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 : n149.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 06:31:43 CDT 2018 0.03/0.23 % CPUTime : 79.96/78.04 ============================== Prover9 =============================== 79.96/78.04 Prover9 (32) version 2009-11A, November 2009. 79.96/78.04 Process 56135 was started by sandbox2 on n149.star.cs.uiowa.edu, 79.96/78.04 Sat Jul 14 06:32:49 2018 79.96/78.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_55995_n149.star.cs.uiowa.edu". 79.96/78.04 ============================== end of head =========================== 79.96/78.04 79.96/78.04 ============================== INPUT ================================= 79.96/78.04 79.96/78.04 % Reading from file /tmp/Prover9_55995_n149.star.cs.uiowa.edu 79.96/78.04 79.96/78.04 set(prolog_style_variables). 79.96/78.04 set(auto2). 79.96/78.04 % set(auto2) -> set(auto). 79.96/78.04 % set(auto) -> set(auto_inference). 79.96/78.04 % set(auto) -> set(auto_setup). 79.96/78.04 % set(auto_setup) -> set(predicate_elim). 79.96/78.04 % set(auto_setup) -> assign(eq_defs, unfold). 79.96/78.04 % set(auto) -> set(auto_limits). 79.96/78.04 % set(auto_limits) -> assign(max_weight, "100.000"). 79.96/78.04 % set(auto_limits) -> assign(sos_limit, 20000). 79.96/78.04 % set(auto) -> set(auto_denials). 79.96/78.04 % set(auto) -> set(auto_process). 79.96/78.04 % set(auto2) -> assign(new_constants, 1). 79.96/78.04 % set(auto2) -> assign(fold_denial_max, 3). 79.96/78.04 % set(auto2) -> assign(max_weight, "200.000"). 79.96/78.04 % set(auto2) -> assign(max_hours, 1). 79.96/78.04 % assign(max_hours, 1) -> assign(max_seconds, 3600). 79.96/78.04 % set(auto2) -> assign(max_seconds, 0). 79.96/78.04 % set(auto2) -> assign(max_minutes, 5). 79.96/78.04 % assign(max_minutes, 5) -> assign(max_seconds, 300). 79.96/78.04 % set(auto2) -> set(sort_initial_sos). 79.96/78.04 % set(auto2) -> assign(sos_limit, -1). 79.96/78.04 % set(auto2) -> assign(lrs_ticks, 3000). 79.96/78.04 % set(auto2) -> assign(max_megs, 400). 79.96/78.04 % set(auto2) -> assign(stats, some). 79.96/78.04 % set(auto2) -> clear(echo_input). 79.96/78.04 % set(auto2) -> set(quiet). 79.96/78.04 % set(auto2) -> clear(print_initial_clauses). 79.96/78.04 % set(auto2) -> clear(print_given). 79.96/78.04 assign(lrs_ticks,-1). 79.96/78.04 assign(sos_limit,10000). 79.96/78.04 assign(order,kbo). 79.96/78.04 set(lex_order_vars). 79.96/78.04 clear(print_given). 79.96/78.04 79.96/78.04 % formulas(sos). % not echoed (35644 formulas) 79.96/78.04 79.96/78.04 ============================== end of input ========================== 79.96/78.04 79.96/78.04 % From the command line: assign(max_seconds, 300). 79.96/78.04 79.96/78.04 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 79.96/78.04 79.96/78.04 % Formulas that are not ordinary clauses: 79.96/78.04 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 2 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 3 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 4 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 7 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 8 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 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]. 79.96/78.04 10 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 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]. 79.96/78.04 12 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 13 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 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]. 79.96/78.04 15 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 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]. 79.96/78.04 17 (all A all B k2_tarski(B,A) = k2_tarski(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 21 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 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]. 79.96/78.04 23 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 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]. 79.96/78.04 25 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 28 (all A all B A = k2_xboole_0(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 29 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 30 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 34 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.04 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]. 79.96/78.05 43 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 46 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 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]. 79.96/78.05 48 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 49 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 52 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 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]. 79.96/78.05 54 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 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]. 79.96/78.05 56 (all A (k1_xboole_0 = A <-> (all B -r2_hidden(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 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]. 79.96/78.05 58 (all A (v1_xboole_0(A) <-> k1_xboole_0 = A)) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 61 (all A k2_xboole_0(A,k1_xboole_0) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 62 (all A all B -(v1_xboole_0(A) & v1_xboole_0(B) & A != B)) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 63 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 64 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 65 (all A k4_xboole_0(A,k1_xboole_0) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 66 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 67 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 68 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 74 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 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]. 79.96/78.05 100 (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]. 79.96/78.05 101 (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]. 79.96/78.05 102 (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]. 79.96/78.05 103 (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]. 79.96/78.05 104 (all A all B k2_xboole_0(A,k3_xboole_0(A,B)) = A) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 105 (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]. 79.96/78.05 106 (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]. 79.96/78.05 107 (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]. 79.96/78.05 108 (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]. 79.96/78.05 109 (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]. 79.96/78.05 110 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 111 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 112 (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]. 79.96/78.05 113 (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]. 79.96/78.05 114 (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]. 79.96/78.05 115 (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]. 79.96/78.05 116 (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]. 79.96/78.05 117 (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]. 79.96/78.05 118 (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]. 79.96/78.05 119 (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]. 79.96/78.05 120 (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]. 79.96/78.05 121 (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]. 79.96/78.05 122 (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]. 79.96/78.05 123 (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]. 79.96/78.05 124 (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]. 79.96/78.05 125 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 126 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 127 (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]. 79.96/78.05 128 (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]. 79.96/78.05 129 (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]. 79.96/78.05 130 (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]. 79.96/78.05 131 (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]. 79.96/78.05 132 (all A k5_xboole_0(A,A) = k1_xboole_0) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 133 (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]. 79.96/78.05 134 (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]. 79.96/78.05 135 (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]. 79.96/78.05 136 (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]. 79.96/78.05 137 (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]. 79.96/78.05 138 (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]. 79.96/78.05 139 (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]. 79.96/78.05 140 (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]. 79.96/78.05 141 (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]. 79.96/78.05 142 (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]. 79.96/78.05 143 (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]. 79.96/78.05 144 (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]. 79.96/78.05 145 (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]. 79.96/78.05 146 (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]. 79.96/78.05 147 (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]. 79.96/78.05 148 (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]. 79.96/78.05 149 (all A all B -(r2_xboole_0(A,B) & r2_xboole_0(B,A))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 150 (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]. 79.96/78.05 151 (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]. 79.96/78.05 152 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 153 (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]. 79.96/78.05 154 (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]. 79.96/78.05 155 (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]. 79.96/78.05 156 (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]. 79.96/78.05 157 (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]. 79.96/78.05 158 (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]. 79.96/78.05 159 (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]. 79.96/78.05 160 (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]. 79.96/78.05 161 (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]. 79.96/78.05 162 (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]. 79.96/78.05 163 (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]. 79.96/78.05 164 (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]. 79.96/78.05 165 (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]. 79.96/78.05 166 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 167 (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]. 79.96/78.05 168 (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]. 79.96/78.05 169 (all A all B k3_xboole_0(A,k2_xboole_0(A,B)) = A) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 170 (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]. 79.96/78.05 171 (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]. 79.96/78.05 172 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 173 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 174 (all A (A != k1_xboole_0 -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 175 (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]. 79.96/78.05 176 (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]. 79.96/78.05 177 (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]. 79.96/78.05 178 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,B) = B)) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 179 (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]. 79.96/78.05 180 (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]. 79.96/78.05 181 (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]. 79.96/78.05 182 (all A all B -(r2_xboole_0(B,A) & r1_tarski(A,B))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 183 (all A k1_tarski(A) = k3_enumset1(A,A,A,A,A)) # label(t87_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 184 (all A all B all C all D all E all F all G k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t59_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 185 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,C,B,D)) # label(t104_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 186 (all A all B k6_enumset1(A,A,A,A,A,A,A,B) = k2_tarski(A,B)) # label(t95_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 187 $T # label(t36_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 188 $T # label(t34_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 189 $T # label(t39_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 190 $T # label(t114_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 191 $T # label(t25_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 192 (all A all B all C all D all E all F all G all H k2_xboole_0(k5_enumset1(A,B,C,D,E,F,G),k1_tarski(H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t68_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 193 $T # label(dt_k5_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 194 $T # label(t27_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 195 $T # label(t115_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 196 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,D,C,A)) # label(t113_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 197 (all A all B all C all D all E all F all G k6_enumset1(A,A,B,C,D,E,F,G) = k5_enumset1(A,B,C,D,E,F,G)) # label(t75_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 198 (all A all B all C all D all E k2_xboole_0(k1_tarski(A),k2_enumset1(B,C,D,E)) = k3_enumset1(A,B,C,D,E)) # label(t47_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 199 $T # label(t30_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 200 $T # label(t24_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 201 $T # label(t11_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 202 (all A all B all C k3_enumset1(A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t78_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 203 (all A k1_tarski(A) = k2_tarski(A,A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 204 $T # label(t16_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 205 $T # label(t14_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 206 $T # label(t18_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 207 $T # label(t9_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 208 $T # label(t124_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 209 (all A k1_enumset1(A,A,A) = k1_tarski(A)) # label(t76_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 210 $T # label(t5_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 211 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,D,C,B)) # label(t107_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 212 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_tarski(A,B),k3_enumset1(C,D,E,F,G))) # label(t57_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 213 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(B,C,A)) # label(t100_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 214 (all A all B all C all D all E all F all G all H k2_xboole_0(k2_enumset1(A,B,C,D),k2_enumset1(E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t65_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 215 (all A k1_tarski(A) = k6_enumset1(A,A,A,A,A,A,A,A)) # label(t96_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 216 $T # label(t40_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 217 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(C,B,A,D)) # label(t116_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 218 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k5_enumset1(A,A,B,C,D,E,F)) # label(t74_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 219 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k2_tarski(A,B),k4_enumset1(C,D,E,F,G,H))) # label(t63_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 220 (all A all B all C all D all E (E = k2_enumset1(A,B,C,D) <-> (all F (-(F != A & F != B & F != D & C != F) <-> r2_hidden(F,E))))) # label(d2_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 221 $T # label(dt_k2_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 222 $T # label(t4_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 223 (all A all B all C k1_enumset1(C,B,A) = k1_enumset1(A,B,C)) # label(t102_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 224 (all A all B all C k5_enumset1(A,A,A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t89_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 225 $T # label(dt_k4_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 226 (all A all B all C all D all E all F all G all H k2_xboole_0(k1_enumset1(A,B,C),k3_enumset1(D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t64_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 227 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_enumset1(F,G,H))) # label(t66_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 228 (all A all B all C all D all E k4_enumset1(A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E)) # label(t73_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 229 $T # label(t37_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 230 $T # label(t8_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 231 (all A all B all C all D all E all F k2_xboole_0(k2_enumset1(A,B,C,D),k2_tarski(E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t54_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 232 (all A all B all C all D k2_enumset1(A,B,D,C) = k2_enumset1(A,B,C,D)) # label(t103_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 233 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k1_tarski(A),k5_enumset1(B,C,D,E,F,G,H))) # label(t62_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 234 $T # label(t121_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 235 (all A all B all C all D all E all F all G all H k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k2_tarski(G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t67_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 236 $T # label(t1_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 237 (all A all B all C all D k4_enumset1(A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t79_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 238 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(C,D,A,B)) # label(t118_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 239 (all A all B all C all D (D = k1_enumset1(A,B,C) <-> (all E (-(E != C & E != B & A != E) <-> r2_hidden(E,D))))) # label(d1_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 240 $T # label(t17_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 241 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k6_enumset1(A,A,A,A,B,C,D,E)) # label(t86_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 242 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(D,B,C,A)) # label(t123_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 243 $T # label(t33_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 244 (all A k4_enumset1(A,A,A,A,A,A) = k1_tarski(A)) # label(t91_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 245 (all A all B all C all D k2_enumset1(C,B,D,A) = k2_enumset1(A,B,C,D)) # label(t117_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 246 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G))) # label(t61_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 247 (all A all B k3_enumset1(A,A,A,A,B) = k2_tarski(A,B)) # label(t83_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 248 $T # label(t35_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 249 (all A all B all C all D k2_enumset1(A,B,C,D) = k3_enumset1(A,A,B,C,D)) # label(t72_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 250 (all A all B k2_tarski(A,B) = k5_enumset1(A,A,A,A,A,A,B)) # label(t92_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 251 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k1_enumset1(A,B,C),k2_enumset1(D,E,F,G))) # label(t58_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 252 (all A all B k2_enumset1(A,A,A,B) = k2_tarski(A,B)) # label(t77_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 253 $T # label(t122_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 254 $T # label(dt_k6_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 255 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_tarski(A,B),k2_enumset1(C,D,E,F))) # label(t52_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 256 (all A all B all C all D all E all F all G (G = k4_enumset1(A,B,C,D,E,F) <-> (all H (-(A != H & D != H & H != E & F != H & H != C & H != B) <-> r2_hidden(H,G))))) # label(d4_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 257 (all A all B all C k2_enumset1(A,A,B,C) = k1_enumset1(A,B,C)) # label(t71_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 258 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,C,A,D)) # label(t110_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 259 (all A all B all C all D k2_enumset1(B,D,A,C) = k2_enumset1(A,B,C,D)) # label(t112_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 260 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_tarski(A,B),k1_enumset1(C,D,E))) # label(t48_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 261 (all A all B all C all D k2_enumset1(C,D,B,A) = k2_enumset1(A,B,C,D)) # label(t119_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 262 $T # label(t22_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 263 (all A all B all C k1_enumset1(A,B,C) = k6_enumset1(A,A,A,A,A,A,B,C)) # label(t93_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 264 (all A all B all C all D all E k2_xboole_0(k2_enumset1(A,B,C,D),k1_tarski(E)) = k3_enumset1(A,B,C,D,E)) # label(t50_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 265 $T # label(t31_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 266 $T # label(t15_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 267 $T # label(t2_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 268 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k6_enumset1(A,A,A,B,C,D,E,F)) # label(t81_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 269 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,A,C,D)) # label(t108_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 270 $T # label(t120_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 271 $T # label(dt_k3_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 272 $T # label(t28_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 273 $T # label(t20_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 274 (all A all B all C all D all E all F (F = k3_enumset1(A,B,C,D,E) <-> (all G (r2_hidden(G,F) <-> -(G != B & G != C & D != G & G != E & G != A))))) # label(d3_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 275 $T # label(t29_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 276 (all A all B all C all D k5_enumset1(A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t85_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 277 (all A all B all C all D k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(A,B,C,D)) # label(t45_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 278 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(B,A,C)) # label(t99_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 279 (all A all B k4_enumset1(A,A,A,A,A,B) = k2_tarski(A,B)) # label(t88_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 280 $T # label(t21_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 281 (all A all B all C all D k2_xboole_0(k1_tarski(A),k1_enumset1(B,C,D)) = k2_enumset1(A,B,C,D)) # label(t44_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 282 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 283 (all A k1_tarski(A) = k2_enumset1(A,A,A,A)) # label(t82_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 284 (all A all B k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B)) # label(t41_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 285 $T # label(t32_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 286 (all A all B all C k1_enumset1(A,B,C) = k2_xboole_0(k1_tarski(A),k2_tarski(B,C))) # label(t42_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 287 (all A all B all C all D all E all F all G all H all I (I = k6_enumset1(A,B,C,D,E,F,G,H) <-> (all J (r2_hidden(J,I) <-> -(J != B & J != C & J != E & J != F & H != J & J != G & D != J & A != J))))) # label(d6_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 288 (all A all B all C all D k2_enumset1(B,C,D,A) = k2_enumset1(A,B,C,D)) # label(t111_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 289 $T # label(t13_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 290 (all A all B all C all D all E all F k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_tarski(F)) = k4_enumset1(A,B,C,D,E,F)) # label(t55_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 291 (all A all B all C all D k2_enumset1(A,B,C,D) = k6_enumset1(A,A,A,A,A,B,C,D)) # label(t90_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 292 $T # label(t97_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 293 $T # label(t19_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 294 $T # label(t6_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 295 (all A all B all C k1_enumset1(A,C,B) = k1_enumset1(A,B,C)) # label(t98_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 296 (all A all B all C all D all E all F all G all H ((all I (-(C != I & D != I & I != F & G != I & I != E & I != B & A != I) <-> r2_hidden(I,H))) <-> k5_enumset1(A,B,C,D,E,F,G) = H)) # label(d5_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 297 (all A all B all C k1_enumset1(A,B,C) = k2_xboole_0(k2_tarski(A,B),k1_tarski(C))) # label(t43_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 298 $T # label(t12_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.05 299 (all A all B all C k4_enumset1(A,A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t84_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 300 (all A all B all C all D all E k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E)) = k3_enumset1(A,B,C,D,E)) # label(t49_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 301 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k1_enumset1(A,B,C),k1_tarski(D))) # label(t46_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 302 $T # label(t7_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 303 $T # label(t38_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 304 $T # label(t26_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 305 $T # label(t101_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 306 (all A all B all C all D all E k5_enumset1(A,A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E)) # label(t80_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 307 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k1_tarski(A),k4_enumset1(B,C,D,E,F,G))) # label(t56_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 308 (all A all B all C all D all E all F k2_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t53_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 309 $T # label(t10_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 310 (all A k5_enumset1(A,A,A,A,A,A,A) = k1_tarski(A)) # label(t94_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 311 (all A all B all C all D k2_enumset1(B,A,D,C) = k2_enumset1(A,B,C,D)) # label(t109_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 312 (all A all B k2_tarski(A,B) = k1_enumset1(A,A,B)) # label(t70_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 313 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_tarski(F,G))) # label(t60_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 314 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(D,C,B,A)) # label(t125_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 315 $T # label(t3_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 316 $T # label(t23_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 317 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_tarski(A),k3_enumset1(B,C,D,E,F))) # label(t51_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 318 (all A all B all C all D k2_enumset1(A,C,D,B) = k2_enumset1(A,B,C,D)) # label(t105_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 319 $T # label(t106_enumset1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 320 (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]. 79.96/78.06 321 (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]. 79.96/78.06 322 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 323 (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]. 79.96/78.06 324 (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]. 79.96/78.06 325 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 326 (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]. 79.96/78.06 327 (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]. 79.96/78.06 328 (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]. 79.96/78.06 329 (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]. 79.96/78.06 330 (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]. 79.96/78.06 331 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 332 (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]. 79.96/78.06 333 (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]. 79.96/78.06 334 (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]. 79.96/78.06 335 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 336 (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]. 79.96/78.06 337 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 338 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 339 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 340 (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]. 79.96/78.06 341 (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]. 79.96/78.06 342 (all A k3_tarski(k1_tarski(A)) = A) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 343 (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]. 79.96/78.06 344 (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]. 79.96/78.06 345 (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]. 79.96/78.06 346 (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]. 79.96/78.06 347 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 348 (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]. 79.96/78.06 349 (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]. 79.96/78.06 350 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 351 (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]. 79.96/78.06 352 (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]. 79.96/78.06 353 (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]. 79.96/78.06 354 (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]. 79.96/78.06 355 (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]. 79.96/78.06 356 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 357 (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]. 79.96/78.06 358 (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]. 79.96/78.06 359 (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]. 79.96/78.06 360 (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]. 79.96/78.06 361 (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]. 79.96/78.06 362 (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]. 79.96/78.06 363 (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]. 79.96/78.06 364 (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]. 79.96/78.06 365 (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]. 79.96/78.06 366 (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]. 79.96/78.06 367 (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]. 79.96/78.06 368 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 369 (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]. 79.96/78.06 370 (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]. 79.96/78.06 371 (all A all B k2_xboole_0(k1_tarski(A),B) != k1_xboole_0) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 372 (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]. 79.96/78.06 373 (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]. 79.96/78.06 374 (all A A = k3_tarski(k1_zfmisc_1(A))) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 375 (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]. 79.96/78.06 376 (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]. 79.96/78.06 377 (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]. 79.96/78.06 378 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 379 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 380 (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]. 79.96/78.06 381 (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]. 79.96/78.06 382 (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]. 79.96/78.06 383 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 384 (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]. 79.96/78.06 385 (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]. 79.96/78.06 386 (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]. 79.96/78.06 387 (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]. 79.96/78.06 388 (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]. 79.96/78.06 389 (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]. 79.96/78.06 390 (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]. 79.96/78.06 391 (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]. 79.96/78.06 392 (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]. 79.96/78.06 393 (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]. 79.96/78.06 394 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 395 (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]. 79.96/78.06 396 (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]. 79.96/78.06 397 (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]. 79.96/78.06 398 (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]. 79.96/78.06 399 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 400 (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]. 79.96/78.06 401 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 402 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 403 (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]. 79.96/78.06 404 (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]. 79.96/78.06 405 (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]. 79.96/78.06 406 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 407 (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]. 79.96/78.06 408 (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]. 79.96/78.06 409 (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]. 79.96/78.06 410 (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]. 79.96/78.06 411 (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]. 79.96/78.06 412 (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]. 79.96/78.06 413 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> A = k1_xboole_0)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 414 (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]. 79.96/78.06 415 (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]. 79.96/78.06 416 (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]. 79.96/78.06 417 (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]. 79.96/78.06 418 (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]. 79.96/78.06 419 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 420 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 421 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 422 (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]. 79.96/78.06 423 (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]. 79.96/78.06 424 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 425 (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]. 79.96/78.06 426 (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]. 79.96/78.06 427 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 79.96/78.06 428 (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]. 80.06/78.06 429 (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]. 80.06/78.06 430 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 431 (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]. 80.06/78.06 432 (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]. 80.06/78.06 433 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 434 (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]. 80.06/78.06 435 (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]. 80.06/78.06 436 (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]. 80.06/78.06 437 (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]. 80.06/78.06 438 (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]. 80.06/78.06 439 (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]. 80.06/78.06 440 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 441 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 442 (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]. 80.06/78.06 443 (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]. 80.06/78.06 444 (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]. 80.06/78.06 445 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 446 (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]. 80.06/78.06 447 (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]. 80.06/78.06 448 (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]. 80.06/78.06 449 (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]. 80.06/78.06 450 (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]. 80.06/78.06 451 (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]. 80.06/78.06 452 (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]. 80.06/78.06 453 (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]. 80.06/78.06 454 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 455 (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]. 80.06/78.06 456 (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]. 80.06/78.06 457 (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]. 80.06/78.06 458 (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]. 80.06/78.06 459 (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]. 80.06/78.06 460 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 461 (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]. 80.06/78.06 462 (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]. 80.06/78.06 463 (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]. 80.06/78.06 464 (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]. 80.06/78.06 465 (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]. 80.06/78.06 466 (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]. 80.06/78.06 467 (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]. 80.06/78.06 468 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 469 (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]. 80.06/78.06 470 (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]. 80.06/78.06 471 (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]. 80.06/78.06 472 (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]. 80.06/78.06 473 (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]. 80.06/78.06 474 (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]. 80.06/78.06 475 (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]. 80.06/78.06 476 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 477 (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]. 80.06/78.06 478 (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]. 80.06/78.06 479 (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]. 80.06/78.06 480 (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]. 80.06/78.06 481 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 482 (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]. 80.06/78.06 483 (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]. 80.06/78.06 484 (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]. 80.06/78.06 485 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 486 (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]. 80.06/78.06 487 (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]. 80.06/78.06 488 (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]. 80.06/78.06 489 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 490 (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]. 80.06/78.06 491 (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]. 80.06/78.06 492 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 493 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 494 (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]. 80.06/78.06 495 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 496 (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]. 80.06/78.06 497 (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]. 80.06/78.06 498 (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]. 80.06/78.06 499 (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]. 80.06/78.06 500 (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]. 80.06/78.06 501 (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]. 80.06/78.06 502 (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]. 80.06/78.06 503 (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]. 80.06/78.06 504 (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]. 80.06/78.06 505 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 506 (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]. 80.06/78.06 507 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 508 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 509 (all A A = k2_subset_1(A)) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 510 (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]. 80.06/78.06 511 (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]. 80.06/78.06 512 (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]. 80.06/78.06 513 (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]. 80.06/78.06 514 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 515 (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]. 80.06/78.06 516 (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]. 80.06/78.06 517 (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]. 80.06/78.06 518 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 519 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 520 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 521 (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]. 80.06/78.06 522 (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]. 80.06/78.06 523 (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]. 80.06/78.06 524 (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]. 80.06/78.06 525 (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]. 80.06/78.06 526 (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]. 80.06/78.06 527 (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]. 80.06/78.06 528 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 529 (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]. 80.06/78.06 530 (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]. 80.06/78.06 531 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 532 (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]. 80.06/78.06 533 (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]. 80.06/78.06 534 (all A k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A))) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.06 535 (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]. 80.06/78.06 536 (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]. 80.06/78.06 537 (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]. 80.06/78.06 538 (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]. 80.06/78.06 539 (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]. 80.06/78.07 540 (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]. 80.06/78.07 541 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 542 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 543 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) -> r1_tarski(C,k3_subset_1(A,B))))))) # label(t35_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 544 (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]. 80.06/78.07 545 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 546 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 547 (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]. 80.06/78.07 548 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 549 (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]. 80.06/78.07 550 (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]. 80.06/78.07 551 (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]. 80.06/78.07 552 (all A k1_subset_1(A) = k1_xboole_0) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 553 (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]. 80.06/78.07 554 (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]. 80.06/78.07 555 (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]. 80.06/78.07 556 (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]. 80.06/78.07 557 (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]. 80.06/78.07 558 (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]. 80.06/78.07 559 (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]. 80.06/78.07 560 (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]. 80.06/78.07 561 (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]. 80.06/78.07 562 (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]. 80.06/78.07 563 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 564 (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]. 80.06/78.07 565 (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]. 80.06/78.07 566 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 567 (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]. 80.06/78.07 568 (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]. 80.06/78.07 569 (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]. 80.06/78.07 570 (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]. 80.06/78.07 571 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 572 (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]. 80.06/78.07 573 (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]. 80.06/78.07 574 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 575 (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]. 80.06/78.07 576 (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]. 80.06/78.07 577 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 578 (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]. 80.06/78.07 579 (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]. 80.06/78.07 580 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 581 (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]. 80.06/78.07 582 (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]. 80.06/78.07 583 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 584 (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]. 80.06/78.07 585 (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]. 80.06/78.07 586 (all A (r1_setfam_1(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 587 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 588 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 589 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 590 (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]. 80.06/78.07 591 (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]. 80.06/78.07 592 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 593 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 594 (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]. 80.06/78.07 595 (all A (v1_setfam_1(A) <-> -r2_hidden(k1_xboole_0,A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 596 (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]. 80.06/78.07 597 (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]. 80.06/78.07 598 (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]. 80.06/78.07 599 (all A A = k1_setfam_1(k1_tarski(A))) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 600 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 601 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 602 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 603 (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]. 80.06/78.07 604 (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]. 80.06/78.07 605 (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]. 80.06/78.07 606 (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]. 80.06/78.07 607 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 608 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 609 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 610 (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]. 80.06/78.07 611 (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]. 80.06/78.07 612 (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]. 80.06/78.07 613 (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]. 80.06/78.07 614 (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]. 80.06/78.07 615 (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]. 80.06/78.07 616 (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]. 80.06/78.07 617 (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]. 80.06/78.07 618 (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]. 80.06/78.07 619 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 620 (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]. 80.06/78.07 621 (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]. 80.06/78.07 622 (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]. 80.06/78.07 623 (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]. 80.06/78.07 624 (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]. 80.06/78.07 625 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 626 (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]. 80.06/78.07 627 (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]. 80.06/78.07 628 (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]. 80.06/78.07 629 (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]. 80.06/78.07 630 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 631 (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]. 80.06/78.07 632 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 633 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 634 (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]. 80.06/78.07 635 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 636 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 637 (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]. 80.06/78.07 638 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 639 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 640 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (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]. 80.06/78.07 641 (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]. 80.06/78.07 642 (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]. 80.06/78.07 643 (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]. 80.06/78.07 644 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 645 (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]. 80.06/78.07 646 (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]. 80.06/78.07 647 (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]. 80.06/78.07 648 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 649 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 650 (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]. 80.06/78.07 651 (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]. 80.06/78.07 652 (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]. 80.06/78.07 653 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 654 (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]. 80.06/78.07 655 (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]. 80.06/78.07 656 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 657 (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]. 80.06/78.07 658 (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]. 80.06/78.07 659 (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]. 80.06/78.07 660 (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]. 80.06/78.07 661 (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]. 80.06/78.07 662 (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]. 80.06/78.07 663 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 664 (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]. 80.06/78.07 665 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 666 (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]. 80.06/78.07 667 (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]. 80.06/78.07 668 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 669 (exists A (-v1_xboole_0(A) & v1_setfam_1(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 670 (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]. 80.06/78.07 671 (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]. 80.06/78.07 672 (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]. 80.06/78.07 673 (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]. 80.06/78.07 674 (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]. 80.06/78.07 675 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 676 (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]. 80.06/78.07 677 (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]. 80.06/78.07 678 (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]. 80.06/78.07 679 (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]. 80.06/78.07 680 (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]. 80.06/78.07 681 (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]. 80.06/78.07 682 (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]. 80.06/78.07 683 (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]. 80.06/78.07 684 (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]. 80.06/78.07 685 (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]. 80.06/78.07 686 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 687 (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]. 80.06/78.07 688 (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]. 80.06/78.07 689 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 690 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k8_relat_1(A,C)),k5_relat_1(B,C)))))) # label(t122_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 691 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 692 (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]. 80.06/78.07 693 (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]. 80.06/78.07 694 (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]. 80.06/78.07 695 (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]. 80.06/78.07 696 (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]. 80.06/78.07 697 (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]. 80.06/78.07 698 (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]. 80.06/78.07 699 (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]. 80.06/78.07 700 (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]. 80.06/78.07 701 (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]. 80.06/78.07 702 (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]. 80.06/78.07 703 (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]. 80.06/78.07 704 (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]. 80.06/78.07 705 (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]. 80.06/78.07 706 (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]. 80.06/78.07 707 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 708 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 709 (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]. 80.06/78.07 710 (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]. 80.06/78.07 711 (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]. 80.06/78.07 712 (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]. 80.06/78.07 713 (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]. 80.06/78.07 714 (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]. 80.06/78.07 715 (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]. 80.06/78.07 716 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 717 (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]. 80.06/78.07 718 (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]. 80.06/78.07 719 (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]. 80.06/78.07 720 (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]. 80.06/78.07 721 (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]. 80.06/78.07 722 (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]. 80.06/78.07 723 (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]. 80.06/78.07 724 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 725 (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]. 80.06/78.07 726 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 727 (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]. 80.06/78.07 728 (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]. 80.06/78.07 729 (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]. 80.06/78.07 730 (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]. 80.06/78.07 731 (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]. 80.06/78.07 732 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k1_relat_1(B)))) # label(t167_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 733 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 734 (all A k7_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 735 (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]. 80.06/78.07 736 (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]. 80.06/78.07 737 (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]. 80.06/78.07 738 (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]. 80.06/78.07 739 (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]. 80.06/78.07 740 (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]. 80.06/78.07 741 (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]. 80.06/78.07 742 (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]. 80.06/78.07 743 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 744 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 745 (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]. 80.06/78.07 746 (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]. 80.06/78.07 747 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 748 (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]. 80.06/78.07 749 (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]. 80.06/78.07 750 (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]. 80.06/78.07 751 (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]. 80.06/78.07 752 (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]. 80.06/78.07 753 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 754 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.07 755 (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]. 80.06/78.07 756 (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]. 80.06/78.07 757 (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]. 80.06/78.07 758 (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]. 80.06/78.07 759 (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]. 80.06/78.08 760 (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]. 80.06/78.08 761 (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]. 80.06/78.08 762 (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]. 80.06/78.08 763 (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]. 80.06/78.08 764 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 765 (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]. 80.06/78.08 766 (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]. 80.06/78.08 767 (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]. 80.06/78.08 768 (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]. 80.06/78.08 769 (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]. 80.06/78.08 770 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 771 (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]. 80.06/78.08 772 (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]. 80.06/78.08 773 (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]. 80.06/78.08 774 (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]. 80.06/78.08 775 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 776 (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]. 80.06/78.08 777 (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]. 80.06/78.08 778 (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]. 80.06/78.08 779 (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]. 80.06/78.08 780 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 781 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 782 (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]. 80.06/78.08 783 (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]. 80.06/78.08 784 (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]. 80.06/78.08 785 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 786 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 787 (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]. 80.06/78.08 788 (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]. 80.06/78.08 789 (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]. 80.06/78.08 790 (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]. 80.06/78.08 791 (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]. 80.06/78.08 792 (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]. 80.06/78.08 793 (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]. 80.06/78.08 794 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 795 (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]. 80.06/78.08 796 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 797 (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]. 80.06/78.08 798 (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]. 80.06/78.08 799 (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]. 80.06/78.08 800 (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]. 80.06/78.08 801 (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]. 80.06/78.08 802 (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]. 80.06/78.08 803 (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]. 80.06/78.08 804 (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]. 80.06/78.08 805 (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]. 80.06/78.08 806 (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]. 80.06/78.08 807 (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]. 80.06/78.08 808 (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]. 80.06/78.08 809 (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]. 80.06/78.08 810 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 811 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 812 (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]. 80.06/78.08 813 (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]. 80.06/78.08 814 (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]. 80.06/78.08 815 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 816 (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]. 80.06/78.08 817 (all A k10_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 818 (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]. 80.06/78.08 819 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 820 (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]. 80.06/78.08 821 (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]. 80.06/78.08 822 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 823 (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]. 80.06/78.08 824 (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]. 80.06/78.08 825 (all A k1_xboole_0 = k9_relat_1(k1_xboole_0,A)) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 826 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 827 (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]. 80.06/78.08 828 (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]. 80.06/78.08 829 (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]. 80.06/78.08 830 (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]. 80.06/78.08 831 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 832 (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]. 80.06/78.08 833 (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]. 80.06/78.08 834 (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]. 80.06/78.08 835 (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]. 80.06/78.08 836 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 837 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 838 (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]. 80.06/78.08 839 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 840 (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]. 80.06/78.08 841 (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]. 80.06/78.08 842 (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]. 80.06/78.08 843 (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]. 80.06/78.08 844 (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]. 80.06/78.08 845 (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]. 80.06/78.08 846 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 847 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 848 (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]. 80.06/78.08 849 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 850 (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]. 80.06/78.08 851 (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]. 80.06/78.08 852 (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]. 80.06/78.08 853 (exists A (v1_relat_1(A) & v3_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 854 (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]. 80.06/78.08 855 (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]. 80.06/78.08 856 (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]. 80.06/78.08 857 (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]. 80.06/78.08 858 (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]. 80.06/78.08 859 (all A k8_relat_1(A,k1_xboole_0) = k1_xboole_0) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 860 (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]. 80.06/78.08 861 (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]. 80.06/78.08 862 (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]. 80.06/78.08 863 (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]. 80.06/78.08 864 (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]. 80.06/78.08 865 (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]. 80.06/78.08 866 (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]. 80.06/78.08 867 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 868 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 869 (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]. 80.06/78.08 870 (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]. 80.06/78.08 871 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 872 (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]. 80.06/78.08 873 (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]. 80.06/78.08 874 (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]. 80.06/78.08 875 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 876 (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]. 80.06/78.08 877 (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]. 80.06/78.08 878 (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]. 80.06/78.08 879 (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]. 80.06/78.08 880 (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]. 80.06/78.08 881 (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]. 80.06/78.08 882 (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]. 80.06/78.08 883 (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]. 80.06/78.08 884 (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]. 80.06/78.08 885 (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]. 80.06/78.08 886 (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]. 80.06/78.08 887 (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]. 80.06/78.08 888 (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]. 80.06/78.08 889 (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]. 80.06/78.08 890 (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]. 80.06/78.08 891 (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]. 80.06/78.08 892 (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]. 80.06/78.08 893 (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]. 80.06/78.08 894 (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]. 80.06/78.08 895 (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]. 80.06/78.08 896 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 897 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 898 (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]. 80.06/78.08 899 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 900 (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]. 80.06/78.08 901 (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]. 80.06/78.08 902 (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]. 80.06/78.08 903 (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]. 80.06/78.08 904 (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]. 80.06/78.08 905 (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]. 80.06/78.08 906 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 907 (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]. 80.06/78.08 908 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 909 (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]. 80.06/78.08 910 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 911 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 912 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 913 (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]. 80.06/78.08 914 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 915 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 916 (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]. 80.06/78.08 917 (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]. 80.06/78.08 918 (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]. 80.06/78.08 919 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 920 (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]. 80.06/78.08 921 (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]. 80.06/78.08 922 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 923 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 924 (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]. 80.06/78.08 925 (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]. 80.06/78.08 926 (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]. 80.06/78.08 927 (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]. 80.06/78.08 928 (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]. 80.06/78.08 929 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 930 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 931 (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]. 80.06/78.08 932 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 933 (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]. 80.06/78.08 934 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 935 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 936 (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]. 80.06/78.08 937 (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]. 80.06/78.08 938 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 939 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 940 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 941 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 942 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 943 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 944 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 945 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 946 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 947 (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]. 80.06/78.08 948 (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]. 80.06/78.08 949 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 950 (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]. 80.06/78.08 951 (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]. 80.06/78.08 952 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 953 (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]. 80.06/78.08 954 (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]. 80.06/78.08 955 (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]. 80.06/78.08 956 (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]. 80.06/78.08 957 (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]. 80.06/78.08 958 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 959 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 960 (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]. 80.06/78.08 961 (exists A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 962 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 963 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 964 (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]. 80.06/78.08 965 (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]. 80.06/78.08 966 (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]. 80.06/78.08 967 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 968 (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]. 80.06/78.08 969 (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]. 80.06/78.08 970 (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]. 80.06/78.08 971 (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]. 80.06/78.08 972 (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]. 80.06/78.08 973 (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]. 80.06/78.08 974 (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]. 80.06/78.08 975 (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]. 80.06/78.08 976 (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]. 80.06/78.08 977 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 978 (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]. 80.06/78.08 979 (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]. 80.06/78.08 980 (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]. 80.06/78.08 981 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.08 982 (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]. 80.06/78.09 983 (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]. 80.06/78.09 984 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 985 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 986 (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]. 80.06/78.09 987 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 988 (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]. 80.06/78.09 989 (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]. 80.06/78.09 990 (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]. 80.06/78.09 991 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 992 (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]. 80.06/78.09 993 (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]. 80.06/78.09 994 (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]. 80.06/78.09 995 (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]. 80.06/78.09 996 (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]. 80.06/78.09 997 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 998 (exists A (v1_xboole_0(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 999 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1000 (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]. 80.06/78.09 1001 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1002 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1003 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1004 (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]. 80.06/78.09 1005 (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]. 80.06/78.09 1006 (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]. 80.06/78.09 1007 (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]. 80.06/78.09 1008 (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]. 80.06/78.09 1009 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1010 (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]. 80.06/78.09 1011 (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]. 80.06/78.09 1012 (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]. 80.06/78.09 1013 (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]. 80.06/78.09 1014 (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]. 80.06/78.09 1015 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1016 (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]. 80.06/78.09 1017 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1018 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1019 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1020 (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]. 80.06/78.09 1021 (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]. 80.06/78.09 1022 (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]. 80.06/78.09 1023 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1024 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1025 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1026 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1027 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1028 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1029 (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]. 80.06/78.09 1030 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1031 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1032 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1033 (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]. 80.06/78.09 1034 (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]. 80.06/78.09 1035 (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]. 80.06/78.09 1036 (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]. 80.06/78.09 1037 (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]. 80.06/78.09 1038 (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]. 80.06/78.09 1039 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1040 (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]. 80.06/78.09 1041 (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]. 80.06/78.09 1042 (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]. 80.06/78.09 1043 (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]. 80.06/78.09 1044 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1045 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1046 (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]. 80.06/78.09 1047 (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]. 80.06/78.09 1048 (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]. 80.06/78.09 1049 (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]. 80.06/78.09 1050 (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]. 80.06/78.09 1051 (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]. 80.06/78.09 1052 (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]. 80.06/78.09 1053 (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]. 80.06/78.09 1054 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1055 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1056 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1057 (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]. 80.06/78.09 1058 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1059 (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]. 80.06/78.09 1060 (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]. 80.06/78.09 1061 (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]. 80.06/78.09 1062 (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]. 80.06/78.09 1063 (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]. 80.06/78.09 1064 (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]. 80.06/78.09 1065 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1066 (exists A (v1_relat_1(A) & v1_funct_1(A) & v3_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1067 (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]. 80.06/78.09 1068 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1069 (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]. 80.06/78.09 1070 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1071 (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]. 80.06/78.09 1072 (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]. 80.06/78.09 1073 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1074 (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]. 80.06/78.09 1075 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1076 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1077 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1078 (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]. 80.06/78.09 1079 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1080 (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]. 80.06/78.09 1081 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1082 (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]. 80.06/78.09 1083 (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]. 80.06/78.09 1084 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1085 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1086 (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]. 80.06/78.09 1087 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1088 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1089 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1090 (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]. 80.06/78.09 1091 (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]. 80.06/78.09 1092 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1093 (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]. 80.06/78.09 1094 (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]. 80.06/78.09 1095 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1096 (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]. 80.06/78.09 1097 (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]. 80.06/78.09 1098 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1099 (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]. 80.06/78.09 1100 (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]. 80.06/78.09 1101 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_tarski(k4_tarski(B,k1_funct_1(A,B))) = k7_relat_1(A,k1_tarski(B)))))) # label(t89_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1102 $T # label(t44_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1103 $T # label(t2_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1104 $T # label(t17_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1105 $T # label(t51_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1106 (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(B,C) -> k7_relat_1(B,A) = k7_relat_1(C,A)))))) # label(t88_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1107 $T # label(t59_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1108 $T # label(t61_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1109 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(B)) & k2_xboole_0(B,D) = C -> k1_funct_1(B,A) = k1_funct_1(C,A)))))))) # label(t34_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1110 $T # label(t55_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1111 (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) -> (A = k3_xboole_0(B,C) -> r1_tarski(k1_relat_1(A),k3_xboole_0(k1_relat_1(B),k1_relat_1(C))) & r1_tarski(k2_relat_1(A),k3_xboole_0(k2_relat_1(B),k2_relat_1(C)))))))))) # label(t28_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1112 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> k7_relat_1(B,k1_relat_1(A)) = A))))) # label(t64_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1113 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B all C (r2_hidden(k4_tarski(C,B),k2_funct_1(A)) <-> r2_hidden(k4_tarski(B,C),A)))))) # label(t47_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1114 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,k1_funct_1(C,A)),k8_relat_1(B,C)) <-> r2_hidden(A,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,A),B)))) # label(t67_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1115 $T # label(t23_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1116 (all A (v1_relat_1(A) & v1_funct_1(A) -> (A = k1_xboole_0 -> k2_funct_1(A) = k1_xboole_0))) # label(t49_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1117 (all A all B all C all D (v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) & v1_funct_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) <-> (A = C -> B = D))) # label(t19_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1118 $T # label(t24_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1119 $T # label(t71_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1120 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k1_funct_1(C,A) = B))) # label(t16_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1121 $T # label(t22_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1122 $T # label(t4_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1123 $T # label(t1_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1124 $T # label(t45_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1125 (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) -> (r2_hidden(A,k1_relat_1(B)) & k3_xboole_0(C,D) = B -> k1_funct_1(D,A) = k1_funct_1(B,A) & k1_funct_1(B,A) = k1_funct_1(C,A)))))))) # label(t29_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1126 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C all D (r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(B,D),A) -> B = C)) <-> v2_funct_1(A)))) # label(t25_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1127 $T # label(t58_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1128 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k4_xboole_0(B,A)) & v1_funct_1(k4_xboole_0(B,A)))) # label(t38_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1129 $T # label(t78_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1130 $T # label(t85_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1131 $T # label(t86_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1132 $T # label(t57_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1133 $T # label(t81_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1134 (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) -> (v2_funct_1(B) & k2_xboole_0(A,B) = C & r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) & v2_funct_1(A) -> v2_funct_1(C)))))))) # label(t37_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1135 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> r1_tarski(k5_relat_1(k7_relat_1(B,A),D),k5_relat_1(B,D)) & r1_tarski(k5_relat_1(C,k7_relat_1(B,A)),k5_relat_1(C,B)))))))) # label(t54_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1136 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B) <-> r2_hidden(k4_tarski(A,k1_funct_1(C,A)),k7_relat_1(C,B))))) # label(t52_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1137 $T # label(t65_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1138 $T # label(t76_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1139 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (C = k2_xboole_0(D,B) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,A) = k1_funct_1(B,A)))))))) # label(t35_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1140 (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) -> (A = k2_xboole_0(B,C) -> k2_xboole_0(k2_relat_1(B),k2_relat_1(C)) = k2_relat_1(A) & k1_relat_1(A) = k2_xboole_0(k1_relat_1(B),k1_relat_1(C))))))))) # label(t33_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1141 $T # label(t68_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1142 (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 = k3_xboole_0(A,B) -> v2_funct_1(C) | -v2_funct_1(B) & -v2_funct_1(A)))))))) # label(t30_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1143 $T # label(t63_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1144 $T # label(t42_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1145 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> v1_funct_1(k2_xboole_0(A,B)) & v1_relat_1(k2_xboole_0(A,B))))))) # label(t31_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1146 $T # label(t43_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1147 $T # label(t14_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1148 $T # label(t56_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1149 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r1_tarski(B,A) -> v1_funct_1(B) & v1_relat_1(B))))) # label(t6_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1150 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k1_funct_1(C,A),B) & r2_hidden(k4_tarski(A,k1_funct_1(C,A)),C) <-> r2_hidden(A,k10_relat_1(C,B))))) # label(t87_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1151 $T # label(t11_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1152 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_relat_1(A) & r1_tarski(A,B) -> A = B))))) # label(t9_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1153 $T # label(t10_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1154 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(D,C)) -> r2_hidden(k4_tarski(k1_funct_1(D,A),B),C) & r2_hidden(k4_tarski(A,k1_funct_1(D,A)),D)))))) # label(t12_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1155 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r1_tarski(A,B) -> v2_funct_1(A)))))) # label(t26_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1156 $T # label(t3_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1157 $T # label(t74_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1158 $T # label(t66_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1159 $T # label(t5_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1160 $T # label(t39_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1161 (all 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) -> r1_tarski(k5_relat_1(k8_relat_1(A,B),D),k5_relat_1(B,D)) & r1_tarski(k5_relat_1(C,k8_relat_1(A,B)),k5_relat_1(C,B)))))))) # label(t69_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1162 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) <-> r1_tarski(A,B)))))) # label(t8_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1163 $T # label(t80_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1164 $T # label(t7_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1165 (all A all B (v1_funct_1(k1_tarski(k4_tarski(A,B))) & v1_relat_1(k1_tarski(k4_tarski(A,B))))) # label(t15_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1166 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_funct_1(k3_xboole_0(B,A)) & v1_relat_1(k3_xboole_0(B,A)))) # label(t27_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1167 $T # label(t50_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1168 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C)) & r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B))))))))) # label(t13_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1169 $T # label(t73_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1170 $T # label(t21_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1171 $T # label(t20_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1172 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_tarski(A) -> k1_tarski(k4_tarski(A,k1_funct_1(B,A))) = B))) # label(t18_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1173 $T # label(t77_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1174 $T # label(t72_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1175 $T # label(t82_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1176 (all A (v1_relat_1(A) & v1_funct_1(A) -> (k1_xboole_0 = A -> v2_funct_1(A)))) # label(t46_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1177 $T # label(t84_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.06/78.09 1178 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) & r1_tarski(C,B) -> v1_funct_1(k2_xboole_0(A,C)) & v1_relat_1(k2_xboole_0(A,C))))))))) # label(t32_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1179 $T # label(t62_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1180 $T # label(t48_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1181 (all 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) -> -(B = k2_xboole_0(C,D) & k1_funct_1(D,A) != k1_funct_1(B,A) & k1_funct_1(C,A) != k1_funct_1(B,A) & r2_hidden(A,k1_relat_1(B))))))))) # label(t36_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1182 $T # label(t41_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1183 $T # label(t53_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1184 $T # label(t60_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1185 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r1_tarski(A,B) -> A = k8_relat_1(k2_relat_1(A),B)))))) # label(t79_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1186 $T # label(t83_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1187 $T # label(t70_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1188 $T # label(t40_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1189 $T # label(t75_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1190 (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]. 80.09/78.10 1191 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1192 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1193 (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]. 80.09/78.10 1194 (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]. 80.09/78.10 1195 (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]. 80.09/78.10 1196 (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]. 80.09/78.10 1197 (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]. 80.09/78.10 1198 (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]. 80.09/78.10 1199 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1200 (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]. 80.09/78.10 1201 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1202 (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]. 80.09/78.10 1203 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1204 (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]. 80.09/78.10 1205 (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]. 80.09/78.10 1206 (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]. 80.09/78.10 1207 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1208 (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]. 80.09/78.10 1209 (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]. 80.09/78.10 1210 (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]. 80.09/78.10 1211 (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]. 80.09/78.10 1212 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1213 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1214 (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]. 80.09/78.10 1215 (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]. 80.09/78.10 1216 (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]. 80.09/78.10 1217 (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]. 80.09/78.10 1218 (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]. 80.09/78.10 1219 (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]. 80.09/78.10 1220 (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]. 80.09/78.10 1221 (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]. 80.09/78.10 1222 (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]. 80.09/78.10 1223 (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]. 80.09/78.10 1224 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1225 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1226 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1227 (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]. 80.09/78.10 1228 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1229 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1230 (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]. 80.09/78.10 1231 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1232 (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]. 80.09/78.10 1233 (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]. 80.09/78.10 1234 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1235 (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]. 80.09/78.10 1236 (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]. 80.09/78.10 1237 (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]. 80.09/78.10 1238 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1239 (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]. 80.09/78.10 1240 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1241 (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]. 80.09/78.10 1242 (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]. 80.09/78.10 1243 (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]. 80.09/78.10 1244 (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]. 80.09/78.10 1245 (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]. 80.09/78.10 1246 (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]. 80.09/78.10 1247 (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]. 80.09/78.10 1248 (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]. 80.09/78.10 1249 (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]. 80.09/78.10 1250 (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]. 80.09/78.10 1251 (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]. 80.09/78.10 1252 (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]. 80.09/78.10 1253 (all A all B (k1_ordinal1(A) = k1_ordinal1(B) -> A = B)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1254 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1255 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1256 (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]. 80.09/78.10 1257 (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]. 80.09/78.10 1258 (all A (v4_ordinal1(A) <-> A = k3_tarski(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1259 (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]. 80.09/78.10 1260 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1261 (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]. 80.09/78.10 1262 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1263 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1264 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1265 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1266 (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]. 80.09/78.10 1267 (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]. 80.09/78.10 1268 (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]. 80.09/78.10 1269 (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]. 80.09/78.10 1270 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1271 (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]. 80.09/78.10 1272 (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]. 80.09/78.10 1273 (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]. 80.09/78.10 1274 (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]. 80.09/78.10 1275 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1276 (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]. 80.09/78.10 1277 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1278 (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]. 80.09/78.10 1279 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]. 80.09/78.10 1280 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1281 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1282 (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]. 80.09/78.10 1283 (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]. 80.09/78.10 1284 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1285 (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]. 80.09/78.10 1286 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1287 (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]. 80.09/78.10 1288 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1289 (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]. 80.09/78.10 1290 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1291 (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]. 80.09/78.10 1292 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1293 (all A (v3_ordinal1(A) <-> v2_ordinal1(A) & v1_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1294 (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]. 80.09/78.10 1295 (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]. 80.09/78.10 1296 (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]. 80.09/78.10 1297 (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]. 80.09/78.10 1298 (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]. 80.09/78.10 1299 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1300 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1301 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1302 (all A -(all B (r2_hidden(B,A) <-> v3_ordinal1(B)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1303 (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]. 80.09/78.10 1304 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1305 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1306 (all A (v1_xboole_0(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1307 (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]. 80.09/78.10 1308 (all A (v3_ordinal1(A) -> v1_ordinal1(A) & v2_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1309 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1310 (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]. 80.09/78.10 1311 (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]. 80.09/78.10 1312 (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]. 80.09/78.10 1313 (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]. 80.09/78.10 1314 (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]. 80.09/78.10 1315 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1316 (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]. 80.09/78.10 1317 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1318 (all A (v1_ordinal1(A) <-> (all B (r2_hidden(B,A) -> r1_tarski(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1319 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1320 (exists A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1321 (all A all B -(r2_hidden(A,B) & r1_tarski(B,A))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1322 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1323 (exists A (v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1324 (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]. 80.09/78.10 1325 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1326 (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]. 80.09/78.10 1327 (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]. 80.09/78.10 1328 (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]. 80.09/78.10 1329 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1330 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1331 (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]. 80.09/78.10 1332 (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]. 80.09/78.10 1333 (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]. 80.09/78.10 1334 (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]. 80.09/78.10 1335 (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]. 80.09/78.10 1336 (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]. 80.09/78.10 1337 $T # label(t44_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1338 (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]. 80.09/78.10 1339 (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]. 80.09/78.10 1340 (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]. 80.09/78.10 1341 (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]. 80.09/78.10 1342 (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]. 80.09/78.10 1343 (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]. 80.09/78.10 1344 (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]. 80.09/78.10 1345 (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]. 80.09/78.10 1346 (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]. 80.09/78.10 1347 (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]. 80.09/78.10 1348 (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]. 80.09/78.10 1349 (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]. 80.09/78.10 1350 $T # label(t4_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1351 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1352 (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]. 80.09/78.10 1353 (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]. 80.09/78.10 1354 $T # label(t46_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1355 (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]. 80.09/78.10 1356 $T # label(t1_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1357 (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]. 80.09/78.10 1358 (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]. 80.09/78.10 1359 (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]. 80.09/78.10 1360 (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]. 80.09/78.10 1361 (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]. 80.09/78.10 1362 (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]. 80.09/78.10 1363 (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]. 80.09/78.10 1364 (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]. 80.09/78.10 1365 (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]. 80.09/78.10 1366 (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]. 80.09/78.10 1367 (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]. 80.09/78.10 1368 (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]. 80.09/78.10 1369 (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]. 80.09/78.10 1370 (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]. 80.09/78.10 1371 (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]. 80.09/78.10 1372 $T # label(t56_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1373 $T # label(t7_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1374 $T # label(t14_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1375 (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]. 80.09/78.10 1376 (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]. 80.09/78.10 1377 (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]. 80.09/78.10 1378 (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]. 80.09/78.10 1379 (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]. 80.09/78.10 1380 (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]. 80.09/78.10 1381 $T # label(t3_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1382 (all A (v1_relat_1(A) -> r4_wellord1(A,A))) # label(t48_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1383 (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]. 80.09/78.10 1384 (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]. 80.09/78.10 1385 (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]. 80.09/78.10 1386 (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]. 80.09/78.10 1387 (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]. 80.09/78.10 1388 (all A (v1_relat_1(A) -> k2_wellord1(A,k3_relat_1(A)) = A)) # label(t30_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.10 1389 (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]. 80.09/78.10 1390 (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]. 80.09/78.10 1391 (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]. 80.09/78.10 1392 (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]. 80.09/78.10 1393 (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]. 80.09/78.11 1394 (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]. 80.09/78.11 1395 (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]. 80.09/78.11 1396 (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]. 80.09/78.11 1397 (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]. 80.09/78.11 1398 $T # label(t34_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1399 (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]. 80.09/78.11 1400 (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]. 80.09/78.11 1401 (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]. 80.09/78.11 1402 $T # label(t6_wellord1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1403 (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]. 80.09/78.11 1404 (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]. 80.09/78.11 1405 (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]. 80.09/78.11 1406 (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]. 80.09/78.11 1407 (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]. 80.09/78.11 1408 (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]. 80.09/78.11 1409 (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]. 80.09/78.11 1410 (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]. 80.09/78.11 1411 (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]. 80.09/78.11 1412 (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]. 80.09/78.11 1413 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1414 (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]. 80.09/78.11 1415 (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]. 80.09/78.11 1416 (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]. 80.09/78.11 1417 (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]. 80.09/78.11 1418 (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]. 80.09/78.11 1419 (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]. 80.09/78.11 1420 (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]. 80.09/78.11 1421 (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]. 80.09/78.11 1422 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1423 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1424 (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]. 80.09/78.11 1425 (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]. 80.09/78.11 1426 (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]. 80.09/78.11 1427 (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]. 80.09/78.11 1428 (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]. 80.09/78.11 1429 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1430 (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]. 80.09/78.11 1431 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1432 (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]. 80.09/78.11 1433 (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]. 80.09/78.11 1434 (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]. 80.09/78.11 1435 (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]. 80.09/78.11 1436 (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]. 80.09/78.11 1437 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1438 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1439 (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]. 80.09/78.11 1440 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1441 (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]. 80.09/78.11 1442 (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]. 80.09/78.11 1443 (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]. 80.09/78.11 1444 (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]. 80.09/78.11 1445 (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]. 80.09/78.11 1446 (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]. 80.09/78.11 1447 (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]. 80.09/78.11 1448 (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]. 80.09/78.11 1449 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1450 (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]. 80.09/78.11 1451 (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]. 80.09/78.11 1452 (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]. 80.09/78.11 1453 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1454 (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]. 80.09/78.11 1455 (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]. 80.09/78.11 1456 (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]. 80.09/78.11 1457 (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]. 80.09/78.11 1458 (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]. 80.09/78.11 1459 (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]. 80.09/78.11 1460 (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]. 80.09/78.11 1461 (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]. 80.09/78.11 1462 (all A (-v1_xboole_0(A) -> k1_xboole_0 != k6_relat_1(A))) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1463 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1464 (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]. 80.09/78.11 1465 (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]. 80.09/78.11 1466 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1467 (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]. 80.09/78.11 1468 (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]. 80.09/78.11 1469 (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]. 80.09/78.11 1470 (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]. 80.09/78.11 1471 (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]. 80.09/78.11 1472 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1473 (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]. 80.09/78.11 1474 (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]. 80.09/78.11 1475 (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]. 80.09/78.11 1476 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1477 (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]. 80.09/78.11 1478 (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]. 80.09/78.11 1479 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1480 (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]. 80.09/78.11 1481 (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]. 80.09/78.11 1482 (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]. 80.09/78.11 1483 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1484 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1485 (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]. 80.09/78.11 1486 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1487 (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]. 80.09/78.11 1488 (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]. 80.09/78.11 1489 (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]. 80.09/78.11 1490 (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]. 80.09/78.11 1491 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1492 (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]. 80.09/78.11 1493 (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]. 80.09/78.11 1494 (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]. 80.09/78.11 1495 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1496 (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]. 80.09/78.11 1497 (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]. 80.09/78.11 1498 (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]. 80.09/78.11 1499 (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]. 80.09/78.11 1500 (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]. 80.09/78.11 1501 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1502 (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]. 80.09/78.11 1503 (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]. 80.09/78.11 1504 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1505 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1506 (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]. 80.09/78.11 1507 (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]. 80.09/78.11 1508 (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]. 80.09/78.11 1509 (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]. 80.09/78.11 1510 (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]. 80.09/78.11 1511 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1512 (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]. 80.09/78.11 1513 (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]. 80.09/78.11 1514 (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]. 80.09/78.11 1515 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1516 (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]. 80.09/78.11 1517 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1518 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1519 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1520 (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]. 80.09/78.11 1521 (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]. 80.09/78.11 1522 (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]. 80.09/78.11 1523 (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]. 80.09/78.11 1524 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1525 (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]. 80.09/78.11 1526 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1527 (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]. 80.09/78.11 1528 (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]. 80.09/78.11 1529 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1530 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1531 (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]. 80.09/78.11 1532 (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]. 80.09/78.11 1533 (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]. 80.09/78.11 1534 (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]. 80.09/78.11 1535 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1536 (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]. 80.09/78.11 1537 (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]. 80.09/78.11 1538 (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]. 80.09/78.11 1539 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1540 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1541 (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]. 80.09/78.11 1542 (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]. 80.09/78.11 1543 (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]. 80.09/78.11 1544 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1545 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1546 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1547 (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]. 80.09/78.11 1548 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1549 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1550 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1551 (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]. 80.09/78.11 1552 (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]. 80.09/78.11 1553 (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]. 80.09/78.11 1554 (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]. 80.09/78.11 1555 (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]. 80.09/78.11 1556 (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]. 80.09/78.11 1557 (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]. 80.09/78.11 1558 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1559 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1560 (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]. 80.09/78.11 1561 (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]. 80.09/78.11 1562 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1563 (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]. 80.09/78.11 1564 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1565 (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]. 80.09/78.11 1566 (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]. 80.09/78.11 1567 (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]. 80.09/78.11 1568 (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]. 80.09/78.11 1569 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1570 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1571 (all A k6_partfun1(A) = k6_relat_1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.11 1572 (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]. 80.09/78.11 1573 (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]. 80.09/78.11 1574 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1575 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1576 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1577 (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]. 80.09/78.12 1578 (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]. 80.09/78.12 1579 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1580 (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]. 80.09/78.12 1581 (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]. 80.09/78.12 1582 (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]. 80.09/78.12 1583 (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]. 80.09/78.12 1584 (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]. 80.09/78.12 1585 (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]. 80.09/78.12 1586 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1587 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1588 (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]. 80.09/78.12 1589 (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]. 80.09/78.12 1590 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1591 (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]. 80.09/78.12 1592 (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]. 80.09/78.12 1593 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1594 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1595 (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]. 80.09/78.12 1596 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1597 (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]. 80.09/78.12 1598 (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]. 80.09/78.12 1599 (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]. 80.09/78.12 1600 (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]. 80.09/78.12 1601 (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]. 80.09/78.12 1602 (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]. 80.09/78.12 1603 (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]. 80.09/78.12 1604 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1605 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1606 (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]. 80.09/78.12 1607 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1608 (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]. 80.09/78.12 1609 (all A k4_partfun1(A,k1_xboole_0) = k1_tarski(k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1610 (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]. 80.09/78.12 1611 (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]. 80.09/78.12 1612 (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]. 80.09/78.12 1613 (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]. 80.09/78.12 1614 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1615 (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]. 80.09/78.12 1616 (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]. 80.09/78.12 1617 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1618 (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]. 80.09/78.12 1619 (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]. 80.09/78.12 1620 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1621 (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]. 80.09/78.12 1622 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1623 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1624 (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]. 80.09/78.12 1625 (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]. 80.09/78.12 1626 (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]. 80.09/78.12 1627 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1628 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1629 (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]. 80.09/78.12 1630 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1631 (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]. 80.09/78.12 1632 (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]. 80.09/78.12 1633 (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]. 80.09/78.12 1634 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1635 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1636 (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]. 80.09/78.12 1637 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1638 (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]. 80.09/78.12 1639 (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]. 80.09/78.12 1640 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1641 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1642 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1643 (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]. 80.09/78.12 1644 (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]. 80.09/78.12 1645 (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]. 80.09/78.12 1646 (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]. 80.09/78.12 1647 (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]. 80.09/78.12 1648 (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]. 80.09/78.12 1649 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1650 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1651 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1652 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1653 (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]. 80.09/78.12 1654 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1655 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1656 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1657 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1658 (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]. 80.09/78.12 1659 (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]. 80.09/78.12 1660 (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]. 80.09/78.12 1661 (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]. 80.09/78.12 1662 (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]. 80.09/78.12 1663 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1664 (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]. 80.09/78.12 1665 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1666 (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]. 80.09/78.12 1667 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1668 (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]. 80.09/78.12 1669 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1670 (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]. 80.09/78.12 1671 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1672 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1673 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1674 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1675 (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]. 80.09/78.12 1676 (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]. 80.09/78.12 1677 (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]. 80.09/78.12 1678 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1679 (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]. 80.09/78.12 1680 (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]. 80.09/78.12 1681 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1682 (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]. 80.09/78.12 1683 (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]. 80.09/78.12 1684 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1685 (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]. 80.09/78.12 1686 (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]. 80.09/78.12 1687 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1688 (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]. 80.09/78.12 1689 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1690 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1691 (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]. 80.09/78.12 1692 (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]. 80.09/78.12 1693 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1694 (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]. 80.09/78.12 1695 (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]. 80.09/78.12 1696 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1697 (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]. 80.09/78.12 1698 (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]. 80.09/78.12 1699 (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]. 80.09/78.12 1700 (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]. 80.09/78.12 1701 (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]. 80.09/78.12 1702 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1703 (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]. 80.09/78.12 1704 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1705 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1706 (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]. 80.09/78.12 1707 (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]. 80.09/78.12 1708 (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]. 80.09/78.12 1709 (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]. 80.09/78.12 1710 (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]. 80.09/78.12 1711 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1712 (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]. 80.09/78.12 1713 (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]. 80.09/78.12 1714 (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]. 80.09/78.12 1715 (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]. 80.09/78.12 1716 (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]. 80.09/78.12 1717 (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]. 80.09/78.12 1718 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1719 (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]. 80.09/78.12 1720 (all A k20_mcart_1(A) = k2_mcart_1(k2_mcart_1(A))) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1721 (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]. 80.09/78.12 1722 (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]. 80.09/78.12 1723 (all A k17_mcart_1(A) = k1_mcart_1(k1_mcart_1(A))) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1724 (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]. 80.09/78.12 1725 (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]. 80.09/78.12 1726 (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]. 80.09/78.12 1727 (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]. 80.09/78.12 1728 (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]. 80.09/78.12 1729 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1730 (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]. 80.09/78.12 1731 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.12 1732 (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]. 80.09/78.12 1733 (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]. 80.09/78.13 1734 (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]. 80.09/78.13 1735 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.13 1736 (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]. 80.09/78.13 1737 (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]. 80.09/78.13 1738 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.13 1739 (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]. 80.09/78.13 1740 (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]. 80.09/78.13 1741 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (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]. 80.09/78.13 1742 (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]. 80.09/78.13 1743 (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]. 80.09/78.13 1744 (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]. 80.09/78.13 1745 (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]. 80.09/78.13 1746 (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]. 80.09/78.13 1747 (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]. 80.09/78.13 1748 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.13 1749 (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]. 80.09/78.13 1750 (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]. 80.09/78.13 1751 (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]. 80.09/78.13 1752 (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]. 80.09/78.13 1753 (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]. 80.09/78.13 1754 (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]. 80.09/78.13 1755 (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]. 80.09/78.13 1756 (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]. 80.09/78.13 1757 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.13 1758 (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]. 80.09/78.13 1759 (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]. 80.09/78.13 1760 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.13 1761 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.13 1762 (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]. 80.09/78.13 1763 (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]. 80.09/78.13 1764 (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]. 80.09/78.13 1765 (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]. 80.09/78.13 1766 (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]. 80.09/78.13 1767 (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]. 80.09/78.13 1768 (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]. 80.09/78.13 1769 (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]. 80.09/78.13 1770 (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]. 80.09/78.13 1771 (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]. 80.09/78.13 1772 (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]. 80.09/78.13 1773 (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]. 80.09/78.13 1774 (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]. 80.09/78.13 1775 (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]. 80.09/78.13 1776 (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]. 80.09/78.13 1777 (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]. 80.09/78.13 1778 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.09/78.13 1779 (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]. 80.09/78.13 1780 (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]. 80.09/78.13 1781 (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]. 80.09/78.13 1782 (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]. 80.09/78.13 1783 (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]. 80.09/78.13 1784 (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]. 80.09/78.13 1785 (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]. 80.09/78.13 1786 (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]. 80.09/78.13 1787 (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]. 80.09/78.13 1788 (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]. 80.09/78.13 1789 (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]. 80.09/78.13 1790 (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]. 80.09/78.13 1791 (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]. 80.09/78.13 1792 (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]. 80.09/78.13 1793 (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]. 80.09/78.13 1794 (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]. 80.09/78.13 1795 (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]. 80.09/78.13 1796 (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]. 80.09/78.13 1797 (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]. 80.09/78.13 1798 (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]. 80.09/78.13 1799 (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]. 80.09/78.13 1800 (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]. 80.09/78.13 1801 (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]. 80.13/78.13 1802 (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]. 80.13/78.13 1803 (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]. 80.13/78.13 1804 (all A k1_mcart_1(k2_mcart_1(A)) = k19_mcart_1(A)) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1805 (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]. 80.13/78.13 1806 (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]. 80.13/78.13 1807 (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]. 80.13/78.13 1808 (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]. 80.13/78.13 1809 (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]. 80.13/78.13 1810 (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]. 80.13/78.13 1811 (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]. 80.13/78.13 1812 (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]. 80.13/78.13 1813 (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]. 80.13/78.13 1814 (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]. 80.13/78.13 1815 (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]. 80.13/78.13 1816 (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]. 80.13/78.13 1817 (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]. 80.13/78.13 1818 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1819 (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]. 80.13/78.13 1820 (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]. 80.13/78.13 1821 (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]. 80.13/78.13 1822 (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]. 80.13/78.13 1823 (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]. 80.13/78.13 1824 (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]. 80.13/78.13 1825 (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]. 80.13/78.13 1826 (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]. 80.13/78.13 1827 (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]. 80.13/78.13 1828 (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]. 80.13/78.13 1829 (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]. 80.13/78.13 1830 (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]. 80.13/78.13 1831 (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]. 80.13/78.13 1832 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1833 (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]. 80.13/78.13 1834 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1835 (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]. 80.13/78.13 1836 (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]. 80.13/78.13 1837 (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]. 80.13/78.13 1838 (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]. 80.13/78.13 1839 (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]. 80.13/78.13 1840 (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]. 80.13/78.13 1841 (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]. 80.13/78.13 1842 (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]. 80.13/78.13 1843 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1844 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1845 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1846 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1847 (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]. 80.13/78.13 1848 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1849 (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]. 80.13/78.13 1850 (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]. 80.13/78.13 1851 (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]. 80.13/78.13 1852 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1853 (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]. 80.13/78.13 1854 (all A all B (r2_tarski(A,B) <-> r2_wellord2(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1855 (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]. 80.13/78.13 1856 (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]. 80.13/78.13 1857 (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]. 80.13/78.13 1858 (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]. 80.13/78.13 1859 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1860 (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]. 80.13/78.13 1861 (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]. 80.13/78.13 1862 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1863 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1864 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1865 (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]. 80.13/78.13 1866 (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]. 80.13/78.13 1867 (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]. 80.13/78.13 1868 (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]. 80.13/78.13 1869 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1870 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1871 (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]. 80.13/78.13 1872 (all A exists B (r2_wellord1(B,A) & v1_relat_1(B))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1873 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1874 (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]. 80.13/78.13 1875 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1876 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1877 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1878 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1879 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1880 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.13 1881 (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]. 80.13/78.14 1882 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1883 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1884 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1885 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1886 (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]. 80.13/78.14 1887 (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]. 80.13/78.14 1888 (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]. 80.13/78.14 1889 (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]. 80.13/78.14 1890 (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]. 80.13/78.14 1891 (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]. 80.13/78.14 1892 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1893 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1894 (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]. 80.13/78.14 1895 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1896 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1897 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1898 (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]. 80.13/78.14 1899 (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]. 80.13/78.14 1900 (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]. 80.13/78.14 1901 (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]. 80.13/78.14 1902 (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]. 80.13/78.14 1903 (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]. 80.13/78.14 1904 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1905 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1906 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1907 (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]. 80.13/78.14 1908 (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]. 80.13/78.14 1909 (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]. 80.13/78.14 1910 (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]. 80.13/78.14 1911 (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]. 80.13/78.14 1912 (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]. 80.13/78.14 1913 (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]. 80.13/78.14 1914 (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]. 80.13/78.14 1915 (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]. 80.13/78.14 1916 (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]. 80.13/78.14 1917 (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]. 80.13/78.14 1918 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1919 (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]. 80.13/78.14 1920 (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]. 80.13/78.14 1921 (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]. 80.13/78.14 1922 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1923 (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]. 80.13/78.14 1924 (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]. 80.13/78.14 1925 (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]. 80.13/78.14 1926 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1927 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1928 (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]. 80.13/78.14 1929 (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]. 80.13/78.14 1930 (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]. 80.13/78.14 1931 (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]. 80.13/78.14 1932 (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]. 80.13/78.14 1933 (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]. 80.13/78.14 1934 (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]. 80.13/78.14 1935 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1936 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1937 (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]. 80.13/78.14 1938 (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]. 80.13/78.14 1939 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1940 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1941 (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]. 80.13/78.14 1942 (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]. 80.13/78.14 1943 (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]. 80.13/78.14 1944 (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]. 80.13/78.14 1945 (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]. 80.13/78.14 1946 (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]. 80.13/78.14 1947 (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]. 80.13/78.14 1948 (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]. 80.13/78.14 1949 (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]. 80.13/78.14 1950 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1951 (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]. 80.13/78.14 1952 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1953 (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]. 80.13/78.14 1954 (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]. 80.13/78.14 1955 (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]. 80.13/78.14 1956 (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]. 80.13/78.14 1957 (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]. 80.13/78.14 1958 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1959 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1960 (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]. 80.13/78.14 1961 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1962 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1963 (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]. 80.13/78.14 1964 (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]. 80.13/78.14 1965 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1966 (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]. 80.13/78.14 1967 (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]. 80.13/78.14 1968 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1969 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1970 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1971 (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]. 80.13/78.14 1972 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]. 80.13/78.14 1973 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1974 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1975 (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]. 80.13/78.14 1976 (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]. 80.13/78.14 1977 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1978 (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]. 80.13/78.14 1979 (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]. 80.13/78.14 1980 (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]. 80.13/78.14 1981 (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]. 80.13/78.14 1982 (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]. 80.13/78.14 1983 (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]. 80.13/78.14 1984 (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]. 80.13/78.14 1985 (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]. 80.13/78.14 1986 (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]. 80.13/78.14 1987 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1988 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1989 (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]. 80.13/78.14 1990 (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]. 80.13/78.14 1991 (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]. 80.13/78.14 1992 (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]. 80.13/78.14 1993 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1994 (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]. 80.13/78.14 1995 (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]. 80.13/78.14 1996 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1997 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1998 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 1999 (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]. 80.13/78.14 2000 (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]. 80.13/78.14 2001 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 2002 (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]. 80.13/78.14 2003 (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]. 80.13/78.14 2004 (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]. 80.13/78.14 2005 (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]. 80.13/78.14 2006 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 2007 (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]. 80.13/78.14 2008 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 2009 (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]. 80.13/78.14 2010 (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]. 80.13/78.14 2011 (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]. 80.13/78.14 2012 (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]. 80.13/78.14 2013 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 2014 (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]. 80.13/78.14 2015 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 2016 (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]. 80.13/78.14 2017 (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]. 80.13/78.14 2018 (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]. 80.13/78.14 2019 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 2020 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 2021 (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]. 80.13/78.14 2022 (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]. 80.13/78.14 2023 (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]. 80.13/78.14 2024 (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]. 80.13/78.14 2025 (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]. 80.13/78.14 2026 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 2027 (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]. 80.13/78.14 2028 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.14 2029 (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]. 80.13/78.15 2030 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2031 (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]. 80.13/78.15 2032 (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]. 80.13/78.15 2033 (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]. 80.13/78.15 2034 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2035 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2036 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2037 (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]. 80.13/78.15 2038 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2039 (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]. 80.13/78.15 2040 (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]. 80.13/78.15 2041 (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]. 80.13/78.15 2042 (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]. 80.13/78.15 2043 (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]. 80.13/78.15 2044 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2045 (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]. 80.13/78.15 2046 (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]. 80.13/78.15 2047 (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]. 80.13/78.15 2048 (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]. 80.13/78.15 2049 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (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]. 80.13/78.15 2050 (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]. 80.13/78.15 2051 (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]. 80.13/78.15 2052 (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]. 80.13/78.15 2053 (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]. 80.13/78.15 2054 (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]. 80.13/78.15 2055 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2056 (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]. 80.13/78.15 2057 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2058 (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]. 80.13/78.15 2059 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2060 (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]. 80.13/78.15 2061 (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]. 80.13/78.15 2062 (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]. 80.13/78.15 2063 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2064 (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]. 80.13/78.15 2065 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2066 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2067 (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]. 80.13/78.15 2068 (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]. 80.13/78.15 2069 (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]. 80.13/78.15 2070 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2071 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2072 (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]. 80.13/78.15 2073 (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]. 80.13/78.15 2074 (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]. 80.13/78.15 2075 (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]. 80.13/78.15 2076 (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]. 80.13/78.15 2077 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2078 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2079 (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]. 80.13/78.15 2080 (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]. 80.13/78.15 2081 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2082 (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]. 80.13/78.15 2083 (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]. 80.13/78.15 2084 (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]. 80.13/78.15 2085 (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]. 80.13/78.15 2086 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2087 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2088 (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]. 80.13/78.15 2089 (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]. 80.13/78.15 2090 (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]. 80.13/78.15 2091 (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]. 80.13/78.15 2092 (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]. 80.13/78.15 2093 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2094 (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]. 80.13/78.15 2095 (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]. 80.13/78.15 2096 (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]. 80.13/78.15 2097 (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]. 80.13/78.15 2098 (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]. 80.13/78.15 2099 (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]. 80.13/78.15 2100 (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]. 80.13/78.15 2101 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2102 (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]. 80.13/78.15 2103 (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]. 80.13/78.15 2104 (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]. 80.13/78.15 2105 (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]. 80.13/78.15 2106 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2107 (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]. 80.13/78.15 2108 (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]. 80.13/78.15 2109 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2110 (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]. 80.13/78.15 2111 (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]. 80.13/78.15 2112 (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]. 80.13/78.15 2113 (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]. 80.13/78.15 2114 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2115 (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]. 80.13/78.15 2116 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2117 (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]. 80.13/78.15 2118 (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]. 80.13/78.15 2119 (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]. 80.13/78.15 2120 (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]. 80.13/78.15 2121 (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]. 80.13/78.15 2122 (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]. 80.13/78.15 2123 (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]. 80.13/78.15 2124 (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]. 80.13/78.15 2125 (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]. 80.13/78.15 2126 (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]. 80.13/78.15 2127 (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]. 80.13/78.15 2128 (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]. 80.13/78.15 2129 (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]. 80.13/78.15 2130 (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]. 80.13/78.15 2131 (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]. 80.13/78.15 2132 (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]. 80.13/78.15 2133 (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]. 80.13/78.15 2134 (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]. 80.13/78.15 2135 (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]. 80.13/78.15 2136 (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]. 80.13/78.15 2137 (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]. 80.13/78.15 2138 (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]. 80.13/78.15 2139 (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]. 80.13/78.15 2140 (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]. 80.13/78.15 2141 (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]. 80.13/78.15 2142 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2143 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2144 (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]. 80.13/78.15 2145 (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]. 80.13/78.15 2146 (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]. 80.13/78.15 2147 (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]. 80.13/78.15 2148 (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]. 80.13/78.15 2149 (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]. 80.13/78.15 2150 (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]. 80.13/78.15 2151 (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]. 80.13/78.15 2152 (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]. 80.13/78.15 2153 (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]. 80.13/78.15 2154 (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]. 80.13/78.15 2155 (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]. 80.13/78.15 2156 (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]. 80.13/78.15 2157 (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]. 80.13/78.15 2158 (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]. 80.13/78.15 2159 (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]. 80.13/78.15 2160 (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]. 80.13/78.15 2161 (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]. 80.13/78.15 2162 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2163 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2164 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2165 (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]. 80.13/78.15 2166 (all A k12_funct_3(A) = k11_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2167 (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]. 80.13/78.15 2168 (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]. 80.13/78.15 2169 (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]. 80.13/78.15 2170 (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]. 80.13/78.15 2171 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2172 (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]. 80.13/78.15 2173 (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]. 80.13/78.15 2174 (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]. 80.13/78.15 2175 (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]. 80.13/78.15 2176 (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]. 80.13/78.15 2177 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2178 (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]. 80.13/78.15 2179 (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]. 80.13/78.15 2180 (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]. 80.13/78.15 2181 (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]. 80.13/78.15 2182 (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]. 80.13/78.15 2183 (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]. 80.13/78.15 2184 (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]. 80.13/78.15 2185 (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]. 80.13/78.15 2186 (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]. 80.13/78.15 2187 (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]. 80.13/78.15 2188 (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]. 80.13/78.15 2189 (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]. 80.13/78.15 2190 (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]. 80.13/78.15 2191 (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]. 80.13/78.15 2192 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.15 2193 (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]. 80.13/78.16 2194 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2195 (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]. 80.13/78.16 2196 (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]. 80.13/78.16 2197 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2198 (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]. 80.13/78.16 2199 (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]. 80.13/78.16 2200 (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]. 80.13/78.16 2201 (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]. 80.13/78.16 2202 (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]. 80.13/78.16 2203 (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]. 80.13/78.16 2204 (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]. 80.13/78.16 2205 (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]. 80.13/78.16 2206 (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]. 80.13/78.16 2207 (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]. 80.13/78.16 2208 (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]. 80.13/78.16 2209 (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]. 80.13/78.16 2210 (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]. 80.13/78.16 2211 (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]. 80.13/78.16 2212 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2213 (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]. 80.13/78.16 2214 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2215 (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]. 80.13/78.16 2216 (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]. 80.13/78.16 2217 (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]. 80.13/78.16 2218 (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]. 80.13/78.16 2219 (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]. 80.13/78.16 2220 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2221 (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]. 80.13/78.16 2222 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2223 (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]. 80.13/78.16 2224 (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]. 80.13/78.16 2225 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2226 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2227 (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]. 80.13/78.16 2228 (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]. 80.13/78.16 2229 (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]. 80.13/78.16 2230 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2231 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & p1_s5_domain_1(C) & A = C)) <-> r2_hidden(A,a_1_3_domain_1(B))))) # label(fraenkel_a_1_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2232 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> m1_subset_1(a_3_8_domain_1(A,B,C),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))))))) # label(s3_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2233 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (k4_domain_1(B,C,D,F,G,H) = E -> H = A))))))) <-> A = k7_mcart_1(B,C,D,E)))))))))) # label(t26_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2234 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E (r2_hidden(E,A) <-> (exists F (m1_subset_1(F,B) & (exists G ((exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))) & m1_subset_1(G,C))))))) -> k3_zfmisc_1(B,C,D) = A))))))))) # label(t16_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2235 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_6_domain_1(A,B,C))))))) # label(t63_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2236 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_domain_1(B)) <-> (exists C (A = C & p1_s1_domain_1(C) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2237 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> H = A))))))))) <-> A = k9_mcart_1(B,C,D,E,F)))))))))))) # label(t41_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2238 (all A ((exists B (m1_subset_1(B,f1_s7_domain_1) & A = B & p1_s7_domain_1(B))) <-> r2_hidden(A,a_0_0_domain_1))) # label(fraenkel_a_0_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2239 (all A all B all C all D all E all F all G all H all I (m1_subset_1(B,A) & m1_subset_1(I,A) & m1_subset_1(H,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k13_domain_1(A,B,C,D,E,F,G,H,I),k1_zfmisc_1(A)))) # label(dt_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2240 $T # label(t39_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2241 $T # label(t27_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2242 (all A all B all C all D all E (m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k9_domain_1(A,B,C,D,E) = k2_enumset1(B,C,D,E))) # label(redefinition_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2243 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(A) -> k16_domain_1(A,B,C,D) = k19_mcart_1(D))) # label(redefinition_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2244 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k8_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> A = G)))))))))))))))))))) # label(t40_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2245 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k1_tarski(B) = k6_domain_1(A,B))) # label(redefinition_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2246 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) -> m1_subset_1(k17_domain_1(A,B,C,D),C))) # label(dt_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2247 (all A all B all C all D all E all F (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,A) & m1_subset_1(E,B) & m1_subset_1(F,C) & -v1_xboole_0(A) -> m1_subset_1(k4_domain_1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)))) # label(dt_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2248 $T # label(t37_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2249 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (m1_subset_1(E,B) & E = A & -(r2_hidden(E,D) <-> r2_hidden(E,C)))) <-> r2_hidden(A,a_3_7_domain_1(B,C,D))))) # label(fraenkel_a_3_7_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2250 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> (all D (m1_subset_1(D,k2_zfmisc_1(A,B)) -> (k2_mcart_1(C) = k2_mcart_1(D) & k1_mcart_1(D) = k1_mcart_1(C) -> C = D))))))))) # label(t12_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2251 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(A) -> k1_mcart_1(C) = k2_domain_1(A,B,C))) # label(redefinition_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2252 $T # label(t5_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2253 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_7_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t64_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2254 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(F,C) & m1_subset_1(E,B) & m1_subset_1(D,A) & -v1_xboole_0(C) & -v1_xboole_0(B) -> k4_domain_1(A,B,C,D,E,F) = k3_mcart_1(D,E,F))) # label(redefinition_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2255 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(E,A) & m1_subset_1(H,D) & m1_subset_1(G,C) & m1_subset_1(F,B) & -v1_xboole_0(D) & -v1_xboole_0(C) -> m1_subset_1(k5_domain_1(A,B,C,D,E,F,G,H),k4_zfmisc_1(A,B,C,D)))) # label(dt_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2256 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> m1_subset_1(a_4_2_domain_1(A,B,C,D),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))))))))) # label(s4_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2257 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k2_zfmisc_1(A,B) = a_2_0_domain_1(A,B))))) # label(t49_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2258 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (r2_hidden(E,C) & r2_hidden(E,D) & A = E & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_1_domain_1(B,C,D))))) # label(fraenkel_a_3_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2259 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> a_6_0_domain_1(A,B,C,D,E,F) = k13_mcart_1(A,B,C,D,E,F))))))))))))) # label(t54_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2260 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> (A = k6_mcart_1(B,C,D,E) <-> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (k4_domain_1(B,C,D,F,G,H) = E -> G = A)))))))))))))))) # label(t25_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2261 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> a_2_2_domain_1(A,B) = k3_subset_1(A,B))))) # label(t57_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2262 $T # label(t19_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2263 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(E,A) -> m1_subset_1(k12_domain_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(A)))) # label(dt_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2264 $T # label(t29_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2265 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_8_domain_1(B,C,D)) <-> (exists E exists F exists G (p1_s3_domain_1(E,F,G) & A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(G,D) & m1_subset_1(F,C) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_8_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2266 (all A (-v1_xboole_0(A) -> a_1_0_domain_1(A) = A)) # label(t48_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2267 $T # label(t23_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2268 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> -(r2_hidden(A,k2_zfmisc_1(B,C)) & (all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,C) -> k4_tarski(D,E) != A))))))))) # label(t9_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2269 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = a_3_3_domain_1(A,B,C))))))) # label(t60_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2270 (all A ((exists B (p2_s10_domain_1(B) & p1_s10_domain_1(B) & B = A & m1_subset_1(B,f1_s10_domain_1))) <-> r2_hidden(A,a_0_3_domain_1))) # label(fraenkel_a_0_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2271 (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) -> k15_domain_1(A,B,C,D) = k18_mcart_1(D))) # label(redefinition_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2272 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = a_3_1_domain_1(A,B,C))))))) # label(t58_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2273 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_4_domain_1(B)) <-> (exists C (A = C & p2_s5_domain_1(C) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2274 $T # label(t34_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2275 (all A (-v1_xboole_0(A) -> k1_subset_1(A) = a_1_1_domain_1(A))) # label(t56_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2276 $T # label(t20_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2277 (all A all B all C all D all E all F all G all H (-v1_xboole_0(D) & m1_subset_1(E,A) & m1_subset_1(G,C) & m1_subset_1(H,D) & m1_subset_1(F,B) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k4_mcart_1(E,F,G,H) = k5_domain_1(A,B,C,D,E,F,G,H))) # label(redefinition_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2278 (all A (r2_hidden(A,a_0_1_domain_1) <-> (exists B (m1_subset_1(B,f1_s8_domain_1) & A = f3_s8_domain_1(B) & p1_s8_domain_1(B))))) # label(fraenkel_a_0_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2279 $T # label(t8_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2280 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> a_2_1_domain_1(A,B) = B)))) # label(t52_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2281 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(E) & -v1_xboole_0(D) -> (r2_hidden(A,a_4_2_domain_1(B,C,D,E)) <-> (exists F exists G exists H exists I (p1_s4_domain_1(F,G,H,I) & k5_domain_1(B,C,D,E,F,G,H,I) = A & m1_subset_1(I,E) & m1_subset_1(H,D) & m1_subset_1(G,C) & m1_subset_1(F,B)))))) # label(fraenkel_a_4_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2282 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & A = C & p1_s6_domain_1(C))) <-> r2_hidden(A,a_1_5_domain_1(B))))) # label(fraenkel_a_1_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2283 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> k3_zfmisc_1(A,B,C) = a_3_0_domain_1(A,B,C))))))) # label(t50_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2284 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> (k5_mcart_1(A,B,C,D) = k5_mcart_1(A,B,C,E) & k7_mcart_1(A,B,C,D) = k7_mcart_1(A,B,C,E) & k6_mcart_1(A,B,C,D) = k6_mcart_1(A,B,C,E) -> E = D))))))))))) # label(t28_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2285 (all A all B all C all D (m1_subset_1(D,B) & m1_subset_1(C,A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)))) # label(dt_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2286 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((exists F (m1_subset_1(F,B) & (exists G (m1_subset_1(G,C) & (exists H ((exists I (m1_subset_1(I,E) & k4_mcart_1(F,G,H,I) = A)) & m1_subset_1(H,D))))))) <-> r2_hidden(A,k4_zfmisc_1(B,C,D,E))))))))))) # label(t31_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2287 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k2_tarski(B,C) = k7_domain_1(A,B,C))) # label(redefinition_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2288 $T # label(t46_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2289 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(C) & -v1_xboole_0(E) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(I,k1_zfmisc_1(E)) & m1_subset_1(H,k1_zfmisc_1(D)) & -v1_xboole_0(D) & -v1_xboole_0(B) -> (r2_hidden(A,a_8_0_domain_1(B,C,D,E,F,G,H,I)) <-> (exists J exists K exists L exists M (m1_subset_1(J,B) & m1_subset_1(K,C) & m1_subset_1(L,D) & A = k5_domain_1(B,C,D,E,J,K,L,M) & r2_hidden(M,I) & r2_hidden(L,H) & r2_hidden(K,G) & r2_hidden(J,F) & m1_subset_1(M,E)))))) # label(fraenkel_a_8_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2290 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) -> ((exists D (m1_subset_1(D,B) & r2_hidden(D,C) & D = A)) <-> r2_hidden(A,a_2_1_domain_1(B,C))))) # label(fraenkel_a_2_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2291 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k7_domain_1(A,B,C) = k7_domain_1(A,C,B))) # label(commutativity_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2292 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> k4_zfmisc_1(A,B,C,D) = a_4_0_domain_1(A,B,C,D))))))))) # label(t51_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2293 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p1_s5_domain_1(B) -> p2_s5_domain_1(B)))) -> r1_tarski(a_1_3_domain_1(A),a_1_4_domain_1(A))))) # label(s5_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2294 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> (k10_mcart_1(A,B,C,D,E) = k10_mcart_1(A,B,C,D,F) & k11_mcart_1(A,B,C,D,E) = k11_mcart_1(A,B,C,D,F) & k9_mcart_1(A,B,C,D,F) = k9_mcart_1(A,B,C,D,E) & k8_mcart_1(A,B,C,D,F) = k8_mcart_1(A,B,C,D,E) -> E = F))))))))))))) # label(t45_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2295 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) -> m1_subset_1(k14_domain_1(A,B,C,D),A))) # label(dt_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2296 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (F = k5_domain_1(B,C,D,E,G,H,I,J) -> J = A))))))))) <-> k11_mcart_1(B,C,D,E,F) = A))))))))))) # label(t43_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2297 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_0_domain_1(B,C)) <-> (exists D exists E (m1_subset_1(D,B) & m1_subset_1(E,C) & k1_domain_1(B,C,D,E) = A))))) # label(fraenkel_a_2_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2298 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (k3_zfmisc_1(B,C,D) = A <-> (all E (r2_hidden(E,A) <-> (exists F ((exists G ((exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))) & m1_subset_1(G,C))) & m1_subset_1(F,B)))))))))))))) # label(t17_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2299 $T # label(t30_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2300 (all A all B all C all D (m1_subset_1(D,B) & m1_subset_1(C,A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k4_tarski(C,D) = k1_domain_1(A,B,C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2301 $T # label(t38_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2302 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (r2_hidden(A,k3_zfmisc_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & (exists F (m1_subset_1(F,C) & (exists G (m1_subset_1(G,D) & A = k3_mcart_1(E,F,G)))))))))))))) # label(t15_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2303 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_4_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & (r2_hidden(E,C) & -r2_hidden(E,D) | r2_hidden(E,D) & -r2_hidden(E,C)) & E = A))))) # label(fraenkel_a_3_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2304 (all A (r2_hidden(A,a_0_2_domain_1) <-> (exists B exists C (m1_subset_1(B,f1_s9_domain_1) & p1_s9_domain_1(B,C) & f4_s9_domain_1(B,C) = A & m1_subset_1(C,f2_s9_domain_1))))) # label(fraenkel_a_0_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2305 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_4_domain_1(A,B,C))))))) # label(t61_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2306 $T # label(t13_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2307 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) -> ((exists E ((r2_hidden(E,D) <-> -r2_hidden(E,C)) & A = E & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_5_domain_1(B,C,D))))) # label(fraenkel_a_3_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2308 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(A) -> m1_subset_1(k15_domain_1(A,B,C,D),B))) # label(dt_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2309 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.16 2310 (all A all B all C all D all E all F all G (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k11_domain_1(A,B,C,D,E,F,G),k1_zfmisc_1(A)))) # label(dt_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2311 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p2_s6_domain_1(B) <-> p1_s6_domain_1(B)))) -> a_1_5_domain_1(A) = a_1_6_domain_1(A)))) # label(s6_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2312 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) -> k10_domain_1(A,B,C,D,E,F) = k3_enumset1(B,C,D,E,F))) # label(redefinition_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2313 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k9_domain_1(A,B,C,D,E),k1_zfmisc_1(A)))) # label(dt_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2314 $T # label(t4_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2315 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F ((exists G ((exists H (m1_subset_1(H,C) & (exists I (m1_subset_1(I,D) & (exists J (k4_mcart_1(G,H,I,J) = F & m1_subset_1(J,E))))))) & m1_subset_1(G,B))) <-> r2_hidden(F,A))) <-> A = k4_zfmisc_1(B,C,D,E)))))))))))) # label(t33_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2316 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> m1_subset_1(a_2_3_domain_1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))))))) # label(s2_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2317 (all A all B all C all D all E all F (m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k10_domain_1(A,B,C,D,E,F),k1_zfmisc_1(A)))) # label(dt_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2318 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(B,A) -> k1_enumset1(B,C,D) = k8_domain_1(A,B,C,D))) # label(redefinition_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2319 $T # label(t35_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2320 $T # label(t18_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2321 (all A all B (-v1_xboole_0(B) -> ((exists C (C = A & -$T & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_1_domain_1(B))))) # label(fraenkel_a_1_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2322 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> k3_domain_1(A,B,C) = k2_mcart_1(C))) # label(redefinition_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2323 (all A all B all C all D all E all F all G (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(E,A) -> k4_enumset1(B,C,D,E,F,G) = k11_domain_1(A,B,C,D,E,F,G))) # label(redefinition_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2324 $T # label(t10_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2325 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & A = C & p2_s6_domain_1(C))) <-> r2_hidden(A,a_1_6_domain_1(B))))) # label(fraenkel_a_1_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2326 $T # label(t21_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2327 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(H,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) -> k12_domain_1(A,B,C,D,E,F,G,H) = k5_enumset1(B,C,D,E,F,G,H))) # label(redefinition_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2328 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(C)) & m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_4_1_domain_1(B,C,D,E)) <-> (exists F exists G (m1_subset_1(F,B) & k1_domain_1(B,C,F,G) = A & r2_hidden(F,D) & r2_hidden(G,E) & m1_subset_1(G,C)))))) # label(fraenkel_a_4_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2329 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_5_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t62_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2330 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (A = k10_mcart_1(B,C,D,E,F) <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (F = k5_domain_1(B,C,D,E,G,H,I,J) -> A = I)))))))))))))))))))) # label(t42_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2331 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k7_domain_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2332 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_0_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & C = A))))) # label(fraenkel_a_1_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2333 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_3_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & E = A & r2_hidden(E,C) & -r2_hidden(E,D)))))) # label(fraenkel_a_3_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2334 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(I,A) & m1_subset_1(H,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(B,A) -> k6_enumset1(B,C,D,E,F,G,H,I) = k13_domain_1(A,B,C,D,E,F,G,H,I))) # label(redefinition_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2335 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> m1_subset_1(k3_domain_1(A,B,C),B))) # label(dt_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2336 $T # label(t36_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2337 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_0_domain_1(B,C,D)) <-> (exists E exists F exists G (A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(G,D) & m1_subset_1(F,C) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2338 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_6_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & (-r2_hidden(E,D) <-> r2_hidden(E,C)) & A = E))))) # label(fraenkel_a_3_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2339 $T # label(t7_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2340 $T # label(t3_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2341 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(B) -> k14_domain_1(A,B,C,D) = k17_mcart_1(D))) # label(redefinition_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2342 $T # label(t11_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2343 $T # label(t1_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2344 (all A all B all C all D all E (-v1_xboole_0(E) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_4_0_domain_1(B,C,D,E)) <-> (exists F exists G exists H exists I (m1_subset_1(H,D) & k5_domain_1(B,C,D,E,F,G,H,I) = A & m1_subset_1(I,E) & m1_subset_1(G,C) & m1_subset_1(F,B)))))) # label(fraenkel_a_4_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2345 $T # label(t22_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2346 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) -> m1_subset_1(k16_domain_1(A,B,C,D),B))) # label(dt_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2347 (all A (r2_hidden(A,a_0_5_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p2_s10_domain_1(B) & B = A)))) # label(fraenkel_a_0_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2348 $T # label(t44_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2349 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_2_domain_1(B,C,D)) <-> (exists E ((r2_hidden(E,C) | r2_hidden(E,D)) & A = E & m1_subset_1(E,B)))))) # label(fraenkel_a_3_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2350 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> a_4_1_domain_1(A,B,C,D) = k12_mcart_1(A,B,C,D))))))))) # label(t53_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2351 $T # label(t2_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2352 $T # label(t14_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2353 $T # label(t47_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2354 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k8_domain_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2355 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(A) -> k17_domain_1(A,B,C,D) = k20_mcart_1(D))) # label(redefinition_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2356 (all A (-v1_xboole_0(A) -> m1_subset_1(a_1_2_domain_1(A),k1_zfmisc_1(A)))) # label(s1_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2357 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_2_domain_1(A,B,C) = k4_subset_1(A,B,C))))))) # label(t59_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2358 (all A (r2_hidden(A,a_0_4_domain_1) <-> (exists B (A = B & p1_s10_domain_1(B) & m1_subset_1(B,f1_s10_domain_1))))) # label(fraenkel_a_0_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2359 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F (r2_hidden(F,A) <-> (exists G (m1_subset_1(G,B) & (exists H (m1_subset_1(H,C) & (exists I ((exists J (F = k4_mcart_1(G,H,I,J) & m1_subset_1(J,E))) & m1_subset_1(I,D))))))))) -> A = k4_zfmisc_1(B,C,D,E)))))))))))) # label(t32_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2360 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> (r2_hidden(A,a_2_3_domain_1(B,C)) <-> (exists D exists E (m1_subset_1(D,B) & m1_subset_1(E,C) & p1_s2_domain_1(D,E) & A = k1_domain_1(B,C,D,E)))))) # label(fraenkel_a_2_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2361 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_2_2_domain_1(B,C)) <-> (exists D (-r2_hidden(D,C) & D = A & m1_subset_1(D,B)))))) # label(fraenkel_a_2_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2362 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = a_8_0_domain_1(A,B,C,D,E,F,G,H))))))))))))))))) # label(t55_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2363 (all A all B all C (m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k2_domain_1(A,B,C),A))) # label(dt_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2364 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> (A = k5_mcart_1(B,C,D,E) <-> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (k4_domain_1(B,C,D,F,G,H) = E -> F = A)))))))))))))))) # label(t24_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2365 (all A all B all C all D all E all F all G (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) & m1_subset_1(G,k1_zfmisc_1(D)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) -> ((exists H exists I exists J (m1_subset_1(I,C) & m1_subset_1(J,D) & A = k4_domain_1(B,C,D,H,I,J) & r2_hidden(I,F) & r2_hidden(J,G) & r2_hidden(H,E) & m1_subset_1(H,B))) <-> r2_hidden(A,a_6_0_domain_1(B,C,D,E,F,G))))) # label(fraenkel_a_6_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2366 $T # label(t6_domain_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2367 (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]. 80.13/78.17 2368 (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]. 80.13/78.17 2369 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2370 (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]. 80.13/78.17 2371 (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]. 80.13/78.17 2372 (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]. 80.13/78.17 2373 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2374 (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]. 80.13/78.17 2375 (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]. 80.13/78.17 2376 (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]. 80.13/78.17 2377 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2378 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2379 (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]. 80.13/78.17 2380 (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]. 80.13/78.17 2381 (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]. 80.13/78.17 2382 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2383 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2384 (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]. 80.13/78.17 2385 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2386 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2387 (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]. 80.13/78.17 2388 (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]. 80.13/78.17 2389 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2390 (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]. 80.13/78.17 2391 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2392 (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]. 80.13/78.17 2393 (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]. 80.13/78.17 2394 (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]. 80.13/78.17 2395 (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]. 80.13/78.17 2396 (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]. 80.13/78.17 2397 (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]. 80.13/78.17 2398 (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]. 80.13/78.17 2399 (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]. 80.13/78.17 2400 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2401 (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]. 80.13/78.17 2402 (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]. 80.13/78.17 2403 (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]. 80.13/78.17 2404 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2405 (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]. 80.13/78.17 2406 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (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]. 80.13/78.17 2407 (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]. 80.13/78.17 2408 (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]. 80.13/78.17 2409 (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]. 80.13/78.17 2410 (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]. 80.13/78.17 2411 (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]. 80.13/78.17 2412 (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]. 80.13/78.17 2413 (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]. 80.13/78.17 2414 (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]. 80.13/78.17 2415 (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]. 80.13/78.17 2416 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2417 (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]. 80.13/78.17 2418 (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]. 80.13/78.17 2419 (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]. 80.13/78.17 2420 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2421 (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]. 80.13/78.17 2422 (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]. 80.13/78.17 2423 (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]. 80.13/78.17 2424 (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]. 80.13/78.17 2425 (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]. 80.13/78.17 2426 (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]. 80.13/78.17 2427 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2428 (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]. 80.13/78.17 2429 (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]. 80.13/78.17 2430 (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]. 80.13/78.17 2431 (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]. 80.13/78.17 2432 (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]. 80.13/78.17 2433 (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]. 80.13/78.17 2434 (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]. 80.13/78.17 2435 (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]. 80.13/78.17 2436 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2437 (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]. 80.13/78.17 2438 (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]. 80.13/78.17 2439 (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]. 80.13/78.17 2440 (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]. 80.13/78.17 2441 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2442 (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]. 80.13/78.17 2443 (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]. 80.13/78.17 2444 (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]. 80.13/78.17 2445 (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]. 80.13/78.17 2446 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2447 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.17 2448 (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]. 80.13/78.18 2449 (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]. 80.13/78.18 2450 (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]. 80.13/78.18 2451 (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]. 80.13/78.18 2452 (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]. 80.13/78.18 2453 (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]. 80.13/78.18 2454 (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]. 80.13/78.18 2455 (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]. 80.13/78.18 2456 (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]. 80.13/78.18 2457 (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]. 80.13/78.18 2458 (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]. 80.13/78.18 2459 (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]. 80.13/78.18 2460 (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]. 80.13/78.18 2461 (exists A (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.18 2462 (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]. 80.13/78.18 2463 (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]. 80.13/78.18 2464 (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]. 80.13/78.18 2465 (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]. 80.13/78.18 2466 (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]. 80.13/78.18 2467 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.18 2468 (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]. 80.13/78.18 2469 (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]. 80.13/78.18 2470 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.18 2471 (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]. 80.13/78.18 2472 (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]. 80.13/78.18 2473 (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]. 80.13/78.18 2474 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.18 2475 (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]. 80.13/78.18 2476 (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]. 80.13/78.18 2477 (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]. 80.13/78.18 2478 (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]. 80.13/78.18 2479 (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]. 80.13/78.18 2480 (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]. 80.13/78.18 2481 (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]. 80.13/78.18 2482 (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]. 80.13/78.18 2483 (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]. 80.13/78.18 2484 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.18 2485 (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]. 80.13/78.18 2486 (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]. 80.13/78.18 2487 (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]. 80.13/78.18 2488 (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]. 80.13/78.18 2489 (all A k12_funct_3(A) = k1_funcop_1(k12_funct_3(A))) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.18 2490 (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]. 80.13/78.18 2491 (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]. 80.13/78.18 2492 (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]. 80.13/78.18 2493 (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]. 80.13/78.18 2494 (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]. 80.13/78.18 2495 (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]. 80.13/78.18 2496 (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]. 80.13/78.18 2497 (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]. 80.13/78.18 2498 (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]. 80.13/78.18 2499 (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]. 80.13/78.18 2500 (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]. 80.13/78.18 2501 (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]. 80.13/78.18 2502 (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]. 80.13/78.18 2503 (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]. 80.13/78.18 2504 (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]. 80.13/78.18 2505 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.18 2506 (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]. 80.13/78.18 2507 (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]. 80.13/78.18 2508 (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]. 80.13/78.18 2509 (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]. 80.13/78.18 2510 (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]. 80.13/78.18 2511 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.18 2512 (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]. 80.13/78.18 2513 (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]. 80.13/78.18 2514 (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]. 80.13/78.18 2515 (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]. 80.13/78.18 2516 (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]. 80.13/78.18 2517 (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]. 80.13/78.18 2518 (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]. 80.13/78.18 2519 (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]. 80.13/78.18 2520 (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]. 80.13/78.18 2521 (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]. 80.13/78.18 2522 (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]. 80.13/78.18 2523 (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]. 80.13/78.18 2524 (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]. 80.13/78.18 2525 (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]. 80.13/78.18 2526 (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]. 80.13/78.18 2527 (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]. 80.13/78.18 2528 (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]. 80.13/78.18 2529 (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]. 80.13/78.18 2530 (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]. 80.13/78.18 2531 (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]. 80.13/78.18 2532 (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]. 80.13/78.18 2533 (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]. 80.13/78.18 2534 (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]. 80.13/78.18 2535 (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]. 80.13/78.18 2536 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 80.13/78.18 2537 (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]. 80.13/78.18 2538 (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]. 80.13/78.18 2539 (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]. 80.13/78.18 2540 (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]. 80.13/78.18 2541 (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]. 80.13/78.18 2542 (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]. 80.13/78.18 2543 (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]. 80.13/78.18 2544 (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]. 80.13/78.18 2545 (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]. 80.13/78.18 2546 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 80.13/78.18 2547 (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]. 80.13/78.18 2548 (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]. 80.13/78.18 2549 (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]. 80.13/78.18 2550 (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]. 80.13/78.18 2551 (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]. 80.13/78.18 2552 (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]. 80.13/78.18 2553 (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]. 80.13/78.18 2554 (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]. 80.13/78.18 2555 (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]. 80.13/78.18 2556 (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]. 80.13/78.18 2557 (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]. 80.13/78.18 2558 (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]. 80.13/78.18 2559 (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]. 80.13/78.18 2560 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 80.13/78.18 2561 (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]. 80.13/78.18 2562 (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]. 80.13/78.18 2563 (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]. 80.13/78.18 2564 (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]. 80.13/78.18 2565 (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]. 80.13/78.18 2566 (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]. 80.13/78.19 2567 (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]. 80.13/78.19 2568 (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]. 80.13/78.19 2569 (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]. 80.13/78.19 2570 (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]. 80.13/78.19 2571 (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]. 80.13/78.19 2572 (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]. 80.13/78.19 2573 (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]. 80.13/78.19 2574 (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]. 80.13/78.19 2575 (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]. 80.13/78.19 2576 (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]. 80.13/78.19 2577 (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]. 80.13/78.19 2578 (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]. 80.13/78.19 2579 (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]. 80.13/78.19 2580 (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]. 80.13/78.19 2581 (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]. 80.13/78.19 2582 (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]. 80.13/78.19 2583 (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]. 80.13/78.19 2584 (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]. 80.13/78.19 2585 (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]. 80.13/78.19 2586 (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]. 80.13/78.19 2587 (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]. 80.13/78.19 2588 (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]. 80.13/78.19 2589 (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]. 80.13/78.19 2590 (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]. 80.13/78.19 2591 (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]. 80.13/78.19 2592 (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]. 80.13/78.19 2593 (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]. 80.13/78.19 2594 (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]. 80.13/78.19 2595 (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]. 80.13/78.19 2596 (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]. 80.13/78.19 2597 (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]. 80.13/78.19 2598 (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]. 80.13/78.19 2599 (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]. 80.13/78.19 2600 (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]. 80.13/78.19 2601 (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]. 80.13/78.19 2602 (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]. 80.13/78.19 2603 (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]. 80.13/78.19 2604 (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]. 80.13/78.19 2605 (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]. 80.13/78.19 2606 (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]. 80.13/78.19 2607 (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]. 80.13/78.19 2608 (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]. 80.13/78.19 2609 (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]. 80.13/78.19 2610 (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]. 80.13/78.19 2611 (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]. 80.13/78.19 2612 (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]. 80.13/78.19 2613 (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]. 80.13/78.19 2614 (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]. 80.13/78.19 2615 (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]. 80.13/78.19 2616 (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]. 80.13/78.19 2617 (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]. 80.13/78.19 2618 (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]. 80.13/78.19 2619 (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]. 80.13/78.19 2620 (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]. 80.13/78.19 2621 (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]. 80.13/78.19 2622 (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]. 80.13/78.19 2623 (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]. 80.13/78.19 2624 (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]. 80.13/78.19 2625 (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]. 80.13/78.19 2626 (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]. 80.13/78.19 2627 (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]. 80.13/78.19 2628 (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]. 80.13/78.19 2629 (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]. 80.13/78.19 2630 (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]. 80.13/78.19 2631 (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]. 80.20/78.27 2632 (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]. 80.20/78.27 2633 (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]. 80.20/78.27 2634 (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]. 80.20/78.27 2635 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.20/78.27 2636 (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]. 80.20/78.27 2637 (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]. 80.20/78.27 2638 (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]. 80.20/78.27 2639 (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]. 80.20/78.27 2640 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.20/78.27 2641 (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]. 80.20/78.27 2642 (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]. 80.20/78.27 2643 (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]. 80.20/78.27 2644 (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]. 80.20/78.27 2645 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.20/78.27 2646 (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]. 80.20/78.27 2647 (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]. 80.20/78.27 2648 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.20/78.27 2649 (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]. 80.27/78.27 2650 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.27/78.27 2651 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.27/78.27 2652 (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]. 80.27/78.27 2653 (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]. 80.27/78.27 2654 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.27/78.27 2655 (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]. 80.27/78.27 2656 (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]. 80.27/78.27 2657 (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]. 80.27/78.27 2658 (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]. 80.27/78.27 2659 (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]. 80.27/78.29 2660 (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]. 80.27/78.29 2661 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.27/78.29 2662 (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]. 80.27/78.29 2663 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.27/78.29 2664 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.27/78.29 2665 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k1_xboole_0) = A)) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.27/78.29 2666 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.27/78.29 2667 (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]. 80.27/78.29 2668 (all A (v3_ordinal1(A) -> A = k7_ordinal2(A))) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.27/78.29 2669 (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]. 80.27/78.29 2670 (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]. 80.27/78.29 2671 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.27/78.29 2672 (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]. 80.27/78.29 2673 (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]. 80.27/78.29 2674 (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]. 80.44/78.43 2675 (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]. 80.44/78.43 2676 (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]. 80.44/78.43 2677 (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]. 80.44/78.43 2678 (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]. 80.44/78.43 2679 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.43 2680 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.43 2681 (all A (v3_ordinal1(A) -> k7_ordinal2(k1_tarski(A)) = k1_ordinal1(A))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.43 2682 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.43 2683 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.43 2684 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.43 2685 (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]. 80.44/78.43 2686 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.43 2687 (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]. 80.44/78.43 2688 (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]. 80.44/78.43 2689 (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]. 80.44/78.43 2690 (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]. 80.44/78.43 2691 (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]. 80.44/78.43 2692 (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]. 80.44/78.43 2693 (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]. 80.44/78.43 2694 (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]. 80.44/78.43 2695 (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]. 80.44/78.43 2696 (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]. 80.44/78.43 2697 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(A,k1_xboole_0))) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.43 2698 (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]. 80.44/78.45 2699 (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]. 80.44/78.45 2700 (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]. 80.44/78.45 2701 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.45 2702 (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]. 80.44/78.45 2703 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.45 2704 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.45 2705 (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]. 80.44/78.45 2706 (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]. 80.44/78.45 2707 (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]. 80.44/78.45 2708 (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]. 80.44/78.45 2709 (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]. 80.44/78.45 2710 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.45 2711 (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]. 80.44/78.45 2712 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k4_ordinal2) = k1_ordinal1(A))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.45 2713 (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]. 80.44/78.45 2714 (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]. 80.44/78.45 2715 (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]. 80.44/78.45 2716 (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]. 80.44/78.45 2717 (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]. 80.44/78.45 2718 (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]. 80.44/78.45 2719 (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]. 80.44/78.45 2720 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.45 2721 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.45 2722 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.45 2723 (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]. 80.44/78.45 2724 (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]. 80.44/78.45 2725 (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]. 80.44/78.45 2726 (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]. 80.44/78.45 2727 (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]. 80.44/78.45 2728 (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]. 80.44/78.45 2729 (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]. 80.44/78.45 2730 (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]. 80.44/78.46 2731 (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]. 80.44/78.46 2732 (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]. 80.44/78.46 2733 (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]. 80.44/78.46 2734 (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]. 80.44/78.46 2735 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.46 2736 (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]. 80.44/78.46 2737 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.46 2738 (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]. 80.44/78.46 2739 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.46 2740 (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]. 80.44/78.46 2741 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.46 2742 (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]. 80.44/78.46 2743 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.46 2744 (all A (v3_ordinal1(A) -> k15_ordinal2(k1_xboole_0,A) = k1_xboole_0)) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.46 2745 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.46 2746 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.46 2747 (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]. 80.44/78.46 2748 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.46 2749 (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]. 80.44/78.46 2750 (exists A (v1_ordinal1(A) & v4_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.46 2751 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2752 (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]. 80.44/78.50 2753 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2754 (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]. 80.44/78.50 2755 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]. 80.44/78.50 2756 (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]. 80.44/78.50 2757 (all A (v3_ordinal1(A) -> k1_xboole_0 = k6_ordinal3(k1_xboole_0,A) & k7_ordinal3(A,k1_xboole_0) = A & k1_xboole_0 = k7_ordinal3(k1_xboole_0,A))) # label(t83_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2758 $T # label(t64_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2759 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> B = k3_xboole_0(A,B) | A = k3_xboole_0(A,B))))) # label(t16_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2760 (all A all B (r1_tarski(k1_ordinal1(A),B) -> r1_tarski(A,B))) # label(t2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2761 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (r2_hidden(C,A) & r2_hidden(E,A) & k14_ordinal2(k15_ordinal2(D,A),E) = k14_ordinal2(k15_ordinal2(B,A),C) -> D = B & C = E))))))))))) # label(t56_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2762 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k2_xboole_0(A,B)) & v2_ordinal1(k2_xboole_0(A,B)) & v1_ordinal1(k2_xboole_0(A,B)))) # label(fc1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2763 $T # label(t62_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2764 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k2_xboole_0(A,B) = A | k2_xboole_0(A,B) = B)))) # label(t15_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2765 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (A != k1_xboole_0 -> k6_ordinal3(k15_ordinal2(B,A),A) = B))))) # label(t81_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2766 $T # label(t46_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2767 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> v4_ordinal1(k15_ordinal2(A,B))))))) # label(t48_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2768 (all A r1_tarski(A,k1_ordinal1(A))) # label(t1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2769 $T # label(d1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2770 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v1_ordinal1(k3_xboole_0(A,B)) & v2_ordinal1(k3_xboole_0(A,B)) & v3_ordinal1(k3_xboole_0(A,B)))) # label(fc2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2771 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -(k14_ordinal2(k15_ordinal2(C,A),D) = B & r2_hidden(D,A)))))) & k1_xboole_0 != A))))) # label(t55_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2772 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k15_ordinal2(k15_ordinal2(A,B),C) = k15_ordinal2(A,k15_ordinal2(B,C)))))))) # label(t58_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2773 $T # label(t63_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2774 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k5_ordinal3(A,B)))) # label(dt_k5_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2775 (all A (v3_ordinal1(A) -> k6_ordinal2(k1_tarski(A)) = A)) # label(t12_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2776 $T # label(t4_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2777 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> -(r2_hidden(A,k14_ordinal2(B,C)) & -r2_hidden(A,B) & (all D (v3_ordinal1(D) -> -(r2_hidden(D,C) & A = k14_ordinal2(B,D))))))))))) # label(t42_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2778 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(k15_ordinal2(A,B),k15_ordinal2(C,B)) -> r2_hidden(A,C)))))))) # label(t37_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2779 $T # label(t45_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2780 (all A (v3_ordinal1(A) -> k1_xboole_0 = k5_ordinal3(k1_xboole_0,A) & k5_ordinal3(A,k1_xboole_0) = A)) # label(t69_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2781 (all A (v3_ordinal1(A) -> k2_ordinal2(k1_tarski(A)) = k1_tarski(A))) # label(t9_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2782 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k4_ordinal2,A) -> B = k1_xboole_0 | (all C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) -> (B = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,B) -> k15_ordinal2(D,A) = k1_funct_1(C,D)))) -> k15_ordinal2(B,A) = k8_ordinal2(C))))))))) # label(t57_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2783 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r2_hidden(A,B) -> -(r1_ordinal1(C,D) & k1_xboole_0 != D) & -r2_hidden(C,D) | r2_hidden(k15_ordinal2(A,C),k15_ordinal2(B,D))))))))))) # label(t22_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2784 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k15_ordinal2(A,B) = k15_ordinal2(C,B) -> k1_xboole_0 = B | A = C))))))) # label(t36_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2785 (all A all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v3_ordinal1(A) -> v1_funct_1(k2_ordinal3(A,B)) & v5_ordinal1(k2_ordinal3(A,B)) & v1_ordinal2(k2_ordinal3(A,B)) & v1_relat_1(k2_ordinal3(A,B)))) # label(dt_k2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2786 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k5_ordinal3(A,C),k5_ordinal3(B,C))))))))) # label(t72_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2787 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r2_hidden(D,C) & k14_ordinal2(k15_ordinal2(B,C),D) = A -> B = k6_ordinal3(A,C) & k7_ordinal3(A,C) = D))))))))) # label(t79_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2788 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (k1_relat_1(A) != k1_xboole_0 -> k14_ordinal2(B,k8_ordinal2(A)) = k8_ordinal2(k1_ordinal3(B,A))))))) # label(t51_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2789 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(k15_ordinal2(A,B),k15_ordinal2(C,B)) -> r1_ordinal1(A,C) | B = k1_xboole_0))))))) # label(t38_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2790 $T # label(t44_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2791 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k1_xboole_0 != A -> k14_ordinal2(B,k3_tarski(A)) = k3_tarski(k14_ordinal2(B,A))))))) # label(t53_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2792 (all A (v3_ordinal1(A) -> -(r1_ordinal1(A,k4_ordinal2) & k4_ordinal2 != A & k1_xboole_0 != A))) # label(t19_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2793 $T # label(t3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2794 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r2_hidden(C,D) -> -r2_hidden(A,B) & -r1_ordinal1(A,B) | r2_hidden(k14_ordinal2(A,C),k14_ordinal2(B,D))))))))))) # label(t20_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2795 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> A = k14_ordinal2(k15_ordinal2(k6_ordinal3(A,B),B),k7_ordinal3(A,B)))))) # label(t78_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2796 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(r1_ordinal1(A,B) & (all C (v3_ordinal1(C) -> k14_ordinal2(A,C) != B))))))) # label(t30_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2797 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k14_ordinal2(k1_funct_1(B,D),A)))) & k1_relat_1(B) = k1_relat_1(C) <-> C = k2_ordinal3(A,B)))))))) # label(d3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2798 $T # label(t59_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2799 $T # label(t61_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2800 (all A (v3_ordinal1(A) -> k6_ordinal2(A) = k1_xboole_0)) # label(t11_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2801 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> -(r2_hidden(A,k15_ordinal2(B,C)) & (all D (v3_ordinal1(D) -> -(r2_hidden(A,k15_ordinal2(D,C)) & r2_hidden(D,B)))) & v4_ordinal1(B)))))))) # label(t49_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2802 $T # label(t40_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2803 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> (all C (v3_ordinal1(C) -> (v4_ordinal1(k8_ordinal2(A)) & (all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (E = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(B,D) = k15_ordinal2(E,C)))))) & k1_relat_1(B) = k1_relat_1(A) -> k8_ordinal2(B) = k15_ordinal2(k8_ordinal2(A),C) | C = k1_xboole_0 | k1_relat_1(A) = k1_xboole_0))))))) # label(t50_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2804 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k1_xboole_0 != A -> r1_ordinal1(B,k15_ordinal2(A,B)) & r1_ordinal1(B,k15_ordinal2(B,A))))))) # label(t39_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2805 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> -r2_hidden(C,A) & -r1_ordinal1(C,A) | r2_hidden(k5_ordinal3(A,C),k5_ordinal3(B,C))))))))) # label(t66_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2806 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k14_ordinal2(k15_ordinal2(A,C),k15_ordinal2(B,C)) = k15_ordinal2(k14_ordinal2(A,B),C))))))) # label(t54_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2807 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(k1_xboole_0 = k15_ordinal2(A,B) & k1_xboole_0 != A & k1_xboole_0 != B))))) # label(t34_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2808 (all A v3_ordinal1(k3_tarski(k2_ordinal2(A)))) # label(t7_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2809 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (-r1_ordinal1(B,A) -> (C = k5_ordinal3(A,B) <-> C = k1_xboole_0)) & (r1_ordinal1(B,A) -> (k14_ordinal2(B,C) = A <-> k5_ordinal3(A,B) = C)))))))) # label(d6_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2810 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k5_ordinal3(A,k14_ordinal2(B,C)) = k5_ordinal3(k5_ordinal3(A,B),C))))))) # label(t70_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2811 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> v4_ordinal1(k14_ordinal2(B,A)) | A = k1_xboole_0))))) # label(t32_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2812 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> B = k14_ordinal2(A,k5_ordinal3(B,A))))))) # label(t60_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2813 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> -(k14_ordinal2(A,C) = B & C != k1_xboole_0))) & r2_hidden(A,B)))))) # label(t31_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2814 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(A,k14_ordinal2(C,B)) & r2_hidden(A,k14_ordinal2(B,C))))))))) # label(t28_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2815 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> v3_ordinal1(k1_setfam_1(B)))))) # label(t13_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2816 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (all C (v3_ordinal1(C) -> ((all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (E = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(B,D) = k14_ordinal2(C,E)))))) & k1_relat_1(A) = k1_relat_1(B) -> k8_ordinal2(B) = k14_ordinal2(C,k8_ordinal2(A)) | k1_xboole_0 = k1_relat_1(A)))))))) # label(t47_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2817 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(k15_ordinal2(k6_ordinal3(A,B),B),A))))) # label(t77_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2818 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(A,k15_ordinal2(B,C)) & r2_hidden(A,k15_ordinal2(C,B)) | C = k1_xboole_0))))))) # label(t35_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2819 (all A (v3_ordinal1(A) -> k1_xboole_0 = k5_ordinal3(A,A))) # label(t67_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2820 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(k14_ordinal2(A,B),C) -> r2_hidden(B,k5_ordinal3(C,A))))))))) # label(t74_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2821 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k14_ordinal2(A,B) = k1_xboole_0 -> B = k1_xboole_0 & A = k1_xboole_0))))) # label(t29_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2822 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r1_ordinal1(C,D) & r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(A,C),k15_ordinal2(B,D))))))))))) # label(t23_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2823 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k5_ordinal3(C,B),k5_ordinal3(C,A))))))))) # label(t71_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2824 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r2_hidden(k1_ordinal1(A),k1_ordinal1(B))))))) # label(t5_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2825 (all A all B (v3_ordinal1(A) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k1_ordinal3(A,B)) & v5_ordinal1(k1_ordinal3(A,B)) & v1_ordinal2(k1_ordinal3(A,B)) & v1_relat_1(k1_ordinal3(A,B)))) # label(dt_k1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2826 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k14_ordinal2(A,C) = k14_ordinal2(A,B) -> C = B))))))) # label(t24_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2827 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k6_ordinal3(A,B)))) # label(dt_k6_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2828 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (B != k1_xboole_0 -> ((exists D (v3_ordinal1(D) & r2_hidden(D,B) & A = k14_ordinal2(k15_ordinal2(C,B),D))) <-> k6_ordinal3(A,B) = C)) & (k1_xboole_0 = B -> (C = k6_ordinal3(A,B) <-> C = k1_xboole_0)))))))) # label(d7_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2829 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v3_ordinal1(A) -> v5_ordinal1(k3_ordinal3(A,B)) & v1_ordinal2(k3_ordinal3(A,B)) & v1_funct_1(k3_ordinal3(A,B)) & v1_relat_1(k3_ordinal3(A,B)))) # label(dt_k3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2830 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(A,k14_ordinal2(A,B)) & r1_ordinal1(B,k14_ordinal2(A,B)))))) # label(t27_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2831 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> k1_xboole_0 != k5_ordinal3(B,A) & r2_hidden(k1_xboole_0,k5_ordinal3(B,A))))))) # label(t68_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2832 (all A (v3_ordinal1(A) -> k6_ordinal3(A,k4_ordinal2) = A & k7_ordinal3(A,k4_ordinal2) = k1_xboole_0)) # label(t84_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2833 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> v3_ordinal1(k3_tarski(B)))))) # label(t6_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2834 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k14_ordinal2(k14_ordinal2(A,B),C) = k14_ordinal2(A,k14_ordinal2(B,C)))))))) # label(t33_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2835 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r1_ordinal1(A,B) & r1_ordinal1(C,D) -> r1_ordinal1(k14_ordinal2(A,C),k14_ordinal2(B,D))))))))))) # label(t21_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2836 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,k14_ordinal2(C,A)) -> r2_hidden(k5_ordinal3(B,C),A) | A = k1_xboole_0))))))) # label(t73_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2837 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(A,k14_ordinal2(B,k5_ordinal3(A,B))))))) # label(t75_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2838 $T # label(t43_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2839 (all A (v3_ordinal1(A) -> (r2_hidden(A,k4_ordinal2) -> k1_xboole_0 = A))) # label(t17_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2840 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k7_ordinal3(k15_ordinal2(A,B),B) = k1_xboole_0)))) # label(t82_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2841 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(k14_ordinal2(A,B),k14_ordinal2(A,C)) -> r2_hidden(B,C)))))))) # label(t25_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2842 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> (all C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k15_ordinal2(k1_funct_1(B,D),A) = k1_funct_1(C,D)))) & k1_relat_1(B) = k1_relat_1(C) <-> k4_ordinal3(A,B) = C))))))) # label(d5_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2843 $T # label(t14_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2844 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> B = k2_ordinal2(B))))) # label(t8_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2845 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k7_ordinal3(A,B)))) # label(dt_k7_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2846 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) -> (all C (v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C) -> (k3_ordinal3(A,B) = C <-> (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k15_ordinal2(A,k1_funct_1(B,D)) = k1_funct_1(C,D)))) & k1_relat_1(B) = k1_relat_1(C)))))))) # label(d4_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2847 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(k14_ordinal2(A,B),k14_ordinal2(A,C)) -> r1_ordinal1(B,C)))))))) # label(t26_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2848 (all A (v3_ordinal1(A) -> (k1_xboole_0 != A -> r2_hidden(k1_xboole_0,A)))) # label(t10_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2849 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> (C = k1_ordinal3(A,B) <-> k1_relat_1(B) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k14_ordinal2(A,k1_funct_1(B,D)))))))))))) # label(d2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2850 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(k8_ordinal2(A)) -> k8_ordinal2(k4_ordinal3(B,A)) = k15_ordinal2(k8_ordinal2(A),B) | k1_xboole_0 = B | k1_relat_1(A) = k1_xboole_0))))) # label(t52_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2851 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> B = k5_ordinal3(k14_ordinal2(A,B),A))))) # label(t65_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2852 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k5_ordinal3(A,k15_ordinal2(k6_ordinal3(A,B),B)) = k7_ordinal3(A,B))))) # label(d8_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2853 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k15_ordinal2(A,B) = k4_ordinal2 -> B = k4_ordinal2 & k4_ordinal2 = A))))) # label(t41_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2854 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,k15_ordinal2(B,C)) -> r2_hidden(k6_ordinal3(A,C),B) & r2_hidden(k7_ordinal3(A,C),C)))))))) # label(t80_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2855 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k5_ordinal3(k15_ordinal2(A,B),k15_ordinal2(C,B)) = k15_ordinal2(k5_ordinal3(A,C),B))))))) # label(t76_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2856 (all A all B (v3_ordinal1(A) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> v1_funct_1(k4_ordinal3(A,B)) & v5_ordinal1(k4_ordinal3(A,B)) & v1_ordinal2(k4_ordinal3(A,B)) & v1_relat_1(k4_ordinal3(A,B)))) # label(dt_k4_ordinal3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2857 (exists A (v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & m1_subset_1(A,k6_arytm_3))) # label(rc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2858 (all A all B (v4_ordinal2(B) & v3_ordinal1(B) & v4_ordinal2(A) & v3_ordinal1(A) -> v3_ordinal1(k2_arytm_3(A,B)))) # label(dt_k2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2859 (all A (m1_subset_1(A,k6_arytm_3) -> (k8_arytm_3(A) = k4_ordinal2 <-> r2_hidden(A,k5_ordinal2)))) # label(t44_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2860 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (A = k2_arytm_3(B,k6_ordinal3(A,B)) <-> r2_arytm_3(B,A)))))) # label(t11_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2861 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> A = k3_arytm_3(A,A) & A = k4_arytm_3(A,A))) # label(t21_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2862 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) -> k2_arytm_3(B,A) = k2_arytm_3(A,B))) # label(commutativity_k2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2863 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> k1_arytm_3(A,B) = k14_ordinal2(A,B))) # label(redefinition_k1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2864 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -((all D (m1_subset_1(D,k6_arytm_3) -> (all E (m1_subset_1(E,k6_arytm_3) -> -(k10_arytm_3(D,E) = A & r3_arytm_3(D,B) & r3_arytm_3(E,C)))))) & r3_arytm_3(A,k10_arytm_3(B,C))))))))) # label(t95_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2865 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> -(k4_tarski(k5_arytm_3(A,B),k5_arytm_3(B,A)) != k9_arytm_3(A,B) & k4_ordinal2 != k5_arytm_3(B,A) & k1_xboole_0 != B) & (k5_arytm_3(B,A) = k4_ordinal2 -> k9_arytm_3(A,B) = k5_arytm_3(A,B)) & (B = k1_xboole_0 -> k1_xboole_0 = k9_arytm_3(A,B)))))) # label(d9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2866 (all A (v3_ordinal1(A) -> (all B (m1_subset_1(B,A) -> v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B))))) # label(cc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2867 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (-(B = k1_xboole_0 & k1_xboole_0 = A) -> r1_arytm_3(k5_arytm_3(A,B),k5_arytm_3(B,A))))))) # label(t27_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2868 (all A (v3_ordinal1(A) -> (r1_arytm_3(k1_xboole_0,A) -> A = k4_ordinal2))) # label(t7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2869 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> -((all C (v4_ordinal2(C) & v3_ordinal1(C) -> (all D (v4_ordinal2(D) & v3_ordinal1(D) -> (all E (v4_ordinal2(E) & v3_ordinal1(E) -> -(A = k2_arytm_3(C,D) & B = k2_arytm_3(C,E) & r1_arytm_3(D,E)))))))) & -(k1_xboole_0 = B & k1_xboole_0 = A)))))) # label(t8_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2870 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -((all C (m1_subset_1(C,k6_arytm_3) -> -(-r3_arytm_3(C,A) & -r3_arytm_3(B,C)))) & -r3_arytm_3(B,A)))))) # label(t101_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2871 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -((all C (m1_subset_1(C,k6_arytm_3) -> -(r2_hidden(C,k5_ordinal2) & r3_arytm_3(B,k11_arytm_3(C,A))))) & A != k12_arytm_3))))) # label(t103_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2872 (all A all B (m1_subset_1(B,k6_arytm_3) & m1_subset_1(A,k6_arytm_3) -> r3_arytm_3(A,B) | r3_arytm_3(B,A))) # label(connectedness_r3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2873 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> k9_arytm_3(B,k4_ordinal2) = B & k9_arytm_3(k1_xboole_0,A) = k1_xboole_0)))) # label(t46_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2874 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (r3_arytm_3(B,A) & r3_arytm_3(A,B) -> B = A))))) # label(t73_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2875 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (A != k1_xboole_0 -> k4_arytm_3(B,A) != k1_xboole_0 & k1_xboole_0 != k6_ordinal3(A,k4_arytm_3(B,A))))))) # label(t23_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2876 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (A != k1_xboole_0 -> k5_arytm_3(A,A) = k4_ordinal2))) # label(t32_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2877 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> k4_ordinal2 = k5_arytm_3(k4_ordinal2,A) & A = k5_arytm_3(A,k4_ordinal2))) # label(t29_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.44/78.50 2878 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> r3_arytm_3(A,k10_arytm_3(A,B)))))) # label(t85_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2879 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (k10_arytm_3(A,B) = B <-> k12_arytm_3 = A))))) # label(t92_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2880 f1_s2_arytm_3 = k12_arytm_3 & r2_hidden(f3_s2_arytm_3,k5_ordinal2) & p1_s2_arytm_3(f1_s2_arytm_3) & -p1_s2_arytm_3(f3_s2_arytm_3) & k13_arytm_3 = f2_s2_arytm_3 -> (exists A (r2_hidden(A,k5_ordinal2) & -p1_s2_arytm_3(k10_arytm_3(A,f2_s2_arytm_3)) & p1_s2_arytm_3(A) & m1_subset_1(A,k6_arytm_3))) # label(s2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2881 (all A (m1_subset_1(A,k6_arytm_3) -> m1_subset_1(k8_arytm_3(A),k5_ordinal2))) # label(dt_k8_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2882 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k5_ordinal2) -> (r2_hidden(A,k5_ordinal2) -> (B = k4_ordinal2 <-> k8_arytm_3(A) = B)) & (-r2_hidden(A,k5_ordinal2) -> (k8_arytm_3(A) = B <-> (exists C (k4_tarski(C,B) = A & v4_ordinal2(C) & v3_ordinal1(C))))))))) # label(d8_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2883 (all A (m1_subset_1(A,k6_arytm_3) -> r1_arytm_3(k7_arytm_3(A),k8_arytm_3(A)))) # label(t40_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2884 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> -(k10_arytm_3(A,B) = k10_arytm_3(C,D) & -r3_arytm_3(A,C) & -r3_arytm_3(B,D)))))))))) # label(t89_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2885 (all A (m1_subset_1(A,k6_arytm_3) -> (exists B (m1_subset_1(B,k6_arytm_3) & A = k10_arytm_3(B,B))))) # label(t66_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2886 (all A all B (v4_ordinal2(B) & v3_ordinal1(B) & v4_ordinal2(A) & v3_ordinal1(A) -> v3_ordinal1(k1_arytm_3(A,B)))) # label(dt_k1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2887 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -((all C (m1_subset_1(C,k6_arytm_3) -> k11_arytm_3(A,C) != B)) & A != k12_arytm_3))))) # label(t61_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2888 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (r2_hidden(k10_arytm_3(A,B),k5_ordinal2) & r2_hidden(A,k5_ordinal2) -> r2_hidden(B,k5_ordinal2)))))) # label(t78_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2889 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k5_ordinal2) -> (r2_hidden(A,k5_ordinal2) -> (B = k7_arytm_3(A) <-> A = B)) & (-r2_hidden(A,k5_ordinal2) -> ((exists C (v3_ordinal1(C) & k4_tarski(B,C) = A & v4_ordinal2(C))) <-> B = k7_arytm_3(A))))))) # label(d7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2890 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (r2_hidden(k1_xboole_0,A) -> r2_hidden(k7_ordinal3(B,A),A)))))) # label(t10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2891 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r2_arytm_3(A,A))) # label(reflexivity_r2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2892 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> k9_arytm_3(k2_arytm_3(k7_arytm_3(A),k7_arytm_3(B)),k2_arytm_3(k8_arytm_3(A),k8_arytm_3(B))) = k11_arytm_3(A,B))))) # label(d11_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2893 (all A (m1_subset_1(A,k6_arytm_3) & v3_ordinal1(A) -> (all B (m1_subset_1(B,k6_arytm_3) & v3_ordinal1(B) -> k11_arytm_3(A,B) = k2_arytm_3(A,B))))) # label(t65_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2894 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) -> v4_ordinal2(k14_ordinal2(A,B)) & v3_ordinal1(k14_ordinal2(A,B)) & v2_ordinal1(k14_ordinal2(A,B)) & v1_ordinal1(k14_ordinal2(A,B)))) # label(fc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.50 2895 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (-(A = k1_xboole_0 & B = k1_xboole_0) -> r1_arytm_3(k6_ordinal3(A,k4_arytm_3(A,B)),k6_ordinal3(B,k4_arytm_3(A,B)))))))) # label(t24_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2896 (all A all B (m1_subset_1(B,k6_arytm_3) & m1_subset_1(A,k6_arytm_3) -> k11_arytm_3(B,A) = k11_arytm_3(A,B))) # label(commutativity_k11_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2897 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> -v1_xboole_0(k1_ordinal1(A)) & v1_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & v4_ordinal2(k1_ordinal1(A)))) # label(fc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2898 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_arytm_3(A,B) <-> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (A = k15_ordinal2(C,D) & B = k15_ordinal2(C,E) -> k4_ordinal2 = C)))))))))))) # label(d1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2899 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) & v4_ordinal2(B) & v4_ordinal2(A) -> m1_subset_1(k5_arytm_3(A,B),k5_ordinal2))) # label(dt_k5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2900 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> r2_arytm_3(k3_arytm_3(A,B),k2_arytm_3(A,B)))))) # label(t17_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2901 (all A (m1_subset_1(A,k6_arytm_3) -> k8_arytm_3(A) != k1_xboole_0)) # label(t41_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2902 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (A != k1_xboole_0 -> k7_arytm_3(k9_arytm_3(B,A)) = k5_arytm_3(B,A) & k5_arytm_3(A,B) = k8_arytm_3(k9_arytm_3(B,A))))))) # label(t48_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2903 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> (r3_arytm_3(A,C) & k10_arytm_3(C,D) = k10_arytm_3(A,B) -> r3_arytm_3(D,B)))))))))) # label(t93_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2904 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -(r3_arytm_3(C,A) & (r3_arytm_3(B,C) & -r3_arytm_3(B,A) | -r3_arytm_3(C,B) & r3_arytm_3(A,B))))))))) # label(t76_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2905 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (r2_arytm_3(A,B) & r2_hidden(k1_xboole_0,B) -> r1_ordinal1(A,B)))))) # label(t15_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2906 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (r2_arytm_3(B,A) & r2_arytm_3(A,B) -> A = B))))) # label(t13_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2907 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (r3_arytm_3(B,C) & r3_arytm_3(A,B) -> r3_arytm_3(A,C)))))))) # label(t74_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2908 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (k1_xboole_0 != A -> k10_arytm_3(k9_arytm_3(B,A),k9_arytm_3(C,A)) = k9_arytm_3(k1_arytm_3(B,C),A)))))))) # label(t53_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2909 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (all D (v4_ordinal2(D) & v3_ordinal1(D) -> -(-(k2_arytm_3(C,A) = k2_arytm_3(B,D) <-> k9_arytm_3(C,B) = k9_arytm_3(D,A)) & A != k1_xboole_0 & B != k1_xboole_0))))))))) # label(t51_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2910 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal2(k15_ordinal2(A,B)) -> v1_xboole_0(k15_ordinal2(A,B)) | r2_hidden(B,k5_ordinal2) & r2_hidden(A,k5_ordinal2)))))) # label(t2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2911 (all A (v3_ordinal1(A) -> (r2_hidden(A,k6_arytm_3) -> r2_hidden(A,k5_ordinal2)))) # label(t37_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2912 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> k15_ordinal2(A,B) = k15_ordinal2(B,A))))) # label(t4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2913 (all A (m1_subset_1(A,k6_arytm_3) -> k10_arytm_3(A,k12_arytm_3) = A)) # label(t56_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2914 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (r1_arytm_3(A,B) -> k5_arytm_3(A,B) = A))))) # label(t28_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2915 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> k4_arytm_3(A,k1_xboole_0) = A & k1_xboole_0 = k3_arytm_3(A,k1_xboole_0))) # label(t19_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2916 (all A ((exists B (A = k4_tarski(B,k4_ordinal2) & m1_subset_1(B,k5_ordinal2))) <-> r2_hidden(A,a_0_1_arytm_3))) # label(fraenkel_a_0_1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2917 (all A all B (v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) & v3_ordinal1(A) -> m1_subset_1(k4_arytm_3(A,B),k5_ordinal2))) # label(dt_k4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2918 $T # label(t84_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2919 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> k11_arytm_3(A,k11_arytm_3(B,C)) = k11_arytm_3(k11_arytm_3(A,B),C))))))) # label(t58_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2920 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (all D (v4_ordinal2(D) & v3_ordinal1(D) -> k11_arytm_3(k9_arytm_3(B,C),k9_arytm_3(D,A)) = k9_arytm_3(k2_arytm_3(B,D),k2_arytm_3(C,A)))))))))) # label(t55_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2921 (all A -r2_hidden(k4_tarski(k12_arytm_3,A),k6_arytm_3)) # label(t68_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2922 (all A (-v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_arytm_3)) -> -((all B (m1_subset_1(B,k6_arytm_3) -> -(r2_hidden(B,A) & (all C (m1_subset_1(C,k6_arytm_3) -> (r2_hidden(C,A) -> r3_arytm_3(C,B))))))) & r2_hidden(A,k6_arytm_3)))) # label(t99_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2923 (all A (m1_subset_1(A,k6_arytm_3) -> k12_arytm_3 = k11_arytm_3(A,k12_arytm_3))) # label(t54_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2924 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) -> k3_arytm_3(A,B) = k3_arytm_3(B,A))) # label(commutativity_k3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2925 (all A all B (v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) & v3_ordinal1(A) -> m1_subset_1(k3_arytm_3(A,B),k5_ordinal2))) # label(dt_k3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2926 (all A (m1_subset_1(A,k6_arytm_3) -> A = k11_arytm_3(A,k13_arytm_3))) # label(t59_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2927 (all A (m1_subset_1(A,k5_ordinal2) -> (all B (m1_subset_1(B,k5_ordinal2) -> (r1_arytm_3(A,B) -> k8_arytm_3(k9_arytm_3(A,B)) = B & k7_arytm_3(k9_arytm_3(A,B)) = A | k1_xboole_0 = B))))) # label(t49_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2928 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> ((exists C (m1_subset_1(C,k6_arytm_3) & B = k10_arytm_3(A,C))) <-> r3_arytm_3(A,B)))))) # label(d12_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2929 (all A (m1_subset_1(A,k6_arytm_3) -> (-r2_hidden(A,k5_ordinal2) -> A = k4_tarski(k7_arytm_3(A),k8_arytm_3(A)) & k4_ordinal2 != k8_arytm_3(A)))) # label(t42_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2930 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (r2_arytm_3(A,k1_arytm_3(B,C)) & r2_arytm_3(A,B) -> r2_arytm_3(A,C)))))))) # label(t16_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2931 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -(k12_arytm_3 != C & (all D (m1_subset_1(D,k6_arytm_3) -> (all E (m1_subset_1(E,k6_arytm_3) -> -(r3_arytm_3(E,C) & C != E & r3_arytm_3(D,B) & A = k10_arytm_3(D,E)))))) & -r3_arytm_3(k10_arytm_3(B,C),A)))))))) # label(t98_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2932 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> k11_arytm_3(A,k10_arytm_3(B,C)) = k10_arytm_3(k11_arytm_3(A,B),k11_arytm_3(A,C)))))))) # label(t63_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2933 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> ((exists C (v3_ordinal1(C) & k2_arytm_3(A,C) = B & v4_ordinal2(C))) <-> r2_arytm_3(A,B)))))) # label(t9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2934 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (k1_xboole_0 != A -> k9_arytm_3(B,C) = k9_arytm_3(k2_arytm_3(B,A),k2_arytm_3(C,A))))))))) # label(t50_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2935 (all A (m1_subset_1(A,k6_arytm_3) -> (r2_hidden(a_1_0_arytm_3(A),k6_arytm_3) <-> k12_arytm_3 = A))) # label(t81_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2936 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (r3_arytm_3(A,B) & B != A <-> -r3_arytm_3(B,A)))))) # label(t75_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2937 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> r2_arytm_3(k4_ordinal2,A) & r2_arytm_3(A,k1_xboole_0))) # label(t14_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2938 (all A all B -v3_ordinal1(k4_tarski(A,B))) # label(t36_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2939 (all A all B (m1_subset_1(B,k6_arytm_3) -> ((exists C (m1_subset_1(C,k6_arytm_3) & A = C & -r3_arytm_3(B,C))) <-> r2_hidden(A,a_1_0_arytm_3(B))))) # label(fraenkel_a_1_0_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2940 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (k10_arytm_3(A,B) = k10_arytm_3(C,B) -> A = C))))))) # label(t69_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2941 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> k9_arytm_3(k1_arytm_3(k2_arytm_3(k7_arytm_3(A),k8_arytm_3(B)),k2_arytm_3(k7_arytm_3(B),k8_arytm_3(A))),k2_arytm_3(k8_arytm_3(A),k8_arytm_3(B))) = k10_arytm_3(A,B))))) # label(d10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2942 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -(r3_arytm_3(A,B) & r3_arytm_3(B,C) & C = A & C != B))))))) # label(t97_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2943 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> -(k5_arytm_3(A,B) = k1_xboole_0 & k1_xboole_0 != A))))) # label(t30_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2944 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) & v4_ordinal2(B) & v4_ordinal2(A) -> v2_ordinal1(k7_ordinal3(A,B)) & v4_ordinal2(k7_ordinal3(A,B)) & v3_ordinal1(k7_ordinal3(A,B)) & v1_ordinal1(k7_ordinal3(A,B)))) # label(fc7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2945 (all A all B (m1_subset_1(A,k6_arytm_3) & m1_subset_1(B,k6_arytm_3) -> m1_subset_1(k10_arytm_3(A,B),k6_arytm_3))) # label(dt_k10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2946 (exists A (m1_subset_1(A,k6_arytm_3) & v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A))) # label(rc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2947 (all A all B -r2_hidden(k4_tarski(A,B),k5_ordinal2)) # label(t38_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2948 (all A (m1_subset_1(A,k6_arytm_3) -> r3_arytm_3(k12_arytm_3,A))) # label(t71_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2949 (all A (m1_subset_1(A,k6_arytm_3) -> A = k9_arytm_3(k7_arytm_3(A),k8_arytm_3(A)))) # label(t45_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2950 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_arytm_3(A,B) <-> (exists C (v3_ordinal1(C) & k15_ordinal2(A,C) = B))))))) # label(d2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2951 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (k1_xboole_0 = k4_arytm_3(A,B) -> A = k1_xboole_0))))) # label(t20_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2952 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -((all D (m1_subset_1(D,k6_arytm_3) -> -(r3_arytm_3(D,C) & -r3_arytm_3(D,A) & r3_arytm_3(D,B)))) & -r3_arytm_3(C,A) & -r3_arytm_3(B,A)))))))) # label(t96_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2953 p1_s1_arytm_3(k1_xboole_0) & (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (p1_s1_arytm_3(A) -> p1_s1_arytm_3(k1_ordinal1(A))))) -> (all A (v3_ordinal1(A) & v4_ordinal2(A) -> p1_s1_arytm_3(A))) # label(s1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2954 (all A (m1_subset_1(A,k1_zfmisc_1(k6_arytm_3)) -> -((exists B (m1_subset_1(B,k6_arytm_3) & r2_hidden(B,A) & B != k12_arytm_3)) & (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> -(r2_hidden(B,A) & r2_hidden(D,A) & C != B & C != D & B != D & r2_hidden(C,A)))))))) & (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (r3_arytm_3(C,B) & r2_hidden(B,A) -> r2_hidden(C,A))))))))) # label(t82_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2955 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (A != k1_xboole_0 -> k5_arytm_3(A,k1_xboole_0) = k4_ordinal2) & k5_arytm_3(k1_xboole_0,A) = k1_xboole_0)) # label(t31_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2956 (all A (m1_subset_1(A,k6_arytm_3) -> -(A != k12_arytm_3 & (all B (m1_subset_1(B,k6_arytm_3) -> k13_arytm_3 != k11_arytm_3(A,B)))))) # label(t60_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2957 (all A (m1_subset_1(A,k6_arytm_3) -> -((all B (m1_subset_1(B,k5_ordinal2) -> (all C (m1_subset_1(C,k5_ordinal2) -> -(r1_arytm_3(B,C) & k4_ordinal2 != C & k1_xboole_0 != C & k4_tarski(B,C) = A))))) & -r2_hidden(A,k5_ordinal2)))) # label(t35_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2958 (all A (m1_subset_1(A,k6_arytm_3) -> -(A != k12_arytm_3 & (all B (m1_subset_1(B,k6_arytm_3) -> -(-r3_arytm_3(A,B) & -r2_hidden(B,k5_ordinal2))))))) # label(t80_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2959 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (m1_subset_1(C,k5_ordinal2) -> (C = k4_arytm_3(A,B) <-> r2_arytm_3(C,A) & r2_arytm_3(C,B) & (all D (v4_ordinal2(D) & v3_ordinal1(D) -> (r2_arytm_3(D,B) & r2_arytm_3(D,A) -> r2_arytm_3(D,C))))))))))) # label(d4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2960 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -((all D (m1_subset_1(D,k6_arytm_3) -> -(B = k10_arytm_3(A,D) & r3_arytm_3(D,C)))) & r3_arytm_3(B,k10_arytm_3(A,C)) & r3_arytm_3(A,B)))))))) # label(t94_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2961 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> k14_ordinal2(A,B) = k14_ordinal2(B,A))))) # label(t3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2962 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (A != k1_xboole_0 -> k4_ordinal2 = k9_arytm_3(A,A)))) # label(t47_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2963 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (r3_arytm_3(k10_arytm_3(A,B),k10_arytm_3(C,B)) <-> r3_arytm_3(A,C)))))))) # label(t83_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2964 $T # label(dt_k6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2965 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -(-r3_arytm_3(B,A) & r3_arytm_3(C,A) & -r3_arytm_3(C,B)))))))) # label(t77_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2966 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> k4_arytm_3(B,A) = k4_arytm_3(A,B))) # label(commutativity_k4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2967 (all A all B (v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) & v3_ordinal1(A) -> k1_arytm_3(B,A) = k1_arytm_3(A,B))) # label(commutativity_k1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2968 (all A (m1_subset_1(A,k6_arytm_3) -> -(A != k1_xboole_0 & k1_xboole_0 = k7_arytm_3(A)) & -(k1_xboole_0 != k7_arytm_3(A) & k1_xboole_0 = A))) # label(t43_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2969 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) -> v1_ordinal1(k5_ordinal3(A,B)) & v2_ordinal1(k5_ordinal3(A,B)) & v4_ordinal2(k5_ordinal3(A,B)) & v3_ordinal1(k5_ordinal3(A,B)))) # label(fc4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2970 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -(all C (m1_subset_1(C,k6_arytm_3) -> A != k10_arytm_3(B,C) & B != k10_arytm_3(A,C))))))) # label(t100_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2971 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (r3_arytm_3(k11_arytm_3(B,A),k11_arytm_3(C,A)) -> r3_arytm_3(B,C) | A = k12_arytm_3))))))) # label(t88_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2972 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (m1_subset_1(C,k5_ordinal2) -> (k3_arytm_3(A,B) = C <-> r2_arytm_3(A,C) & r2_arytm_3(B,C) & (all D (v4_ordinal2(D) & v3_ordinal1(D) -> (r2_arytm_3(B,D) & r2_arytm_3(A,D) -> r2_arytm_3(C,D))))))))))) # label(d3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2973 (all A (m1_subset_1(A,k6_arytm_3) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & m1_subset_1(B,k6_arytm_3) -> k10_arytm_3(A,B) = k1_arytm_3(A,B))))) # label(t64_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2974 (all A (v3_ordinal1(A) -> r1_arytm_3(k4_ordinal2,A))) # label(t6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2975 (all A (m1_subset_1(A,k6_arytm_3) -> -(all B (m1_subset_1(B,k6_arytm_3) -> r3_arytm_3(B,A))))) # label(t102_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2976 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> k2_arytm_3(k4_arytm_3(A,C),B) = k4_arytm_3(k2_arytm_3(A,B),k2_arytm_3(C,B)))))))) # label(t22_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2977 (all A all B (v3_ordinal1(B) & v4_ordinal2(B) & v4_ordinal2(A) & v3_ordinal1(A) -> k15_ordinal2(A,B) = k2_arytm_3(A,B))) # label(redefinition_k2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2978 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (k10_arytm_3(A,B) = k12_arytm_3 -> A = k12_arytm_3))))) # label(t70_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2979 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_arytm_3(A,B) -> r1_arytm_3(B,A)))) # label(symmetry_r1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2980 (all A (m1_subset_1(A,k5_ordinal2) -> v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_ordinal1(A))) # label(cc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2981 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) -> v2_ordinal1(k15_ordinal2(A,B)) & v4_ordinal2(k15_ordinal2(A,B)) & v3_ordinal1(k15_ordinal2(A,B)) & v1_ordinal1(k15_ordinal2(A,B)))) # label(fc5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2982 (all A (m1_subset_1(A,k6_arytm_3) -> (v3_ordinal1(A) -> v2_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(A) & v1_ordinal1(A)))) # label(cc4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2983 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> -(-r3_arytm_3(B,D) & -r3_arytm_3(A,C) & k11_arytm_3(A,B) = k11_arytm_3(C,D)))))))))) # label(t91_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2984 (all A (v3_ordinal1(A) & v1_xboole_0(A) -> v4_ordinal2(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2985 (all A (m1_subset_1(A,k6_arytm_3) -> (r3_arytm_3(A,k12_arytm_3) -> k12_arytm_3 = A))) # label(t72_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2986 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> A = k2_arytm_3(k5_arytm_3(A,B),k4_arytm_3(A,B)))))) # label(t26_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2987 (all A all B (m1_subset_1(B,k6_arytm_3) & m1_subset_1(A,k6_arytm_3) -> m1_subset_1(k11_arytm_3(A,B),k6_arytm_3))) # label(dt_k11_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2988 (all A (m1_subset_1(A,k5_ordinal2) -> (all B (m1_subset_1(B,k5_ordinal2) -> (k1_xboole_0 != B & B != k4_ordinal2 & r1_arytm_3(A,B) <-> r2_hidden(k4_tarski(A,B),k6_arytm_3)))))) # label(t39_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2989 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> k5_arytm_3(A,B) = k6_ordinal3(A,k4_arytm_3(A,B)))))) # label(d5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2990 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) & v3_ordinal1(B) -> -(-r3_arytm_3(A,B) & r2_hidden(A,k5_ordinal2) & -r3_arytm_3(k10_arytm_3(B,k13_arytm_3),A)))))) # label(t79_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2991 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) -> v1_ordinal1(k6_ordinal3(A,B)) & v4_ordinal2(k6_ordinal3(A,B)) & v3_ordinal1(k6_ordinal3(A,B)) & v2_ordinal1(k6_ordinal3(A,B)))) # label(fc6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2992 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -(k12_arytm_3 != B & k12_arytm_3 != A & k11_arytm_3(A,B) = k12_arytm_3))))) # label(t86_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2993 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (r3_arytm_3(A,B) -> r3_arytm_3(k11_arytm_3(A,C),k11_arytm_3(B,C))))))))) # label(t90_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2994 (all A (m1_subset_1(A,k6_arytm_3) -> m1_subset_1(k7_arytm_3(A),k5_ordinal2))) # label(dt_k7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2995 (exists A (-v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(A))) # label(rc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2996 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (k11_arytm_3(A,B) = k11_arytm_3(A,C) -> C = B | k12_arytm_3 = A))))))) # label(t62_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2997 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (k1_xboole_0 != A -> r2_arytm_3(k6_ordinal3(k2_arytm_3(B,A),k3_arytm_3(B,A)),B)))))) # label(t18_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2998 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> k10_arytm_3(A,k10_arytm_3(B,C)) = k10_arytm_3(k10_arytm_3(A,B),C))))))) # label(t57_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 2999 $T # label(t12_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3000 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (all D (v4_ordinal2(D) & v3_ordinal1(D) -> -(k1_xboole_0 != B & k10_arytm_3(k9_arytm_3(C,B),k9_arytm_3(D,A)) != k9_arytm_3(k1_arytm_3(k2_arytm_3(C,A),k2_arytm_3(B,D)),k2_arytm_3(B,A)) & A != k1_xboole_0))))))))) # label(t52_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3001 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -((all D (m1_subset_1(D,k6_arytm_3) -> -(A = k11_arytm_3(B,D) & r3_arytm_3(D,C)))) & r3_arytm_3(A,k11_arytm_3(B,C))))))))) # label(t87_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3002 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal2(k14_ordinal2(A,B)) -> r2_hidden(A,k5_ordinal2) & r2_hidden(B,k5_ordinal2)))))) # label(t1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3003 (all A ((exists B exists C (m1_subset_1(B,k5_ordinal2) & m1_subset_1(C,k5_ordinal2) & A = k4_tarski(B,C) & C != k1_xboole_0 & r1_arytm_3(B,C))) <-> r2_hidden(A,a_0_0_arytm_3))) # label(fraenkel_a_0_0_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3004 $T # label(t67_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3005 (all A all B (m1_subset_1(A,k6_arytm_3) & m1_subset_1(B,k6_arytm_3) -> k10_arytm_3(A,B) = k10_arytm_3(B,A))) # label(commutativity_k10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3006 (all A all B (v3_ordinal1(A) & v4_ordinal2(B) & v3_ordinal1(B) & v4_ordinal2(A) -> m1_subset_1(k9_arytm_3(A,B),k6_arytm_3))) # label(dt_k9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3007 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (k1_xboole_0 != A -> k5_arytm_3(k2_arytm_3(B,A),k2_arytm_3(C,A)) = k5_arytm_3(B,C)))))))) # label(t33_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3008 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (r1_arytm_3(A,B) <-> k4_ordinal2 = k4_arytm_3(A,B)))))) # label(t25_arytm_3) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3009 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> k7_arytm_2(A,k7_arytm_2(B,C)) = k7_arytm_2(k7_arytm_2(A,B),C))))))) # label(t7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3010 (all A (m1_subset_1(A,k1_zfmisc_1(k2_arytm_2)) -> (all B (m1_subset_1(B,k1_zfmisc_1(k2_arytm_2)) -> -((all C (m1_subset_1(C,k2_arytm_2) -> (all D (m1_subset_1(D,k2_arytm_2) -> (r2_hidden(C,A) & r2_hidden(D,B) -> r1_arytm_2(C,D)))))) & (all C (m1_subset_1(C,k2_arytm_2) -> (exists D ((exists E (r2_hidden(E,B) & -(r1_arytm_2(C,E) & r1_arytm_2(D,C)) & r2_hidden(D,A) & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,k2_arytm_2))))) & (exists C (m1_subset_1(C,k2_arytm_2) & r2_hidden(C,B))) & (exists C (r2_hidden(C,A) & m1_subset_1(C,k2_arytm_2)))))))) # label(t9_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3011 (all A (m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (all B (m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> k6_arytm_2(A,B) = a_2_1_arytm_2(A,B))))) # label(d7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3012 (all A (m1_subset_1(A,k1_arytm_2) -> m1_subset_1(k4_arytm_2(A),k2_arytm_2))) # label(dt_k4_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3013 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (A = k7_arytm_2(B,C) -> r1_arytm_2(C,A)))))))) # label(t20_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3014 (all A all B (m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) -> r1_arytm_2(A,B) | r1_arytm_2(B,A))) # label(connectedness_r1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3015 (all A (r2_hidden(A,a_0_1_arytm_2) <-> (exists B (m1_subset_1(B,k6_arytm_3) & A = a_1_0_arytm_2(B) & B != k12_arytm_3)))) # label(fraenkel_a_0_1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3016 (all A (m1_subset_1(A,k2_arytm_2) -> -(A != k12_arytm_3 & (all B (m1_subset_1(B,k2_arytm_2) -> k13_arytm_3 != k8_arytm_2(A,B)))))) # label(t15_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3017 (all A all B (m1_subset_1(A,k1_arytm_2) & m1_subset_1(B,k1_arytm_2) -> k6_arytm_2(B,A) = k6_arytm_2(A,B))) # label(commutativity_k6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3018 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> k8_arytm_2(A,k7_arytm_2(B,C)) = k7_arytm_2(k8_arytm_2(A,B),k8_arytm_2(A,C)))))))) # label(t14_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3019 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (k7_arytm_2(A,B) = k7_arytm_2(A,C) -> B = C))))))) # label(t12_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3020 (all A (m1_subset_1(A,k2_arytm_2) -> m2_subset_1(k3_arytm_2(A),k1_zfmisc_1(k6_arytm_3),k1_arytm_2))) # label(dt_k3_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3021 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(B != k12_arytm_3 & k12_arytm_3 != A & k7_arytm_2(A,B) != k4_arytm_2(k5_arytm_2(k3_arytm_2(A),k3_arytm_2(B)))) & (A = k12_arytm_3 -> B = k7_arytm_2(A,B)) & (k12_arytm_3 = B -> A = k7_arytm_2(A,B)))))) # label(d8_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3022 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(r1_arytm_2(A,B) & (all C (m1_subset_1(C,k2_arytm_2) -> k7_arytm_2(A,C) != B))))))) # label(t10_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3023 (all A all B (m1_subset_1(B,k2_arytm_2) & m1_subset_1(A,k2_arytm_2) -> m1_subset_1(k7_arytm_2(A,B),k2_arytm_2))) # label(dt_k7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3024 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r2_hidden(A,k5_ordinal2) & r2_hidden(B,k5_ordinal2) -> r2_hidden(k7_arytm_2(B,A),k5_ordinal2)))))) # label(t17_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3025 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k13_arytm_3 = A -> B = k8_arytm_2(A,B)))))) # label(t16_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3026 (all A all B (m1_subset_1(B,k2_arytm_2) & m1_subset_1(A,k2_arytm_2) -> k8_arytm_2(B,A) = k8_arytm_2(A,B))) # label(commutativity_k8_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3027 $T # label(t5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3028 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(all C (m1_subset_1(C,k2_arytm_2) -> k7_arytm_2(B,C) != A & B != k7_arytm_2(A,C))))))) # label(t11_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3029 $T # label(dt_k2_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3030 (all A (m1_subset_1(A,k1_zfmisc_1(k2_arytm_2)) -> (r2_hidden(k12_arytm_3,A) & (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r2_hidden(B,A) & C = k13_arytm_3 -> r2_hidden(k7_arytm_2(B,C),A)))))) -> r1_tarski(k5_ordinal2,A)))) # label(t18_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3031 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> k4_arytm_2(k6_arytm_2(k3_arytm_2(A),k3_arytm_2(B))) = k8_arytm_2(A,B))))) # label(d9_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3032 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k7_arytm_2(A,B) = k12_arytm_3 -> k12_arytm_3 = A))))) # label(t6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3033 (all A (m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (all B (m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> k5_arytm_2(A,B) = a_2_0_arytm_2(A,B))))) # label(d6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.51 3034 (all A all B all C (m2_subset_1(C,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) & m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> ((exists D exists E (m1_subset_1(E,k6_arytm_3) & A = k10_arytm_3(D,E) & r2_hidden(D,B) & r2_hidden(E,C) & m1_subset_1(D,k6_arytm_3))) <-> r2_hidden(A,a_2_0_arytm_2(B,C))))) # label(fraenkel_a_2_0_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3035 (all A all B (m1_subset_1(A,k1_arytm_2) & m1_subset_1(B,k1_arytm_2) -> k5_arytm_2(A,B) = k5_arytm_2(B,A))) # label(commutativity_k5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3036 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (-r2_hidden(A,k6_arytm_3) -> (A = B <-> k3_arytm_2(A) = B)) & (r2_hidden(A,k6_arytm_3) -> (k3_arytm_2(A) = B <-> (exists C (m1_subset_1(C,k6_arytm_3) & a_1_0_arytm_2(C) = B & A = C)))))))) # label(d3_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3037 (all A all B (m1_subset_1(B,k6_arytm_3) -> ((exists C (m1_subset_1(C,k6_arytm_3) & A = C & -r3_arytm_3(B,C))) <-> r2_hidden(A,a_1_0_arytm_2(B))))) # label(fraenkel_a_1_0_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3038 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(r2_hidden(A,k6_arytm_3) & r2_hidden(B,k6_arytm_3) & (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> -(C = A & k8_arytm_2(A,B) = k11_arytm_3(C,D) & B = D)))))))))) # label(t22_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3039 (all A ((exists B ((all C (m1_subset_1(C,k6_arytm_3) -> (r2_hidden(C,B) -> (all D (m1_subset_1(D,k6_arytm_3) -> (r3_arytm_3(D,C) -> r2_hidden(D,B)))) & (exists D (m1_subset_1(D,k6_arytm_3) & -r3_arytm_3(D,C) & r2_hidden(D,B)))))) & A = B & m1_subset_1(B,k1_zfmisc_1(k6_arytm_3)))) <-> r2_hidden(A,a_0_0_arytm_2))) # label(fraenkel_a_0_0_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3040 (all A all B all C (m2_subset_1(C,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) & m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> ((exists D exists E (m1_subset_1(D,k6_arytm_3) & k11_arytm_3(D,E) = A & r2_hidden(D,B) & r2_hidden(E,C) & m1_subset_1(E,k6_arytm_3))) <-> r2_hidden(A,a_2_1_arytm_2(B,C))))) # label(fraenkel_a_2_1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3041 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r2_hidden(A,k6_arytm_3) & r2_hidden(B,k6_arytm_3) -> (r1_arytm_2(A,B) <-> (exists C (m1_subset_1(C,k6_arytm_3) & (exists D (A = C & B = D & r3_arytm_3(C,D) & m1_subset_1(D,k6_arytm_3))))))) & (r2_hidden(B,k6_arytm_3) -> r2_hidden(A,k6_arytm_3) | (r1_arytm_2(A,B) <-> -r2_hidden(B,A))) & -(-(r1_arytm_2(A,B) <-> r1_tarski(A,B)) & -(-r2_hidden(A,k6_arytm_3) & r2_hidden(B,k6_arytm_3)) & -(-r2_hidden(B,k6_arytm_3) & r2_hidden(A,k6_arytm_3)) & -(r2_hidden(A,k6_arytm_3) & r2_hidden(B,k6_arytm_3))) & (r2_hidden(A,k6_arytm_3) -> (r1_arytm_2(A,B) <-> r2_hidden(A,B)) | r2_hidden(B,k6_arytm_3)))))) # label(d5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3042 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (A = k12_arytm_3 -> k8_arytm_2(A,B) = k12_arytm_3))))) # label(t4_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3043 (all A (m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> ((all C (m1_subset_1(C,k6_arytm_3) -> -(all D (m1_subset_1(D,k6_arytm_3) -> (-r3_arytm_3(C,D) <-> r2_hidden(D,A)))))) -> (B = A <-> k4_arytm_2(A) = B)) & ((exists C (m1_subset_1(C,k6_arytm_3) & (all D (m1_subset_1(D,k6_arytm_3) -> (-r3_arytm_3(C,D) <-> r2_hidden(D,A)))))) -> (k4_arytm_2(A) = B <-> (exists C (m1_subset_1(C,k6_arytm_3) & (all D (m1_subset_1(D,k6_arytm_3) -> (r2_hidden(D,A) <-> -r3_arytm_3(C,D)))) & B = C)))))))) # label(d4_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3044 (all A (m1_subset_1(A,k2_arytm_2) -> (r2_hidden(A,k5_ordinal2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (A != B & r1_arytm_2(B,A) & r2_hidden(B,k5_ordinal2) <-> r2_hidden(B,A))))))) # label(t19_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3045 (all A all B (m1_subset_1(A,k1_arytm_2) & m1_subset_1(B,k1_arytm_2) -> m2_subset_1(k5_arytm_2(A,B),k1_zfmisc_1(k6_arytm_3),k1_arytm_2))) # label(dt_k5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3046 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> k8_arytm_2(k8_arytm_2(A,B),C) = k8_arytm_2(A,k8_arytm_2(B,C)))))))) # label(t13_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3047 (all A all B (m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) -> k7_arytm_2(A,B) = k7_arytm_2(B,A))) # label(commutativity_k7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3048 (all A all B (m1_subset_1(B,k1_arytm_2) & m1_subset_1(A,k1_arytm_2) -> m2_subset_1(k6_arytm_2(A,B),k1_zfmisc_1(k6_arytm_3),k1_arytm_2))) # label(dt_k6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3049 (all A -r2_hidden(k4_tarski(k12_arytm_3,A),k2_arytm_2)) # label(t3_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3050 (all A all B (m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) -> m1_subset_1(k8_arytm_2(A,B),k2_arytm_2))) # label(dt_k8_arytm_2) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3051 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k7_arytm_2(A,B) = B -> A = k1_xboole_0))))) # label(t1_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3052 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r1_arytm_2(B,A) -> k1_arytm_1(A,B) = k2_arytm_1(A,B)) & (-r1_arytm_2(B,A) -> k4_tarski(k1_xboole_0,k1_arytm_1(B,A)) = k2_arytm_1(A,B)))))) # label(d2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3053 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r1_arytm_2(B,A) & r1_arytm_2(A,B) -> B = A))))) # label(t4_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3054 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(C,B) & r1_arytm_2(A,B) -> k2_arytm_1(k1_arytm_1(B,C),A) = k2_arytm_1(k1_arytm_1(B,A),C)))))))) # label(t25_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3055 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(B,A) -> k1_xboole_0 = k1_arytm_1(A,B) | C = k1_xboole_0 | k4_tarski(k1_xboole_0,k8_arytm_2(C,k1_arytm_1(A,B))) = k2_arytm_1(k8_arytm_2(C,B),k8_arytm_2(C,A))))))))) # label(t28_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3056 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(k1_arytm_1(A,B) = k1_xboole_0 & -r1_arytm_2(A,B)))))) # label(t9_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3057 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r1_arytm_2(A,B) & k1_xboole_0 = k1_arytm_1(B,A) -> A = B))))) # label(t10_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3058 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) & r1_arytm_2(A,C) -> k7_arytm_2(k1_arytm_1(C,A),B) = k7_arytm_2(k1_arytm_1(B,A),C)))))))) # label(t15_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3059 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (-r1_arytm_2(A,B) -> k2_arytm_1(k7_arytm_2(C,B),A) = k2_arytm_1(C,k1_arytm_1(A,B))))))))) # label(t21_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3060 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(k7_arytm_2(A,C),k7_arytm_2(B,C)) <-> r1_arytm_2(A,B)))))))) # label(t7_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3061 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> r1_arytm_2(k8_arytm_2(A,C),k8_arytm_2(B,C))))))))) # label(t8_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3062 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k1_xboole_0 = A -> r1_arytm_2(A,B)))))) # label(t6_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3063 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,C) & r1_arytm_2(A,B) -> k7_arytm_2(k1_arytm_1(B,A),C) = k7_arytm_2(B,k1_arytm_1(C,A))))))))) # label(t12_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3064 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> r1_arytm_2(k1_arytm_1(A,B),A))))) # label(t11_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3065 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r1_arytm_2(A,B) & B = k1_xboole_0 -> A = k1_xboole_0))))) # label(t5_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3066 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> r1_arytm_2(k1_arytm_1(A,C),k1_arytm_1(B,C))))))))) # label(t17_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3067 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> -(k4_tarski(k1_xboole_0,k8_arytm_2(C,k1_arytm_1(A,B))) != k2_arytm_1(k8_arytm_2(C,B),k8_arytm_2(C,A)) & k1_xboole_0 != C & -r1_arytm_2(A,B)))))))) # label(t27_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3068 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> k2_arytm_1(B,k7_arytm_2(A,C)) = k2_arytm_1(k1_arytm_1(B,A),C)))))))) # label(t24_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3069 (all A all B (m1_subset_1(B,k2_arytm_2) & m1_subset_1(A,k2_arytm_2) -> m1_subset_1(k1_arytm_1(A,B),k2_arytm_2))) # label(dt_k1_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3070 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) & r1_arytm_2(C,A) -> k1_arytm_1(B,k1_arytm_1(A,C)) = k7_arytm_2(k1_arytm_1(B,A),C)))))))) # label(t14_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3071 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k1_xboole_0 = A -> k1_xboole_0 = B | k2_arytm_1(A,B) = k4_tarski(k1_xboole_0,B)))))) # label(t19_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3072 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(B != k1_xboole_0 & A != k1_xboole_0 & k1_xboole_0 = k8_arytm_2(A,B)))))) # label(t2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3073 (all A (m1_subset_1(A,k2_arytm_2) -> k2_arytm_1(A,A) = k1_xboole_0)) # label(t18_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3074 $T # label(dt_k2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3075 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> k8_arytm_2(C,k1_arytm_1(B,A)) = k2_arytm_1(k8_arytm_2(C,B),k8_arytm_2(C,A))))))))) # label(t26_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3076 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) & r1_arytm_2(B,C) -> r1_arytm_2(A,C)))))))) # label(t3_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3077 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> k7_arytm_2(C,k1_arytm_1(B,A)) = k1_arytm_1(k7_arytm_2(C,B),A)))))))) # label(t13_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3078 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> k7_arytm_2(k1_arytm_1(B,A),C) = k2_arytm_1(B,k1_arytm_1(A,C)) | r1_arytm_2(A,C)))))))) # label(t22_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3079 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> -(-r1_arytm_2(A,C) & k2_arytm_1(C,k1_arytm_1(A,B)) != k2_arytm_1(B,k1_arytm_1(A,C)) & -r1_arytm_2(A,B)))))))) # label(t23_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3080 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (-r1_arytm_2(B,A) -> (k1_xboole_0 = C <-> k1_arytm_1(A,B) = C)) & (r1_arytm_2(B,A) -> (C = k1_arytm_1(A,B) <-> A = k7_arytm_2(C,B))))))))) # label(d1_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3081 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> r1_arytm_2(k1_arytm_1(C,B),k1_arytm_1(C,A))))))))) # label(t16_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3082 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) -> k2_arytm_1(k7_arytm_2(C,B),A) = k7_arytm_2(C,k1_arytm_1(B,A))))))))) # label(t20_arytm_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3083 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3084 (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]. 80.51/78.52 3085 (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]. 80.51/78.52 3086 (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]. 80.51/78.52 3087 (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]. 80.51/78.52 3088 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3089 (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]. 80.51/78.52 3090 (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]. 80.51/78.52 3091 (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]. 80.51/78.52 3092 (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]. 80.51/78.52 3093 (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]. 80.51/78.52 3094 (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]. 80.51/78.52 3095 (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]. 80.51/78.52 3096 (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]. 80.51/78.52 3097 (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]. 80.51/78.52 3098 (all A (v1_finset_1(A) <-> v1_finset_1(k1_zfmisc_1(A)))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3099 (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]. 80.51/78.52 3100 (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]. 80.51/78.52 3101 (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]. 80.51/78.52 3102 (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]. 80.51/78.52 3103 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3104 (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]. 80.51/78.52 3105 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3106 (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]. 80.51/78.52 3107 (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]. 80.51/78.52 3108 (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]. 80.51/78.52 3109 (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]. 80.51/78.52 3110 (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]. 80.51/78.52 3111 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3112 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3113 (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]. 80.51/78.52 3114 (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]. 80.51/78.52 3115 (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]. 80.51/78.52 3116 (all A (v1_finset_1(k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3117 (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]. 80.51/78.52 3118 (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]. 80.51/78.52 3119 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3120 (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]. 80.51/78.52 3121 (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]. 80.51/78.52 3122 (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]. 80.51/78.52 3123 (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]. 80.51/78.52 3124 (exists A (v1_finset_1(A) & -v1_xboole_0(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3125 (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]. 80.51/78.52 3126 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3127 (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]. 80.51/78.52 3128 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3129 (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]. 80.51/78.52 3130 (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]. 80.51/78.52 3131 (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]. 80.51/78.52 3132 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3133 (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]. 80.51/78.52 3134 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3135 (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]. 80.51/78.52 3136 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3137 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3138 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3139 (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]. 80.51/78.52 3140 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> m1_subset_1(k2_finsub_1(A,B,C),A))) # label(dt_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3141 $T # label(t12_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3142 (all A all B (v4_finsub_1(B) -> (B = k5_finsub_1(A) <-> (all C (v1_finset_1(C) & r1_tarski(C,A) <-> r2_hidden(C,B)))))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3143 $T # label(t5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3144 (all A all B k5_finsub_1(k3_xboole_0(A,B)) = k3_xboole_0(k5_finsub_1(A),k5_finsub_1(B))) # label(t24_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3145 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) -> k4_finsub_1(A,B,C) = k5_xboole_0(B,C))) # label(redefinition_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3146 (all A v4_finsub_1(k5_finsub_1(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3147 $T # label(t29_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3148 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k4_xboole_0(B,C),A) & r2_hidden(k5_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t15_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3149 (all A all B (r1_tarski(A,B) -> r1_tarski(k5_finsub_1(A),k5_finsub_1(B)))) # label(t23_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3150 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> k4_finsub_1(A,B,C) = k4_finsub_1(A,C,B))) # label(commutativity_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3151 (all A (-v1_xboole_0(A) & v4_finsub_1(A) -> (all B (v4_finsub_1(B) & -v1_xboole_0(B) -> -v1_xboole_0(k3_xboole_0(A,B)) & v4_finsub_1(k3_xboole_0(A,B)))))) # label(t21_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3152 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k3_finsub_1(A,B,C),A))) # label(dt_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3153 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_finset_1(A) -> m1_subset_1(B,k5_finsub_1(A))))) # label(t34_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3154 (all A (v3_finsub_1(A) <-> (all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k4_xboole_0(B,C),A))))) # label(d3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3155 $T # label(t7_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3156 (all A (v1_finsub_1(A) & v3_finsub_1(A) <-> v4_finsub_1(A))) # label(d4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3157 (all A (v4_finsub_1(A) & -v1_xboole_0(A) -> r2_hidden(k1_xboole_0,A))) # label(t18_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3158 $T # label(t19_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3159 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k2_finsub_1(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3160 (all A (v3_finsub_1(A) & v1_finsub_1(A) -> v4_finsub_1(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3161 (all A all B all C (v4_finsub_1(C) & -v1_xboole_0(C) -> (m1_subset_1(A,C) & m1_subset_1(B,C) -> m1_subset_1(k3_xboole_0(A,B),C)))) # label(t13_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3162 $T # label(t31_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3163 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> k3_finsub_1(A,B,B) = B)) # label(idempotence_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3164 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> m1_subset_1(k4_finsub_1(A,B,C),A))) # label(dt_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3165 $T # label(t11_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3166 $T # label(t4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3167 (all A all B all C (-v1_xboole_0(C) & v4_finsub_1(C) -> (m1_subset_1(A,C) & m1_subset_1(B,C) -> m1_subset_1(k5_xboole_0(A,B),C)))) # label(t14_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3168 (all A r1_tarski(k5_finsub_1(A),k1_zfmisc_1(A))) # label(t26_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3169 $T # label(t2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3170 (all A v4_finsub_1(k1_zfmisc_1(A))) # label(t20_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3171 $T # label(t1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3172 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k3_xboole_0(B,C),A))) <-> v2_finsub_1(A))) # label(d2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3173 (all A (v4_finsub_1(A) -> v1_finsub_1(A) & v3_finsub_1(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3174 (all A (v4_finsub_1(A) <-> (all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k4_xboole_0(B,C),A) & r2_hidden(k2_xboole_0(B,C),A))))) # label(t10_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3175 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k3_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t16_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3176 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) -> k1_finsub_1(A,B,C) = k1_finsub_1(A,C,B))) # label(commutativity_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3177 (all A (v1_finsub_1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k2_xboole_0(B,C),A))))) # label(d1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3178 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k3_finsub_1(A,B,C) = k3_finsub_1(A,C,B))) # label(commutativity_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3179 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k2_xboole_0(B,C) = k1_finsub_1(A,B,C))) # label(redefinition_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3180 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> m1_subset_1(B,k1_zfmisc_1(A)))) # label(t32_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3181 (all A (v3_finsub_1(k5_finsub_1(A)) & v4_finsub_1(k5_finsub_1(A)) & v1_finsub_1(k5_finsub_1(A)) & -v1_xboole_0(k5_finsub_1(A)))) # label(fc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3182 $T # label(t6_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3183 (exists A (-v1_xboole_0(A) & v2_finsub_1(A) & v3_finsub_1(A) & v4_finsub_1(A) & v1_finsub_1(A))) # label(rc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3184 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k3_xboole_0(B,C) = k3_finsub_1(A,B,C))) # label(redefinition_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3185 (all A all B r1_tarski(k2_xboole_0(k5_finsub_1(A),k5_finsub_1(B)),k5_finsub_1(k2_xboole_0(A,B)))) # label(t25_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3186 (all A (v1_finset_1(A) -> k1_zfmisc_1(A) = k5_finsub_1(A))) # label(t27_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3187 (all A (v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)) & -v1_xboole_0(k1_zfmisc_1(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3188 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k2_xboole_0(B,C),A) & r2_hidden(k5_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t17_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3189 $T # label(t22_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3190 $T # label(t9_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3191 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k1_finsub_1(A,B,C),A))) # label(dt_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3192 $T # label(t8_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3193 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(cc3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3194 $T # label(t33_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3195 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(t30_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3196 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> B = k1_finsub_1(A,B,B))) # label(idempotence_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3197 $T # label(t3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3198 (all A all B all C r1_tarski(k1_tarski(A),k1_enumset1(A,B,C))) # label(t3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3199 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (v2_binop_1(C,A) & v1_binop_1(C,A) & v3_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F)))) | D = k1_xboole_0))))))))))) # label(t29_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3200 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> k10_setwiseo(A,A,B,k11_setwiseo(A)) = B)))) # label(t71_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3201 $T # label(t46_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3202 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,C) -> r2_hidden(k8_funct_2(A,B,E,F),D)))) -> r1_tarski(k2_funct_2(A,B,E,C),D)))))))))) # label(t15_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3203 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,B,A) & v1_funct_2(C,B,A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (k2_funct_2(B,A,C,D) = k1_xboole_0 -> k1_xboole_0 = D))))))))) # label(t19_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3204 $T # label(t24_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3205 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (r6_binop_1(A,D,C) & v2_binop_1(C,A) & v1_binop_1(C,A) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (m2_relset_1(F,B,A) & v1_funct_2(F,B,A) & v1_funct_1(F) -> (all G (m1_subset_1(G,A) -> k2_binop_1(A,A,A,D,k7_setwiseo(B,A,C,E,F),G) = k7_setwiseo(B,A,C,E,k7_funcop_1(A,B,D,F,G)))))))))))))))))) # label(t37_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3206 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (v3_binop_1(C,A) & v1_binop_1(C,A) & v2_binop_1(C,A) & v1_setwiseo(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D))))))))))))))) # label(t42_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3207 $T # label(t66_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3208 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & m2_relset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) -> (B = k9_setwiseo(A) <-> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k2_binop_1(k5_finsub_1(A),k5_finsub_1(A),k5_finsub_1(A),B,C,D) = k5_setwiseo(A,C,D)))))))) # label(d4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3209 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,B,k5_finsub_1(C)) & m2_relset_1(F,B,k5_finsub_1(C)) -> k10_setwiseo(B,C,k8_setwiseo(A,B,E,D),F) = k10_setwiseo(A,C,D,k7_funct_2(A,B,k5_finsub_1(C),E,F)))))))))))) # label(t63_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3210 $T # label(t47_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3211 (all A (v1_funct_2(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & m2_relset_1(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_1(k9_setwiseo(A)))) # label(dt_k9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3212 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (r2_hidden(C,B) -> m1_subset_1(C,A))))))) # label(t14_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3213 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k5_setwiseo(A,C,B) = k5_setwiseo(A,B,C))) # label(commutativity_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3214 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (v1_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> k7_setwiseo(B,A,C,k2_setwiseo(B,E),D) = k8_funct_2(B,A,D,E)))))))))))) # label(t26_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3215 (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,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (v2_binop_1(D,A) & v1_binop_1(D,A) & v3_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (k1_xboole_0 != E -> (all F (v1_funct_1(F) & v1_funct_2(F,B,C) & m2_relset_1(F,B,C) -> (all G (v1_funct_2(G,C,A) & m2_relset_1(G,C,A) & v1_funct_1(G) -> k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G)) = k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G))))))))))))))))) # label(t38_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3216 (all A all B all C (r2_hidden(A,k2_xboole_0(B,k1_tarski(C))) <-> r2_hidden(A,B) | C = A)) # label(t6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3217 (all A k1_xboole_0 = k1_setwiseo(A)) # label(d1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3218 $T # label(t48_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3219 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> -(k1_xboole_0 != E & F != k1_xboole_0 & k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D) != k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)))))))))))))))) # label(t30_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3220 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & v1_funct_1(E) & v1_funct_2(E,A,B) & m1_relset_1(E,A,B) & m1_subset_1(D,k5_finsub_1(A)) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> m1_subset_1(k7_setwiseo(A,B,C,D,E),B))) # label(dt_k7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3221 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k1_tarski(B) = k2_setwiseo(A,B))) # label(redefinition_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3222 $T # label(t21_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3223 (all A (m2_relset_1(k11_setwiseo(A),A,k5_finsub_1(A)) & v1_funct_2(k11_setwiseo(A),A,k5_finsub_1(A)) & v1_funct_1(k11_setwiseo(A)))) # label(dt_k11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3224 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)))) # label(dt_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3225 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (v2_binop_1(C,B) & v3_binop_1(C,B) & v1_binop_1(C,B) -> (all F (m1_subset_1(F,B) -> (k2_funct_2(A,B,E,D) = k2_setwiseo(B,F) -> k7_setwiseo(A,B,C,D,E) = F)))))))))))))) # label(t34_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3226 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)) = k7_setwiseo(B,A,C,k3_setwiseo(B,E,F),D)))))))))))))) # label(t27_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3227 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> m1_subset_1(k6_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.52 3228 (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) -> (v2_binop_1(C,B) & v3_binop_1(C,B) & v1_setwiseo(C,B) & v1_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(D,D),D) & m2_relset_1(E,k2_zfmisc_1(D,D),D) -> (v3_binop_1(E,D) & v1_setwiseo(E,D) & v2_binop_1(E,D) & v1_binop_1(E,D) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (all G (v1_funct_2(G,B,D) & m2_relset_1(G,B,D) & v1_funct_1(G) -> ((all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)) = k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)))))) & k8_funct_2(B,D,G,k3_binop_1(B,C)) = k3_binop_1(D,E) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)) = k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G))))))))))))))))))))) # label(t45_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3229 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (v2_binop_1(C,A) & v3_binop_1(C,A) & v1_binop_1(C,A) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> (r2_hidden(G,D) -> k8_funct_2(B,A,E,G) = F))) -> k7_setwiseo(B,A,C,D,E) = F))) | k1_xboole_0 = D))))))))))) # label(t33_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3230 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> k1_xboole_0 = k10_setwiseo(A,B,k1_setwiseo(A),C))))) # label(t59_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3231 (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) -> ((exists C (m1_subset_1(C,A) & r3_binop_1(A,C,B))) <-> v1_setwiseo(B,A)))))) # label(d2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3232 $T # label(t2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3233 (all A all B (v1_funct_2(B,A,k5_finsub_1(A)) & m2_relset_1(B,A,k5_finsub_1(A)) & v1_funct_1(B) -> (k11_setwiseo(A) = B <-> (all C (r2_hidden(C,A) -> k1_funct_1(B,C) = k1_tarski(C)))))) # label(d6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3234 (all A all B all C all D (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k1_enumset1(B,C,D) = k4_setwiseo(A,B,C,D))) # label(redefinition_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3235 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k10_setwiseo(A,B,k5_setwiseo(A,D,E),C) = k5_setwiseo(B,k10_setwiseo(A,B,D,C),k10_setwiseo(A,B,E,C)))))))))) # label(t62_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3236 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) & r2_hidden(C,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) -> B = C))))))))) # label(t69_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3237 (all A v3_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t49_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3238 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> (r2_hidden(F,D) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,F),k7_setwiseo(B,A,C,D,E)) = k7_setwiseo(B,A,C,D,E))))))))))))))) # label(t31_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3239 (all A (m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo)) -> (all B (m1_subset_1(B,k5_finsub_1(f1_s3_setwiseo)) -> (p1_s3_setwiseo(B) & p1_s3_setwiseo(A) -> k1_xboole_0 = A | p1_s3_setwiseo(k5_setwiseo(f1_s3_setwiseo,A,B)) | k1_xboole_0 = B))))) & (all A (m1_subset_1(A,f1_s3_setwiseo) -> p1_s3_setwiseo(k2_setwiseo(f1_s3_setwiseo,A)))) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo)) -> (A != k1_xboole_0 -> p1_s3_setwiseo(A)))) # label(s3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3240 (all A (m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo)) -> (all B (m1_subset_1(B,f1_s4_setwiseo) -> (p1_s4_setwiseo(A) -> p1_s4_setwiseo(k5_setwiseo(f1_s4_setwiseo,A,k2_setwiseo(f1_s4_setwiseo,B)))))))) & p1_s4_setwiseo(k1_setwiseo(f1_s4_setwiseo)) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo)) -> p1_s4_setwiseo(A))) # label(s4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3241 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v1_setwiseo(C,A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> k7_setwiseo(B,A,C,k1_setwiseo(B),D) = k3_binop_1(A,C)))))))))) # label(t40_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3242 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k10_setwiseo(A,B,k3_setwiseo(A,D,E),C) = k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)))))))))) # label(t57_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3243 (all A (-v1_xboole_0(A) -> (exists B (v1_finset_1(B) & -v1_xboole_0(B) & m1_subset_1(B,k5_finsub_1(A)))))) # label(rc2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3244 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k5_setwiseo(B,k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)),k8_funct_2(A,k5_finsub_1(B),C,F)) = k10_setwiseo(A,B,k4_setwiseo(A,D,E,F),C))))))))))) # label(t58_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3245 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) & v1_funct_2(C,B,A) & v1_funct_1(C) -> (all D (m1_subset_1(D,B) -> r2_hidden(D,k3_funct_2(B,A,C,k1_tarski(k8_funct_2(B,A,C,D)))))))))))) # label(t12_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3246 $T # label(t20_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3247 (all A all B all C -(-r2_hidden(C,A) & -r1_tarski(A,B) & r1_tarski(A,k2_xboole_0(B,k1_tarski(C))))) # label(t5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3248 (all A (m1_subset_1(k1_setwiseo(A),k5_finsub_1(A)) & v1_xboole_0(k1_setwiseo(A)))) # label(dt_k1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3249 (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) -> (r3_binop_1(A,k3_binop_1(A,B),B) <-> v1_setwiseo(B,A)))))) # label(t22_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3250 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (v1_binop_1(D,A) & v3_binop_1(D,A) & v2_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (m2_relset_1(F,B,k5_finsub_1(C)) & v1_funct_2(F,B,k5_finsub_1(C)) & v1_funct_1(F) -> (all G (m2_relset_1(G,k5_finsub_1(C),A) & v1_funct_2(G,k5_finsub_1(C),A) & v1_funct_1(G) -> ((all H (m1_subset_1(H,k5_finsub_1(C)) -> (all I (m1_subset_1(I,k5_finsub_1(C)) -> k2_binop_1(A,A,A,D,k8_funct_2(k5_finsub_1(C),A,G,H),k8_funct_2(k5_finsub_1(C),A,G,I)) = k8_funct_2(k5_finsub_1(C),A,G,k5_setwiseo(C,H,I)))))) -> k7_setwiseo(B,A,D,E,k7_funct_2(B,k5_finsub_1(C),A,F,G)) = k8_funct_2(k5_finsub_1(C),A,G,k10_setwiseo(B,C,E,F))))))))))))))))) # label(t64_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.53 3251 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all 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) -> (v1_binop_1(D,B) & v1_setwiseo(D,B) & v3_binop_1(D,B) & v2_binop_1(D,B) -> (all E (v1_funct_2(E,A,k5_finsub_1(C)) & m2_relset_1(E,A,k5_finsub_1(C)) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k5_finsub_1(C),B) & m2_relset_1(F,k5_finsub_1(C),B) -> (k8_funct_2(k5_finsub_1(C),B,F,k1_setwiseo(C)) = k3_binop_1(B,D) & (all G (m1_subset_1(G,k5_finsub_1(C)) -> (all H (m1_subset_1(H,k5_finsub_1(C)) -> k8_funct_2(k5_finsub_1(C),B,F,k5_setwiseo(C,G,H)) = k2_binop_1(B,B,B,D,k8_funct_2(k5_finsub_1(C),B,F,G),k8_funct_2(k5_finsub_1(C),B,F,H)))))) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> k8_funct_2(k5_finsub_1(C),B,F,k10_setwiseo(A,C,G,E)) = k7_setwiseo(A,B,D,G,k7_funct_2(A,k5_finsub_1(C),B,E,F)))))))))))))))) # label(t65_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.54 3252 (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 (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (v2_binop_1(C,B) & v1_binop_1(C,B) -> (all F (m1_subset_1(F,B) -> ((exists G (m2_relset_1(G,k5_finsub_1(A),B) & k8_funct_2(k5_finsub_1(A),B,G,D) = F & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> H = k1_xboole_0 | (all I (m1_subset_1(I,A) -> (r2_hidden(I,k6_setwiseo(A,D,H)) -> k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))) = k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)))))))) & (all H (m1_subset_1(H,A) -> k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)) = k8_funct_2(A,B,E,H))) & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> k1_funct_1(G,k1_xboole_0) = H))) & v1_funct_2(G,k5_finsub_1(A),B) & v1_funct_1(G))) <-> k7_setwiseo(A,B,C,D,E) = F))) | -v1_setwiseo(C,B) & k1_xboole_0 = D))))))))))) # label(d3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.54 3253 (all A exists B (m1_subset_1(B,k5_finsub_1(A)) & v1_xboole_0(B) & v1_finset_1(B))) # label(rc1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.54 3254 (all A v2_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t51_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.54 3255 $T # label(t1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.54 3256 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k3_setwiseo(A,B,C) = k3_setwiseo(A,C,B))) # label(commutativity_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.54 3257 (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,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & r6_binop_1(A,D,C) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (v1_funct_2(F,B,A) & m2_relset_1(F,B,A) & v1_funct_1(F) -> (all G (m1_subset_1(G,A) -> k7_setwiseo(B,A,C,E,k8_funcop_1(A,B,D,G,F)) = k2_binop_1(A,A,A,D,G,k7_setwiseo(B,A,C,E,F)))))))))))))))))) # label(t36_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.54 3258 (all A (-v1_xboole_0(A) -> (all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,k5_finsub_1(B)) & m2_relset_1(D,A,k5_finsub_1(B)) -> (all E (v1_funct_2(E,k5_finsub_1(B),k5_finsub_1(C)) & m2_relset_1(E,k5_finsub_1(B),k5_finsub_1(C)) & v1_funct_1(E) -> (k1_setwiseo(C) = k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k1_setwiseo(B)) & (all F (m1_subset_1(F,k5_finsub_1(B)) -> (all G (m1_subset_1(G,k5_finsub_1(B)) -> k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k5_setwiseo(B,F,G)) = k5_setwiseo(C,k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,F),k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,G)))))) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> k10_setwiseo(A,C,F,k7_funct_2(A,k5_finsub_1(B),k5_finsub_1(C),D,E)) = k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k10_setwiseo(A,B,F,D))))))))))) # label(t72_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.54 3259 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)),k8_funct_2(B,A,D,G)) = k7_setwiseo(B,A,C,k4_setwiseo(B,E,F,G),D)))))))))))))))) # label(t28_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.54 3260 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v3_binop_1(D,A) & v2_binop_1(D,A) & v1_setwiseo(D,A) & v1_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m2_relset_1(F,B,C) & v1_funct_2(F,B,C) & v1_funct_1(F) -> (all G (v1_funct_2(G,C,A) & m2_relset_1(G,C,A) & v1_funct_1(G) -> k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G) = k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G))))))))))))))))) # label(t44_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3261 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> k6_setwiseo(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3262 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> m1_subset_1(k5_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3263 (all A all B all C (r2_hidden(B,C) & r1_tarski(A,C) <-> r1_tarski(k2_xboole_0(A,k1_tarski(B)),C))) # label(t8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3264 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))))) # label(t18_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3265 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k10_setwiseo(A,B,D,C) = k3_tarski(k8_setwiseo(A,k5_finsub_1(B),C,D)))))))) # label(t61_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3266 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (v3_binop_1(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> -v1_setwiseo(C,B) & k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> ((exists G (m2_relset_1(G,k5_finsub_1(A),B) & k8_funct_2(k5_finsub_1(A),B,G,D) = F & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> H = k1_funct_1(G,k1_xboole_0)))) & (all H (m1_subset_1(H,A) -> k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)) = k8_funct_2(A,B,E,H))) & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> k1_xboole_0 = H | (all I (m1_subset_1(I,A) -> (r2_hidden(I,D) -> k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)) = k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))))))))) & v1_funct_2(G,k5_finsub_1(A),B) & v1_funct_1(G))) <-> k7_setwiseo(A,B,C,D,E) = F)))))))))))))) # label(t25_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3267 (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 (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (v2_binop_1(C,A) & v1_setwiseo(C,A) & v1_binop_1(C,A) & v3_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F))))))))))))))) # label(t41_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3268 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v1_setwiseo(B,A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,k3_binop_1(A,B),C) = C & k2_binop_1(A,A,A,B,C,k3_binop_1(A,B)) = C))))))) # label(t23_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3269 (all A r3_binop_1(k5_finsub_1(A),k1_setwiseo(A),k9_setwiseo(A))) # label(t52_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3270 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(C,A) -> m1_subset_1(k4_setwiseo(A,B,C,D),k5_finsub_1(A)))) # label(dt_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3271 (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) -> (v3_binop_1(C,B) & v1_setwiseo(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> (k8_setwiseo(A,B,E,G) = k8_setwiseo(A,B,D,F) -> k7_setwiseo(A,B,C,F,D) = k7_setwiseo(A,B,C,G,E))))))))))))))))) # label(t43_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3272 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> k5_setwiseo(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3273 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (v1_funct_2(D,A,k5_finsub_1(B)) & m2_relset_1(D,A,k5_finsub_1(B)) & v1_funct_1(D) -> k10_setwiseo(A,B,C,D) = k7_setwiseo(A,k5_finsub_1(B),k9_setwiseo(B),C,D))))))) # label(d5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3274 (exists A (v1_funct_2(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo)) & (all B (m1_subset_1(B,f1_s1_setwiseo) -> (all C (m1_subset_1(C,f1_s1_setwiseo) -> (p1_s1_setwiseo(C,B) & r2_hidden(C,f2_s1_setwiseo) <-> r2_hidden(C,k8_funct_2(f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo),A,B))))))) & m2_relset_1(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo)) & v1_funct_1(A))) # label(s1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3275 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (r1_tarski(C,B) -> m1_subset_1(C,k5_finsub_1(A)))))) # label(t16_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3276 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> (r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),C)) <-> B = C))))) # label(t68_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3277 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k5_setwiseo(A,B,B) = B)) # label(idempotence_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3278 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,A) -> k8_funct_2(A,k5_finsub_1(B),C,D) = k10_setwiseo(A,B,k2_setwiseo(A,D),C))))))) # label(t56_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3279 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k3_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3280 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(D,k5_finsub_1(A)) & m1_relset_1(C,A,B) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k9_relat_1(C,D) = k8_setwiseo(A,B,C,D))) # label(redefinition_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3281 (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) -> (v1_binop_1(C,B) & v2_binop_1(C,B) & v3_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(D,D),D) & v1_funct_2(E,k2_zfmisc_1(D,D),D) & v1_funct_1(E) -> (v3_binop_1(E,D) & v2_binop_1(E,D) & v1_binop_1(E,D) -> (all F (m2_relset_1(F,A,B) & v1_funct_2(F,A,B) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,B,D) & v1_funct_2(G,B,D) -> ((all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)) = k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)))))) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> (k1_xboole_0 != H -> k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)) = k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)))))))))))))))))))))) # label(t39_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3282 $T # label(t9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3283 (all A all B all C r1_tarski(k2_tarski(A,B),k1_enumset1(A,B,C))) # label(t4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3284 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E ((exists F (m1_subset_1(F,A) & r2_hidden(E,k8_funct_2(A,k5_finsub_1(B),C,F)) & r2_hidden(F,D))) <-> r2_hidden(E,k10_setwiseo(A,B,D,C)))))))))) # label(t70_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3285 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(C,k5_finsub_1(A)) & m1_relset_1(D,A,k5_finsub_1(B)) & v1_funct_2(D,A,k5_finsub_1(B)) & v1_funct_1(D) -> m1_subset_1(k10_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3286 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,B,A) & m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,B) -> k1_tarski(k8_funct_2(B,A,C,D)) = k2_funct_2(B,A,C,k1_tarski(D)))))))))) # label(t13_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3287 $T # label(t17_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3288 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> (r1_tarski(E,F) -> k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) = k7_setwiseo(B,A,C,F,D) | k1_xboole_0 = E)))))))))))))) # label(t32_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3289 $T # label(t10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3290 (all A k1_xboole_0 = k3_binop_1(k5_finsub_1(A),k9_setwiseo(A))) # label(t55_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3291 (all A v1_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t50_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3292 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,A,k5_finsub_1(A)) & v1_funct_2(B,A,k5_finsub_1(A)) & v1_funct_1(B) -> (B = k11_setwiseo(A) <-> (all C (m1_subset_1(C,A) -> k2_setwiseo(A,C) = k8_funct_2(A,k5_finsub_1(A),B,C)))))))) # label(t67_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3293 (all A r3_binop_1(k5_finsub_1(A),k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)),k9_setwiseo(A))) # label(t54_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3294 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k5_finsub_1(A)) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(A) -> m1_subset_1(k8_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3295 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k4_xboole_0(k9_relat_1(C,B),A) = k9_relat_1(C,k4_xboole_0(B,k10_relat_1(C,A))))) # label(t11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3296 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k10_setwiseo(A,B,k5_setwiseo(A,E,k2_setwiseo(A,D)),C) = k5_setwiseo(B,k10_setwiseo(A,B,E,C),k8_funct_2(A,k5_finsub_1(B),C,D)))))))))) # label(t60_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3297 (all A v1_setwiseo(k9_setwiseo(A),k5_finsub_1(A))) # label(t53_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3298 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k2_tarski(B,C) = k3_setwiseo(A,B,C))) # label(redefinition_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3299 (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) -> (v1_binop_1(C,B) & v2_binop_1(C,B) & v3_binop_1(C,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> (k2_funct_2(A,B,D,F) = k2_funct_2(A,B,E,G) -> k7_setwiseo(A,B,C,G,E) = k7_setwiseo(A,B,C,F,D) | k1_xboole_0 = F)))))))))))))))) # label(t35_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3300 $T # label(t7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3301 p1_s2_setwiseo(k1_setwiseo(f1_s2_setwiseo)) & (all A (m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo)) -> (all B (m1_subset_1(B,f1_s2_setwiseo) -> (p1_s2_setwiseo(A) -> r2_hidden(B,A) | p1_s2_setwiseo(k5_setwiseo(f1_s2_setwiseo,A,k2_setwiseo(f1_s2_setwiseo,B)))))))) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo)) -> p1_s2_setwiseo(A))) # label(s2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3302 (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]. 80.51/78.56 3303 (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]. 80.51/78.56 3304 (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]. 80.51/78.56 3305 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3306 (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]. 80.51/78.56 3307 (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]. 80.51/78.56 3308 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3309 (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]. 80.51/78.56 3310 (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]. 80.51/78.56 3311 (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]. 80.51/78.56 3312 (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]. 80.51/78.56 3313 (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]. 80.51/78.56 3314 (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]. 80.51/78.56 3315 (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]. 80.51/78.56 3316 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3317 (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]. 80.51/78.56 3318 (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]. 80.51/78.56 3319 (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]. 80.51/78.56 3320 (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]. 80.51/78.56 3321 (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]. 80.51/78.56 3322 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3323 (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]. 80.51/78.56 3324 (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]. 80.51/78.56 3325 (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]. 80.51/78.56 3326 (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]. 80.51/78.56 3327 (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]. 80.51/78.56 3328 (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]. 80.51/78.56 3329 (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]. 80.51/78.56 3330 (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]. 80.51/78.56 3331 (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]. 80.51/78.56 3332 (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]. 80.51/78.56 3333 (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]. 80.51/78.56 3334 (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]. 80.51/78.56 3335 (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]. 80.51/78.56 3336 (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]. 80.51/78.56 3337 (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]. 80.51/78.56 3338 (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]. 80.51/78.56 3339 (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]. 80.51/78.56 3340 (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]. 80.51/78.56 3341 (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]. 80.51/78.56 3342 (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]. 80.51/78.56 3343 (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]. 80.51/78.56 3344 (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]. 80.51/78.56 3345 (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]. 80.51/78.56 3346 (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]. 80.51/78.56 3347 (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]. 80.51/78.56 3348 (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]. 80.51/78.56 3349 (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]. 80.51/78.56 3350 (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]. 80.51/78.56 3351 (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]. 80.51/78.56 3352 (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]. 80.51/78.56 3353 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]. 80.51/78.56 3354 (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]. 80.51/78.56 3355 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3356 (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]. 80.51/78.56 3357 (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]. 80.51/78.56 3358 (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]. 80.51/78.56 3359 (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]. 80.51/78.56 3360 (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]. 80.51/78.56 3361 (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]. 80.51/78.56 3362 (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]. 80.51/78.56 3363 (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]. 80.51/78.56 3364 (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]. 80.51/78.56 3365 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3366 (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]. 80.51/78.56 3367 (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]. 80.51/78.56 3368 (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]. 80.51/78.56 3369 (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]. 80.51/78.56 3370 (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]. 80.51/78.56 3371 (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]. 80.51/78.56 3372 (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]. 80.51/78.56 3373 (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]. 80.51/78.56 3374 (exists A (v1_fraenkel(A) & -v1_xboole_0(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3375 (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]. 80.51/78.56 3376 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3377 (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]. 80.51/78.56 3378 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]. 80.51/78.56 3379 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3380 (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]. 80.51/78.56 3381 (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]. 80.51/78.56 3382 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3383 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]. 80.51/78.56 3384 (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]. 80.51/78.56 3385 (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]. 80.51/78.56 3386 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3387 (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]. 80.51/78.56 3388 (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]. 80.51/78.56 3389 (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]. 80.51/78.56 3390 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3391 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3392 (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]. 80.51/78.56 3393 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3394 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3395 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3396 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3397 (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]. 80.51/78.56 3398 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (np__0 = B -> A = k1_arytm_0(A,B)))))) # label(t13_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3399 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k3_arytm_0(k2_arytm_0(A,B)) = k2_arytm_0(k3_arytm_0(A),B))))) # label(t17_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3400 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (r2_hidden(k5_arytm_0(A,B),k1_numbers) -> B = np__0))))) # label(t26_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3401 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k1_arytm_0(A,B),k1_numbers))) # label(dt_k1_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3402 (all A all B k13_arytm_3 != k4_tarski(A,B)) # label(t7_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3403 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k2_arytm_0(A,B),k1_numbers))) # label(dt_k2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3404 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k4_arytm_0(A),k1_numbers))) # label(dt_k4_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.56 3405 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_arytm_0(k2_arytm_0(A,B),C) = k2_arytm_0(A,k2_arytm_0(B,C)))))))) # label(t15_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3406 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k2_arytm_1(A,B) = k12_arytm_3 -> B = A))))) # label(t6_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3407 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (B = k13_arytm_3 -> k2_arytm_0(A,B) = A))))) # label(t21_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3408 (all A (m1_subset_1(A,k2_numbers) -> (exists B ((exists C (k5_arytm_0(B,C) = A & m1_subset_1(C,k1_numbers))) & m1_subset_1(B,k1_numbers))))) # label(t11_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3409 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2) -> (C = k1_arytm_0(A,B) <-> (exists D (m1_subset_1(D,k2_arytm_2) & (exists E (m1_subset_1(E,k2_arytm_2) & A = D & C = k7_arytm_2(D,E) & E = B)))))) & -(-(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2)) & -(r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(C = k1_arytm_0(A,B) <-> (exists D (m1_subset_1(D,k2_arytm_2) & (exists E (A = k4_tarski(np__0,D) & B = k4_tarski(np__0,E) & C = k4_tarski(np__0,k7_arytm_2(D,E)) & m1_subset_1(E,k2_arytm_2)))))) & -(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)))) & (r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_arytm_2) -> (C = k1_arytm_0(A,B) <-> (exists D ((exists E (C = k2_arytm_1(E,D) & B = E & A = k4_tarski(np__0,D) & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,k2_arytm_2))))) & (r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_arytm_2) -> (C = k1_arytm_0(A,B) <-> (exists D ((exists E (A = D & B = k4_tarski(np__0,E) & C = k2_arytm_1(D,E) & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,k2_arytm_2))))))))))) # label(d2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3410 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_arytm_0(A,k1_arytm_0(B,C)) = k1_arytm_0(k2_arytm_0(A,B),k2_arytm_0(A,C)))))))) # label(t16_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3411 (all A (m1_subset_1(A,k2_arytm_2) -> (k12_arytm_3 != A -> r2_hidden(k4_tarski(k12_arytm_3,A),k1_numbers)))) # label(t2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3412 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (B = k3_arytm_0(A) <-> np__0 = k1_arytm_0(A,B)))))) # label(d4_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3413 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k3_arytm_0(A),k1_numbers))) # label(dt_k3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3414 (all A (m1_subset_1(A,k1_numbers) -> k4_arytm_0(k4_arytm_0(A)) = A)) # label(involutiveness_k4_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3415 $T # label(d6_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3416 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (B != np__0 -> A = k2_arytm_0(k2_arytm_0(A,B),k4_arytm_0(B))))))) # label(t22_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3417 (all A -(A = k12_arytm_3 & r2_hidden(k4_tarski(k12_arytm_3,A),k1_numbers))) # label(t3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3418 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (k8_arytm_2(A,B) = k8_arytm_2(A,C) -> C = B | k12_arytm_3 = A))))))) # label(t8_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3419 $T # label(t9_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3420 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k2_arytm_0(A,B) = k2_arytm_0(B,A))) # label(commutativity_k2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.51/78.57 3421 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (B = np__0 -> k2_arytm_0(A,B) = np__0))))) # label(t14_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3422 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k4_arytm_0(k2_arytm_0(A,B)) = k2_arytm_0(k4_arytm_0(A),k4_arytm_0(B)))))) # label(t24_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3423 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (k1_arytm_0(k2_arytm_0(A,A),k2_arytm_0(B,B)) = np__0 -> A = np__0))))) # label(t19_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3424 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k1_numbers) -> (k5_arytm_0(C,D) = k5_arytm_0(A,B) -> B = D & C = A))))))))) # label(t12_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3425 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) -> ((exists D ((exists E (A = D & E = B & k8_arytm_2(D,E) = C & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,k2_arytm_2))) <-> k2_arytm_0(A,B) = C)) & (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> A = np__0 | (C = k2_arytm_0(A,B) <-> (exists D ((exists E (A = D & k4_tarski(np__0,E) = B & C = k4_tarski(np__0,k8_arytm_2(D,E)) & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,k2_arytm_2))))) & -(-(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2)) & -(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(np__0 = C <-> C = k2_arytm_0(A,B)) & -(r2_hidden(B,k2_arytm_2) & np__0 != B & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r2_hidden(A,k2_arytm_2) & np__0 != A & 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(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> ((exists D (m1_subset_1(D,k2_arytm_2) & (exists E (k4_tarski(np__0,E) = B & k8_arytm_2(E,D) = C & k4_tarski(np__0,D) = A & m1_subset_1(E,k2_arytm_2))))) <-> C = k2_arytm_0(A,B))) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> ((exists D (m1_subset_1(D,k2_arytm_2) & (exists E (m1_subset_1(E,k2_arytm_2) & A = k4_tarski(np__0,D) & B = E & C = k4_tarski(np__0,k8_arytm_2(E,D)))))) <-> C = k2_arytm_0(A,B)) | np__0 = B))))))) # label(d3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3426 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> -(np__0 = k2_arytm_0(A,B) & B != np__0 & np__0 != A))))) # label(t23_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3427 (all A (m1_subset_1(A,k1_numbers) -> A = k3_arytm_0(k3_arytm_0(A)))) # label(involutiveness_k3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3428 (all A (m1_subset_1(A,k1_numbers) -> r2_hidden(k2_arytm_0(A,A),k2_arytm_2))) # label(t18_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3429 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> -r2_hidden(k5_funct_4(k1_numbers,np__0,k13_arytm_3,A,B),k1_numbers))))) # label(t10_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3430 $T # label(d1_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3431 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (np__0 = B -> A = k5_arytm_0(A,B)) & (np__0 != B -> k5_arytm_0(A,B) = k5_funct_4(k1_numbers,np__0,k13_arytm_3,A,B)))))) # label(d7_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3432 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> r2_hidden(k2_arytm_1(A,B),k1_numbers))))) # label(t4_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3433 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k1_arytm_0(B,A) = k1_arytm_0(A,B))) # label(commutativity_k1_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3434 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k5_arytm_0(A,B),k2_numbers))) # label(dt_k5_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3435 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k1_arytm_0(k3_arytm_0(A),k3_arytm_0(B)) = k3_arytm_0(k1_arytm_0(A,B)))))) # label(t27_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3436 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (k2_arytm_0(A,B) = k13_arytm_3 & k2_arytm_0(A,C) = k13_arytm_3 -> A = np__0 | B = C))))))) # label(t20_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3437 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (A != np__0 -> (B = k4_arytm_0(A) <-> k2_arytm_0(A,B) = k13_arytm_3)) & (np__0 = A -> (B = k4_arytm_0(A) <-> np__0 = B)))))) # label(d5_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3438 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k1_arytm_0(k1_arytm_0(A,B),C) = k1_arytm_0(A,k1_arytm_0(B,C)))))))) # label(t25_arytm_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3439 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3440 (all A (r2_hidden(A,k2_numbers) <-> v1_xcmplx_0(A))) # label(d2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3441 (all A (m1_subset_1(A,k1_numbers) -> v1_xcmplx_0(A))) # label(cc1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3442 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C ((exists D (m1_subset_1(D,k1_numbers) & (exists E ((exists F ((exists G (m1_subset_1(G,k1_numbers) & A = k5_arytm_0(D,E) & k5_arytm_0(k1_arytm_0(k2_arytm_0(D,F),k3_arytm_0(k2_arytm_0(E,G))),k1_arytm_0(k2_arytm_0(D,G),k2_arytm_0(E,F))) = C & B = k5_arytm_0(F,G))) & m1_subset_1(F,k1_numbers))) & m1_subset_1(E,k1_numbers))))) <-> C = k3_xcmplx_0(A,B))))))) # label(d5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3443 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,k5_xcmplx_0(B)) = k7_xcmplx_0(A,B))))) # label(d9_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3444 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C ((exists D ((exists E (m1_subset_1(E,k1_numbers) & (exists F (m1_subset_1(F,k1_numbers) & (exists G (k5_arytm_0(k1_arytm_0(D,F),k1_arytm_0(E,G)) = C & B = k5_arytm_0(F,G) & A = k5_arytm_0(D,E) & m1_subset_1(G,k1_numbers))))))) & m1_subset_1(D,k1_numbers))) <-> k2_xcmplx_0(A,B) = C)))))) # label(d4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3445 $T # label(dt_k2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3446 (all A (v1_xcmplx_0(A) -> k5_xcmplx_0(k5_xcmplx_0(A)) = A)) # label(involutiveness_k5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3447 (all A (v1_xcmplx_0(A) -> A = k4_xcmplx_0(k4_xcmplx_0(A)))) # label(involutiveness_k4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3448 $T # label(dt_k3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3449 (all A (-v1_xboole_0(A) & v1_xcmplx_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & -v1_xboole_0(k5_xcmplx_0(A)))) # label(fc7_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3450 (exists A v1_xcmplx_0(A)) # label(rc1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3451 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> (np__1 = k3_xcmplx_0(A,B) <-> B = k5_xcmplx_0(A))) & (np__0 = A -> (B = k5_xcmplx_0(A) <-> np__0 = B)))))) # label(d7_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3452 (exists A (-v1_xboole_0(A) & v1_xcmplx_0(A))) # label(rc2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3453 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3454 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3455 (all A (v4_ordinal2(A) -> v1_xcmplx_0(A))) # label(cc2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3456 $T # label(dt_k1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3457 (all A (v1_xcmplx_0(A) -> (A = np__0 <-> v1_xboole_0(A)))) # label(d3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3458 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> k3_xcmplx_0(B,A) = k3_xcmplx_0(A,B))) # label(commutativity_k3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3459 $T # label(dt_k6_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3460 (all A (-v1_xboole_0(A) & v1_xcmplx_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & -v1_xboole_0(k4_xcmplx_0(A)))) # label(fc6_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3461 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(A,k4_xcmplx_0(B)) = k6_xcmplx_0(A,B))))) # label(d8_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3462 (all A all B (-v1_xboole_0(B) & v1_xcmplx_0(B) & v1_xcmplx_0(A) & -v1_xboole_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & -v1_xboole_0(k3_xcmplx_0(A,B)))) # label(fc8_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3463 (all A all B (-v1_xboole_0(B) & v1_xcmplx_0(B) & v1_xcmplx_0(A) & -v1_xboole_0(A) -> -v1_xboole_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc9_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3464 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3465 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)))) # label(dt_k5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3466 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A))) # label(commutativity_k2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3467 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (B = k4_xcmplx_0(A) <-> np__0 = k2_xcmplx_0(A,B)))))) # label(d6_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3468 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)))) # label(dt_k4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3469 $T # label(dt_k7_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3470 (all A (v1_xcmplx_0(A) -> A = k3_xcmplx_0(np__1,A))) # label(t3_arithm) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3471 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(A,np__1))) # label(t6_arithm) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3472 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(A,np__0) = A)) # label(t1_arithm) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3473 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(A,np__0) = A)) # label(t4_arithm) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3474 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(A,np__0) = np__0)) # label(t2_arithm) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3475 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(np__0,A) = np__0)) # label(t5_arithm) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3476 (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]. 80.59/78.57 3477 (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]. 80.59/78.57 3478 (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]. 80.59/78.57 3479 (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]. 80.59/78.57 3480 (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]. 80.59/78.57 3481 (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]. 80.59/78.57 3482 (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]. 80.59/78.57 3483 (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]. 80.59/78.57 3484 (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]. 80.59/78.57 3485 (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]. 80.59/78.57 3486 (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]. 80.59/78.57 3487 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3488 (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]. 80.59/78.57 3489 (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]. 80.59/78.57 3490 (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]. 80.59/78.57 3491 (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]. 80.59/78.57 3492 (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]. 80.59/78.57 3493 (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]. 80.59/78.57 3494 (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]. 80.59/78.57 3495 (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]. 80.59/78.57 3496 (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]. 80.59/78.57 3497 (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]. 80.59/78.57 3498 (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]. 80.59/78.57 3499 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3500 (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]. 80.59/78.57 3501 (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]. 80.59/78.57 3502 (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]. 80.59/78.57 3503 (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]. 80.59/78.57 3504 (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]. 80.59/78.57 3505 (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]. 80.59/78.57 3506 (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]. 80.59/78.57 3507 (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]. 80.59/78.57 3508 (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]. 80.59/78.57 3509 (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]. 80.59/78.57 3510 (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]. 80.59/78.57 3511 (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]. 80.59/78.57 3512 (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]. 80.59/78.57 3513 (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]. 80.59/78.57 3514 (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]. 80.59/78.57 3515 (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]. 80.59/78.57 3516 (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]. 80.59/78.57 3517 (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]. 80.59/78.57 3518 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3519 (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]. 80.59/78.57 3520 (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]. 80.59/78.57 3521 (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]. 80.59/78.57 3522 (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]. 80.59/78.57 3523 (all A (v1_xreal_0(A) <-> r2_hidden(A,k1_numbers))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3524 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> v2_xreal_0(B) | v3_xreal_0(A) | v1_xboole_0(B)))))) # label(t5_real) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3525 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-v2_xreal_0(A) & -v3_xreal_0(B) & -r1_xreal_0(A,B)))))) # label(t8_real) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3526 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> v2_xreal_0(B) | v3_xreal_0(A) | v1_xboole_0(A)))))) # label(t6_real) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3527 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(v2_xreal_0(A) & -v2_xreal_0(B) & r1_xreal_0(A,B)))))) # label(t4_real) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3528 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,B) & -v3_xreal_0(B) & -v2_xreal_0(A)))))) # label(t7_real) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3529 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & v3_xreal_0(B) -> v3_xreal_0(A)))))) # label(t2_real) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3530 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,B) & v3_xreal_0(B) & -v3_xreal_0(A)))))) # label(t3_real) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3531 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & v2_xreal_0(A) -> v2_xreal_0(B)))))) # label(t1_real) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3532 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C)))))))) # label(t167_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3533 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B)) = k2_xcmplx_0(A,B))))) # label(t164_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3534 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> k3_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(np__1,A)) = B))))) # label(t108_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3535 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k7_xcmplx_0(A,np__4),k7_xcmplx_0(A,np__4)) = k7_xcmplx_0(A,np__2))) # label(t72_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3536 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k7_xcmplx_0(A,B))))) # label(t192_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3537 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)))))))))) # label(t77_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3538 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(A,C),B))))))) # label(t29_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3539 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)))))))))) # label(t126_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3540 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),A),B) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t166_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3541 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),C),B))))))) # label(t146_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3542 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k4_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(B,A),C)) = k3_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t186_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3543 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k6_xcmplx_0(C,D) = k2_xcmplx_0(A,B) -> k2_xcmplx_0(A,D) = k6_xcmplx_0(C,B)))))))))) # label(t35_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3544 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k5_xcmplx_0(A),B) = k5_xcmplx_0(k3_xcmplx_0(A,k5_xcmplx_0(B))))))) # label(t206_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3545 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != A & np__0 != B & np__0 = k3_xcmplx_0(A,k5_xcmplx_0(B))))))) # label(t208_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3546 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(A,B) = k4_xcmplx_0(A) -> B = k4_xcmplx_0(np__1) | np__0 = A))))) # label(t197_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3547 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k6_xcmplx_0(B,A),k4_xcmplx_0(C)) = k3_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t185_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3548 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),np__3))) # label(t68_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3549 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k6_xcmplx_0(A,B) = np__0 -> B = A))))) # label(t15_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3550 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != A & np__0 = k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) & B != np__0))))) # label(t209_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3551 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),A) = k4_xcmplx_0(B))))) # label(t233_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3552 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k6_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))))))) # label(t152_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3553 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k6_xcmplx_0(A,B) = k6_xcmplx_0(C,D) -> k2_xcmplx_0(B,C) = k2_xcmplx_0(A,D)))))))))) # label(t34_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3554 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) = k3_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),D))))))))) # label(t43_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3555 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),B),A))))))) # label(t165_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3556 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k7_xcmplx_0(B,A))))) # label(t216_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3557 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(A),B)))))) # label(t191_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3558 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,B) = k7_xcmplx_0(A,k7_xcmplx_0(np__1,B)))))) # label(t101_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3559 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),A),B) = k6_xcmplx_0(k2_xcmplx_0(A,B),C))))))) # label(t155_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3560 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k6_xcmplx_0(C,D) = k6_xcmplx_0(A,B) -> k6_xcmplx_0(A,C) = k6_xcmplx_0(B,D)))))))))) # label(t24_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3561 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k4_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C)))))))) # label(t168_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3562 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(B) = k6_xcmplx_0(k6_xcmplx_0(A,A),B))))) # label(t230_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3563 (all A (v1_xcmplx_0(A) -> k4_xcmplx_0(A) = k6_xcmplx_0(np__0,A))) # label(t150_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3564 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(k3_xcmplx_0(k2_xcmplx_0(A,B),k5_xcmplx_0(k3_xcmplx_0(A,B))) != k2_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) & B != np__0 & A != np__0))))) # label(t213_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3565 (all A (v1_xcmplx_0(A) -> k5_xcmplx_0(k4_xcmplx_0(A)) = k4_xcmplx_0(k5_xcmplx_0(A)))) # label(t224_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3566 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) = k3_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)))))))))) # label(t47_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3567 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(np__1)) = A)) # label(t181_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3568 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(A,B),C) = k4_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C)))))))) # label(t173_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3569 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k6_xcmplx_0(B,C) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)),A)))))))) # label(t130_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3570 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> B = k6_xcmplx_0(A,k6_xcmplx_0(A,B)))))) # label(t18_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3571 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(k7_xcmplx_0(C,B),A))))))) # label(t81_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.57 3572 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),A),B) = A)))) # label(t139_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3573 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k6_xcmplx_0(A,C) = k6_xcmplx_0(A,B) -> C = B))))))) # label(t20_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3574 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(np__1,k3_xcmplx_0(A,B)) = k3_xcmplx_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(np__1,B)))))) # label(t103_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3575 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(A,B) = np__1 -> A = B))))) # label(t58_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3576 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,B),C),C),A) = B))))))) # label(t133_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3577 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k6_xcmplx_0(A,B),A) = k4_xcmplx_0(B))))) # label(t232_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3578 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_xcmplx_0(B,A) = k4_xcmplx_0(A) -> A = np__0 | k4_xcmplx_0(np__1) = B))))) # label(t182_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3579 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,C) = k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),B))))))) # label(t228_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3580 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),B),A) = k6_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t160_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3581 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(np__1,k7_xcmplx_0(A,B)) = k7_xcmplx_0(B,A))))) # label(t57_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3582 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,k6_xcmplx_0(k4_xcmplx_0(B),C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C))))))) # label(t157_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3583 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k4_xcmplx_0(A),k3_xcmplx_0(np__2,A)) = A)) # label(t184_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3584 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))) = A)))) # label(t138_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3585 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = k3_xcmplx_0(B,A) -> A = np__0 | B = np__1))))) # label(t7_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3586 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(np__1,A) = k5_xcmplx_0(A))) # label(t217_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3587 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> k2_xcmplx_0(A,B) = k3_xcmplx_0(A,k2_xcmplx_0(np__1,k7_xcmplx_0(B,A)))))))) # label(t118_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3588 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(B) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),A),B))))) # label(t231_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3589 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k2_xcmplx_0(A,B) = k2_xcmplx_0(C,B) -> A = C))))))) # label(t2_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3590 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),A),B))))))) # label(t159_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3591 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k2_xcmplx_0(A,B) = k2_xcmplx_0(C,D) -> k6_xcmplx_0(A,C) = k6_xcmplx_0(D,B)))))))))) # label(t33_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3592 (all A (v1_xcmplx_0(A) -> A = k5_xcmplx_0(k7_xcmplx_0(np__1,A)))) # label(t219_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3593 (all A (v1_xcmplx_0(A) -> A = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,np__4),k7_xcmplx_0(A,np__4)),k7_xcmplx_0(A,np__4)),k7_xcmplx_0(A,np__4)))) # label(t71_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3594 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k3_xcmplx_0(A,k4_xcmplx_0(B))) = k3_xcmplx_0(A,B))))) # label(t178_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3595 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(A,k3_xcmplx_0(B,C)) = k3_xcmplx_0(k3_xcmplx_0(A,B),C))))))) # label(t4_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3596 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D))))))))) # label(t64_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3597 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> B = k7_xcmplx_0(k3_xcmplx_0(B,A),A)))))) # label(t90_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3598 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,B) = k7_xcmplx_0(A,k5_xcmplx_0(B)))))) # label(t221_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3599 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> k3_xcmplx_0(A,k6_xcmplx_0(np__1,k7_xcmplx_0(B,A))) = k6_xcmplx_0(A,B)))))) # label(t132_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3600 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(np__1,k5_xcmplx_0(A)) = A)) # label(t218_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3601 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(C,k7_xcmplx_0(A,B)))))))) # label(t82_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3602 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(A,k3_xcmplx_0(B,C)) = k7_xcmplx_0(k7_xcmplx_0(A,B),C))))))) # label(t79_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3603 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k4_xcmplx_0(k7_xcmplx_0(A,k4_xcmplx_0(B))))))) # label(t190_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3604 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(C,B),A))))))) # label(t76_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3605 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k5_xcmplx_0(A),k7_xcmplx_0(B,C)) = k7_xcmplx_0(B,k3_xcmplx_0(A,C)))))))) # label(t222_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3606 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k6_xcmplx_0(B,k7_xcmplx_0(C,A)) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(B,A),C),A)))))))) # label(t128_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3607 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k3_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(C,A)),A) = k7_xcmplx_0(B,C)))))))) # label(t93_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3608 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) = k4_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C)))))))) # label(t170_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3609 (all A (v1_xcmplx_0(A) -> A = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,np__3),k7_xcmplx_0(A,np__3)),k7_xcmplx_0(A,np__3)))) # label(t69_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3610 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(A,B) = A -> B = np__1 | np__0 = A))))) # label(t61_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3611 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> B = k7_xcmplx_0(A,k7_xcmplx_0(A,B))))))) # label(t52_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3612 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__1 = k3_xcmplx_0(A,B) -> A = k5_xcmplx_0(B)))))) # label(t211_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3613 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_xcmplx_0(k3_xcmplx_0(A,B)) = k7_xcmplx_0(k5_xcmplx_0(A),B))))) # label(t223_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3614 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(A,B) != np__0 -> k7_xcmplx_0(A,k7_xcmplx_0(A,B)) = B))))) # label(t54_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3615 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(B,C)) = k7_xcmplx_0(B,k3_xcmplx_0(C,A)))))))) # label(t104_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3616 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k6_xcmplx_0(A,B) = k2_xcmplx_0(C,k4_xcmplx_0(B)) -> C = A))))))) # label(t153_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3617 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(np__1,k7_xcmplx_0(np__1,A)) = A)) # label(t56_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3618 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k4_xcmplx_0(A),B) = k4_xcmplx_0(k6_xcmplx_0(A,B)))))) # label(t162_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3619 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != B & k6_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) != k3_xcmplx_0(k6_xcmplx_0(B,A),k5_xcmplx_0(k3_xcmplx_0(A,B))) & np__0 != A))))) # label(t214_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3620 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),D))))))))) # label(t123_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3621 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) = k3_xcmplx_0(A,k6_xcmplx_0(B,C)))))))) # label(t40_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3622 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> k7_xcmplx_0(B,k3_xcmplx_0(A,k7_xcmplx_0(np__1,A))) = B))))) # label(t111_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3623 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k3_xcmplx_0(A,C),B) = k7_xcmplx_0(A,k7_xcmplx_0(B,C)))))))) # label(t78_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3624 (all A (v1_xcmplx_0(A) -> (A != np__0 -> k7_xcmplx_0(A,k4_xcmplx_0(A)) = k4_xcmplx_0(np__1)))) # label(t199_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3625 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k6_xcmplx_0(A,k6_xcmplx_0(B,B)))))) # label(t17_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3626 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 = k2_xcmplx_0(A,k4_xcmplx_0(B)) -> B = A))))) # label(t136_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3627 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k6_xcmplx_0(A,B),B) = A)))) # label(t27_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3628 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k5_xcmplx_0(B) = k5_xcmplx_0(A) -> B = A))))) # label(t202_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3629 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(k2_xcmplx_0(A,A),np__2))) # label(t65_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3630 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k3_xcmplx_0(B,A) = k3_xcmplx_0(C,A) -> C = B | np__0 = A))))))) # label(t5_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3631 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> -(np__0 != B & k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)),k3_xcmplx_0(A,B)) != k6_xcmplx_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) & np__0 != A))))))))) # label(t131_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3632 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B))) = k2_xcmplx_0(A,B))))) # label(t142_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3633 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(np__1,A) = k7_xcmplx_0(np__1,B) -> B = A))))) # label(t59_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3634 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k3_xcmplx_0(A,B))))) # label(t177_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3635 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k3_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(C,B)))))))))) # label(t86_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3636 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k3_xcmplx_0(B,C) = k3_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(C,A))))))))) # label(t91_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3637 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_xcmplx_0(A) = k4_xcmplx_0(B) -> B = A))))) # label(t134_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3638 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(k3_xcmplx_0(A,B) = np__0 & B != np__0 & A != np__0))))) # label(t6_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3639 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(np__1,B),C),A))))))) # label(t102_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3640 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (all E (v1_xcmplx_0(E) -> k3_xcmplx_0(k7_xcmplx_0(E,C),k7_xcmplx_0(A,k3_xcmplx_0(B,D))) = k7_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(B,C),k7_xcmplx_0(D,E))))))))))))) # label(t235_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3641 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> -(np__0 != A & B != np__0 & k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)),k3_xcmplx_0(A,B)) != k2_xcmplx_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B))))))))))) # label(t117_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3642 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(A,k7_xcmplx_0(C,B)) = k7_xcmplx_0(A,k7_xcmplx_0(B,C)))))))) # label(t80_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3643 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(np__4,A) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A))) # label(t13_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3644 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(C,B) = k6_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(A,C)))))))) # label(t23_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3645 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(A != np__0 & B != np__0 & k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(B,A)) != np__1))))) # label(t113_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3646 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (all E (v1_xcmplx_0(E) -> k3_xcmplx_0(k7_xcmplx_0(E,C),k7_xcmplx_0(A,k3_xcmplx_0(B,D))) = k7_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(B,C),k7_xcmplx_0(D,E))))))))))))) # label(t87_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3647 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),B) = k6_xcmplx_0(A,C))))))) # label(t229_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3648 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(A,C),k6_xcmplx_0(C,B)) = k6_xcmplx_0(A,B))))))) # label(t39_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3649 (all A (v1_xcmplx_0(A) -> k4_xcmplx_0(A) = k6_xcmplx_0(A,k3_xcmplx_0(np__2,A)))) # label(t187_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3650 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(A,k2_xcmplx_0(B,C)))))))) # label(t36_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3651 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k5_xcmplx_0(k3_xcmplx_0(A,B)))))) # label(t205_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3652 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) = k3_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),D))))))))) # label(t44_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3653 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k3_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C)) = k3_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)))))))))) # label(t41_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3654 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> B = k7_xcmplx_0(B,k7_xcmplx_0(A,A))))))) # label(t51_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3655 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C)))))))) # label(t171_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3656 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k2_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k2_xcmplx_0(B,k7_xcmplx_0(C,A)))))))))) # label(t237_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3657 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)))))))))) # label(t125_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3658 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),C),A))))))) # label(t147_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3659 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(k4_xcmplx_0(A),B) = k4_xcmplx_0(k7_xcmplx_0(A,B)))))) # label(t188_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3660 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k3_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)))))))))) # label(t9_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3661 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(B != np__0 & (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(B,C) != A))))))) # label(t234_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3662 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)))))))) # label(t1_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3663 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k4_xcmplx_0(B),A) = k6_xcmplx_0(k4_xcmplx_0(A),B))))) # label(t144_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3664 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B)) = k2_xcmplx_0(A,k4_xcmplx_0(B)))))) # label(t141_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3665 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(A,C)) = k4_xcmplx_0(k6_xcmplx_0(B,C)))))))) # label(t149_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3666 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(A,np__0) = np__0)) # label(t62_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3667 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k6_xcmplx_0(A,B)) = k6_xcmplx_0(B,A))))) # label(t143_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3668 (all A (v1_xcmplx_0(A) -> np__0 = k7_xcmplx_0(A,np__0))) # label(t49_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3669 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(A,B) = k6_xcmplx_0(k2_xcmplx_0(A,C),k6_xcmplx_0(C,B)))))))) # label(t31_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3670 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k6_xcmplx_0(k4_xcmplx_0(B),k6_xcmplx_0(k4_xcmplx_0(A),B)))))) # label(t145_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3671 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k2_xcmplx_0(A,B),k4_xcmplx_0(B)) = A)))) # label(t137_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3672 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> B = k3_xcmplx_0(k3_xcmplx_0(B,A),k5_xcmplx_0(A))))))) # label(t204_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3673 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k2_xcmplx_0(B,C) = k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)),A)))))))) # label(t116_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3674 (all A (v1_xcmplx_0(A) -> A = k2_xcmplx_0(k7_xcmplx_0(A,np__2),k7_xcmplx_0(A,np__2)))) # label(t66_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3675 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(A,k4_xcmplx_0(B)) = k2_xcmplx_0(A,B))))) # label(t151_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3676 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k4_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C)))))))) # label(t174_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3677 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(np__2,A) = k2_xcmplx_0(A,A))) # label(t11_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3678 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,B) = k4_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(A),B)))))) # label(t179_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3679 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),C),A) = k2_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t156_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3680 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(A,k4_xcmplx_0(B)))))) # label(t189_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3681 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)) = k3_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(C,D)))))))))) # label(t45_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3682 (all A (v1_xcmplx_0(A) -> -(np__1 = k3_xcmplx_0(A,A) & A != k4_xcmplx_0(np__1) & np__1 != A))) # label(t183_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3683 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A),np__4))) # label(t70_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3684 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k4_xcmplx_0(A),B) = k3_xcmplx_0(A,k4_xcmplx_0(B)))))) # label(t176_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3685 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k7_xcmplx_0(k2_xcmplx_0(B,k3_xcmplx_0(A,C)),A) = k2_xcmplx_0(k7_xcmplx_0(B,A),C)))))))) # label(t114_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3686 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != B & k7_xcmplx_0(A,B) = np__0 & A != np__0))))) # label(t50_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3687 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k4_xcmplx_0(A),B) = k4_xcmplx_0(k3_xcmplx_0(A,B)))))) # label(t175_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3688 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k7_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,C)) = k7_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)))))))))) # label(t85_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3689 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(A,B) = k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B)))))) # label(t163_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3690 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k2_xcmplx_0(A,C),B) = k2_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,B)))))))) # label(t63_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3691 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(A,k6_xcmplx_0(B,C)))))))) # label(t37_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3692 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k7_xcmplx_0(np__1,B),k7_xcmplx_0(A,C)) = k7_xcmplx_0(k7_xcmplx_0(A,B),C))))))) # label(t105_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3693 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k2_xcmplx_0(A,A),A) = k3_xcmplx_0(np__3,A))) # label(t12_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3694 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k5_xcmplx_0(B) = k7_xcmplx_0(np__1,A) -> B = A))))) # label(t220_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3695 (all A (v1_xcmplx_0(A) -> (np__0 != A -> k7_xcmplx_0(A,A) = np__1))) # label(t60_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3696 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k2_xcmplx_0(A,k6_xcmplx_0(B,B)))))) # label(t25_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3697 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k7_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(A,C)) = k3_xcmplx_0(B,C)))))))) # label(t94_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3698 (all A (v1_xcmplx_0(A) -> (A != np__0 -> np__1 = k3_xcmplx_0(A,k7_xcmplx_0(np__1,A))))) # label(t107_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3699 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(k2_xcmplx_0(A,B),np__2) = A -> B = A))))) # label(t67_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3700 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,B) = k6_xcmplx_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)))))))) # label(t22_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3701 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(A,k6_xcmplx_0(C,B)) = k6_xcmplx_0(A,k6_xcmplx_0(B,C)))))))) # label(t38_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3702 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,B) = k5_xcmplx_0(k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B))))))) # label(t207_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3703 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k6_xcmplx_0(A,B) = A -> B = np__0))))) # label(t16_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3704 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) = k6_xcmplx_0(A,B))))))) # label(t32_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3705 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),C),A))))))) # label(t158_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3706 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k7_xcmplx_0(B,C) = k3_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(A,C))))))))) # label(t99_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3707 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k6_xcmplx_0(k2_xcmplx_0(A,B),B))))) # label(t26_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3708 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k2_xcmplx_0(A,B)) = k6_xcmplx_0(k4_xcmplx_0(B),A))))) # label(t161_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3709 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(C,B),A) = k2_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t30_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3710 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),B),A))))))) # label(t148_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3711 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),B) = k2_xcmplx_0(A,C))))))) # label(t227_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3712 (all A (v1_xcmplx_0(A) -> np__0 = k6_xcmplx_0(A,A))) # label(t14_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3713 (all A (v1_xcmplx_0(A) -> k4_xcmplx_0(A) = k3_xcmplx_0(k4_xcmplx_0(np__1),A))) # label(t180_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3714 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_xcmplx_0(np__1) = k7_xcmplx_0(A,B) -> B = k4_xcmplx_0(A) & A = k4_xcmplx_0(B)))))) # label(t196_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3715 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k6_xcmplx_0(A,C),B) = k6_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,B)))))))) # label(t121_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3716 (all A (v1_xcmplx_0(A) -> (k4_xcmplx_0(A) = np__0 -> np__0 = A))) # label(t135_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3717 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(np__1,C),k7_xcmplx_0(A,B)))))))) # label(t106_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3718 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> k3_xcmplx_0(B,k7_xcmplx_0(A,A)) = B))))) # label(t89_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3719 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C))))))) # label(t75_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3720 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k7_xcmplx_0(D,A) = k7_xcmplx_0(C,B) -> A = np__0 | B = np__0 | k3_xcmplx_0(D,B) = k3_xcmplx_0(C,A)))))))))) # label(t96_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3721 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k2_xcmplx_0(B,C) = k3_xcmplx_0(A,k2_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)))))))))) # label(t115_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3722 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = k2_xcmplx_0(A,B) -> B = np__0))))) # label(t3_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3723 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,k7_xcmplx_0(D,C)),B),k3_xcmplx_0(k7_xcmplx_0(D,C),A)) = k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(A,B),C),D),B))))))))) # label(t236_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3724 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k7_xcmplx_0(D,B) = k7_xcmplx_0(C,A) -> k7_xcmplx_0(C,A) = k7_xcmplx_0(k2_xcmplx_0(C,D),k2_xcmplx_0(A,B)) | A = k4_xcmplx_0(B) | B = np__0 | A = np__0))))))))) # label(t201_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3725 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,k3_xcmplx_0(np__3,B)),k7_xcmplx_0(A,k3_xcmplx_0(np__3,B))),k7_xcmplx_0(A,k3_xcmplx_0(np__3,B))))))) # label(t120_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3726 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(np__1)) = A)) # label(t195_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3727 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k7_xcmplx_0(D,B) = k3_xcmplx_0(C,A) -> np__0 = A | k7_xcmplx_0(D,A) = k3_xcmplx_0(C,B) | B = np__0))))))))) # label(t97_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3728 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k3_xcmplx_0(A,k7_xcmplx_0(k7_xcmplx_0(B,A),C)) = k7_xcmplx_0(B,C)))))))) # label(t98_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3729 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> k3_xcmplx_0(B,k3_xcmplx_0(k7_xcmplx_0(np__1,A),A)) = B))))) # label(t109_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3730 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__1 = k3_xcmplx_0(A,k5_xcmplx_0(B)) -> B = A))))) # label(t210_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3731 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> B = k3_xcmplx_0(k7_xcmplx_0(B,A),A)))))) # label(t88_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3732 (all A (v1_xcmplx_0(A) -> k4_xcmplx_0(A) = k7_xcmplx_0(A,k4_xcmplx_0(np__1)))) # label(t194_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3733 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) = k3_xcmplx_0(A,k2_xcmplx_0(B,C)))))))) # label(t8_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3734 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k6_xcmplx_0(A,B) = k2_xcmplx_0(A,k4_xcmplx_0(C)) -> B = C))))))) # label(t154_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3735 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k7_xcmplx_0(C,A) = k7_xcmplx_0(B,A) -> C = B | A = np__0))))))) # label(t53_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3736 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 = k7_xcmplx_0(np__1,k3_xcmplx_0(A,B)) & B != np__0 & A != np__0))))) # label(t112_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3737 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)))))) # label(t140_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3738 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k7_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)) = k7_xcmplx_0(B,C)))))))) # label(t55_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3739 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(k2_xcmplx_0(A,A),np__4) = k7_xcmplx_0(A,np__2))) # label(t73_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3740 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k4_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C)) = k2_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t172_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3741 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k3_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)))))))))) # label(t10_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3742 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) = k4_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C)))))))) # label(t169_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3743 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(k4_xcmplx_0(A),B) = k7_xcmplx_0(A,k4_xcmplx_0(B)))))) # label(t193_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3744 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> B = k3_xcmplx_0(k3_xcmplx_0(B,k7_xcmplx_0(np__1,A)),A)))))) # label(t110_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3745 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k3_xcmplx_0(C,A) = k3_xcmplx_0(D,B) -> np__0 = A | k7_xcmplx_0(D,A) = k7_xcmplx_0(C,B) | B = np__0))))))))) # label(t95_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3746 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k3_xcmplx_0(A,k6_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))) = k6_xcmplx_0(B,C)))))))) # label(t129_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3747 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k7_xcmplx_0(C,A) = k7_xcmplx_0(D,B) -> np__0 = A | k7_xcmplx_0(C,A) = k7_xcmplx_0(k6_xcmplx_0(C,D),k6_xcmplx_0(A,B)) | B = A | np__0 = B))))))))) # label(t124_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3748 $T # label(t212_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3749 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(B,A) = k5_xcmplx_0(k7_xcmplx_0(A,B)))))) # label(t215_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3750 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(A,np__2) = k6_xcmplx_0(A,k7_xcmplx_0(A,np__2)))) # label(t122_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3751 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(A,B) = k2_xcmplx_0(k2_xcmplx_0(A,C),k6_xcmplx_0(B,C)))))))) # label(t28_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3752 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k7_xcmplx_0(k6_xcmplx_0(B,k3_xcmplx_0(C,A)),A) = k6_xcmplx_0(k7_xcmplx_0(B,A),C)))))))) # label(t127_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3753 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(A,C),B) = k6_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t21_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3754 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k7_xcmplx_0(k7_xcmplx_0(A,C),B))))))) # label(t48_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3755 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,k7_xcmplx_0(np__1,B)) = k7_xcmplx_0(A,B))))) # label(t100_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3756 (all A (v1_xcmplx_0(A) -> (np__0 != A -> k4_xcmplx_0(np__1) = k7_xcmplx_0(k4_xcmplx_0(A),A)))) # label(t198_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3757 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k7_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(A,C),B),D))))))))) # label(t84_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3758 (all A (v1_xcmplx_0(A) -> -(k7_xcmplx_0(np__1,A) = A & A != np__1 & A != k4_xcmplx_0(np__1) & np__0 != A))) # label(t200_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3759 (all A (v1_xcmplx_0(A) -> -(A = k5_xcmplx_0(A) & A != k4_xcmplx_0(np__1) & np__1 != A & np__0 != A))) # label(t225_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3760 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k6_xcmplx_0(C,B) = k6_xcmplx_0(A,B) -> C = A))))))) # label(t19_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3761 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k7_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)) = k7_xcmplx_0(B,C)))))))) # label(t92_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3762 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_xcmplx_0(A,B) = np__1 -> k7_xcmplx_0(np__1,B) = A))))) # label(t74_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3763 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k2_xcmplx_0(k7_xcmplx_0(A,k3_xcmplx_0(np__2,B)),k7_xcmplx_0(A,k3_xcmplx_0(np__2,B))))))) # label(t119_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3764 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k3_xcmplx_0(k6_xcmplx_0(A,B),k2_xcmplx_0(C,D)) = k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)),k3_xcmplx_0(B,C)),k3_xcmplx_0(B,D)))))))))) # label(t46_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3765 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) = k3_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),D))))))))) # label(t42_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3766 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),B) = k2_xcmplx_0(A,C))))))) # label(t226_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3767 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k7_xcmplx_0(A,B),C) = k7_xcmplx_0(A,k7_xcmplx_0(B,C)))))))) # label(t83_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3768 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(A,B) & r1_xreal_0(np__1,k7_xcmplx_0(B,A))))))) # label(t193_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3769 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(k6_xcmplx_0(C,A),B) & -r1_xreal_0(C,B) & r1_xreal_0(A,np__0)))))))) # label(t55_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3770 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(np__0,B) & r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) & -r1_xreal_0(B,C) & -r1_xreal_0(np__0,A)))))))) # label(t103_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3771 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k6_xcmplx_0(B,A),B) & -r1_xreal_0(np__0,A)))))) # label(t48_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3772 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,k4_xcmplx_0(A)) & r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) & -r1_xreal_0(np__0,A)))))) # label(t209_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3773 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,k4_xcmplx_0(B)) & r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) & -r1_xreal_0(A,np__0)))))) # label(t200_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3774 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(B,C) & r1_xreal_0(k6_xcmplx_0(C,A),B)))))))) # label(t56_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3775 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & r1_xreal_0(B,np__0) -> r1_xreal_0(k7_xcmplx_0(B,A),np__1)))))) # label(t186_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.58 3776 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,k4_xcmplx_0(B)) -> r1_xreal_0(k2_xcmplx_0(A,B),np__0)))))) # label(t61_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3777 (all A (v1_xreal_0(A) -> (r1_xreal_0(k7_xcmplx_0(np__1,np__2),A) -> r1_xreal_0(np__0,k6_xcmplx_0(k3_xcmplx_0(np__2,A),np__1))))) # label(t221_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3778 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,k2_xcmplx_0(A,B)) & -r1_xreal_0(k4_xcmplx_0(B),A)))))) # label(t63_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3779 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-(-r1_xreal_0(np__0,B) & -r1_xreal_0(np__0,A)) & -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,np__0)) & -r1_xreal_0(k3_xcmplx_0(A,B),np__0)))))) # label(t136_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3780 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(B,k6_xcmplx_0(B,A)) & -r1_xreal_0(A,np__0)))))) # label(t46_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3781 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k6_xcmplx_0(A,B),C) <-> r1_xreal_0(A,k2_xcmplx_0(B,C))))))))) # label(t22_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3782 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(A,np__2),np__0)))) # label(t217_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3783 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) <-> r1_xreal_0(A,B)))))))) # label(t11_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3784 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & r1_xreal_0(B,A) -> A = B))))) # label(t1_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3785 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)) & -r1_xreal_0(C,B) & -r1_xreal_0(np__0,A)))))))) # label(t71_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3786 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,B) & r1_xreal_0(k2_xcmplx_0(A,C),B) & r1_xreal_0(np__0,A)))))))) # label(t42_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3787 (all A (v1_xreal_0(A) -> r1_xreal_0(np__0,k3_xcmplx_0(A,A)))) # label(t65_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3788 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__1,A) -> r1_xreal_0(k5_xcmplx_0(A),np__1)))) # label(t213_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3789 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,B) & r1_xreal_0(k2_xcmplx_0(B,np__1),A)))))) # label(t147_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3790 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k7_xcmplx_0(A,np__4),np__0) & -r1_xreal_0(A,np__0)))) # label(t226_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3791 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,np__1) & r1_xreal_0(B,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C))) & r1_xreal_0(np__0,A) -> np__0 = A | r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),C)))))))) # label(t181_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3792 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(B,np__0) & -r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A)) & r1_xreal_0(k3_xcmplx_0(C,B),k7_xcmplx_0(D,A))))))))))) # label(t116_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3793 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) & -r1_xreal_0(C,B) & -r1_xreal_0(B,np__0)))))))) # label(t102_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3794 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (np__0 = k2_xcmplx_0(A,B) & r1_xreal_0(B,np__0) & r1_xreal_0(A,np__0) -> A = np__0))))) # label(t30_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3795 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,B) & r1_xreal_0(k7_xcmplx_0(B,A),np__1) & -r1_xreal_0(np__0,A)))))) # label(t190_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3796 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,C) & r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) & r1_xreal_0(A,B)))))))))) # label(t17_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3797 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(C,np__1) -> r1_xreal_0(k7_xcmplx_0(A,C),B)))) -> r1_xreal_0(A,B)))))) # label(t212_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3798 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,np__0) & r1_xreal_0(B,C) -> r1_xreal_0(k2_xcmplx_0(B,A),C)))))))) # label(t37_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3799 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__1,B) & r1_xreal_0(np__0,A) -> r1_xreal_0(A,k3_xcmplx_0(A,B))))))) # label(t153_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3800 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,B) & r1_xreal_0(np__0,C) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C))))))))) # label(t66_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3801 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,C) & r1_xreal_0(A,B) -> r1_xreal_0(A,C)))))))) # label(t2_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3802 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(A,B) & r1_xreal_0(C,D) -> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D))))))))))) # label(t9_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3803 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(k6_xcmplx_0(A,B),np__0)))))) # label(t49_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3804 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,B) & r1_xreal_0(B,k6_xcmplx_0(A,np__1))))))) # label(t149_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3805 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(B,np__0) | r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) | r1_xreal_0(A,np__0)))))))))) # label(t104_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3806 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(np__0,A) | r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) | r1_xreal_0(np__0,B)))))))))) # label(t105_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3807 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(k4_xcmplx_0(B),A) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t196_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3808 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(np__0,A) & r1_xreal_0(C,D) & r1_xreal_0(np__0,C) & r1_xreal_0(A,B) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D))))))))))) # label(t68_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3809 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & r1_xreal_0(A,np__0) -> r1_xreal_0(k7_xcmplx_0(B,A),np__1)))))) # label(t188_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3810 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(B,C) & r1_xreal_0(k2_xcmplx_0(A,C),B) & -r1_xreal_0(A,np__0)))))))) # label(t41_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3811 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(C,k2_xcmplx_0(B,A)) & r1_xreal_0(B,C) & -r1_xreal_0(np__0,A)))))))) # label(t39_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3812 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(A,k7_xcmplx_0(A,np__4))))) # label(t225_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3813 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(A),B) -> r1_xreal_0(np__0,A) | r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))))))) # label(t205_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3814 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k7_xcmplx_0(A,np__3),np__0) & -r1_xreal_0(A,np__0)))) # label(t224_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3815 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,k4_xcmplx_0(B)) & r1_xreal_0(A,np__0) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t198_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3816 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,np__0) & r1_xreal_0(np__0,A) -> r1_xreal_0(k7_xcmplx_0(A,B),np__0)))))) # label(t139_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3817 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k6_xcmplx_0(B,A),np__0) & -r1_xreal_0(B,A)))))) # label(t52_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3818 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(A,C) & -r1_xreal_0(D,B) & r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & -r1_xreal_0(B,np__0) & -r1_xreal_0(A,np__0)))))))))) # label(t100_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3819 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(A,np__0) -> r1_xreal_0(k7_xcmplx_0(A,B),np__0)))))) # label(t140_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3820 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k6_xcmplx_0(A,B),k2_xcmplx_0(C,D)) -> r1_xreal_0(k6_xcmplx_0(A,D),k2_xcmplx_0(C,B))))))))))) # label(t25_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3821 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,C) & r1_xreal_0(np__0,A) -> r1_xreal_0(B,k2_xcmplx_0(A,C))))))))) # label(t40_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3822 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,np__0) & r1_xreal_0(k7_xcmplx_0(A,B),np__0) & -r1_xreal_0(A,np__0)))))) # label(t141_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3823 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,np__0) & r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) & -r1_xreal_0(np__0,A)))))) # label(t126_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3824 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> -(-r1_xreal_0(np__1,C) & -r1_xreal_0(A,k3_xcmplx_0(C,B)) & -r1_xreal_0(C,np__0)))) -> r1_xreal_0(A,np__0)))))) # label(t171_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3825 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,A) & r1_xreal_0(np__0,k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A))) & -r1_xreal_0(A,B) & -r1_xreal_0(B,k4_xcmplx_0(A))))))) # label(t97_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3826 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,C) & r1_xreal_0(A,np__0) -> r1_xreal_0(B,k6_xcmplx_0(C,A))))))))) # label(t54_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3827 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) -> r1_xreal_0(A,B) | r1_xreal_0(np__0,k5_xcmplx_0(A))))))) # label(t92_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3828 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k4_xcmplx_0(A),np__0) & -r1_xreal_0(np__0,A)) & -(r1_xreal_0(np__0,A) & -r1_xreal_0(k4_xcmplx_0(A),np__0)))) # label(t60_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3829 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(k4_xcmplx_0(A),B) & r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t207_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3830 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) & -r1_xreal_0(k4_xcmplx_0(B),A)))))) # label(t202_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3831 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k3_xcmplx_0(A,B),np__1) & r1_xreal_0(B,k4_xcmplx_0(np__1)) & -r1_xreal_0(k4_xcmplx_0(np__1),A)))))) # label(t166_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3832 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,k4_xcmplx_0(np__1)) & r1_xreal_0(B,k4_xcmplx_0(np__1)) -> r1_xreal_0(np__1,k3_xcmplx_0(A,B))))))) # label(t165_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3833 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)) & -r1_xreal_0(C,B) & -r1_xreal_0(np__0,A)))))))) # label(t77_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3834 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(D,B)) <-> r1_xreal_0(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D))))))))))) # label(t23_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3835 (all A (v1_xreal_0(A) -> -(all B (v1_xreal_0(B) -> r1_xreal_0(A,B))))) # label(t4_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3836 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k2_xcmplx_0(A,B),k6_xcmplx_0(C,D)) -> r1_xreal_0(k2_xcmplx_0(A,D),k6_xcmplx_0(C,B))))))))))) # label(t24_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3837 (all A (v1_xreal_0(A) -> (r1_xreal_0(k7_xcmplx_0(np__1,np__2),A) -> r1_xreal_0(k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,A)),np__0)))) # label(t222_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3838 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k7_xcmplx_0(B,A),C) & -r1_xreal_0(k3_xcmplx_0(C,A),B)))))))) # label(t86_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3839 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) & -r1_xreal_0(C,B) & -r1_xreal_0(B,np__0)))))))) # label(t78_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3840 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,k4_xcmplx_0(np__1)) -> r1_xreal_0(k4_xcmplx_0(np__1),k5_xcmplx_0(A))))) # label(t215_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3841 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,k4_xcmplx_0(A)) & r1_xreal_0(A,np__0) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t197_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3842 (all A (v1_xreal_0(A) -> -(all B (v1_xreal_0(B) -> r1_xreal_0(B,A))))) # label(t3_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3843 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,np__0) & -r1_xreal_0(A,k4_xcmplx_0(np__1)) & r1_xreal_0(B,np__0) & r1_xreal_0(np__1,k3_xcmplx_0(A,B)) & r1_xreal_0(k4_xcmplx_0(np__1),B)))))) # label(t168_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3844 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k3_xcmplx_0(A,B),A) & -r1_xreal_0(np__1,B) & -r1_xreal_0(np__0,A)))))) # label(t158_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3845 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(C,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,D))) & -r1_xreal_0(C,D) & -r1_xreal_0(C,B) & r1_xreal_0(A,np__1) & r1_xreal_0(np__0,A)))))))))) # label(t178_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3846 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,np__0) & r1_xreal_0(A,np__0) -> r1_xreal_0(np__0,k7_xcmplx_0(A,B))))))) # label(t137_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3847 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(A),B) -> r1_xreal_0(k4_xcmplx_0(B),A)))))) # label(t28_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3848 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(A,k4_xcmplx_0(B)) & r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t210_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3849 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(C,A),k3_xcmplx_0(D,B)) & -r1_xreal_0(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B)) & -r1_xreal_0(np__0,B)))))))))) # label(t119_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3850 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(np__0,A) & -r1_xreal_0(C,B) & r1_xreal_0(C,k6_xcmplx_0(B,A))))))))) # label(t53_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3851 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) -> r1_xreal_0(k6_xcmplx_0(D,B),k6_xcmplx_0(C,A))))))))))) # label(t19_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3852 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,np__0) & r1_xreal_0(C,B) -> r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) | r1_xreal_0(np__0,B)))))))) # label(t123_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3853 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B)) & r1_xreal_0(k3_xcmplx_0(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(B,np__0) & -r1_xreal_0(A,np__0)))))))))) # label(t115_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3854 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-(-r1_xreal_0(np__0,A) & -r1_xreal_0(np__0,B)) & -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,np__0)) & -r1_xreal_0(k7_xcmplx_0(A,B),np__0)))))) # label(t146_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3855 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(k6_xcmplx_0(B,A),B)))))) # label(t45_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3856 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B)) & r1_xreal_0(k7_xcmplx_0(C,A),k3_xcmplx_0(D,B)) & -r1_xreal_0(B,np__0)))))))))) # label(t118_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3857 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(np__0,A) & r1_xreal_0(C,B) -> r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) | r1_xreal_0(np__0,B)))))))) # label(t121_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3858 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(np__0,A) & r1_xreal_0(A,np__1) & r1_xreal_0(B,C) -> r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),C)))))))) # label(t174_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3859 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k3_xcmplx_0(B,D),k3_xcmplx_0(A,C)) & -r1_xreal_0(C,D) & -r1_xreal_0(np__0,C) & r1_xreal_0(B,A)))))))))) # label(t72_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3860 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k5_xcmplx_0(A),k4_xcmplx_0(np__1)) & -r1_xreal_0(k4_xcmplx_0(np__1),A)))) # label(t216_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3861 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A)) & r1_xreal_0(k3_xcmplx_0(C,B),k7_xcmplx_0(D,A)) & -r1_xreal_0(np__0,B) & -r1_xreal_0(A,np__0)))))))))) # label(t117_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3862 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) & -r1_xreal_0(B,A) & -r1_xreal_0(A,np__0)))))) # label(t90_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3863 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(np__0,A) & np__0 = k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(k6_xcmplx_0(np__1,A),C)) & -(C = np__0 & B = np__0) & -(B = np__0 & A = np__1) & -(A = np__0 & C = np__0) & r1_xreal_0(np__0,C) & r1_xreal_0(np__0,B) & r1_xreal_0(A,np__1)))))))) # label(t172_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3864 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,k6_xcmplx_0(B,C)) -> r1_xreal_0(C,k6_xcmplx_0(B,A))))))))) # label(t13_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3865 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(np__1,k7_xcmplx_0(B,A)) & -r1_xreal_0(B,A)))))) # label(t194_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3866 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,C) & r1_xreal_0(A,np__0) -> r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A))))))))) # label(t75_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3867 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> -(-r1_xreal_0(np__1,C) & -r1_xreal_0(k3_xcmplx_0(A,C),B) & -r1_xreal_0(C,np__0)))) -> r1_xreal_0(A,B)))))) # label(t170_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3868 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) & -r1_xreal_0(B,np__0)))))))))) # label(t111_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3869 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(C,np__0) -> r1_xreal_0(k6_xcmplx_0(A,C),B)))) -> r1_xreal_0(A,B)))))) # label(t59_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3870 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(np__0,k3_xcmplx_0(A,B)) & -r1_xreal_0(np__0,B)))))) # label(t134_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3871 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (exists C (v1_xreal_0(C) & -r1_xreal_0(A,C) & -r1_xreal_0(B,C))))))) # label(t6_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3872 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & r1_xreal_0(np__0,A) -> r1_xreal_0(k7_xcmplx_0(A,B),np__1)))))) # label(t185_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3873 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,k3_xcmplx_0(C,A)) -> r1_xreal_0(A,np__0) | r1_xreal_0(k7_xcmplx_0(B,A),C)))))))) # label(t81_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3874 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k2_xcmplx_0(np__1,A),np__0) & -r1_xreal_0(A,k4_xcmplx_0(np__1))))) # label(t150_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3875 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k3_xcmplx_0(A,B),np__1) & r1_xreal_0(np__1,B) & -r1_xreal_0(A,np__1)))))) # label(t163_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3876 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,k7_xcmplx_0(np__1,np__2)) -> r1_xreal_0(k6_xcmplx_0(k3_xcmplx_0(np__2,A),np__1),np__0)))) # label(t219_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3877 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(B,k7_xcmplx_0(C,A)) & -r1_xreal_0(C,k3_xcmplx_0(B,A))))))))) # label(t84_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3878 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) <-> r1_xreal_0(A,B)))))))) # label(t8_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3879 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,B) & r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),C),k3_xcmplx_0(A,D)),B) & r1_xreal_0(B,C) & -r1_xreal_0(np__1,A) & -r1_xreal_0(A,np__0)))))))))) # label(t179_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3880 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(A),B) -> r1_xreal_0(np__0,k2_xcmplx_0(A,B))))))) # label(t62_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3881 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,k4_xcmplx_0(A)) -> r1_xreal_0(A,np__0) | r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))))))) # label(t203_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3882 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (exists C (v1_xreal_0(C) & -r1_xreal_0(C,B) & -r1_xreal_0(C,A))))))) # label(t5_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3883 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k2_xcmplx_0(A,B))))))) # label(t35_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3884 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,np__0) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A))))))))))) # label(t108_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3885 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(np__0,B) & r1_xreal_0(np__0,C) & r1_xreal_0(np__0,D) & C != np__0 & A != np__0 & k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) = np__0 & r1_xreal_0(np__0,A)))))))))) # label(t73_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3886 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) -> r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,D))))))))))) # label(t18_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3887 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> -r1_xreal_0(B,k4_xcmplx_0(A)) & -r1_xreal_0(A,B) | r1_xreal_0(np__0,k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A)))))))) # label(t96_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3888 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) & -r1_xreal_0(k4_xcmplx_0(A),B)))))) # label(t201_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3889 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(np__0 != B & (all C (v1_xreal_0(C) -> k7_xcmplx_0(B,C) != A))))))) # label(t227_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3890 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(A,np__0) & r1_xreal_0(C,np__0) & r1_xreal_0(D,C) & r1_xreal_0(B,A) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D))))))))))) # label(t69_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3891 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,np__0) & r1_xreal_0(A,np__0) -> r1_xreal_0(np__0,k3_xcmplx_0(A,B))))))) # label(t130_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3892 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(B),A) -> r1_xreal_0(np__0,A) | r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))))))) # label(t206_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3893 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(np__0,A) & r1_xreal_0(A,np__1) & r1_xreal_0(B,C) -> r1_xreal_0(B,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)))))))))) # label(t173_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3894 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(C,np__0) & r1_xreal_0(A,B) -> r1_xreal_0(k3_xcmplx_0(B,C),k3_xcmplx_0(A,C))))))))) # label(t67_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3895 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(C,k3_xcmplx_0(B,A)) & r1_xreal_0(k7_xcmplx_0(C,A),B)))))))) # label(t83_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3896 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),B) & r1_xreal_0(A,np__1) & r1_xreal_0(np__0,A) -> np__0 = A | r1_xreal_0(C,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)))))))))) # label(t182_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3897 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k5_xcmplx_0(A),np__0)) & -(r1_xreal_0(A,np__0) & -r1_xreal_0(k5_xcmplx_0(A),np__0)))) # label(t124_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3898 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) | r1_xreal_0(B,np__0) | r1_xreal_0(np__0,A)))))))))) # label(t107_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3899 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(B,np__0) -> r1_xreal_0(k3_xcmplx_0(A,B),np__0)))))) # label(t133_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3900 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) | r1_xreal_0(A,np__0)))))) # label(t87_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3901 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) & -r1_xreal_0(B,k4_xcmplx_0(A))))))) # label(t199_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3902 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(A,k7_xcmplx_0(A,np__2))))) # label(t218_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3903 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__1,B) & r1_xreal_0(A,np__0) -> r1_xreal_0(k3_xcmplx_0(A,B),A)))))) # label(t156_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3904 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(np__0,C) -> r1_xreal_0(A,k6_xcmplx_0(B,C))))) -> r1_xreal_0(A,B)))))) # label(t58_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3905 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,np__0) & r1_xreal_0(k3_xcmplx_0(A,B),np__0) & -r1_xreal_0(A,np__0)))))) # label(t131_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3906 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__1,A) & -r1_xreal_0(C,B) & r1_xreal_0(D,C) & r1_xreal_0(C,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,D))) & -r1_xreal_0(A,np__0)))))))))) # label(t180_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3907 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(np__0,B) | r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) | r1_xreal_0(A,np__0)))))))))) # label(t106_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3908 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-(-r1_xreal_0(A,np__0) & -r1_xreal_0(np__0,B)) & -(-r1_xreal_0(np__0,A) & -r1_xreal_0(B,np__0)) & -r1_xreal_0(np__0,k3_xcmplx_0(A,B))))))) # label(t135_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3909 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) -> r1_xreal_0(k6_xcmplx_0(D,C),k6_xcmplx_0(B,A))))))))))) # label(t20_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3910 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,k5_xcmplx_0(A)) & -r1_xreal_0(k5_xcmplx_0(B),np__0) & r1_xreal_0(B,A)))))) # label(t127_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3911 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(np__0,B) & r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) & -r1_xreal_0(B,C)))))))) # label(t101_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3912 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) -> r1_xreal_0(k2_xcmplx_0(A,B),B)))))) # label(t34_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3913 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__1,B) & r1_xreal_0(np__1,A) -> r1_xreal_0(np__1,k3_xcmplx_0(A,B))))))) # label(t161_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3914 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k6_xcmplx_0(A,B),C) -> r1_xreal_0(k6_xcmplx_0(A,C),B)))))))) # label(t14_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3915 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A)) & -r1_xreal_0(C,B) & -r1_xreal_0(A,np__0)))))))) # label(t76_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3916 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) & r1_xreal_0(C,D) & -r1_xreal_0(B,A)))))))))) # label(t10_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3917 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,k4_xcmplx_0(B)) -> r1_xreal_0(B,k4_xcmplx_0(A))))))) # label(t27_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3918 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(C,D) & r1_xreal_0(A,B) -> r1_xreal_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C))))))))))) # label(t15_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3919 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k3_xcmplx_0(B,A),C) -> r1_xreal_0(np__0,A) | r1_xreal_0(k7_xcmplx_0(C,A),B)))))))) # label(t80_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3920 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(B,k2_xcmplx_0(A,B)) & -r1_xreal_0(np__0,A)))))) # label(t32_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3921 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__1) & r1_xreal_0(np__1,k5_xcmplx_0(A))))) # label(t214_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3922 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(np__0,k6_xcmplx_0(B,A))))))) # label(t50_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3923 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(B,np__1) -> r1_xreal_0(A,k3_xcmplx_0(A,B))))))) # label(t154_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3924 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(C,B) & r1_xreal_0(k3_xcmplx_0(C,A),k3_xcmplx_0(B,A))))))))) # label(t70_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3925 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) & r1_xreal_0(B,np__1) & r1_xreal_0(A,np__1) -> r1_xreal_0(k3_xcmplx_0(A,B),np__1)))))) # label(t162_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3926 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,np__0) & r1_xreal_0(np__0,k7_xcmplx_0(B,A)) & -r1_xreal_0(np__0,A)))))) # label(t144_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3927 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A)),np__0) & r1_xreal_0(np__0,A) -> r1_xreal_0(B,A) & r1_xreal_0(k4_xcmplx_0(A),B)))))) # label(t95_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3928 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & -r1_xreal_0(np__1,C) & -r1_xreal_0(A,k7_xcmplx_0(B,C))))) -> r1_xreal_0(A,B)))))) # label(t211_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3929 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(np__1,A) & r1_xreal_0(k6_xcmplx_0(np__1,A),np__0)))) # label(t151_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3930 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(np__0,B) & r1_xreal_0(k3_xcmplx_0(A,B),np__0)))))) # label(t132_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3931 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,B) & r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) & -r1_xreal_0(np__0,A)))))) # label(t89_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3932 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) & r1_xreal_0(C,D) & -r1_xreal_0(B,A)))))))))) # label(t16_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3933 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k3_xcmplx_0(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B)) & -r1_xreal_0(np__0,B)))))))))) # label(t114_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3934 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(A,np__0) | r1_xreal_0(np__1,k7_xcmplx_0(B,A))))))) # label(t183_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3935 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,np__1) & r1_xreal_0(np__0,A) -> r1_xreal_0(k3_xcmplx_0(A,B),A)))))) # label(t155_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3936 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) & -r1_xreal_0(C,A) & -r1_xreal_0(D,B) & r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B))))))))))) # label(t98_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3937 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,C) & r1_xreal_0(np__0,B) -> r1_xreal_0(A,np__0) | r1_xreal_0(k7_xcmplx_0(B,C),k7_xcmplx_0(B,A))))))))) # label(t120_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3938 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,B) & r1_xreal_0(np__1,k7_xcmplx_0(A,B)) & r1_xreal_0(A,np__0)))))) # label(t192_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3939 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,k6_xcmplx_0(A,B)) & -r1_xreal_0(B,A)))))) # label(t51_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3940 (all A (v1_xreal_0(A) -> -(r1_xreal_0(np__0,A) & -r1_xreal_0(np__0,k5_xcmplx_0(A))) & -(r1_xreal_0(np__0,k5_xcmplx_0(A)) & -r1_xreal_0(np__0,A)))) # label(t125_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3941 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(A,np__1) & r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),C),k3_xcmplx_0(A,D)),B) & -r1_xreal_0(D,B) & -r1_xreal_0(C,B) & r1_xreal_0(np__0,A)))))))))) # label(t177_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3942 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,k7_xcmplx_0(np__1,np__2)) -> r1_xreal_0(np__0,k6_xcmplx_0(np__1,k3_xcmplx_0(np__2,A)))))) # label(t220_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3943 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k6_xcmplx_0(A,B),np__0) & r1_xreal_0(k6_xcmplx_0(B,A),np__0) & A != B))))) # label(t57_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3944 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,B) & r1_xreal_0(C,k2_xcmplx_0(B,A)) & r1_xreal_0(A,np__0)))))))) # label(t38_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.59 3945 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(A),B) & r1_xreal_0(np__0,A) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t195_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3946 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) <-> r1_xreal_0(k4_xcmplx_0(B),k4_xcmplx_0(A))))))) # label(t26_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3947 (all A (v1_xreal_0(A) -> -(r1_xreal_0(A,k7_xcmplx_0(A,np__3)) & -r1_xreal_0(A,np__0)))) # label(t223_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3948 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(np__0,A) -> k3_xcmplx_0(A,B) = np__0))))) # label(t128_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3949 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__1,A) & r1_xreal_0(np__0,B) & r1_xreal_0(B,np__1) & r1_xreal_0(np__1,k3_xcmplx_0(A,B)) & r1_xreal_0(np__0,A)))))) # label(t164_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3950 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,C) & r1_xreal_0(A,np__0) -> r1_xreal_0(B,np__0) | r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C))))))))) # label(t122_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3951 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) & r1_xreal_0(B,A) & -r1_xreal_0(np__0,k5_xcmplx_0(A))))))) # label(t94_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3952 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k3_xcmplx_0(A,B))))))) # label(t129_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3953 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,B) <-> r1_xreal_0(k6_xcmplx_0(C,B),k6_xcmplx_0(C,A))))))))) # label(t12_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3954 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(C,k7_xcmplx_0(B,A)) & -r1_xreal_0(k3_xcmplx_0(C,A),B)))))))) # label(t85_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3955 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(k4_xcmplx_0(B),A) & r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t208_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3956 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(C,np__1) -> r1_xreal_0(A,k3_xcmplx_0(B,C))))) -> r1_xreal_0(A,B)))))) # label(t169_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3957 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,B) & r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & -r1_xreal_0(np__0,A)))))))))) # label(t109_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3958 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,k4_xcmplx_0(B)) -> r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) | r1_xreal_0(A,np__0)))))) # label(t204_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3959 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) -> r1_xreal_0(B,k6_xcmplx_0(B,A))))))) # label(t47_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3960 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(k4_xcmplx_0(np__1),A) & r1_xreal_0(k4_xcmplx_0(np__1),B) & r1_xreal_0(B,np__0) -> r1_xreal_0(k3_xcmplx_0(A,B),np__1)))))) # label(t167_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3961 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__1) & r1_xreal_0(np__0,B) & r1_xreal_0(B,np__1) & np__1 = k3_xcmplx_0(A,B) & r1_xreal_0(np__0,A) -> np__1 = A))))) # label(t152_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3962 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k3_xcmplx_0(B,A),C) -> r1_xreal_0(A,np__0) | r1_xreal_0(B,k7_xcmplx_0(C,A))))))))) # label(t79_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3963 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__1,B) & r1_xreal_0(A,k3_xcmplx_0(A,B)) & -r1_xreal_0(A,np__0)))))) # label(t159_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3964 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,B) & r1_xreal_0(k7_xcmplx_0(A,B),np__0) & -r1_xreal_0(np__0,A)))))) # label(t142_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3965 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(B,C) & r1_xreal_0(B,D) & r1_xreal_0(A,np__1) & r1_xreal_0(np__0,A) -> r1_xreal_0(B,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),C),k3_xcmplx_0(A,D)))))))))))) # label(t175_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3966 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k7_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & -r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A)) & -r1_xreal_0(np__0,B)))))))))) # label(t112_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3967 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,A) & r1_xreal_0(k2_xcmplx_0(A,B),np__0) & -r1_xreal_0(B,np__0)))))) # label(t36_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3968 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,np__1) & r1_xreal_0(A,k3_xcmplx_0(A,B)) & -r1_xreal_0(np__0,A)))))) # label(t160_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3969 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,k3_xcmplx_0(C,A)) -> r1_xreal_0(C,k7_xcmplx_0(B,A)) | r1_xreal_0(np__0,A)))))))) # label(t82_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3970 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(B,k2_xcmplx_0(A,B))))))) # label(t33_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3971 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,A) -> r1_xreal_0(np__0,A) | r1_xreal_0(np__1,k7_xcmplx_0(B,A))))))) # label(t184_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3972 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(D,C) & r1_xreal_0(B,C) & r1_xreal_0(A,np__1) & r1_xreal_0(np__0,A) -> r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,D)),C)))))))))) # label(t176_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3973 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(np__0,k7_xcmplx_0(A,B)) & -r1_xreal_0(B,np__0)))))) # label(t143_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3974 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,np__1) & r1_xreal_0(k3_xcmplx_0(A,B),A) & -r1_xreal_0(A,np__0)))))) # label(t157_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3975 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,A) & -r1_xreal_0(B,C)))) & -r1_xreal_0(B,A)))))) # label(t7_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3976 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) -> r1_xreal_0(k5_xcmplx_0(A),np__0) | r1_xreal_0(B,A)))))) # label(t91_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3977 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k2_xcmplx_0(A,B),C) <-> r1_xreal_0(A,k6_xcmplx_0(C,B))))))))) # label(t21_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3978 (all A (v1_xreal_0(A) -> -r1_xreal_0(A,k6_xcmplx_0(A,np__1)))) # label(t148_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3979 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k2_xcmplx_0(B,A),np__0) & -r1_xreal_0(B,k4_xcmplx_0(A))))))) # label(t64_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3980 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,k7_xcmplx_0(A,B)) & -(-r1_xreal_0(np__0,B) & -r1_xreal_0(A,np__0)) & -(-r1_xreal_0(np__0,A) & -r1_xreal_0(B,np__0))))))) # label(t145_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3981 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,A) -> r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) | r1_xreal_0(np__0,A)))))) # label(t88_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3982 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(np__0,C) -> r1_xreal_0(k2_xcmplx_0(A,C),B)))) -> r1_xreal_0(A,B)))))) # label(t44_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3983 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k7_xcmplx_0(B,A),np__1) & -r1_xreal_0(B,A) & -r1_xreal_0(A,np__0)))))) # label(t189_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3984 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(np__0,A) & r1_xreal_0(B,C) -> r1_xreal_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))))))))) # label(t74_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3985 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k2_xcmplx_0(B,A),B) & -r1_xreal_0(A,np__0)))))) # label(t31_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3986 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(B,A) -> r1_xreal_0(k7_xcmplx_0(B,A),np__1)))))) # label(t187_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3987 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,A) & r1_xreal_0(np__1,k7_xcmplx_0(A,B)) & -r1_xreal_0(B,A)))))) # label(t191_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3988 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(np__0,A) & -r1_xreal_0(B,np__0) & r1_xreal_0(B,D) & r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & -r1_xreal_0(C,A)))))))))) # label(t99_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3989 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(np__0,B) & r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B))))))))))) # label(t110_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3990 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> r1_xreal_0(np__0,k7_xcmplx_0(A,B))))))) # label(t138_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3991 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (-r1_xreal_0(C,np__0) -> r1_xreal_0(A,k2_xcmplx_0(B,C))))) -> r1_xreal_0(A,B)))))) # label(t43_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3992 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,B) & -r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) & -r1_xreal_0(k5_xcmplx_0(A),np__0)))))) # label(t93_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3993 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) & k2_xcmplx_0(A,B) = np__0 -> A = np__0))))) # label(t29_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3994 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(B,np__0) & r1_xreal_0(k7_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & -r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A)) & -r1_xreal_0(A,np__0)))))))))) # label(t113_xreal_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3995 $T # label(t8_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3996 $T # label(t10_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3997 $T # label(t13_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3998 (all A all B (v4_ordinal2(B) -> (r2_hidden(A,a_1_0_axioms(B)) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & A = C & -r1_xreal_0(B,C)))))) # label(fraenkel_a_1_0_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 3999 $T # label(t1_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4000 $T # label(t17_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4001 $T # label(t2_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4002 (all A (v1_xreal_0(A) -> -((all B (v1_xreal_0(B) -> k3_xcmplx_0(A,B) != np__1)) & A != np__0))) # label(t20_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4003 (all A (v1_xreal_0(A) -> (exists B (v1_xreal_0(B) & k2_xcmplx_0(A,B) = np__0)))) # label(t19_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4004 $T # label(t27_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4005 $T # label(t7_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4006 $T # label(t14_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4007 $T # label(t18_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4008 $T # label(t3_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4009 $T # label(t21_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4010 $T # label(t15_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4011 $T # label(t24_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4012 $T # label(t16_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4013 $T # label(t23_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4014 $T # label(t6_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4015 (all A (v4_ordinal2(A) -> A = a_1_0_axioms(A))) # label(t30_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4016 $T # label(t25_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4017 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_numbers)) -> -((all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r2_hidden(D,B) & r2_hidden(C,A) -> r1_xreal_0(C,D)))))) & (all C (v1_xreal_0(C) -> (exists D (v1_xreal_0(D) & (exists E (v1_xreal_0(E) & r2_hidden(D,A) & r2_hidden(E,B) & -(r1_xreal_0(D,C) & r1_xreal_0(C,E))))))))))))) # label(t26_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4018 $T # label(t11_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4019 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> ((all B (v1_xreal_0(B) -> (r2_hidden(B,A) -> r2_hidden(k2_xcmplx_0(B,np__1),A)))) & r2_hidden(np__0,A) -> r1_tarski(k5_numbers,A)))) # label(t29_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4020 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(A,k5_numbers) & r2_hidden(B,k5_numbers) -> r2_hidden(k2_xcmplx_0(A,B),k5_numbers)))))) # label(t28_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4021 $T # label(t5_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4022 $T # label(t9_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4023 $T # label(t4_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4024 $T # label(t12_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4025 $T # label(t22_axioms) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4026 $T # label(t54_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4027 $T # label(t90_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4028 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k4_real_1(A,B),k1_numbers))) # label(dt_k4_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4029 (all A (m1_subset_1(A,k1_numbers) -> k1_real_1(A) = k4_xcmplx_0(A))) # label(redefinition_k1_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4030 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) <-> -(B != A & r1_xreal_0(B,A))))))) # label(d5_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4031 $T # label(t51_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4032 $T # label(t91_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4033 $T # label(t24_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4034 $T # label(t71_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4035 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (-r1_xreal_0(A,np__0) -> -(-r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A)) & r1_xreal_0(C,B)) & -(r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A)) & -r1_xreal_0(C,B))))))))) # label(t73_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4036 $T # label(t23_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4037 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k6_real_1(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k6_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4038 $T # label(t8_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4039 $T # label(t83_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4040 (all A (m1_subset_1(A,k1_numbers) -> k1_real_1(k1_real_1(A)) = A)) # label(involutiveness_k1_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4041 $T # label(t34_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4042 $T # label(t4_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4043 $T # label(t47_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4044 $T # label(t79_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4045 $T # label(t88_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4046 $T # label(t13_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4047 $T # label(t9_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4048 $T # label(t28_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4049 $T # label(t27_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4050 $T # label(t78_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4051 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k2_real_1(A),k1_numbers))) # label(dt_k2_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4052 $T # label(t35_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4053 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(A,B) & r1_xreal_0(C,D) -> r1_xreal_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C))) & -(r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) & (r1_xreal_0(C,D) & -r1_xreal_0(B,A) | -r1_xreal_0(D,C) & r1_xreal_0(A,B))))))))))) # label(t92_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4054 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k4_real_1(B,A) = k4_real_1(A,B))) # label(commutativity_k4_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4055 $T # label(d3_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4056 $T # label(t45_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4057 $T # label(t33_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4058 $T # label(t72_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4059 $T # label(t17_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4060 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (-r1_xreal_0(np__0,A) -> -(-r1_xreal_0(C,B) & r1_xreal_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))) & -(r1_xreal_0(C,B) & -r1_xreal_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)))))))))) # label(t74_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4061 $T # label(t64_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4062 $T # label(t46_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4063 $T # label(t20_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4064 $T # label(t77_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4065 $T # label(t30_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4066 (exists A ((all B (m1_subset_1(B,k1_numbers) -> (r2_hidden(B,A) <-> p1_s1_real_1(B)))) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)))) # label(s1_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4067 $T # label(t84_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4068 $T # label(t1_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4069 $T # label(t58_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4070 $T # label(t6_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4071 $T # label(t10_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4072 $T # label(t86_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4073 (all A (m1_subset_1(A,k1_numbers) -> k2_real_1(k2_real_1(A)) = A)) # label(involutiveness_k2_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4074 $T # label(t76_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4075 $T # label(t87_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4076 $T # label(t38_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4077 $T # label(t29_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4078 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k6_real_1(A,B),k1_numbers))) # label(dt_k6_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4079 $T # label(t53_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4080 $T # label(t59_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4081 $T # label(t5_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4082 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k3_real_1(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k3_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4083 $T # label(t67_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4084 $T # label(t85_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4085 $T # label(t19_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4086 $T # label(t68_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4087 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k5_real_1(A,B),k1_numbers))) # label(dt_k5_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4088 $T # label(d4_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4089 (all A (m1_subset_1(A,k1_numbers) -> k2_real_1(A) = k5_xcmplx_0(A))) # label(redefinition_k2_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4090 (all A (m1_subset_1(A,k1_numbers) -> v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc1_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4091 $T # label(t81_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4092 $T # label(t82_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4093 $T # label(t61_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4094 $T # label(t18_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4095 $T # label(t14_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4096 $T # label(t50_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4097 $T # label(t70_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4098 $T # label(t37_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4099 $T # label(t31_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4100 $T # label(t66_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4101 $T # label(t40_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4102 $T # label(t44_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4103 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k3_real_1(B,A) = k3_real_1(A,B))) # label(commutativity_k3_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4104 $T # label(t65_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4105 $T # label(t80_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4106 $T # label(t22_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4107 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k3_real_1(A,B),k1_numbers))) # label(dt_k3_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4108 $T # label(t16_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4109 $T # label(t49_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4110 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k6_xcmplx_0(A,B) = k5_real_1(A,B))) # label(redefinition_k5_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4111 $T # label(t21_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4112 $T # label(t39_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4113 $T # label(t3_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4114 $T # label(t63_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4115 $T # label(t89_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4116 $T # label(t69_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4117 $T # label(t42_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4118 $T # label(t60_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4119 $T # label(t7_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4120 $T # label(t12_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4121 $T # label(t41_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4122 $T # label(t32_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4123 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k3_xcmplx_0(A,B) = k4_real_1(A,B))) # label(redefinition_k4_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4124 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k1_real_1(A),k1_numbers))) # label(dt_k1_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4125 $T # label(d2_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4126 $T # label(t56_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4127 $T # label(t2_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4128 $T # label(t43_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4129 $T # label(t15_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4130 (all A (v1_xreal_0(A) -> A = k6_xcmplx_0(A,np__0))) # label(t25_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4131 $T # label(t62_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4132 $T # label(t36_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4133 $T # label(t55_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4134 $T # label(t11_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4135 $T # label(t75_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4136 $T # label(t52_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4137 $T # label(t57_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4138 $T # label(t48_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4139 $T # label(d1_real_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4140 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k5_square_1(A)))) # label(fc1_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4141 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> A = k1_square_1(A,A))) # label(idempotence_k1_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4142 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(A,B) -> r1_xreal_0(k8_square_1(A),k8_square_1(B))))))) # label(t94_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4143 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (p1_s1_square_1(A) & p2_s1_square_1(B) -> r1_xreal_0(A,B)))))) -> (exists A ((all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (p1_s1_square_1(B) & p2_s1_square_1(C) -> r1_xreal_0(A,C) & r1_xreal_0(B,A)))))) & v1_xreal_0(A))) # label(s1_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4144 $T # label(t20_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4145 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,A) & r1_xreal_0(k5_square_1(B),k5_square_1(A)) & -r1_xreal_0(B,A)))))) # label(t78_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4146 $T # label(t4_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4147 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k6_xcmplx_0(k5_square_1(A),k5_square_1(B)) != np__0 -> k7_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(k5_square_1(A),k5_square_1(B))) = k7_xcmplx_0(np__1,k6_xcmplx_0(A,B))))))) # label(t71_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4148 (all A (v1_xreal_0(A) -> (-r1_xreal_0(A,np__0) -> k8_square_1(k7_xcmplx_0(np__1,A)) = k7_xcmplx_0(np__1,k8_square_1(A))))) # label(t101_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4149 (all A (v1_xreal_0(A) -> v1_xreal_0(k5_square_1(A)) & v1_xcmplx_0(k5_square_1(A)))) # label(fc2_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4150 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> k8_square_1(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k8_square_1(A),k8_square_1(B))))))) # label(t99_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4151 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k2_xcmplx_0(A,B) = k2_xcmplx_0(k1_square_1(A,B),k2_square_1(A,B)))))) # label(t53_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4152 $T # label(t14_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4153 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_square_1(k6_xcmplx_0(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k5_square_1(A),k3_xcmplx_0(k3_xcmplx_0(np__2,A),B)),k5_square_1(B)))))) # label(t64_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4154 $T # label(t29_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4155 $T # label(t21_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4156 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k6_xcmplx_0(k5_square_1(A),k5_square_1(B)) != np__0 -> k7_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(k5_square_1(A),k5_square_1(B))) = k7_xcmplx_0(np__1,k2_xcmplx_0(A,B))))))) # label(t70_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4157 $T # label(t47_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4158 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_square_1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k2_xcmplx_0(k5_square_1(A),k3_xcmplx_0(k3_xcmplx_0(np__2,A),B)),k5_square_1(B)))))) # label(t63_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4159 $T # label(t5_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4160 (all A (v1_xcmplx_0(A) -> (k5_square_1(A) = np__0 -> np__0 = A))) # label(t73_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4161 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> r1_xreal_0(k1_square_1(A,B),A))))) # label(t35_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4162 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> A = k4_square_1(A,A))) # label(idempotence_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4163 $T # label(t88_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4164 $T # label(t10_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4165 $T # label(t98_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4166 $T # label(t15_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4167 $T # label(t34_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4168 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> k2_square_1(A,k2_square_1(B,C)) = k2_square_1(k2_square_1(A,B),C))))))) # label(t51_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4169 $T # label(t11_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4170 $T # label(t79_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4171 $T # label(t45_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4172 $T # label(t48_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4173 (all A (v1_xreal_0(A) -> r1_xreal_0(np__0,k5_square_1(A)))) # label(t72_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4174 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> k2_square_1(A,B) = k2_square_1(B,A))) # label(commutativity_k2_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4175 $T # label(t17_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4176 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,np__0) -> k4_xcmplx_0(A) = k8_square_1(k5_square_1(A))))) # label(t90_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4177 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k3_square_1(A,B),k1_numbers))) # label(dt_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4178 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> k1_square_1(A,B) = A) & (-r1_xreal_0(A,B) -> k1_square_1(A,B) = B))))) # label(d1_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4179 $T # label(t26_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4180 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> k7_xcmplx_0(np__1,k6_xcmplx_0(k8_square_1(A),k8_square_1(B))) = k7_xcmplx_0(k2_xcmplx_0(k8_square_1(A),k8_square_1(B)),k6_xcmplx_0(A,B))))))) # label(t107_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4181 $T # label(t6_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4182 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k7_square_1(A),k1_numbers))) # label(dt_k7_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4183 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k6_square_1(A),k2_numbers))) # label(dt_k6_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4184 (all A (v1_xreal_0(A) -> v1_xreal_0(k8_square_1(A)))) # label(dt_k8_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4185 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> (all B (v1_xreal_0(B) -> (k8_square_1(A) = B <-> A = k5_square_1(B) & r1_xreal_0(np__0,B))))))) # label(d4_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4186 $T # label(t13_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4187 $T # label(t23_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4188 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(B,A) | k7_xcmplx_0(k2_xcmplx_0(k8_square_1(B),k8_square_1(A)),k6_xcmplx_0(B,A)) = k7_xcmplx_0(np__1,k6_xcmplx_0(k8_square_1(B),k8_square_1(A)))))))) # label(t108_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4189 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> B = k2_square_1(A,B) | A = k2_square_1(A,B))))) # label(t49_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4190 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xreal_0(k1_square_1(A,B)))) # label(dt_k1_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4191 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k2_square_1(A,C),B) <-> r1_xreal_0(C,B) & r1_xreal_0(A,B)))))))) # label(t50_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4192 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k1_square_1(A,B) = k3_square_1(A,B))) # label(redefinition_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4193 $T # label(t37_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4194 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k2_square_1(A,B) = k4_square_1(A,B))) # label(redefinition_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4195 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> k3_xcmplx_0(k6_xcmplx_0(k8_square_1(A),k8_square_1(B)),k2_xcmplx_0(k8_square_1(A),k8_square_1(B))) = k6_xcmplx_0(A,B)))))) # label(t104_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4196 $T # label(t42_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4197 $T # label(t32_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4198 $T # label(t7_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4199 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k1_square_1(A,B) = A | B = k1_square_1(A,B))))) # label(t38_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4200 $T # label(t3_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4201 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> A = B | k7_xcmplx_0(k6_xcmplx_0(k8_square_1(A),k8_square_1(B)),k6_xcmplx_0(A,B)) = k7_xcmplx_0(np__1,k2_xcmplx_0(k8_square_1(A),k8_square_1(B)))))))) # label(t105_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4202 (all A (v1_xcmplx_0(A) -> k5_square_1(A) = k5_square_1(k4_xcmplx_0(A)))) # label(t61_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4203 $T # label(t43_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4204 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> k2_square_1(k1_square_1(A,B),k1_square_1(A,C)) = k1_square_1(A,k2_square_1(B,C)))))))) # label(t56_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4205 (all A (m1_subset_1(A,k2_numbers) -> k6_square_1(A) = k5_square_1(A))) # label(redefinition_k6_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4206 $T # label(t1_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4207 (all A (v1_xreal_0(A) -> -(r1_xreal_0(np__1,k7_xcmplx_0(np__1,A)) & -r1_xreal_0(A,np__1)))) # label(t2_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4208 (all A (m1_subset_1(A,k1_numbers) -> k8_square_1(A) = k9_square_1(A))) # label(redefinition_k9_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4209 $T # label(t91_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4210 $T # label(t12_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4211 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k6_xcmplx_0(k5_square_1(A),k3_xcmplx_0(np__2,A)),np__1) = k5_square_1(k6_xcmplx_0(A,np__1)))) # label(t66_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4212 $T # label(t52_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4213 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k8_square_1(A),np__0) & -r1_xreal_0(A,np__0)))) # label(t93_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4214 $T # label(t28_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4215 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k5_square_1(A),A) & -r1_xreal_0(A,np__1)))) # label(t76_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4216 $T # label(t18_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4217 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k1_square_1(A,k2_square_1(A,B)) = A)))) # label(t55_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4218 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) -> k8_square_1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k8_square_1(A),k8_square_1(B))))))) # label(t97_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4219 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k4_square_1(A,B) = k4_square_1(B,A))) # label(commutativity_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4220 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> k1_square_1(A,B) = k1_square_1(B,A))) # label(commutativity_k1_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4221 $T # label(t19_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4222 (all A (m1_subset_1(A,k2_numbers) -> v1_xcmplx_0(A))) # label(cc1_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4223 (all A (v1_xreal_0(A) -> (k8_square_1(A) = np__0 & r1_xreal_0(np__0,A) -> np__0 = A))) # label(t92_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4224 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k5_square_1(A),np__0) & A != np__0))) # label(t74_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4225 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-(r1_xreal_0(B,np__0) & r1_xreal_0(A,np__0)) & -(r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A)) & r1_xreal_0(np__0,k3_xcmplx_0(A,B))))))) # label(t25_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4226 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k9_square_1(A),k1_numbers))) # label(dt_k9_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4227 $T # label(t62_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4228 $T # label(t31_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4229 $T # label(t100_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4230 (all A (v1_xreal_0(A) -> (-r1_xreal_0(A,np__0) -> k7_xcmplx_0(A,k8_square_1(A)) = k8_square_1(A)))) # label(t103_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4231 $T # label(t87_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4232 $T # label(t8_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4233 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> r1_xreal_0(A,k2_square_1(A,B)))))) # label(t46_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4234 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k3_square_1(A,B) = k3_square_1(B,A))) # label(commutativity_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4235 $T # label(t27_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4236 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xreal_0(k2_square_1(A,B)))) # label(dt_k2_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4237 (all A (v1_xcmplx_0(A) -> k5_square_1(A) = k3_xcmplx_0(A,A))) # label(d3_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4238 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k4_square_1(A,B),k1_numbers))) # label(dt_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4239 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> A = k2_square_1(A,A))) # label(idempotence_k2_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4240 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_square_1(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k5_square_1(A),k5_square_1(B)))))) # label(t69_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4241 (all A (m1_subset_1(A,k1_numbers) -> k7_square_1(A) = k5_square_1(A))) # label(redefinition_k7_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4242 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> A = k2_square_1(A,k1_square_1(A,B)))))) # label(t54_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4243 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> k7_xcmplx_0(np__1,k2_xcmplx_0(k8_square_1(B),k8_square_1(A))) = k7_xcmplx_0(k6_xcmplx_0(k8_square_1(B),k8_square_1(A)),k6_xcmplx_0(B,A)) | r1_xreal_0(B,A)))))) # label(t106_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4244 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B)) = k6_xcmplx_0(k5_square_1(A),k5_square_1(B)))))) # label(t67_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4245 $T # label(t81_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4246 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> A = k8_square_1(k5_square_1(A))))) # label(t89_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4247 $T # label(dt_k5_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4248 $T # label(t41_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4249 $T # label(t30_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4250 $T # label(t58_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4251 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k5_square_1(A),k5_square_1(B)) = k5_square_1(k3_xcmplx_0(A,B)))))) # label(t68_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4252 $T # label(t36_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4253 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> A = k3_square_1(A,A))) # label(idempotence_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4254 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k8_square_1(B),k8_square_1(A)) & -r1_xreal_0(B,A) & r1_xreal_0(np__0,A)))))) # label(t95_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4255 $T # label(t22_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4256 $T # label(t24_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4257 $T # label(t33_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4258 $T # label(t80_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.60 4259 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,B) & r1_xreal_0(A,C) <-> r1_xreal_0(A,k1_square_1(B,C))))))))) # label(t39_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4260 $T # label(t44_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4261 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,A) -> A = k2_square_1(A,B)) & (-r1_xreal_0(B,A) -> B = k2_square_1(A,B)))))) # label(d2_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4262 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> k2_square_1(A,k1_square_1(B,C)) = k1_square_1(k2_square_1(A,B),k2_square_1(A,C)))))))) # label(t57_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4263 $T # label(t9_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4264 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> k1_square_1(A,k1_square_1(B,C)) = k1_square_1(k1_square_1(A,B),C))))))) # label(t40_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4265 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(np__1,A) & r1_xreal_0(A,k5_square_1(A))))) # label(t75_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4266 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & r1_xreal_0(np__0,A) -> r1_xreal_0(k5_square_1(A),k5_square_1(B))))))) # label(t77_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4267 $T # label(t16_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4268 (all A (v1_xcmplx_0(A) -> k5_square_1(k2_xcmplx_0(A,np__1)) = k2_xcmplx_0(k2_xcmplx_0(k5_square_1(A),k3_xcmplx_0(np__2,A)),np__1))) # label(t65_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4269 (all A (v1_xreal_0(A) -> (-r1_xreal_0(A,np__0) -> k7_xcmplx_0(np__1,k8_square_1(A)) = k7_xcmplx_0(k8_square_1(A),A)))) # label(t102_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4270 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (k8_square_1(A) = k8_square_1(B) & r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) -> A = B))))) # label(t96_square_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4271 $T # label(t24_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4272 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,k2_xcmplx_0(B,C)) & r1_nat_1(A,B) -> r1_nat_1(A,C)))))))) # label(t57_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4273 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)))) # label(fc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4274 $T # label(t31_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4275 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k3_xcmplx_0(A,B) = k2_nat_1(A,B))) # label(redefinition_k2_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4276 (exists A (m1_subset_1(A,k5_numbers) & v3_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4277 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(B,A) -> m2_subset_1(k6_xcmplx_0(B,np__1),k1_numbers,k5_numbers)))))) # label(t60_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4278 $T # label(t12_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4279 (all A (v4_ordinal2(A) -> -r1_xreal_0(k2_xcmplx_0(A,np__1),np__0))) # label(t21_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4280 (exists A (-v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4281 $T # label(t25_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4282 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> m2_subset_1(k4_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k4_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4283 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> k4_nat_1(A,B) = k4_nat_1(k2_xcmplx_0(k3_xcmplx_0(B,C),A),B))))))) # label(t73_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4284 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,B) & r1_nat_1(A,C) -> r1_nat_1(A,k2_xcmplx_0(B,C))))))))) # label(t55_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4285 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(np__0 != A & r1_xreal_0(k2_xcmplx_0(B,A),B)))))) # label(t41_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4286 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) <-> -r1_xreal_0(k2_xcmplx_0(B,np__1),A)))))) # label(t38_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4287 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (k4_nat_1(A,C) = np__0 & k6_xcmplx_0(A,k3_xcmplx_0(D,C)) = B -> np__0 = k4_nat_1(B,C)))))))))) # label(t65_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4288 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (k4_nat_1(A,C) = np__0 -> k4_nat_1(B,C) = k4_nat_1(k2_xcmplx_0(A,B),C)))))))) # label(t67_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4289 $T # label(t34_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4290 (all A (v4_ordinal2(A) -> r1_xreal_0(np__0,A))) # label(t18_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4291 -r1_xreal_0(f3_s8_nat_1,np__0) & f1_s8_nat_1(np__0) = f2_s8_nat_1 & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k4_nat_1(f1_s8_nat_1(A),f1_s8_nat_1(k1_nat_1(A,np__1))) = f1_s8_nat_1(k1_nat_1(A,np__2)))) & f1_s8_nat_1(np__1) = f3_s8_nat_1 & -r1_xreal_0(f2_s8_nat_1,f3_s8_nat_1) -> (exists A (k6_nat_1(f2_s8_nat_1,f3_s8_nat_1) = f1_s8_nat_1(A) & np__0 = f1_s8_nat_1(k1_nat_1(A,np__1)) & m2_subset_1(A,k1_numbers,k5_numbers))) # label(s8_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4292 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (np__0 = k4_nat_1(A,C) -> r1_xreal_0(C,B) | B = k4_nat_1(k2_xcmplx_0(A,B),C) | C = np__0))))))) # label(t66_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4293 (exists A (p1_s5_nat_1(A) & m2_subset_1(A,k1_numbers,k5_numbers))) -> (exists A (p1_s5_nat_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (p1_s5_nat_1(B) -> r1_xreal_0(A,B)))) & m2_subset_1(A,k1_numbers,k5_numbers))) # label(s5_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4294 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k2_xcmplx_0(A,B) = k1_nat_1(A,B))) # label(redefinition_k1_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4295 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r1_xreal_0(k1_nat_1(B,np__1),A) & A != B & r1_xreal_0(B,A)))))) # label(t70_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4296 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k6_nat_1(B,A) = k6_nat_1(A,B))) # label(commutativity_k6_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4297 $T # label(t15_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4298 $T # label(t35_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4299 (all A (v4_ordinal2(A) -> (-r1_xreal_0(np__1,A) -> np__0 = A))) # label(t39_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4300 $T # label(t6_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4301 (exists A (m2_subset_1(A,k1_numbers,k5_numbers) & p1_s7_nat_1(A))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(np__0 != A & p1_s7_nat_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r1_xreal_0(A,B) & p1_s7_nat_1(B))))))) -> p1_s7_nat_1(np__0) # label(s7_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4302 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> ((all B (m1_subset_1(B,k1_numbers) -> (r2_hidden(B,A) -> r2_hidden(k3_real_1(B,np__1),A)))) & r2_hidden(np__0,A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r2_hidden(B,A)))))) # label(t2_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4303 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_nat_1(A,B) <-> B = k3_xcmplx_0(A,k3_nat_1(B,A))))))) # label(t49_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4304 p1_s2_nat_1(np__0) & (all A (v4_ordinal2(A) -> (p1_s2_nat_1(A) -> p1_s2_nat_1(k2_xcmplx_0(A,np__1))))) -> (all A (v4_ordinal2(A) -> p1_s2_nat_1(A))) # label(s2_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4305 $T # label(t11_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4306 $T # label(t9_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4307 $T # label(t17_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4308 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,B) -> r1_nat_1(A,k3_xcmplx_0(B,C))))))))) # label(t56_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4309 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_nat_1(B,A) -> r1_xreal_0(A,np__0) | r1_xreal_0(B,A)))))) # label(t54_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4310 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & B = k3_xcmplx_0(A,C))) <-> r1_nat_1(A,B)))))) # label(d3_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4311 (all A (v4_ordinal2(A) -> np__1 = k4_nat_1(A,np__2) | np__0 = k4_nat_1(A,np__2))) # label(t62_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4312 $T # label(t7_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4313 (all A all B (v4_ordinal2(A) & -v1_xboole_0(B) & v4_ordinal2(B) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)))) # label(fc3_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4314 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> A = k6_nat_1(A,A))) # label(idempotence_k6_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4315 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(A,np__1) -> k4_nat_1(np__1,A) = np__1))))) # label(t64_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4316 $T # label(t3_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4317 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (np__1 = k3_xcmplx_0(A,B) -> np__1 = A & np__1 = B))))) # label(t40_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4318 $T # label(t14_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4319 (exists A (v3_ordinal1(A) & -v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)))) # label(rc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4320 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (-(-(f1_s3_nat_1 = B & A = np__0) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(k1_nat_1(C,np__1) = A & p1_s3_nat_1(C,D) & f2_s3_nat_1(A,D) = B)))))) <-> p1_s3_nat_1(A,B)))))) -> (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) -> (p1_s3_nat_1(A,C) & p1_s3_nat_1(A,B) -> B = C))))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (exists B (p1_s3_nat_1(A,B) & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(s3_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4321 $T # label(t50_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4322 (all A (v4_ordinal2(A) -> v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & -v3_xreal_0(A))) # label(cc3_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4323 $T # label(t36_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4324 $T # label(t13_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4325 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(r1_xreal_0(A,k4_nat_1(B,A)) & -r1_xreal_0(A,np__0)))))) # label(t46_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4326 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v4_ordinal2(k3_xcmplx_0(A,B)))) # label(fc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4327 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (-r1_xreal_0(A,np__0) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (exists C ((exists D (m2_subset_1(D,k1_numbers,k5_numbers) & -r1_xreal_0(A,D) & k1_nat_1(k2_nat_1(A,C),D) = B)) & m2_subset_1(C,k1_numbers,k5_numbers)))))))) # label(t42_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4328 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> m2_subset_1(k6_xcmplx_0(B,A),k1_numbers,k5_numbers)))))) # label(t61_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4329 (all A all B (v4_ordinal2(B) & -v1_xboole_0(B) & v4_ordinal2(A) -> v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)))) # label(fc4_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4330 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (np__0 != B -> k3_nat_1(k2_nat_1(A,B),B) = A))))) # label(t72_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4331 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(-r1_xreal_0(np__2,A) & np__1 != A & np__0 != A))) # label(t71_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4332 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(A,B) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C))))))))) # label(t20_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4333 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k6_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k6_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4334 p1_s1_nat_1(np__0) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (p1_s1_nat_1(A) -> p1_s1_nat_1(k1_nat_1(A,np__1))))) -> (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> p1_s1_nat_1(A))) # label(s1_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4335 $T # label(t44_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4336 (all A (v4_ordinal2(A) -> np__0 = k4_nat_1(np__0,A))) # label(t78_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4337 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(A,B) -> r1_xreal_0(A,k2_xcmplx_0(B,C))))))))) # label(t37_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4338 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(A,B) -> B = k4_nat_1(B,A)))))) # label(t76_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4339 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (np__0 = k2_xcmplx_0(A,B) -> A = np__0 & B = np__0))))) # label(t23_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4340 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(k2_xcmplx_0(A,B),A) <-> r1_xreal_0(np__1,B)))))) # label(t59_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4341 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B != k2_xcmplx_0(A,C))) & r1_xreal_0(A,B)))))) # label(t28_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4342 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> k4_nat_1(k3_xcmplx_0(A,B),A) = np__0)))) # label(t63_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4343 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (np__0 != A -> k3_nat_1(k3_xcmplx_0(A,B),A) = B))))) # label(t68_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4344 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k1_nat_1(A,B) = k1_nat_1(B,A))) # label(commutativity_k1_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4345 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k5_nat_1(B,A) = k5_nat_1(A,B))) # label(commutativity_k5_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4346 (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) -> p1_s4_nat_1(B)))) -> p1_s4_nat_1(A)))) -> (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> p1_s4_nat_1(A))) # label(s4_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4347 $T # label(t45_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4348 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (-((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(k2_xcmplx_0(k3_xcmplx_0(B,C),D) = A & -r1_xreal_0(B,D)))) & -(B = np__0 & np__0 = C)) <-> k3_nat_1(A,B) = C))))))) # label(d1_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4349 (all A (v4_ordinal2(A) -> k4_nat_1(A,A) = np__0)) # label(t77_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4350 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> r1_nat_1(A,A))) # label(reflexivity_r1_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4351 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> m2_subset_1(k3_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k3_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4352 $T # label(t1_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4353 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k5_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k5_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4354 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(A != k2_xcmplx_0(B,np__1) & -r1_xreal_0(A,B) & r1_xreal_0(A,k2_xcmplx_0(B,np__1))))))) # label(t26_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4355 $T # label(t33_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4356 $T # label(t16_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4357 (all A (v4_ordinal2(A) -> -(A != np__0 & r1_xreal_0(A,np__0)))) # label(t19_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4358 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(A,np__0) -> B = k2_xcmplx_0(k3_xcmplx_0(A,k3_nat_1(B,A)),k4_nat_1(B,A))))))) # label(t47_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4359 $T # label(t32_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4360 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> m2_subset_1(k2_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k2_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4361 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> (k2_xcmplx_0(k3_xcmplx_0(B,D),F) = A & A = k2_xcmplx_0(k3_xcmplx_0(B,C),E) -> E = F & D = C | r1_xreal_0(B,F) | r1_xreal_0(B,E)))))))))))))) # label(t43_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4362 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_nat_1(B,A) & r1_nat_1(A,B) -> B = A))))) # label(t52_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4363 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(B,C) & r1_nat_1(A,B) -> r1_nat_1(A,C)))))))) # label(t51_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4364 $T # label(t10_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4365 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k2_nat_1(A,B) = k2_nat_1(B,A))) # label(commutativity_k2_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4366 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(r1_xreal_0(A,B) & B != A & k2_xcmplx_0(A,np__1) != B & r1_xreal_0(B,k2_xcmplx_0(A,np__1))))))) # label(t27_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4367 $T # label(t8_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4368 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> k4_nat_1(k2_xcmplx_0(A,B),C) = k4_nat_1(k2_xcmplx_0(k4_nat_1(A,C),B),C))))))) # label(t74_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4369 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k1_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4370 $T # label(t30_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4371 $T # label(t4_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4372 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r1_xreal_0(A,k2_xcmplx_0(A,B)))))) # label(t29_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4373 $T # label(t5_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4374 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_nat_1(D,B) & r1_nat_1(D,A) -> r1_nat_1(D,C)))) & r1_nat_1(C,B) & r1_nat_1(C,A) <-> C = k6_nat_1(A,B)))))))) # label(d5_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4375 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v3_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v4_ordinal2(A) & v2_ordinal1(A))) # label(cc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4376 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> k4_nat_1(k2_xcmplx_0(A,B),C) = k4_nat_1(k2_xcmplx_0(A,k4_nat_1(B,C)),C))))))) # label(t75_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4377 (all A (v4_ordinal2(A) -> -(np__0 != A & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> A != k1_nat_1(B,np__1)))))) # label(t22_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4378 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (-(-(B = np__0 & C = np__0) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(A = k2_xcmplx_0(k3_xcmplx_0(B,D),C) & -r1_xreal_0(B,C))))) <-> C = k4_nat_1(A,B)))))))) # label(d2_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4379 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,B) & r1_nat_1(A,C) -> r1_nat_1(A,k4_nat_1(B,C))))))))) # label(t58_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4380 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(cc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4381 $T # label(t48_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4382 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (k4_nat_1(A,B) = np__0 -> k3_nat_1(k2_xcmplx_0(A,C),B) = k1_nat_1(k3_nat_1(A,B),k3_nat_1(C,B))))))))) # label(t69_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4383 (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) -> (k5_nat_1(A,B) = C <-> r1_nat_1(B,C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_nat_1(B,D) & r1_nat_1(A,D) -> r1_nat_1(C,D)))) & r1_nat_1(A,C)))))))) # label(d4_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4384 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (p1_s6_nat_1(A) -> r1_xreal_0(A,f1_s6_nat_1)))) & (exists A (m2_subset_1(A,k1_numbers,k5_numbers) & p1_s6_nat_1(A))) -> (exists A ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (p1_s6_nat_1(B) -> r1_xreal_0(B,A)))) & p1_s6_nat_1(A) & m2_subset_1(A,k1_numbers,k5_numbers))) # label(s6_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4385 (all A (v4_ordinal2(A) -> r1_nat_1(np__1,A) & r1_nat_1(A,np__0))) # label(t53_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4386 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k5_nat_1(A,A) = A)) # label(idempotence_k5_nat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4387 (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]. 80.59/78.61 4388 (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]. 80.59/78.61 4389 (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]. 80.59/78.61 4390 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4391 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4392 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4393 (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]. 80.59/78.61 4394 (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]. 80.59/78.61 4395 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4396 (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]. 80.59/78.61 4397 (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]. 80.59/78.61 4398 (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]. 80.59/78.61 4399 (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]. 80.59/78.61 4400 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4401 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4402 (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]. 80.59/78.61 4403 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4404 (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]. 80.59/78.61 4405 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4406 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4407 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4408 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4409 (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]. 80.59/78.61 4410 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]. 80.59/78.61 4411 (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]. 80.59/78.61 4412 (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]. 80.59/78.61 4413 (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]. 80.59/78.61 4414 (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]. 80.59/78.61 4415 (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]. 80.59/78.61 4416 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4417 (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]. 80.59/78.61 4418 (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]. 80.59/78.61 4419 (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]. 80.59/78.61 4420 (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]. 80.59/78.61 4421 (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]. 80.59/78.61 4422 (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]. 80.59/78.61 4423 (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]. 80.59/78.61 4424 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]. 80.59/78.61 4425 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4426 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4427 (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]. 80.59/78.61 4428 (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]. 80.59/78.61 4429 (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]. 80.59/78.61 4430 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4431 (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]. 80.59/78.61 4432 (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]. 80.59/78.61 4433 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4434 (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]. 80.59/78.61 4435 (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]. 80.59/78.61 4436 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4437 (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]. 80.59/78.61 4438 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4439 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4440 (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]. 80.59/78.61 4441 (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]. 80.59/78.61 4442 (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]. 80.59/78.61 4443 (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]. 80.59/78.61 4444 (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]. 80.59/78.61 4445 (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]. 80.59/78.61 4446 (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]. 80.59/78.61 4447 (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]. 80.59/78.61 4448 (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]. 80.59/78.61 4449 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4450 (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]. 80.59/78.61 4451 (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]. 80.59/78.61 4452 (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]. 80.59/78.61 4453 (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]. 80.59/78.61 4454 (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]. 80.59/78.61 4455 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4456 (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]. 80.59/78.61 4457 (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]. 80.59/78.61 4458 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4459 (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]. 80.59/78.61 4460 (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]. 80.59/78.61 4461 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4462 (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]. 80.59/78.61 4463 (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]. 80.59/78.61 4464 (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]. 80.59/78.61 4465 (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]. 80.59/78.61 4466 (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]. 80.59/78.61 4467 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.61 4468 (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]. 80.59/78.62 4469 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4470 (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]. 80.59/78.62 4471 (all A (v1_int_1(A) -> v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4472 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]. 80.59/78.62 4473 (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]. 80.59/78.62 4474 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4475 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4476 (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]. 80.59/78.62 4477 (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]. 80.59/78.62 4478 (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]. 80.59/78.62 4479 (all A (v1_int_1(A) -> np__0 = k5_int_1(A,np__0))) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4480 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4481 (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]. 80.59/78.62 4482 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4483 (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]. 80.59/78.62 4484 (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]. 80.59/78.62 4485 (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]. 80.59/78.62 4486 (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]. 80.59/78.62 4487 (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]. 80.59/78.62 4488 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4489 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4490 (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]. 80.59/78.62 4491 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4492 (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]. 80.59/78.62 4493 (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]. 80.59/78.62 4494 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4495 (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]. 80.59/78.62 4496 (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]. 80.59/78.62 4497 (all A (v1_int_1(A) -> np__0 = k6_int_1(A,A))) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4498 (all A (r2_hidden(A,k4_numbers) <-> v1_int_1(A))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4499 (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]. 80.59/78.62 4500 (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]. 80.59/78.62 4501 (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]. 80.59/78.62 4502 (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]. 80.59/78.62 4503 (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]. 80.59/78.62 4504 (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]. 80.59/78.62 4505 (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]. 80.59/78.62 4506 (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]. 80.59/78.62 4507 (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]. 80.59/78.62 4508 (all A (v1_rat_1(A) -> -(r1_xreal_0(np__1,A) & -r1_xreal_0(k1_rat_1(A),k2_rat_1(A))) & -(-r1_xreal_0(np__1,A) & r1_xreal_0(k1_rat_1(A),k2_rat_1(A))))) # label(t72_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4509 $T # label(t82_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4510 $T # label(t85_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4511 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (k4_xcmplx_0(k2_rat_1(A)) = k1_rat_1(B) & k2_rat_1(B) = k1_real_1(k1_rat_1(A)) -> -r1_xreal_0(np__0,A) & B = k7_xcmplx_0(np__1,A)) & (B = k7_xcmplx_0(np__1,A) -> r1_xreal_0(np__0,A) | k4_xcmplx_0(k2_rat_1(A)) = k1_rat_1(B) & k2_rat_1(B) = k1_real_1(k1_rat_1(A))))))) # label(t89_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4512 $T # label(t13_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4513 (all A (v1_rat_1(A) -> v1_rat_1(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc18_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4514 (all A (r2_hidden(A,k3_numbers) <-> v1_rat_1(A))) # label(d2_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4515 (exists A v1_rat_1(A)) # label(rc2_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4516 $T # label(t55_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4517 $T # label(t70_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4518 $T # label(t4_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4519 (all A (v1_rat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B = k1_rat_1(A) <-> B != np__0 & (exists C (k7_xcmplx_0(C,B) = A & v1_int_1(C))) & (all C (v1_int_1(C) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k7_xcmplx_0(C,D) = A -> np__0 = D | r1_xreal_0(B,D))))))))))) # label(d3_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4520 (all A (v1_rat_1(A) -> (r1_xreal_0(k2_rat_1(A),np__0) <-> r1_xreal_0(A,np__0)))) # label(t77_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4521 $T # label(t17_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4522 (all A all B (v1_int_1(A) & v1_rat_1(B) -> v1_rat_1(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc8_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4523 (all A (v1_rat_1(A) -> (exists B (v1_int_1(B) & (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & np__0 != C & k7_xcmplx_0(B,C) = A)))))) # label(t24_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4524 (all A (v1_rat_1(A) -> k3_xcmplx_0(k1_rat_1(A),A) = k2_rat_1(A))) # label(d4_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4525 (all A (A = k3_numbers <-> (all B ((exists C (v1_int_1(C) & (exists D (B = k7_xcmplx_0(C,D) & v1_int_1(D))))) <-> r2_hidden(B,A))))) # label(d1_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4526 $T # label(t14_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4527 (all A (v1_rat_1(A) -> m2_subset_1(k1_rat_1(A),k1_numbers,k5_numbers))) # label(dt_k1_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4528 (all A all B (v1_int_1(A) & v1_rat_1(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_rat_1(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc7_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4529 (all A (v1_rat_1(A) -> (k1_rat_1(A) = np__1 <-> A = k2_rat_1(A)))) # label(t42_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4530 $T # label(t28_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4531 (all A (v1_rat_1(A) -> (r1_xreal_0(k2_rat_1(A),k1_real_1(k1_rat_1(A))) <-> r1_xreal_0(A,k1_real_1(np__1))))) # label(t65_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4532 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v1_rat_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc1_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4533 $T # label(t15_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4534 $T # label(t39_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4535 $T # label(t83_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4536 (all A (v1_rat_1(A) -> -(v1_int_1(A) & -r1_xreal_0(np__1,k2_real_1(k1_rat_1(A)))) & -(-v1_int_1(A) & r1_xreal_0(np__1,k2_real_1(k1_rat_1(A)))))) # label(t46_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4537 (all A (v1_rat_1(A) -> (exists B (v1_int_1(B) & (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & k7_xcmplx_0(B,C) = A & (all D (v1_int_1(D) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (k7_xcmplx_0(D,E) = A -> E = np__0 | r1_xreal_0(C,E)))))) & C != np__0)))))) # label(t25_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4538 (all A all B (m1_subset_1(B,k5_numbers) & v1_rat_1(A) -> v1_rat_1(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc10_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4539 (all A (v1_rat_1(A) -> A = k7_xcmplx_0(k2_rat_1(A),k1_rat_1(A)) & A = k3_xcmplx_0(k2_real_1(k1_rat_1(A)),k2_rat_1(A)) & k3_xcmplx_0(k2_rat_1(A),k2_real_1(k1_rat_1(A))) = A)) # label(t37_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4540 $T # label(t10_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4541 $T # label(t23_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4542 (all A (v1_rat_1(A) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc1_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4543 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_rat_1(C) -> -(C = k7_xcmplx_0(A,B) & B != np__0 & (all D (v1_int_1(D) -> -(B = k3_xcmplx_0(k1_rat_1(C),D) & k3_xcmplx_0(k2_rat_1(C),D) = A)))))))))) # label(t61_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4544 (all A (v1_rat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r1_xreal_0(B,np__1) & (exists C (v1_int_1(C) & (exists D (k2_nat_1(D,B) = k1_rat_1(A) & k3_xcmplx_0(C,B) = k2_rat_1(A) & m2_subset_1(D,k1_numbers,k5_numbers)))))))))) # label(t62_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4545 (all A (v1_rat_1(A) -> (k1_real_1(np__1) = A <-> k1_real_1(k1_rat_1(A)) = k2_rat_1(A)))) # label(t48_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4546 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> -(r1_xreal_0(B,A) & -r1_xreal_0(k3_xcmplx_0(k2_rat_1(B),k1_rat_1(A)),k3_xcmplx_0(k2_rat_1(A),k1_rat_1(B)))) & -(r1_xreal_0(k3_xcmplx_0(k2_rat_1(B),k1_rat_1(A)),k3_xcmplx_0(k2_rat_1(A),k1_rat_1(B))) & -r1_xreal_0(B,A)))))) # label(t86_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4547 (all A (v1_int_1(A) -> v1_rat_1(A))) # label(t7_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4548 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (B = k7_xcmplx_0(np__1,A) -> r1_xreal_0(A,np__0) | k1_rat_1(B) = k2_rat_1(A) & k1_rat_1(A) = k2_rat_1(B)) & (k1_rat_1(B) = k2_rat_1(A) & k2_rat_1(B) = k1_rat_1(A) -> -r1_xreal_0(A,np__0) & B = k7_xcmplx_0(np__1,A)))))) # label(t88_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4549 (all A (v1_rat_1(A) -> -(-r1_xreal_0(k1_real_1(np__1),A) & r1_xreal_0(k1_real_1(k1_rat_1(A)),k2_rat_1(A))) & -(-r1_xreal_0(k1_real_1(k1_rat_1(A)),k2_rat_1(A)) & r1_xreal_0(k1_real_1(np__1),A)))) # label(t64_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4550 $T # label(t20_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4551 (all A (v1_rat_1(A) -> (A != np__0 -> k7_xcmplx_0(k2_rat_1(A),A) = k1_rat_1(A)))) # label(t38_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4552 $T # label(t5_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4553 (all A (v1_rat_1(A) -> -(-r1_xreal_0(k1_real_1(np__1),A) & r1_xreal_0(k4_xcmplx_0(k2_rat_1(A)),k1_rat_1(A))) & -(-r1_xreal_0(k4_xcmplx_0(k2_rat_1(A)),k1_rat_1(A)) & r1_xreal_0(k1_real_1(np__1),A)))) # label(t66_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4554 $T # label(t43_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4555 $T # label(t56_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4556 (all A -(v1_rat_1(A) & (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> -(k7_xcmplx_0(B,C) = A & C != np__0))))))) # label(t3_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4557 (all A ((exists B ((exists C (k7_xcmplx_0(B,C) = A & v1_int_1(C))) & v1_int_1(B))) -> v1_rat_1(A))) # label(t6_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4558 (all A (v1_rat_1(A) -> -(r1_xreal_0(np__0,k2_rat_1(A)) & -r1_xreal_0(np__0,A)) & -(r1_xreal_0(np__0,A) & -r1_xreal_0(np__0,k2_rat_1(A))))) # label(t76_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4559 $T # label(t78_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4560 (all A (v1_rat_1(A) -> (k1_rat_1(A) = np__1 | A = k2_rat_1(A) -> v1_int_1(A)))) # label(t41_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4561 (all A (v1_rat_1(A) -> v1_int_1(k2_rat_1(A)))) # label(dt_k2_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4562 (exists A (v1_rat_1(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & m1_subset_1(A,k1_numbers))) # label(rc1_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4563 (all A (v1_rat_1(A) -> (k1_rat_1(A) = k2_rat_1(A) <-> A = np__1))) # label(t47_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4564 (all A all B (m1_subset_1(A,k5_numbers) & v1_rat_1(B) -> v1_rat_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc15_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4565 $T # label(t8_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4566 (all A (v1_rat_1(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_rat_1(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc16_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4567 $T # label(t26_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4568 $T # label(t2_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4569 (all A (v1_rat_1(A) -> v1_rat_1(k5_xcmplx_0(A)))) # label(t21_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4570 (all A (v1_int_1(A) -> v1_xreal_0(A) & v1_rat_1(A) & v1_xcmplx_0(A))) # label(cc2_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4571 (all A (v1_rat_1(A) -> (r1_xreal_0(k1_rat_1(A),k4_xcmplx_0(k2_rat_1(A))) <-> r1_xreal_0(A,k1_real_1(np__1))))) # label(t67_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4572 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -((all C (v1_rat_1(C) -> -(-r1_xreal_0(C,A) & -r1_xreal_0(B,C)))) & -r1_xreal_0(B,A)))))) # label(t22_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4573 $T # label(t19_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4574 (all A (v1_rat_1(A) -> -(-v1_int_1(A) & r1_xreal_0(k1_rat_1(A),np__1)) & -(v1_int_1(A) & -r1_xreal_0(k1_rat_1(A),np__1)))) # label(t45_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4575 (all A all B (m1_subset_1(B,k5_numbers) & v1_rat_1(A) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_rat_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc11_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4576 $T # label(t57_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4577 $T # label(t75_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4578 (all A (v1_rat_1(A) -> (v1_int_1(A) -> k1_rat_1(A) = np__1 & A = k2_rat_1(A)))) # label(t40_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4579 $T # label(t11_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4580 (all A all B (m1_subset_1(A,k5_numbers) & v1_rat_1(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_rat_1(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc14_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4581 (all A all B (v1_int_1(A) & v1_rat_1(B) -> v1_rat_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc9_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4582 $T # label(t9_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4583 (all A (v1_rat_1(A) -> r1_xreal_0(np__1,k1_rat_1(A)))) # label(t29_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4584 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_rat_1(C) -> -((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(k3_xcmplx_0(k2_rat_1(C),D) = B & k2_nat_1(k1_rat_1(C),D) = A))) & C = k7_xcmplx_0(B,A) & np__0 != A))))))) # label(t60_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4585 $T # label(t52_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4586 $T # label(t69_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4587 (all A (v1_rat_1(A) -> (k2_rat_1(A) = np__0 <-> A = np__0))) # label(t36_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4588 (all A (v1_rat_1(A) -> (r1_xreal_0(k2_rat_1(A),k1_rat_1(A)) <-> r1_xreal_0(A,np__1)))) # label(t73_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4589 $T # label(t54_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4590 (all A all B (v1_rat_1(A) & v1_int_1(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_rat_1(k3_xcmplx_0(A,B)))) # label(fc6_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4591 $T # label(t71_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4592 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (k1_rat_1(A) = k1_rat_1(B) & k2_rat_1(B) = k2_rat_1(A) -> A = B))))) # label(t84_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4593 (all A (v1_rat_1(A) -> (r1_xreal_0(np__0,A) -> np__1 != k1_rat_1(A) & A != k2_rat_1(A) | m2_subset_1(A,k1_numbers,k5_numbers)))) # label(t44_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4594 (all A all B (v1_int_1(B) & v1_rat_1(A) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_rat_1(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc4_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4595 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_rat_1(C) -> (k7_xcmplx_0(B,A) = C & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -((exists E (v1_int_1(E) & (exists F (m2_subset_1(F,k1_numbers,k5_numbers) & B = k3_xcmplx_0(E,D) & A = k2_nat_1(F,D))))) & -r1_xreal_0(D,np__1)))) -> np__0 = A | k1_rat_1(C) = A & B = k2_rat_1(C)))))))) # label(t63_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4596 (all A (v1_rat_1(A) -> r1_xreal_0(k2_real_1(k1_rat_1(A)),np__1))) # label(t34_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4597 $T # label(t32_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4598 (all A all B (v1_rat_1(A) & v1_int_1(B) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_rat_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc5_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4599 (all A (v1_rat_1(A) -> -r1_xreal_0(k2_real_1(k1_rat_1(A)),np__0))) # label(t30_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4600 $T # label(t33_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4601 $T # label(t68_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4602 (all A all B (v1_rat_1(B) & v1_rat_1(A) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_rat_1(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc2_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4603 $T # label(t59_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4604 $T # label(t18_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4605 (all A all B (m1_subset_1(A,k5_numbers) & v1_rat_1(B) -> v1_rat_1(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc13_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4606 (all A (v1_xreal_0(A) -> (all B (v1_rat_1(B) -> (r1_xreal_0(k3_xcmplx_0(A,k1_rat_1(B)),k2_rat_1(B)) <-> r1_xreal_0(A,B)))))) # label(t81_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4607 $T # label(t74_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4608 $T # label(t79_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4609 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_rat_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc3_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4610 (all A (v1_int_1(A) -> (all B (v1_rat_1(B) -> (A != np__0 -> B = k7_xcmplx_0(k3_xcmplx_0(k2_rat_1(B),A),k3_xcmplx_0(k1_rat_1(B),A))))))) # label(t50_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4611 $T # label(t31_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4612 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> v1_rat_1(k7_xcmplx_0(A,B)))))) # label(t16_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4613 (all A (v1_rat_1(A) -> k1_rat_1(A) = k1_rat_1(k4_xcmplx_0(A)) & k2_rat_1(k4_xcmplx_0(A)) = k4_xcmplx_0(k2_rat_1(A)))) # label(t87_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4614 $T # label(t35_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4615 $T # label(t51_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4616 (all A (v1_rat_1(A) -> -r1_xreal_0(k1_rat_1(A),np__0))) # label(t27_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4617 (all A -((all B (v1_int_1(B) -> (all C (v1_int_1(C) -> -(k7_xcmplx_0(B,C) = A & np__0 != C))))) & r2_hidden(A,k3_numbers))) # label(t1_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4618 $T # label(t12_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4619 $T # label(t58_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4620 (all A (v1_xreal_0(A) -> (all B (v1_rat_1(B) -> -(-r1_xreal_0(B,A) & r1_xreal_0(k2_rat_1(B),k3_xcmplx_0(A,k1_rat_1(B)))) & -(-r1_xreal_0(k2_rat_1(B),k3_xcmplx_0(A,k1_rat_1(B))) & r1_xreal_0(B,A)))))) # label(t80_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4621 (all A all B (m1_subset_1(B,k5_numbers) & v1_rat_1(A) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_rat_1(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc12_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4622 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & v1_rat_1(k7_xcmplx_0(A,B)))) # label(fc17_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4623 (all A (v1_rat_1(A) -> (k4_xcmplx_0(k2_rat_1(A)) = k1_rat_1(A) <-> k1_real_1(np__1) = A))) # label(t49_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4624 $T # label(t53_rat_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4625 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k17_binop_2(A,B),k3_numbers))) # label(dt_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4626 (all A (v1_funct_1(A) & m2_relset_1(A,k3_numbers,k3_numbers) & v1_funct_2(A,k3_numbers,k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> k14_binop_2(B) = k8_funct_2(k3_numbers,k3_numbers,A,B))) <-> k38_binop_2 = A))) # label(d14_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4627 (all A (m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k4_binop_2(B,C))))) <-> A = k28_binop_2))) # label(d4_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4628 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> (A = k30_binop_2 <-> (all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k6_binop_2(B,C) = k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C)))))))) # label(d6_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4629 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k22_binop_2(A,B) = k22_binop_2(B,A))) # label(commutativity_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4630 (all A (m1_subset_1(A,k2_numbers) -> k4_xcmplx_0(A) = k1_binop_2(A))) # label(redefinition_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4631 (all A (m1_subset_1(A,k1_numbers) -> k8_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4632 (all A (v1_funct_1(A) & m2_relset_1(A,f1_s1_binop_2,f2_s1_binop_2) & v1_funct_2(A,f1_s1_binop_2,f2_s1_binop_2) -> (all B (v1_funct_1(B) & v1_funct_2(B,f1_s1_binop_2,f2_s1_binop_2) & m2_relset_1(B,f1_s1_binop_2,f2_s1_binop_2) -> ((all C (m1_subset_1(C,f1_s1_binop_2) -> f3_s1_binop_2(C) = k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,B,C))) & (all C (m1_subset_1(C,f1_s1_binop_2) -> f3_s1_binop_2(C) = k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,A,C))) -> A = B))))) # label(s1_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4633 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k21_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4634 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k3_xcmplx_0(A,B) = k24_binop_2(A,B))) # label(redefinition_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4635 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k24_binop_2(B,C) = k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C))))) <-> A = k48_binop_2))) # label(d24_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4636 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k12_binop_2(A,B),k1_numbers))) # label(dt_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4637 (all A (m2_relset_1(A,k2_numbers,k2_numbers) & v1_funct_2(A,k2_numbers,k2_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k2_numbers) -> k8_funct_2(k2_numbers,k2_numbers,A,B) = k2_binop_2(B))) <-> k26_binop_2 = A))) # label(d2_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4638 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k16_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k16_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4639 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k10_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k10_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4640 (all A (v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k16_binop_2(B,C))))) <-> A = k40_binop_2))) # label(d16_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4641 (all A (m1_subset_1(A,k3_numbers) -> k14_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4642 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k2_xcmplx_0(A,B) = k15_binop_2(A,B))) # label(redefinition_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4643 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k10_binop_2(A,B),k1_numbers))) # label(dt_k10_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4644 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k11_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4645 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k5_binop_2(A,B) = k5_binop_2(B,A))) # label(commutativity_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4646 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k18_binop_2(B,C))))) <-> A = k42_binop_2))) # label(d18_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4647 (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) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k9_binop_2(B,C))))) <-> A = k33_binop_2))) # label(d9_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4648 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k3_binop_2(B,A) = k3_binop_2(A,B))) # label(commutativity_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4649 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k8_binop_2(A),k1_numbers))) # label(dt_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4650 (all A (m1_subset_1(A,k1_numbers) -> k4_xcmplx_0(A) = k7_binop_2(A))) # label(redefinition_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4651 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k23_binop_2(B,A) = k23_binop_2(A,B))) # label(commutativity_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4652 (all A (m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k15_binop_2(B,C))))) <-> k39_binop_2 = A))) # label(d15_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4653 (all A (m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> (A = k44_binop_2 <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k20_binop_2(B,C) = k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C)))))))) # label(d20_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4654 (all A (v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_1(A) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k23_binop_2(B,C) = k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C))))) <-> A = k47_binop_2))) # label(d23_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4655 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k16_binop_2(A,B),k3_numbers))) # label(dt_k16_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4656 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k2_xcmplx_0(A,B) = k9_binop_2(A,B))) # label(redefinition_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4657 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k2_xcmplx_0(A,B) = k23_binop_2(A,B))) # label(redefinition_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4658 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> m1_subset_1(k18_binop_2(A,B),k3_numbers))) # label(dt_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4659 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k11_binop_2(A,B) = k11_binop_2(B,A))) # label(commutativity_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4660 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k7_binop_2(A),k1_numbers))) # label(dt_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4661 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k9_binop_2(A,B),k1_numbers))) # label(dt_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4662 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k18_binop_2(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4663 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k5_binop_2(A,B),k2_numbers))) # label(dt_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4664 (all A (m2_relset_1(A,k3_numbers,k3_numbers) & v1_funct_2(A,k3_numbers,k3_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k3_numbers) -> k13_binop_2(B) = k8_funct_2(k3_numbers,k3_numbers,A,B))) <-> k37_binop_2 = A))) # label(d13_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4665 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k2_xcmplx_0(A,B) = k3_binop_2(A,B))) # label(redefinition_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4666 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> m1_subset_1(k20_binop_2(A,B),k4_numbers))) # label(dt_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4667 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> (A = k27_binop_2 <-> (all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k3_binop_2(B,C)))))))) # label(d3_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4668 (all A (m1_subset_1(A,k1_numbers) -> k8_binop_2(k8_binop_2(A)) = A)) # label(involutiveness_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4669 (all A (m1_subset_1(A,k3_numbers) -> m1_subset_1(k14_binop_2(A),k3_numbers))) # label(dt_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4670 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k11_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C))))) <-> A = k35_binop_2))) # label(d11_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4671 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> ((all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k5_binop_2(B,C))))) <-> k29_binop_2 = A))) # label(d5_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4672 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> k20_binop_2(A,B) = k20_binop_2(B,A))) # label(commutativity_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4673 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> (A = k41_binop_2 <-> (all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k17_binop_2(B,C) = k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C)))))))) # label(d17_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4674 (all A (m1_subset_1(A,k2_numbers) -> A = k2_binop_2(k2_binop_2(A)))) # label(involutiveness_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4675 (all A (m1_subset_1(A,k3_numbers) -> m1_subset_1(k13_binop_2(A),k3_numbers))) # label(dt_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4676 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k17_binop_2(A,B) = k17_binop_2(B,A))) # label(commutativity_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4677 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k1_binop_2(A),k2_numbers))) # label(dt_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4678 (all A (m1_subset_1(A,k2_numbers) -> A = k1_binop_2(k1_binop_2(A)))) # label(involutiveness_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4679 (all A (v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k21_binop_2(B,C) = k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C))))) <-> k45_binop_2 = A))) # label(d21_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4680 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers))) # label(dt_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4681 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k3_binop_2(A,B),k2_numbers))) # label(dt_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4682 (all A (m1_subset_1(A,k3_numbers) -> A = k13_binop_2(k13_binop_2(A)))) # label(involutiveness_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4683 (all A (m1_subset_1(A,k3_numbers) -> v1_xreal_0(A) & v1_rat_1(A) & v1_xcmplx_0(A))) # label(cc1_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4684 (all A (m1_subset_1(A,k3_numbers) -> A = k14_binop_2(k14_binop_2(A)))) # label(involutiveness_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4685 (all A (m1_subset_1(A,k4_numbers) -> m1_subset_1(k19_binop_2(A),k4_numbers))) # label(dt_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4686 (all A (v1_funct_2(A,k1_numbers,k1_numbers) & m2_relset_1(A,k1_numbers,k1_numbers) & v1_funct_1(A) -> (k31_binop_2 = A <-> (all B (m1_subset_1(B,k1_numbers) -> k7_binop_2(B) = k8_funct_2(k1_numbers,k1_numbers,A,B)))))) # label(d7_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.62 4687 (all A (v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_1(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_2(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_1(B) -> ((all C (m1_subset_1(C,f1_s2_binop_2) -> (all D (m1_subset_1(D,f1_s2_binop_2) -> f2_s2_binop_2(C,D) = k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,A,C,D))))) & (all C (m1_subset_1(C,f1_s2_binop_2) -> (all D (m1_subset_1(D,f1_s2_binop_2) -> f2_s2_binop_2(C,D) = k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,B,C,D))))) -> A = B))))) # label(s2_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4688 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k2_binop_2(A),k2_numbers))) # label(dt_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4689 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> m1_subset_1(k15_binop_2(A,B),k3_numbers))) # label(dt_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4690 (all A (m1_subset_1(A,k4_numbers) -> A = k19_binop_2(k19_binop_2(A)))) # label(involutiveness_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4691 (all A (v1_funct_2(A,k2_numbers,k2_numbers) & m2_relset_1(A,k2_numbers,k2_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k2_numbers) -> k8_funct_2(k2_numbers,k2_numbers,A,B) = k1_binop_2(B))) <-> A = k25_binop_2))) # label(d1_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4692 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> m1_subset_1(k21_binop_2(A,B),k4_numbers))) # label(dt_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4693 (all A (m1_subset_1(A,k3_numbers) -> k13_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4694 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k6_binop_2(A,B),k2_numbers))) # label(dt_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4695 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k3_xcmplx_0(A,B) = k17_binop_2(A,B))) # label(redefinition_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4696 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> m2_subset_1(k24_binop_2(A,B),k1_numbers,k5_numbers))) # label(dt_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4697 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k7_xcmplx_0(A,B) = k6_binop_2(A,B))) # label(redefinition_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4698 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k4_binop_2(A,B),k2_numbers))) # label(dt_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4699 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k9_binop_2(A,B) = k9_binop_2(B,A))) # label(commutativity_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4700 (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) -> (A = k36_binop_2 <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k12_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C)))))))) # label(d12_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4701 (all A (v1_funct_1(A) & m2_relset_1(A,k4_numbers,k4_numbers) & v1_funct_2(A,k4_numbers,k4_numbers) -> ((all B (m1_subset_1(B,k4_numbers) -> k19_binop_2(B) = k8_funct_2(k4_numbers,k4_numbers,A,B))) <-> k43_binop_2 = A))) # label(d19_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4702 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k3_xcmplx_0(A,B) = k22_binop_2(A,B))) # label(redefinition_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4703 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k20_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4704 (all A (m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> (k34_binop_2 = A <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k10_binop_2(B,C)))))))) # label(d10_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4705 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> m1_subset_1(k22_binop_2(A,B),k4_numbers))) # label(dt_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4706 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) -> ((all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k22_binop_2(B,C))))) <-> k46_binop_2 = A))) # label(d22_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4707 (all A (m1_subset_1(A,k4_numbers) -> k4_xcmplx_0(A) = k19_binop_2(A))) # label(redefinition_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4708 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k12_binop_2(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4709 (all A (m1_subset_1(A,k2_numbers) -> k2_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4710 (all A (v1_funct_1(A) & v1_funct_2(A,k1_numbers,k1_numbers) & m2_relset_1(A,k1_numbers,k1_numbers) -> (A = k32_binop_2 <-> (all B (m1_subset_1(B,k1_numbers) -> k8_binop_2(B) = k8_funct_2(k1_numbers,k1_numbers,A,B)))))) # label(d8_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4711 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k24_binop_2(A,B) = k24_binop_2(B,A))) # label(commutativity_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4712 (all A (m1_subset_1(A,k1_numbers) -> A = k7_binop_2(k7_binop_2(A)))) # label(involutiveness_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4713 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k15_binop_2(B,A) = k15_binop_2(A,B))) # label(commutativity_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4714 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k3_xcmplx_0(A,B) = k5_binop_2(A,B))) # label(redefinition_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4715 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k4_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4716 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k11_binop_2(A,B),k1_numbers))) # label(dt_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4717 (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]. 80.59/78.63 4718 (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]. 80.59/78.63 4719 (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]. 80.59/78.63 4720 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4721 (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]. 80.59/78.63 4722 (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]. 80.59/78.63 4723 (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]. 80.59/78.63 4724 (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]. 80.59/78.63 4725 (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]. 80.59/78.63 4726 (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]. 80.59/78.63 4727 (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]. 80.59/78.63 4728 (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]. 80.59/78.63 4729 (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]. 80.59/78.63 4730 (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]. 80.59/78.63 4731 (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]. 80.59/78.63 4732 (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]. 80.59/78.63 4733 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4734 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4735 (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]. 80.59/78.63 4736 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4737 (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]. 80.59/78.63 4738 (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]. 80.59/78.63 4739 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4740 (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]. 80.59/78.63 4741 (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]. 80.59/78.63 4742 (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]. 80.59/78.63 4743 (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]. 80.59/78.63 4744 (all A ((all B (r2_hidden(B,A) -> v1_int_1(B))) <-> v4_membered(A))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4745 (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]. 80.59/78.63 4746 (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]. 80.59/78.63 4747 (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]. 80.59/78.63 4748 (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]. 80.59/78.63 4749 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4750 (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]. 80.59/78.63 4751 (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]. 80.59/78.63 4752 (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]. 80.59/78.63 4753 (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]. 80.59/78.63 4754 (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]. 80.59/78.63 4755 (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]. 80.59/78.63 4756 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4757 (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]. 80.59/78.63 4758 (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]. 80.59/78.63 4759 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4760 (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]. 80.59/78.63 4761 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4762 (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]. 80.59/78.63 4763 (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]. 80.59/78.63 4764 (all A (v1_membered(A) <-> (all B (r2_hidden(B,A) -> v1_xcmplx_0(B))))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4765 (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]. 80.59/78.63 4766 (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]. 80.59/78.63 4767 (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]. 80.59/78.63 4768 (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]. 80.59/78.63 4769 (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]. 80.59/78.63 4770 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4771 (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]. 80.59/78.63 4772 (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]. 80.59/78.63 4773 (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]. 80.59/78.63 4774 (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]. 80.59/78.63 4775 (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]. 80.59/78.63 4776 (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]. 80.59/78.63 4777 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4778 (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]. 80.59/78.63 4779 (all A ((all B (r2_hidden(B,A) -> v4_ordinal2(B))) <-> v5_membered(A))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4780 (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]. 80.59/78.63 4781 (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]. 80.59/78.63 4782 (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]. 80.59/78.63 4783 (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]. 80.59/78.63 4784 (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]. 80.59/78.63 4785 (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]. 80.59/78.63 4786 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4787 (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]. 80.59/78.63 4788 (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]. 80.59/78.63 4789 (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]. 80.59/78.63 4790 (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]. 80.59/78.63 4791 (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]. 80.59/78.63 4792 (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]. 80.59/78.63 4793 (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]. 80.59/78.63 4794 (all A ((all B (r2_hidden(B,A) -> v1_rat_1(B))) <-> v3_membered(A))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4795 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4796 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4797 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4798 (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]. 80.59/78.63 4799 (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]. 80.59/78.63 4800 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4801 (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]. 80.59/78.63 4802 (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]. 80.59/78.63 4803 (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]. 80.59/78.63 4804 (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]. 80.59/78.63 4805 (all A ((all B (r2_hidden(B,A) -> v1_xreal_0(B))) <-> v2_membered(A))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4806 (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]. 80.59/78.63 4807 (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]. 80.59/78.63 4808 (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]. 80.59/78.63 4809 (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]. 80.59/78.63 4810 (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]. 80.59/78.63 4811 (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]. 80.59/78.63 4812 (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]. 80.59/78.63 4813 (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]. 80.59/78.63 4814 (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]. 80.59/78.63 4815 (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]. 80.59/78.63 4816 (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]. 80.59/78.63 4817 (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]. 80.59/78.63 4818 (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]. 80.59/78.63 4819 (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]. 80.59/78.63 4820 (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]. 80.59/78.63 4821 (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]. 80.59/78.63 4822 (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]. 80.59/78.63 4823 (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]. 80.59/78.63 4824 (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]. 80.59/78.63 4825 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4826 (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]. 80.59/78.63 4827 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4828 (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]. 80.59/78.63 4829 (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]. 80.59/78.63 4830 (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]. 80.59/78.63 4831 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4832 (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]. 80.59/78.63 4833 (all A (m1_subset_1(A,k2_numbers) -> k4_xcmplx_0(A) = k10_complex1(A))) # label(redefinition_k10_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4834 $T # label(t89_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4835 $T # label(t95_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4836 (all A (m1_subset_1(A,k1_numbers) -> A = k4_complex1(k3_xcmplx_0(A,k7_complex1)))) # label(t26_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4837 (all A (v1_xcmplx_0(A) -> k1_real_1(k3_complex1(A)) = k3_complex1(k4_xcmplx_0(A)) & k1_real_1(k4_complex1(A)) = k4_complex1(k4_xcmplx_0(A)))) # label(t34_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4838 (all A (m1_subset_1(A,k2_numbers) -> (np__0 = k3_complex1(A) -> k4_complex1(A) = np__0 | k1_real_1(k2_real_1(k4_complex1(A))) = k4_complex1(k12_complex1(A)) & np__0 = k3_complex1(k12_complex1(A))))) # label(t80_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4839 (all A (m1_subset_1(A,k2_numbers) -> k4_real_1(np__2,k3_complex1(A)) = k3_complex1(k8_complex1(A,k15_complex1(A))) & k4_complex1(k8_complex1(A,k15_complex1(A))) = np__0)) # label(t127_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4840 (all A (m1_subset_1(A,k2_numbers) -> k4_real_1(np__2,k4_real_1(k3_complex1(A),k4_complex1(A))) = k4_complex1(k9_complex1(A,A)) & k3_complex1(k9_complex1(A,A)) = k5_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))))) # label(t32_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4841 $T # label(t4_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4842 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_complex1(k3_xcmplx_0(A,B)) = k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k3_complex1(B),k4_complex1(A))) & k3_complex1(k3_xcmplx_0(A,B)) = k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))))))) # label(t24_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4843 (all A (v1_xcmplx_0(A) -> k6_real_1(k1_real_1(k4_complex1(A)),k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A)))) = k4_complex1(k5_xcmplx_0(A)) & k6_real_1(k3_complex1(A),k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A)))) = k3_complex1(k5_xcmplx_0(A)))) # label(t64_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4844 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k17_complex1(k6_xcmplx_0(B,A)) = k17_complex1(k6_xcmplx_0(A,B)))))) # label(t146_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4845 (all A (m1_subset_1(A,k2_numbers) -> k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_xcmplx_0(k1_real_1(k4_complex1(A)),k7_complex1)) = k10_complex1(A))) # label(d11_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4846 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> r1_xreal_0(k17_complex1(k6_xcmplx_0(A,B)),k3_real_1(k17_complex1(A),k17_complex1(B))))))) # label(t143_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4847 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k17_complex1(k6_xcmplx_0(A,B)) = np__0 <-> A = B))))) # label(t147_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4848 $T # label(t83_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4849 $T # label(t100_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4850 $T # label(t69_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4851 $T # label(t111_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4852 $T # label(t59_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4853 $T # label(t21_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4854 $T # label(t46_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4855 $T # label(t84_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4856 $T # label(t10_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4857 (all A (v1_xreal_0(A) -> r1_xreal_0(k1_real_1(k17_complex1(A)),A) & r1_xreal_0(A,k17_complex1(A)))) # label(t162_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4858 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_complex1(k2_xcmplx_0(A,B)) = k3_real_1(k4_complex1(A),k4_complex1(B)) & k3_real_1(k3_complex1(A),k3_complex1(B)) = k3_complex1(k2_xcmplx_0(A,B)))))) # label(t19_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4859 (all A (v1_funct_2(A,np__2,k1_numbers) & m2_relset_1(A,np__2,k1_numbers) & v1_funct_1(A) -> (exists B ((exists C (m1_subset_1(C,k1_numbers) & A = k5_funct_4(k1_numbers,np__0,np__1,B,C))) & m1_subset_1(B,k1_numbers))))) # label(t5_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4860 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k11_complex1(k15_complex1(A),k15_complex1(B)) = k15_complex1(k11_complex1(A,B)))))) # label(t120_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4861 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,np__0) -> k17_complex1(A) = k4_xcmplx_0(A)))) # label(t156_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4862 $T # label(t50_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4863 (all A (v1_xcmplx_0(A) -> k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))) = k17_complex1(k3_xcmplx_0(A,A)))) # label(t154_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4864 $T # label(t57_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4865 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k4_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = B & k3_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = A)))) # label(t28_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4866 (all A (m1_subset_1(A,k2_numbers) -> v1_xcmplx_0(A))) # label(cc1_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4867 $T # label(t90_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4868 (all A (m1_subset_1(A,k1_numbers) -> k3_complex1(k3_xcmplx_0(A,k7_complex1)) = np__0)) # label(t25_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4869 (all A (v1_xcmplx_0(A) -> r1_xreal_0(k3_complex1(A),k17_complex1(A)))) # label(t140_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4870 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k8_complex1(A,B) = k8_complex1(B,A))) # label(commutativity_k8_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4871 (all A (v1_xcmplx_0(A) -> v1_xreal_0(k16_complex1(A)) & v1_xcmplx_0(k16_complex1(A)))) # label(fc4_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4872 $T # label(t85_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4873 (all A (v1_xcmplx_0(A) -> (k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))) = np__0 <-> np__0 = A))) # label(t13_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4874 $T # label(t93_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4875 (all A (v1_xcmplx_0(A) -> A = k15_complex1(k15_complex1(A)))) # label(involutiveness_k15_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4876 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) = k5_arytm_0(A,B))))) # label(t27_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4877 (all A (v1_xreal_0(A) -> k4_xcmplx_0(A) = k17_complex1(A) | k17_complex1(A) = A)) # label(t157_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4878 (all A (v1_xcmplx_0(A) -> (all B ((r2_hidden(A,k1_numbers) -> (np__0 = B <-> k2_complex1(A) = B)) & (-r2_hidden(A,k1_numbers) -> (k2_complex1(A) = B <-> (exists C (v1_funct_2(C,np__2,k1_numbers) & A = C & B = k1_funct_1(C,np__1) & m2_relset_1(C,np__2,k1_numbers) & v1_funct_1(C))))))))) # label(d3_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4879 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),k17_complex1(k6_xcmplx_0(A,B))),np__2) = k1_square_1(A,B))))) # label(t159_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4880 $T # label(t98_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4881 $T # label(t3_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4882 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_complex1(A) = k4_complex1(B) & k3_complex1(A) = k3_complex1(B) <-> A = B))))) # label(d5_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4883 $T # label(t6_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4884 $T # label(t11_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4885 $T # label(t78_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4886 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> r1_xreal_0(k17_complex1(k5_real_1(k17_complex1(A),k17_complex1(B))),k17_complex1(k6_xcmplx_0(A,B))))))) # label(t150_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4887 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k1_numbers) -> (k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) = k2_xcmplx_0(C,k3_xcmplx_0(D,k7_complex1)) -> B = D & A = C))))))))) # label(t163_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4888 $T # label(t23_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4889 $T # label(t8_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4890 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k8_complex1(k15_complex1(A),k15_complex1(B)) = k15_complex1(k2_xcmplx_0(A,B)))))) # label(t118_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4891 $T # label(t75_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4892 $T # label(t101_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4893 $T # label(t105_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4894 $T # label(d4_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4895 $T # label(t68_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4896 (all A (v1_xcmplx_0(A) -> m1_subset_1(k18_complex1(A),k1_numbers))) # label(dt_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4897 $T # label(t102_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4898 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k14_complex1(A)))) # label(dt_k14_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4899 $T # label(t54_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4900 $T # label(t1_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.63 4901 $T # label(t103_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4902 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k13_complex1(k15_complex1(A),k15_complex1(B)) = k15_complex1(k13_complex1(A,B)))))) # label(t123_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4903 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> r1_xreal_0(k5_real_1(k17_complex1(A),k17_complex1(B)),k17_complex1(k2_xcmplx_0(A,B))))))) # label(t144_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4904 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k11_complex1(A,B),k2_numbers))) # label(dt_k11_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4905 (all A (v1_xcmplx_0(A) -> k17_complex1(k3_xcmplx_0(A,k15_complex1(A))) = k17_complex1(k3_xcmplx_0(A,A)))) # label(t155_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4906 $T # label(t18_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4907 (all A (v1_xcmplx_0(A) -> k17_complex1(A) = k17_complex1(k4_xcmplx_0(A)))) # label(t138_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4908 (all A (v1_xcmplx_0(A) -> -(-r1_xreal_0(k17_complex1(A),np__0) & A = np__0) & -(A != np__0 & r1_xreal_0(k17_complex1(A),np__0)))) # label(t133_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4909 (all A (m1_subset_1(A,k2_numbers) -> A = k12_complex1(k12_complex1(A)))) # label(involutiveness_k12_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4910 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k12_complex1(A),k2_numbers))) # label(dt_k12_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4911 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k11_complex1(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k11_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4912 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 = k3_complex1(A) & np__0 = k3_complex1(B) -> k3_complex1(k3_xcmplx_0(A,B)) = k1_real_1(k4_real_1(k4_complex1(A),k4_complex1(B))) & k4_complex1(k3_xcmplx_0(A,B)) = np__0))))) # label(t31_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4913 $T # label(t104_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4914 $T # label(t99_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4915 $T # label(t49_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4916 $T # label(t108_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4917 (all A (v1_xcmplx_0(A) -> k16_complex1(A) = k17_complex1(A))) # label(redefinition_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4918 $T # label(t45_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4919 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k2_xcmplx_0(A,B) = k8_complex1(A,B))) # label(redefinition_k8_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4920 (all A (v1_xcmplx_0(A) -> k2_real_1(k17_complex1(A)) = k17_complex1(k5_xcmplx_0(A)))) # label(t152_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4921 (all A (v1_xcmplx_0(A) -> m1_subset_1(k4_complex1(A),k1_numbers))) # label(dt_k4_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4922 $T # label(t35_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4923 (all A (v1_xcmplx_0(A) -> k4_complex1(A) = k2_complex1(A))) # label(redefinition_k4_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4924 $T # label(t87_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4925 $T # label(t65_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4926 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k9_complex1(A,B),k2_numbers))) # label(dt_k9_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4927 $T # label(t47_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4928 (all A (v1_xcmplx_0(A) -> (k15_complex1(A) = np__0 -> A = np__0))) # label(t114_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4929 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k2_square_1(A,B) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),k17_complex1(k6_xcmplx_0(A,B))),np__2))))) # label(t160_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4930 $T # label(t43_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4931 $T # label(t55_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4932 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_complex1(A) = np__0 & k4_complex1(B) = np__0 -> k4_real_1(k3_complex1(A),k3_complex1(B)) = k3_complex1(k3_xcmplx_0(A,B)) & k4_complex1(k3_xcmplx_0(A,B)) = np__0))))) # label(t30_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4933 $T # label(t77_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4934 $T # label(t67_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4935 $T # label(d1_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4936 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k5_real_1(k3_complex1(A),k3_complex1(B)) = k3_complex1(k11_complex1(A,B)) & k5_real_1(k4_complex1(A),k4_complex1(B)) = k4_complex1(k11_complex1(A,B)))))) # label(t48_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4937 (all A (v1_xcmplx_0(A) -> k17_complex1(k15_complex1(A)) = k17_complex1(A))) # label(t139_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4938 (all A (v1_xcmplx_0(A) -> (all B ((-r2_hidden(A,k1_numbers) -> ((exists C (v1_funct_1(C) & v1_funct_2(C,np__2,k1_numbers) & C = A & k1_funct_1(C,np__0) = B & m2_relset_1(C,np__2,k1_numbers))) <-> B = k1_complex1(A))) & (r2_hidden(A,k1_numbers) -> (B = k1_complex1(A) <-> B = A)))))) # label(d2_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4939 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k6_real_1(k3_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B)))) = k3_complex1(k13_complex1(A,B)) & k6_real_1(k5_real_1(k4_real_1(k3_complex1(B),k4_complex1(A)),k4_real_1(k3_complex1(A),k4_complex1(B))),k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B)))) = k4_complex1(k13_complex1(A,B)))))) # label(t82_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4940 (all A (m1_subset_1(A,k2_numbers) -> k15_complex1(k12_complex1(A)) = k12_complex1(k15_complex1(A)))) # label(t122_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4941 $T # label(t63_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4942 $T # label(dt_k2_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4943 $T # label(t39_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4944 $T # label(t41_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4945 $T # label(t117_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4946 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k1_complex1(A)) & v1_xreal_0(k1_complex1(A)))) # label(fc1_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4947 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> (np__0 = k4_complex1(B) & np__0 = k4_complex1(A) -> np__0 = k4_complex1(k13_complex1(A,B)) & k6_real_1(k3_complex1(A),k3_complex1(B)) = k3_complex1(k13_complex1(A,B)) | k3_complex1(B) = np__0))))) # label(t109_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4948 $T # label(t76_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4949 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k2_xcmplx_0(k3_real_1(k3_complex1(A),k3_complex1(B)),k3_xcmplx_0(k3_real_1(k4_complex1(A),k4_complex1(B)),k7_complex1)) = k8_complex1(A,B))))) # label(d9_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4950 (all A (m1_subset_1(A,k2_numbers) -> k10_complex1(k10_complex1(A)) = A)) # label(involutiveness_k10_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4951 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> r1_xreal_0(k17_complex1(k2_xcmplx_0(A,B)),k3_real_1(k17_complex1(A),k17_complex1(B))))))) # label(t142_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4952 $T # label(t53_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4953 $T # label(t60_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4954 $T # label(t20_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4955 (all A (m1_subset_1(A,k2_numbers) -> k10_complex1(k15_complex1(A)) = k15_complex1(k10_complex1(A)))) # label(t119_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4956 (all A (m1_subset_1(A,k2_numbers) -> k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))) = k3_complex1(k9_complex1(A,k15_complex1(A))) & np__0 = k4_complex1(k9_complex1(A,k15_complex1(A))))) # label(t126_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4957 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k17_complex1(k7_xcmplx_0(A,B)) = k6_real_1(k17_complex1(A),k17_complex1(B)))))) # label(t153_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4958 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_real_1(k17_complex1(A),k17_complex1(B)) = k17_complex1(k3_xcmplx_0(A,B)))))) # label(t151_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4959 (all A (v1_xcmplx_0(A) -> k15_complex1(A) = k14_complex1(A))) # label(redefinition_k15_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4960 $T # label(t71_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4961 $T # label(t16_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4962 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k13_complex1(A,B),k2_numbers))) # label(dt_k13_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4963 $T # label(t42_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4964 (all A (v1_xcmplx_0(A) -> k16_complex1(A) = k16_complex1(k16_complex1(A)))) # label(projectivity_k16_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4965 $T # label(t81_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4966 $T # label(t73_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4967 (all A (v1_xcmplx_0(A) -> k16_complex1(A) = k18_complex1(A))) # label(redefinition_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4968 (all A (m1_subset_1(A,k2_numbers) -> k12_complex1(A) = k2_xcmplx_0(k6_real_1(k3_complex1(A),k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A)))),k3_xcmplx_0(k6_real_1(k1_real_1(k4_complex1(A)),k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A)))),k7_complex1)))) # label(d13_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4969 (all A (v1_xcmplx_0(A) -> k17_complex1(k17_complex1(A)) = k17_complex1(A))) # label(projectivity_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4970 $T # label(t33_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4971 (all A (m1_subset_1(A,k2_numbers) -> k4_complex1(k11_complex1(A,k15_complex1(A))) = k4_real_1(np__2,k4_complex1(A)) & k3_complex1(k11_complex1(A,k15_complex1(A))) = np__0)) # label(t128_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4972 $T # label(t56_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4973 (all A (m1_subset_1(A,k2_numbers) -> (k4_complex1(A) = np__0 -> k3_complex1(A) = np__0 | np__0 = k4_complex1(k12_complex1(A)) & k3_complex1(k12_complex1(A)) = k2_real_1(k3_complex1(A))))) # label(t79_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4974 (all A (v1_xcmplx_0(A) -> k3_complex1(k15_complex1(A)) = k3_complex1(A) & k4_complex1(k15_complex1(A)) = k1_real_1(k4_complex1(A)))) # label(t112_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4975 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k13_complex1(A,B) = k2_xcmplx_0(k6_real_1(k3_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B)))),k3_xcmplx_0(k6_real_1(k5_real_1(k4_real_1(k3_complex1(B),k4_complex1(A)),k4_real_1(k3_complex1(A),k4_complex1(B))),k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B)))),k7_complex1)))))) # label(d14_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4976 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k16_complex1(A)))) # label(dt_k16_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4977 (all A (v1_xcmplx_0(A) -> k16_complex1(A) = k9_square_1(k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A)))))) # label(d16_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4978 $T # label(t58_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4979 $T # label(t94_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4980 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k9_complex1(A,B) = k2_xcmplx_0(k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k3_xcmplx_0(k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k3_complex1(B),k4_complex1(A))),k7_complex1)))))) # label(d10_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4981 $T # label(t92_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4982 $T # label(t97_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4983 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> (k3_complex1(B) = np__0 & k3_complex1(A) = np__0 -> k4_complex1(B) = np__0 | k3_complex1(k13_complex1(A,B)) = k6_real_1(k4_complex1(A),k4_complex1(B)) & k4_complex1(k13_complex1(A,B)) = np__0))))) # label(t110_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4984 $T # label(t88_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4985 $T # label(t61_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4986 (all A (v1_xcmplx_0(A) -> (np__0 = k3_complex1(A) -> k17_complex1(A) = k17_complex1(k4_complex1(A))))) # label(t137_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4987 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k13_complex1(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k13_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4988 (all A (v1_xcmplx_0(A) -> m1_subset_1(k3_complex1(A),k1_numbers))) # label(dt_k3_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4989 (all A (v1_xcmplx_0(A) -> r1_xreal_0(np__0,k17_complex1(A)))) # label(t132_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4990 $T # label(t62_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4991 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> r1_xreal_0(k5_real_1(k17_complex1(A),k17_complex1(B)),k17_complex1(k6_xcmplx_0(A,B))))))) # label(t145_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4992 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k10_complex1(A),k2_numbers))) # label(dt_k10_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4993 $T # label(t36_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4994 $T # label(t51_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4995 (all A (v1_xcmplx_0(A) -> A = k14_complex1(k14_complex1(A)))) # label(involutiveness_k14_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4996 (all A (v1_xcmplx_0(A) -> r1_xreal_0(k4_complex1(A),k17_complex1(A)))) # label(t141_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4997 (all A (v1_xcmplx_0(A) -> m1_subset_1(k17_complex1(A),k1_numbers))) # label(dt_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4998 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k9_complex1(B,A) = k9_complex1(A,B))) # label(commutativity_k9_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 4999 $T # label(dt_k1_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5000 (all A (m1_subset_1(A,k2_numbers) -> (k4_complex1(A) = np__0 -> A = k15_complex1(A)))) # label(t124_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5001 $T # label(t14_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5002 $T # label(t44_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5003 $T # label(t38_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5004 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k2_xcmplx_0(k5_real_1(k3_complex1(A),k3_complex1(B)),k3_xcmplx_0(k5_real_1(k4_complex1(A),k4_complex1(B)),k7_complex1)) = k11_complex1(A,B))))) # label(d12_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5005 $T # label(t96_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5006 (all A (v1_xreal_0(A) -> k5_square_1(A) = k7_square_1(k17_complex1(A)))) # label(t161_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5007 (all A (v1_xcmplx_0(A) -> m1_subset_1(k15_complex1(A),k2_numbers))) # label(dt_k15_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5008 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k3_xcmplx_0(A,B) = k9_complex1(A,B))) # label(redefinition_k9_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5009 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (B = np__0 & A = np__0 <-> k2_xcmplx_0(k5_square_1(A),k5_square_1(B)) = np__0))))) # label(t2_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5010 (all A (v1_xcmplx_0(A) -> (np__0 = k17_complex1(A) -> np__0 = A))) # label(t131_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5011 (all A (v1_xcmplx_0(A) -> k18_complex1(k18_complex1(A)) = k18_complex1(A))) # label(projectivity_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5012 (all A (m1_subset_1(A,k2_numbers) -> k5_xcmplx_0(A) = k12_complex1(A))) # label(redefinition_k12_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5013 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> k17_complex1(A) = A))) # label(t129_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5014 $T # label(t107_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5015 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> r1_xreal_0(k17_complex1(k6_xcmplx_0(B,C)),k3_real_1(k17_complex1(k6_xcmplx_0(B,A)),k17_complex1(k6_xcmplx_0(A,C)))))))))) # label(t149_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5016 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(k3_complex1(A),k3_xcmplx_0(k4_complex1(A),k7_complex1)) = k14_complex1(A))) # label(d15_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5017 (all A (v1_xcmplx_0(A) -> v1_xreal_0(k2_complex1(A)) & v1_xcmplx_0(k2_complex1(A)))) # label(fc2_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5018 $T # label(t74_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5019 (all A (v1_xreal_0(A) -> k17_complex1(A) = k8_square_1(k5_square_1(A)))) # label(t158_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5020 $T # label(t66_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5021 $T # label(t106_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5022 $T # label(t22_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5023 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k3_complex1(A),k3_xcmplx_0(k4_complex1(A),k7_complex1)) = A)) # label(t29_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5024 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k15_complex1(k9_complex1(A,B)) = k9_complex1(k15_complex1(A),k15_complex1(B)))))) # label(t121_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5025 $T # label(t91_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5026 $T # label(t86_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5027 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(r1_xreal_0(k17_complex1(k6_xcmplx_0(A,B)),np__0) & A != B) & -(B = A & -r1_xreal_0(k17_complex1(k6_xcmplx_0(A,B)),np__0)))))) # label(t148_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5028 (all A (v1_xcmplx_0(A) -> k1_complex1(A) = k3_complex1(A))) # label(redefinition_k3_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5029 $T # label(t52_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5030 (all A (v1_xcmplx_0(A) -> (k4_complex1(A) = np__0 -> k17_complex1(A) = k17_complex1(k3_complex1(A))))) # label(t136_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5031 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_complex1(B) = k3_complex1(A) & k4_complex1(A) = k4_complex1(B) -> B = A))))) # label(t9_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5032 (all A (m1_subset_1(A,k2_numbers) -> (k3_complex1(A) = np__0 -> k15_complex1(A) = k10_complex1(A)))) # label(t125_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5033 $T # label(t40_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5034 $T # label(t7_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5035 $T # label(t70_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5036 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k8_complex1(A,B),k2_numbers))) # label(dt_k8_complex1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5037 (all A (v1_xreal_0(A) -> (A = np__0 <-> np__0 = k18_complex1(A)))) # label(t7_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5038 $T # label(t10_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5039 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> r1_xreal_0(k6_xcmplx_0(k2_xcmplx_0(k1_absvalue(A),k1_absvalue(B)),np__1),k1_absvalue(k2_xcmplx_0(A,B))))))) # label(t40_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5040 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,A) & r1_xreal_0(k4_xcmplx_0(A),B) <-> r1_xreal_0(k18_complex1(B),A)))))) # label(t12_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5041 (all A (v1_xreal_0(A) -> v1_xreal_0(k1_absvalue(A)) & v1_xcmplx_0(k1_absvalue(A)))) # label(fc1_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5042 $T # label(t5_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5043 (all A (v1_xreal_0(A) -> -(r1_xreal_0(np__0,A) & A != np__0 & k4_xcmplx_0(A) = k18_complex1(A)))) # label(t9_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5044 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (k3_real_1(k18_complex1(A),k18_complex1(B)) = k18_complex1(k2_xcmplx_0(A,B)) -> r1_xreal_0(np__0,k3_xcmplx_0(A,B))))))) # label(t25_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5045 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k1_absvalue(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k1_absvalue(A),k1_absvalue(B)))))) # label(t42_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5046 $T # label(t19_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5047 $T # label(t16_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5048 (all A (v1_xreal_0(A) -> (np__0 = k1_absvalue(A) -> A = np__0))) # label(t33_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5049 $T # label(t28_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5050 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> r1_xreal_0(k6_real_1(k18_complex1(k2_xcmplx_0(A,B)),k3_real_1(np__1,k18_complex1(k2_xcmplx_0(A,B)))),k3_real_1(k6_real_1(k18_complex1(A),k3_real_1(np__1,k18_complex1(A))),k6_real_1(k18_complex1(B),k3_real_1(np__1,k18_complex1(B))))))))) # label(t26_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5051 (all A (v1_xreal_0(A) -> k1_absvalue(k7_xcmplx_0(np__1,A)) = k7_xcmplx_0(np__1,k1_absvalue(A)))) # label(t39_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5052 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k2_absvalue(A),k1_numbers))) # label(dt_k2_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5053 (all A (v1_xreal_0(A) -> (-r1_xreal_0(A,np__0) -> np__1 = k1_absvalue(A)) & (-r1_xreal_0(np__0,A) -> k1_absvalue(A) = k1_real_1(np__1)) & (r1_xreal_0(np__0,A) & r1_xreal_0(A,np__0) -> k1_absvalue(A) = np__0))) # label(d2_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5054 (all A (v1_xreal_0(A) -> k1_absvalue(A) = k1_absvalue(k1_absvalue(A)))) # label(t36_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5055 $T # label(t29_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5056 (all A (v1_xreal_0(A) -> k1_absvalue(A) = k1_absvalue(k7_xcmplx_0(np__1,A)))) # label(t41_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5057 (all A (v1_xreal_0(A) -> -(r1_xreal_0(A,np__0) & k1_absvalue(A) = np__1))) # label(t31_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5058 (all A (v1_xreal_0(A) -> -(r1_xreal_0(np__0,A) & k1_real_1(np__1) = k1_absvalue(A)))) # label(t32_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5059 $T # label(dt_k1_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5060 $T # label(t13_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5061 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k18_complex1(A),B) & r1_xreal_0(k18_complex1(C),D) -> r1_xreal_0(k18_complex1(k2_xcmplx_0(A,C)),k2_xcmplx_0(B,D))))))))))) # label(t21_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5062 (all A (v1_xreal_0(A) -> k18_complex1(k7_xcmplx_0(np__1,A)) = k6_real_1(np__1,k18_complex1(A)))) # label(t15_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5063 (all A (v1_xreal_0(A) -> (np__0 != A -> np__1 = k3_xcmplx_0(k1_absvalue(A),k1_absvalue(k7_xcmplx_0(np__1,A)))))) # label(t38_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5064 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> r1_xreal_0(k1_absvalue(k2_xcmplx_0(A,B)),k2_xcmplx_0(k2_xcmplx_0(k1_absvalue(A),k1_absvalue(B)),np__1)))))) # label(t37_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5065 (all A (v1_xreal_0(A) -> (np__0 != A -> k4_real_1(k18_complex1(A),k18_complex1(k7_xcmplx_0(np__1,A))) = np__1))) # label(t14_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5066 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (-r1_xreal_0(k7_xcmplx_0(A,B),np__0) -> k8_square_1(k7_xcmplx_0(A,B)) = k6_real_1(k9_square_1(k18_complex1(A)),k9_square_1(k18_complex1(B)))))))) # label(t23_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5067 $T # label(t6_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5068 (all A (v1_xreal_0(A) -> (-r1_xreal_0(np__0,A) -> k16_complex1(A) = k4_xcmplx_0(A)) & (r1_xreal_0(np__0,A) -> k16_complex1(A) = A))) # label(d1_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5069 $T # label(t30_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5070 (all A (m1_subset_1(A,k1_numbers) -> k2_absvalue(A) = k1_absvalue(A))) # label(redefinition_k2_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5071 $T # label(t18_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5072 $T # label(t3_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5073 $T # label(t2_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5074 $T # label(t22_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5075 $T # label(t17_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5076 $T # label(t4_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5077 $T # label(t27_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5078 (all A (v1_xreal_0(A) -> r1_xreal_0(A,k18_complex1(A)) & r1_xreal_0(k1_real_1(k18_complex1(A)),A))) # label(t11_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5079 (all A (v1_xreal_0(A) -> k3_xcmplx_0(k18_complex1(A),k1_absvalue(A)) = A)) # label(t34_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5080 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,k3_xcmplx_0(A,B)) -> k4_real_1(k9_square_1(k18_complex1(A)),k9_square_1(k18_complex1(B))) = k8_square_1(k3_xcmplx_0(A,B))))))) # label(t20_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5081 (all A (v1_xreal_0(A) -> k18_complex1(A) = A | k18_complex1(A) = k4_xcmplx_0(A))) # label(t1_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5082 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,k3_xcmplx_0(A,B)) -> k18_complex1(k2_xcmplx_0(A,B)) = k3_real_1(k18_complex1(A),k18_complex1(B))))))) # label(t24_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5083 $T # label(t8_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5084 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k3_xcmplx_0(k1_absvalue(A),k1_absvalue(B)) = k1_absvalue(k3_xcmplx_0(A,B)))))) # label(t35_absvalue) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5085 (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]. 80.59/78.64 5086 (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]. 80.59/78.64 5087 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5088 (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]. 80.59/78.64 5089 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5090 (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]. 80.59/78.64 5091 (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]. 80.59/78.64 5092 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5093 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5094 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5095 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5096 (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]. 80.59/78.64 5097 (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]. 80.59/78.64 5098 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5099 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5100 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5101 (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]. 80.59/78.64 5102 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5103 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5104 (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]. 80.59/78.64 5105 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5106 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5107 (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]. 80.59/78.64 5108 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5109 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5110 (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]. 80.59/78.64 5111 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5112 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5113 (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]. 80.59/78.64 5114 (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]. 80.59/78.64 5115 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5116 (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]. 80.59/78.64 5117 (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]. 80.59/78.64 5118 (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]. 80.59/78.64 5119 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5120 (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]. 80.59/78.64 5121 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5122 (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]. 80.59/78.64 5123 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5124 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5125 (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]. 80.59/78.64 5126 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5127 (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]. 80.59/78.64 5128 (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]. 80.59/78.64 5129 (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]. 80.59/78.64 5130 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5131 (all A exists B (v3_ordinal1(B) & r2_wellord2(A,B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5132 (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]. 80.59/78.64 5133 (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]. 80.59/78.64 5134 (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]. 80.59/78.64 5135 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5136 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5137 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5138 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5139 (all A k4_ordinal2 = k1_card_1(k1_tarski(A))) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5140 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5141 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5142 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5143 (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]. 80.59/78.64 5144 (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]. 80.59/78.64 5145 (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]. 80.59/78.64 5146 (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]. 80.59/78.64 5147 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5148 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5149 (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]. 80.59/78.64 5150 (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]. 80.59/78.64 5151 (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]. 80.59/78.64 5152 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5153 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5154 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.64 5155 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5156 (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]. 80.59/78.65 5157 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5158 (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]. 80.59/78.65 5159 (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]. 80.59/78.65 5160 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5161 (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]. 80.59/78.65 5162 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5163 (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]. 80.59/78.65 5164 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5165 (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]. 80.59/78.65 5166 (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]. 80.59/78.65 5167 (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]. 80.59/78.65 5168 (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]. 80.59/78.65 5169 (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]. 80.59/78.65 5170 (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]. 80.59/78.65 5171 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5172 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5173 (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]. 80.59/78.65 5174 (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]. 80.59/78.65 5175 (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]. 80.59/78.65 5176 (all A (r2_wellord2(A,k1_xboole_0) <-> A = k1_xboole_0)) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5177 (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]. 80.59/78.65 5178 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5179 (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]. 80.59/78.65 5180 (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]. 80.59/78.65 5181 (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]. 80.59/78.65 5182 (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]. 80.59/78.65 5183 (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]. 80.59/78.65 5184 (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]. 80.59/78.65 5185 (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]. 80.59/78.65 5186 (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]. 80.59/78.65 5187 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5188 (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]. 80.59/78.65 5189 (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]. 80.59/78.65 5190 (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]. 80.59/78.65 5191 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5192 (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]. 80.59/78.65 5193 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5194 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5195 (all A k1_xboole_0 = k6_finseq_1(A)) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5196 (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]. 80.59/78.65 5197 (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]. 80.59/78.65 5198 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5199 (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]. 80.59/78.65 5200 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5201 (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]. 80.59/78.65 5202 (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]. 80.59/78.65 5203 (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]. 80.59/78.65 5204 (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]. 80.59/78.65 5205 (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]. 80.59/78.65 5206 (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]. 80.59/78.65 5207 (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]. 80.59/78.65 5208 (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]. 80.59/78.65 5209 (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]. 80.59/78.65 5210 (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]. 80.59/78.65 5211 (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]. 80.59/78.65 5212 (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]. 80.59/78.65 5213 (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]. 80.59/78.65 5214 (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]. 80.59/78.65 5215 (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]. 80.59/78.65 5216 (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]. 80.59/78.65 5217 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5218 (all A (v4_ordinal2(A) -> A = k4_card_1(k2_finseq_1(A)))) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5219 (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]. 80.59/78.65 5220 (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]. 80.59/78.65 5221 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5222 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5223 (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]. 80.59/78.65 5224 (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]. 80.59/78.65 5225 (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]. 80.59/78.65 5226 (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]. 80.59/78.65 5227 (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]. 80.59/78.65 5228 (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]. 80.59/78.65 5229 (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]. 80.59/78.65 5230 (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]. 80.59/78.65 5231 (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]. 80.59/78.65 5232 (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]. 80.59/78.65 5233 (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]. 80.59/78.65 5234 (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]. 80.59/78.65 5235 (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]. 80.59/78.65 5236 (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]. 80.59/78.65 5237 (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]. 80.59/78.65 5238 (all A k9_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5239 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5240 (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]. 80.59/78.65 5241 (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]. 80.59/78.65 5242 (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]. 80.59/78.65 5243 (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]. 80.59/78.65 5244 (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]. 80.59/78.65 5245 (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]. 80.59/78.65 5246 (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]. 80.59/78.65 5247 (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]. 80.59/78.65 5248 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5249 (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]. 80.59/78.65 5250 (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]. 80.59/78.65 5251 (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]. 80.59/78.65 5252 (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]. 80.59/78.65 5253 (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]. 80.59/78.65 5254 (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]. 80.59/78.65 5255 (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]. 80.59/78.65 5256 (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]. 80.59/78.65 5257 (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]. 80.59/78.65 5258 (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]. 80.59/78.65 5259 (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]. 80.59/78.65 5260 (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]. 80.59/78.65 5261 (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]. 80.59/78.65 5262 (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]. 80.59/78.65 5263 (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]. 80.59/78.65 5264 (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]. 80.59/78.65 5265 (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]. 80.59/78.65 5266 (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]. 80.59/78.65 5267 (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]. 80.59/78.65 5268 (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]. 80.59/78.65 5269 (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]. 80.59/78.65 5270 (all A k5_finseq_1(A) = k9_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5271 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5272 (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]. 80.59/78.65 5273 (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]. 80.59/78.65 5274 (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]. 80.59/78.65 5275 (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]. 80.59/78.65 5276 (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]. 80.59/78.65 5277 (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]. 80.59/78.65 5278 (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]. 80.59/78.65 5279 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5280 (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]. 80.59/78.65 5281 (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]. 80.59/78.65 5282 (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]. 80.59/78.65 5283 (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]. 80.59/78.65 5284 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5285 (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]. 80.59/78.65 5286 (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]. 80.59/78.65 5287 (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]. 80.59/78.65 5288 (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]. 80.59/78.65 5289 (exists A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5290 (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]. 80.59/78.65 5291 (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]. 80.59/78.65 5292 (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]. 80.59/78.65 5293 (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]. 80.59/78.65 5294 (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]. 80.59/78.65 5295 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5296 (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]. 80.59/78.65 5297 (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]. 80.59/78.65 5298 (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]. 80.59/78.65 5299 (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]. 80.59/78.65 5300 (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]. 80.59/78.65 5301 (all A k5_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5302 (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]. 80.59/78.65 5303 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5304 (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]. 80.59/78.65 5305 (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]. 80.59/78.65 5306 (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]. 80.59/78.65 5307 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.65 5308 (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]. 80.59/78.65 5309 (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]. 80.59/78.65 5310 (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]. 80.59/78.66 5311 (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]. 80.59/78.66 5312 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5313 (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]. 80.59/78.66 5314 (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]. 80.59/78.66 5315 (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]. 80.59/78.66 5316 (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]. 80.59/78.66 5317 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5318 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5319 (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]. 80.59/78.66 5320 (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]. 80.59/78.66 5321 (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]. 80.59/78.66 5322 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5323 (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]. 80.59/78.66 5324 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5325 (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]. 80.59/78.66 5326 (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]. 80.59/78.66 5327 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = k2_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5328 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5329 (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]. 80.59/78.66 5330 (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]. 80.59/78.66 5331 (exists A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5332 (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]. 80.59/78.66 5333 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5334 (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]. 80.59/78.66 5335 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5336 (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]. 80.59/78.66 5337 (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]. 80.59/78.66 5338 (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]. 80.59/78.66 5339 (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]. 80.59/78.66 5340 (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]. 80.59/78.66 5341 (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]. 80.59/78.66 5342 (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]. 80.59/78.66 5343 (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]. 80.59/78.66 5344 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5345 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5346 (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]. 80.59/78.66 5347 (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]. 80.59/78.66 5348 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5349 (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]. 80.59/78.66 5350 (all A (r2_hidden(A,k9_zf_lang) <-> v1_zf_lang(A) & m2_finseq_1(A,k5_numbers))) # label(t14_zf_lang) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5351 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v6_zf_lang(A) -> k1_funct_1(A,np__1) = np__4))) # label(t39_zf_lang) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5352 $T # label(t21_zf_lang) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5353 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,np__1),k3_zf_lang(A)),k3_zf_lang(B)) = k5_zf_lang(A,B))))) # label(d4_zf_lang) # label(axiom) # label(non_clause). [assumption]. 80.59/78.66 5354 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (k29_zf_lang(A) = B <-> (all C ((exists D (m2_finseq_1(D,k5_numbers) & C = D & r2_zf_lang(D,A) & v1_zf_lang(D))) <-> r2_hidden(C,B))))))) # label(d42_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5355 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> m2_finseq_1(k22_zf_lang(A),k5_numbers) & v1_zf_lang(k22_zf_lang(A)))) # label(dt_k22_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5356 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> m2_finseq_1(k27_zf_lang(A),k5_numbers) & v1_zf_lang(k27_zf_lang(A)))) # label(dt_k27_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5357 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v8_zf_lang(A) | v5_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (v5_zf_lang(A) -> (k22_zf_lang(A) = B <-> (exists C (k7_zf_lang(C,B) = A & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))))) & (-v5_zf_lang(A) -> ((exists C (k10_zf_lang(C,B) = A & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) <-> B = k22_zf_lang(A)))))))) # label(d32_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5358 (all A all B (m1_subset_1(A,k1_zf_lang) & m1_finseq_1(B,k5_numbers) -> m2_finseq_1(k8_zf_lang(A,B),k5_numbers))) # label(dt_k8_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5359 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r3_zf_lang(A,B) & r3_zf_lang(B,C) -> r3_zf_lang(A,C)))))))) # label(t85_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5360 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k29_zf_lang(k8_zf_lang(A,B)) = k2_xboole_0(k29_zf_lang(B),k1_tarski(k8_zf_lang(A,B))))))) # label(t106_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5361 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_relat_1(k6_zf_lang(A)) & v1_funct_1(k6_zf_lang(A)) & v1_finseq_1(k6_zf_lang(A)) & v1_zf_lang(k6_zf_lang(A)) & v1_finset_1(k6_zf_lang(A)))) # label(fc4_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5362 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m2_subset_1(k19_zf_lang(A),k5_numbers,k1_zf_lang))) # label(dt_k19_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5363 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v4_zf_lang(A) -> (k20_zf_lang(A) = B <-> r1_zf_lang(B,A))))))) # label(t75_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5364 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v11_zf_lang(A) -> k13_zf_lang(k23_zf_lang(A),k24_zf_lang(A)) = A))) # label(t63_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5365 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v10_zf_lang(A) -> A = k12_zf_lang(k27_zf_lang(A),k28_zf_lang(A))))) # label(t67_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5366 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r2_zf_lang(A,B) -> r1_tarski(k29_zf_lang(A),k29_zf_lang(B))))))) # label(t101_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5367 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v10_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> ((exists C (k12_zf_lang(C,B) = A & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) <-> B = k28_zf_lang(A))))))) # label(d38_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5368 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> -(r1_xreal_0(k3_finseq_1(B),k3_finseq_1(A)) & r3_zf_lang(A,B)))))) # label(t83_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5369 (all A (-v1_xboole_0(A) -> ((all B (m2_finseq_1(B,k5_numbers) -> (all C (m2_finseq_1(C,k5_numbers) -> (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k7_zf_lang(B,C),A)))))) & (all B (-v1_xboole_0(B) -> ((all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> r2_hidden(k5_zf_lang(C,D),B) & r2_hidden(k4_zf_lang(C,D),B))))) & (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_finseq_1(D,k5_numbers) -> (r2_hidden(D,B) -> r2_hidden(k8_zf_lang(C,D),B)))))) & (all C (m2_finseq_1(C,k5_numbers) -> (all D (m2_finseq_1(D,k5_numbers) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k7_zf_lang(C,D),B)))))) & (all C (m2_finseq_1(C,k5_numbers) -> (r2_hidden(C,B) -> r2_hidden(k6_zf_lang(C),B)))) & (all C (r2_hidden(C,B) -> m2_finseq_1(C,k5_numbers))) -> r1_tarski(A,B)))) & (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_finseq_1(C,k5_numbers) -> (r2_hidden(C,A) -> r2_hidden(k8_zf_lang(B,C),A)))))) & (all B (m2_finseq_1(B,k5_numbers) -> (r2_hidden(B,A) -> r2_hidden(k6_zf_lang(B),A)))) & (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> r2_hidden(k4_zf_lang(B,C),A) & r2_hidden(k5_zf_lang(B,C),A))))) & (all B (r2_hidden(B,A) -> m2_finseq_1(B,k5_numbers))) <-> A = k9_zf_lang))) # label(d8_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5370 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r1_zf_lang(B,k8_zf_lang(A,C)) <-> C = B))))))) # label(t73_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5371 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_zf_lang(k20_zf_lang(A)) & m2_finseq_1(k20_zf_lang(A),k5_numbers))) # label(dt_k20_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5372 $T # label(t5_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5373 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (k7_zf_lang(A,B) = k7_zf_lang(C,D) -> A = C & B = D))))))))) # label(t47_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5374 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> m2_subset_1(k23_zf_lang(A),k5_numbers,k1_zf_lang))) # label(dt_k23_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5375 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (v6_zf_lang(B) -> -(k23_zf_lang(B) = A & (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> k8_zf_lang(A,D) != B))) & ((exists D (m2_subset_1(D,k5_numbers,k1_zf_lang) & k8_zf_lang(D,C) = B)) -> k24_zf_lang(B) = C) & -((all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> k8_zf_lang(D,C) != B)) & C = k24_zf_lang(B)) & ((exists D (k8_zf_lang(A,D) = B & m2_finseq_1(D,k5_numbers) & v1_zf_lang(D))) -> A = k23_zf_lang(B))))))))) # label(t60_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5376 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v7_zf_lang(A) -> k1_funct_1(A,np__3) = k19_zf_lang(A) & k18_zf_lang(A) = k1_funct_1(A,np__2)))) # label(t52_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5377 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> ((exists B (m2_finseq_1(B,k5_numbers) & (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & A = k12_zf_lang(B,C))) & v1_zf_lang(B))) <-> v10_zf_lang(A)))) # label(d22_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5378 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m2_subset_1(k18_zf_lang(A),k5_numbers,k1_zf_lang))) # label(dt_k18_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5379 $T # label(t99_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5380 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> -(r3_zf_lang(B,A) & v7_zf_lang(A)))))) # label(t93_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5381 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,np__0),k3_zf_lang(A)),k3_zf_lang(B)) = k4_zf_lang(A,B))))) # label(d3_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5382 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r1_zf_lang(A,B) -> r3_zf_lang(A,B)))))) # label(t82_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5383 (all A all B (m1_subset_1(A,k1_zf_lang) & v1_zf_lang(B) & m1_finseq_1(B,k5_numbers) -> v1_finseq_1(k8_zf_lang(A,B)) & v1_zf_lang(k8_zf_lang(A,B)) & v1_finset_1(k8_zf_lang(A,B)) & v1_funct_1(k8_zf_lang(A,B)) & v1_relat_1(k8_zf_lang(A,B)))) # label(fc6_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5384 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (r2_zf_lang(A,B) & r2_zf_lang(B,C) -> r2_zf_lang(A,C)))))))) # label(t86_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5385 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v5_zf_lang(A) -> k29_zf_lang(A) = k2_xboole_0(k2_xboole_0(k29_zf_lang(k21_zf_lang(A)),k29_zf_lang(k22_zf_lang(A))),k1_tarski(A))))) # label(t109_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5386 (all A (m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) -> k7_zf_lang(A,B) = k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,np__3),A),B))))) # label(d6_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5387 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> -(-v4_zf_lang(A) & -v6_zf_lang(A) & -v5_zf_lang(A) & -v7_zf_lang(A)))) # label(t26_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5388 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (v11_zf_lang(B) -> -((all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> B != k13_zf_lang(A,D))) & k23_zf_lang(B) = A) & -(k24_zf_lang(B) = C & (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> B != k13_zf_lang(D,C)))) & ((exists D (m2_subset_1(D,k5_numbers,k1_zf_lang) & B = k13_zf_lang(D,C))) -> C = k24_zf_lang(B)) & ((exists D (v1_zf_lang(D) & k13_zf_lang(A,D) = B & m2_finseq_1(D,k5_numbers))) -> A = k23_zf_lang(B))))))))) # label(t61_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5389 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v11_zf_lang(A) | v6_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (-v6_zf_lang(A) -> (k24_zf_lang(A) = B <-> (exists C (k13_zf_lang(C,B) = A & m2_subset_1(C,k5_numbers,k1_zf_lang))))) & (v6_zf_lang(A) -> (k24_zf_lang(A) = B <-> (exists C (m2_subset_1(C,k5_numbers,k1_zf_lang) & k8_zf_lang(C,B) = A))))))))) # label(d34_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5390 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (r2_hidden(B,k29_zf_lang(C)) -> -r1_zf_lang(A,B) & -r2_zf_lang(A,B) & -r3_zf_lang(A,B) | r2_hidden(A,k29_zf_lang(C))))))))) # label(t111_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5391 $T # label(t15_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5392 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v3_zf_lang(A) <-> (exists B ((exists C (m2_subset_1(C,k5_numbers,k1_zf_lang) & k5_zf_lang(B,C) = A)) & m2_subset_1(B,k5_numbers,k1_zf_lang)))))) # label(d11_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5393 (all A (m1_finseq_1(A,k5_numbers) -> m2_finseq_1(k6_zf_lang(A),k5_numbers))) # label(dt_k6_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5394 (all A all B all C (m1_subset_1(A,k1_zf_lang) & m1_finseq_1(C,k5_numbers) & v1_zf_lang(C) & m1_subset_1(B,k1_zf_lang) -> m2_finseq_1(k14_zf_lang(A,B,C),k5_numbers) & v1_zf_lang(k14_zf_lang(A,B,C)))) # label(dt_k14_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5395 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v2_zf_lang(A) -> k1_funct_1(A,np__1) = np__0))) # label(t35_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5396 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (A = k7_finseq_1(B,C) -> B = A))))))) # label(t46_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5397 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> k16_zf_lang(A,B,C,D) = k8_zf_lang(A,k14_zf_lang(B,C,D)))))))))) # label(d26_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5398 (all A all B (m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) -> v1_relat_1(k5_zf_lang(A,B)) & v1_funct_1(k5_zf_lang(A,B)) & v1_finseq_1(k5_zf_lang(A,B)) & v1_zf_lang(k5_zf_lang(A,B)) & v1_finset_1(k5_zf_lang(A,B)))) # label(fc3_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5399 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> ((all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (r3_zf_lang(B,A) -> p1_s2_zf_lang(B)))) -> p1_s2_zf_lang(A)))) -> (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> p1_s2_zf_lang(A))) # label(s2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5400 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> r2_zf_lang(A,A))) # label(t79_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5401 $T # label(t18_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5402 $T # label(dt_k29_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5403 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k1_funct_1(k7_zf_lang(A,B),np__1) = np__3)))) # label(t33_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5404 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -(-(k1_funct_1(A,np__1) = np__1 & v3_zf_lang(A)) & -(v6_zf_lang(A) & k1_funct_1(A,np__1) = np__4) & -(v5_zf_lang(A) & np__3 = k1_funct_1(A,np__1)) & -(v4_zf_lang(A) & np__2 = k1_funct_1(A,np__1)) & -(v2_zf_lang(A) & np__0 = k1_funct_1(A,np__1))))) # label(t40_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5405 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v5_zf_lang(A) -> A = k7_zf_lang(k21_zf_lang(A),k22_zf_lang(A))))) # label(t58_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5406 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v5_zf_lang(A) -> k1_funct_1(A,np__1) = np__3))) # label(t38_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5407 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v2_zf_lang(A) -> A = k4_zf_lang(k18_zf_lang(A),k19_zf_lang(A))))) # label(t53_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5408 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (np__1 = k1_funct_1(A,np__1) -> v3_zf_lang(A)))) # label(t42_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5409 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v9_zf_lang(A) <-> (exists B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) & (exists C (m2_finseq_1(C,k5_numbers) & A = k11_zf_lang(B,C) & v1_zf_lang(C)))))))) # label(d21_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5410 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> -r3_zf_lang(C,k5_zf_lang(A,B)))))))) # label(t89_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5411 (all A all B (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(B) & m1_finseq_1(B,k5_numbers) -> v1_relat_1(k7_zf_lang(A,B)) & v1_finseq_1(k7_zf_lang(A,B)) & v1_zf_lang(k7_zf_lang(A,B)) & v1_finset_1(k7_zf_lang(A,B)) & v1_funct_1(k7_zf_lang(A,B)))) # label(fc5_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5412 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> ((exists B (m2_finseq_1(B,k5_numbers) & A = k6_zf_lang(B) & v1_zf_lang(B))) <-> v4_zf_lang(A)))) # label(d12_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5413 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v6_zf_lang(A) -> (k24_zf_lang(A) = B <-> r1_zf_lang(B,A))))))) # label(t77_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5414 (all A all B (m1_subset_1(A,k1_zf_lang) & m1_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> v1_zf_lang(k13_zf_lang(A,B)) & m2_finseq_1(k13_zf_lang(A,B),k5_numbers))) # label(dt_k13_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5415 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> k14_zf_lang(A,B,C) = k8_zf_lang(A,k8_zf_lang(B,C)))))))) # label(d24_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5416 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> k17_zf_lang(A,B,C,D) = k13_zf_lang(A,k15_zf_lang(B,C,D)) & k16_zf_lang(A,B,C,D) = k8_zf_lang(A,k14_zf_lang(B,C,D)))))))))) # label(t24_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5417 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (r2_zf_lang(A,B) <-> (exists C ((exists D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & k1_funct_1(D,np__1) = A & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> -(r1_xreal_0(np__1,E) & (all F (m2_finseq_1(F,k5_numbers) & v1_zf_lang(F) -> (all G (v1_zf_lang(G) & m2_finseq_1(G,k5_numbers) -> -(G = k1_funct_1(D,k1_nat_1(E,np__1)) & r1_zf_lang(F,G) & F = k1_funct_1(D,E)))))) & -r1_xreal_0(C,E)))) & k1_funct_1(D,C) = B & k3_finseq_1(D) = C & r1_xreal_0(np__1,C))) & m2_subset_1(C,k1_numbers,k5_numbers)))))))) # label(d40_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5418 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (np__2 = k1_funct_1(A,np__1) -> v4_zf_lang(A)))) # label(t43_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5419 $T # label(t2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5420 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (k4_zf_lang(C,D) = k4_zf_lang(A,B) -> D = B & C = A))))))))) # label(t6_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5421 (exists A (v1_finset_1(A) & v1_zf_lang(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) & m1_finseq_1(A,k5_numbers))) # label(rc1_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5422 (all A all B all C (m1_subset_1(A,k1_zf_lang) & m1_finseq_1(C,k5_numbers) & v1_zf_lang(C) & m1_subset_1(B,k1_zf_lang) -> m2_finseq_1(k15_zf_lang(A,B,C),k5_numbers) & v1_zf_lang(k15_zf_lang(A,B,C)))) # label(dt_k15_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5423 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (r1_zf_lang(A,B) <-> -(B != k6_zf_lang(A) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> k7_zf_lang(A,C) != B & k7_zf_lang(C,A) != B)) & (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> k8_zf_lang(C,A) != B)))))))) # label(d39_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5424 (all A (m1_subset_1(A,k1_zf_lang) -> m2_finseq_1(k3_zf_lang(A),k5_numbers))) # label(dt_k3_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5425 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v10_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> ((exists C (v1_zf_lang(C) & k12_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers))) <-> k27_zf_lang(A) = B)))))) # label(d37_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5426 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k13_zf_lang(A,B) = k6_zf_lang(k8_zf_lang(A,k6_zf_lang(B))))))) # label(d19_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5427 $T # label(t4_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5428 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_finseq_1(B,k5_numbers) -> k8_zf_lang(A,B) = k8_finseq_1(k5_numbers,k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,np__4),k3_zf_lang(A)),B))))) # label(d7_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5429 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r2_hidden(A,k29_zf_lang(B)) -> r2_zf_lang(A,B)))))) # label(t100_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5430 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v6_zf_lang(A) -> r3_zf_lang(k24_zf_lang(A),A)))) # label(t96_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5431 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k2_xboole_0(k2_xboole_0(k29_zf_lang(A),k29_zf_lang(B)),k1_tarski(k7_zf_lang(A,B))) = k29_zf_lang(k7_zf_lang(A,B)))))) # label(t105_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5432 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,A)) = k12_zf_lang(A,B))))) # label(d18_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5433 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v9_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (B = k26_zf_lang(A) <-> (exists C (v1_zf_lang(C) & k11_zf_lang(C,B) = A & m2_finseq_1(C,k5_numbers))))))))) # label(d36_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5434 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v2_zf_lang(A) | v3_zf_lang(A) <-> v7_zf_lang(A)))) # label(d15_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5435 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> k2_xboole_0(k29_zf_lang(A),k1_tarski(k6_zf_lang(A))) = k29_zf_lang(k6_zf_lang(A)))) # label(t104_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5436 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v8_zf_lang(A) -> k10_zf_lang(k21_zf_lang(A),k22_zf_lang(A)) = A))) # label(t59_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5437 (all A all B all C all D (m1_subset_1(C,k1_zf_lang) & v1_zf_lang(D) & m1_finseq_1(D,k5_numbers) & m1_subset_1(B,k1_zf_lang) & m1_subset_1(A,k1_zf_lang) -> m2_finseq_1(k16_zf_lang(A,B,C,D),k5_numbers) & v1_zf_lang(k16_zf_lang(A,B,C,D)))) # label(dt_k16_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5438 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v2_zf_lang(A) <-> (exists B (m2_subset_1(B,k5_numbers,k1_zf_lang) & (exists C (m2_subset_1(C,k5_numbers,k1_zf_lang) & A = k4_zf_lang(B,C)))))))) # label(d10_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5439 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> -r3_zf_lang(C,k4_zf_lang(A,B)))))))) # label(t88_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5440 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (r3_zf_lang(A,B) <-> r2_zf_lang(A,B) & A != B))))) # label(d41_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5441 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k6_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B))) = k10_zf_lang(A,B))))) # label(d16_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5442 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r3_zf_lang(B,k8_zf_lang(A,C)) -> r2_zf_lang(B,C)))))))) # label(t92_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5443 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -((all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> -r1_xreal_0(k1_nat_1(k3_finseq_1(B),np__1),k3_finseq_1(A)))) & -v7_zf_lang(A)))) # label(t28_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.81 5444 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v8_zf_lang(A) | v5_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (-v5_zf_lang(A) -> ((exists C (k10_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) <-> k21_zf_lang(A) = B)) & (v5_zf_lang(A) -> (k21_zf_lang(A) = B <-> (exists C (v1_zf_lang(C) & k7_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers)))))))))) # label(d31_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5445 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> k13_zf_lang(A,k13_zf_lang(B,C)) = k15_zf_lang(A,B,C))))))) # label(d25_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5446 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -((all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> k4_zf_lang(B,C) != A)))) & v2_zf_lang(A)) & -(v3_zf_lang(A) & (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> k5_zf_lang(B,C) != A))))) & -((all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k6_zf_lang(B) != A)) & v4_zf_lang(A)) & ((exists B (m2_finseq_1(B,k5_numbers) & A = k6_zf_lang(B) & v1_zf_lang(B))) -> v4_zf_lang(A)) & -((all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> k7_zf_lang(B,C) != A)))) & v5_zf_lang(A)) & -((all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> A != k8_zf_lang(B,C))))) & v6_zf_lang(A)) & ((exists B ((exists C (m2_finseq_1(C,k5_numbers) & k8_zf_lang(B,C) = A & v1_zf_lang(C))) & m2_subset_1(B,k5_numbers,k1_zf_lang))) -> v6_zf_lang(A)) & ((exists B (v1_zf_lang(B) & (exists C (v1_zf_lang(C) & k7_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers))) & m2_finseq_1(B,k5_numbers))) -> v5_zf_lang(A)) & ((exists B ((exists C (k5_zf_lang(B,C) = A & m2_subset_1(C,k5_numbers,k1_zf_lang))) & m2_subset_1(B,k5_numbers,k1_zf_lang))) -> v3_zf_lang(A)) & ((exists B (m2_subset_1(B,k5_numbers,k1_zf_lang) & (exists C (m2_subset_1(C,k5_numbers,k1_zf_lang) & k4_zf_lang(B,C) = A)))) -> v2_zf_lang(A)))) # label(t16_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5447 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v4_zf_lang(A) -> np__2 = k1_funct_1(A,np__1)))) # label(t37_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5448 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k1_tarski(k5_zf_lang(A,B)) = k29_zf_lang(k5_zf_lang(A,B)))))) # label(t103_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5449 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (np__3 = k1_funct_1(A,np__1) -> v5_zf_lang(A)))) # label(t44_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5450 $T # label(t8_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5451 (all A ((exists B (r1_xreal_0(np__5,B) & B = A & m2_subset_1(B,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_0_0_zf_lang))) # label(fraenkel_a_0_0_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5452 (all A (m2_finseq_1(A,k5_numbers) -> k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,np__2),A) = k6_zf_lang(A))) # label(d5_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5453 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v6_zf_lang(A) <-> (exists B (m2_subset_1(B,k5_numbers,k1_zf_lang) & (exists C (v1_zf_lang(C) & A = k8_zf_lang(B,C) & m2_finseq_1(C,k5_numbers)))))))) # label(d14_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5454 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v9_zf_lang(A) -> ((exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k11_zf_lang(B,C) = A)) -> B = k25_zf_lang(A)) & -(B = k26_zf_lang(A) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> A != k11_zf_lang(C,B)))) & ((exists C (A = k11_zf_lang(C,B) & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) -> k26_zf_lang(A) = B) & -(B = k25_zf_lang(A) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> k11_zf_lang(B,C) != A)))))))) # label(t64_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5455 $T # label(t17_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5456 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v5_zf_lang(A) -> ((exists C (v1_zf_lang(C) & k7_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers))) -> k21_zf_lang(A) = B) & -(B = k22_zf_lang(A) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> k7_zf_lang(C,B) != A))) & ((exists C (v1_zf_lang(C) & k7_zf_lang(C,B) = A & m2_finseq_1(C,k5_numbers))) -> k22_zf_lang(A) = B) & -(k21_zf_lang(A) = B & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> k7_zf_lang(B,C) != A)))))))) # label(t56_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5457 $T # label(t1_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5458 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v5_zf_lang(A) -> (B = k21_zf_lang(A) | k22_zf_lang(A) = B <-> r1_zf_lang(B,A))))))) # label(t76_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5459 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r2_zf_lang(C,k5_zf_lang(A,B)) <-> C = k5_zf_lang(A,B)))))))) # label(t98_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5460 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> -(-r2_zf_lang(A,B) & -r2_zf_lang(A,C) & r3_zf_lang(A,k7_zf_lang(B,C))))))))) # label(t91_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5461 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (k5_zf_lang(C,D) = k5_zf_lang(A,B) -> C = A & B = D))))))))) # label(t7_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5462 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v7_zf_lang(A) -> k1_funct_1(A,np__3) = k19_zf_lang(A)))) # label(d29_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5463 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v3_zf_lang(A) -> np__1 = k1_funct_1(A,np__1)))) # label(t36_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5464 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -((all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> A != k10_zf_lang(B,C))))) & v8_zf_lang(A)) & ((exists B ((exists C (A = k10_zf_lang(B,C) & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) & m2_finseq_1(B,k5_numbers) & v1_zf_lang(B))) -> v8_zf_lang(A)) & -(v9_zf_lang(A) & (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> A != k11_zf_lang(B,C)))))) & ((exists B (v1_zf_lang(B) & (exists C (A = k11_zf_lang(B,C) & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) & m2_finseq_1(B,k5_numbers))) -> v9_zf_lang(A)) & -((all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> A != k12_zf_lang(B,C))))) & v10_zf_lang(A)) & ((exists B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) & (exists C (A = k12_zf_lang(B,C) & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))))) -> v10_zf_lang(A)) & -((all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> A != k13_zf_lang(B,C))))) & v11_zf_lang(A)) & ((exists B ((exists C (m2_finseq_1(C,k5_numbers) & A = k13_zf_lang(B,C) & v1_zf_lang(C))) & m2_subset_1(B,k5_numbers,k1_zf_lang))) -> v11_zf_lang(A)))) # label(t22_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5465 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> np__0 = k1_funct_1(k4_zf_lang(A,B),np__1) & k1_funct_1(k5_zf_lang(A,B),np__1) = np__1)))) # label(t31_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5466 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> v1_zf_lang(k24_zf_lang(A)) & m2_finseq_1(k24_zf_lang(A),k5_numbers))) # label(dt_k24_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5467 (all A all B (m1_finseq_1(B,k5_numbers) & v1_zf_lang(B) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m2_finseq_1(k12_zf_lang(A,B),k5_numbers) & v1_zf_lang(k12_zf_lang(A,B)))) # label(dt_k12_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5468 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v9_zf_lang(A) -> k11_zf_lang(k25_zf_lang(A),k26_zf_lang(A)) = A))) # label(t65_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5469 $T # label(t20_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5470 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (k11_zf_lang(A,B) = k11_zf_lang(C,D) -> B = D & A = C))))))))) # label(t49_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5471 (all A (m1_subset_1(A,k1_zf_lang) -> k5_finseq_1(A) = k3_zf_lang(A))) # label(redefinition_k3_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5472 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> np__2 = k1_funct_1(k6_zf_lang(A),np__1))) # label(t32_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5473 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m2_finseq_1(k26_zf_lang(A),k5_numbers) & v1_zf_lang(k26_zf_lang(A)))) # label(dt_k26_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5474 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -(-v5_zf_lang(A) & -v6_zf_lang(A) & -v4_zf_lang(A) & -v3_zf_lang(A) & -v2_zf_lang(A)))) # label(t25_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5475 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v6_zf_lang(A) | v11_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (v6_zf_lang(A) -> ((exists C (v1_zf_lang(C) & k8_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers))) <-> k23_zf_lang(A) = B)) & (-v6_zf_lang(A) -> (B = k23_zf_lang(A) <-> (exists C (m2_finseq_1(C,k5_numbers) & A = k13_zf_lang(B,C) & v1_zf_lang(C)))))))))) # label(d33_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5476 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (k3_finseq_1(A) = np__3 -> v7_zf_lang(A)))) # label(t30_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5477 $T # label(t55_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5478 (all A all B (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(B) & m1_finseq_1(B,k5_numbers) -> v1_zf_lang(k11_zf_lang(A,B)) & m2_finseq_1(k11_zf_lang(A,B),k5_numbers))) # label(dt_k11_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5479 (all A all B (m1_finseq_1(B,k5_numbers) & m1_finseq_1(A,k5_numbers) -> m2_finseq_1(k7_zf_lang(A,B),k5_numbers))) # label(dt_k7_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5480 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> -(r1_zf_lang(B,A) & v7_zf_lang(A)))))) # label(t74_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5481 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v5_zf_lang(A) <-> (exists B (m2_finseq_1(B,k5_numbers) & (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & A = k7_zf_lang(B,C))) & v1_zf_lang(B)))))) # label(d13_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5482 (all A (m2_finseq_1(A,k5_numbers) -> (v1_zf_lang(A) <-> m1_subset_1(A,k9_zf_lang)))) # label(d9_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5483 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> m2_finseq_1(k25_zf_lang(A),k5_numbers) & v1_zf_lang(k25_zf_lang(A)))) # label(dt_k25_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5484 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> r1_xreal_0(np__3,k3_finseq_1(A)))) # label(t29_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5485 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v6_zf_lang(A) -> k29_zf_lang(A) = k2_xboole_0(k29_zf_lang(k24_zf_lang(A)),k1_tarski(A))))) # label(t110_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5486 $T # label(t19_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.82 5487 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r2_zf_lang(C,k4_zf_lang(A,B)) <-> C = k4_zf_lang(A,B)))))))) # label(t97_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5488 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v4_zf_lang(A) -> r3_zf_lang(k20_zf_lang(A),A)))) # label(t94_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5489 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v6_zf_lang(A) -> A = k8_zf_lang(k23_zf_lang(A),k24_zf_lang(A))))) # label(t62_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5490 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (v10_zf_lang(A) -> -(B = k27_zf_lang(A) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> A != k12_zf_lang(B,C)))) & ((exists C (v1_zf_lang(C) & A = k12_zf_lang(C,B) & m2_finseq_1(C,k5_numbers))) -> B = k28_zf_lang(A)) & -(k28_zf_lang(A) = B & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> A != k12_zf_lang(C,B)))) & ((exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k12_zf_lang(B,C) = A)) -> B = k27_zf_lang(A))))))) # label(t66_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5491 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_zf_lang(k21_zf_lang(A)) & m2_finseq_1(k21_zf_lang(A),k5_numbers))) # label(dt_k21_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5492 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r1_zf_lang(A,k7_zf_lang(B,C)) <-> A = B | A = C))))))) # label(t72_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5493 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (r2_zf_lang(A,B) & r2_zf_lang(B,A) -> A = B))))) # label(t87_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5494 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> k15_zf_lang(A,B,C) = k13_zf_lang(A,k13_zf_lang(B,C)) & k8_zf_lang(A,k8_zf_lang(B,C)) = k14_zf_lang(A,B,C))))))) # label(t23_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5495 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (np__4 = k1_funct_1(A,np__1) -> v6_zf_lang(A)))) # label(t45_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5496 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k29_zf_lang(k4_zf_lang(A,B)) = k1_tarski(k4_zf_lang(A,B)))))) # label(t102_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5497 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (k29_zf_lang(A) = k1_tarski(A) <-> v7_zf_lang(A)))) # label(t107_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5498 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v7_zf_lang(A) -> k1_funct_1(A,np__2) = k18_zf_lang(A)))) # label(d28_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5499 (all A all B (m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) -> v1_zf_lang(k4_zf_lang(A,B)) & v1_finseq_1(k4_zf_lang(A,B)) & v1_finset_1(k4_zf_lang(A,B)) & v1_funct_1(k4_zf_lang(A,B)) & v1_relat_1(k4_zf_lang(A,B)))) # label(fc2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5500 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v7_zf_lang(A) -> np__3 = k3_finseq_1(A)))) # label(t27_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5501 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v11_zf_lang(A) <-> (exists B (m2_subset_1(B,k5_numbers,k1_zf_lang) & (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k13_zf_lang(B,C) = A))))))) # label(d23_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.86 5502 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (p1_s1_zf_lang(k20_zf_lang(A)) & v4_zf_lang(A) -> p1_s1_zf_lang(A)))) & (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v6_zf_lang(A) & p1_s1_zf_lang(k24_zf_lang(A)) -> p1_s1_zf_lang(A)))) & (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (p1_s1_zf_lang(k21_zf_lang(A)) & p1_s1_zf_lang(k22_zf_lang(A)) & v5_zf_lang(A) -> p1_s1_zf_lang(A)))) & (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v7_zf_lang(A) -> p1_s1_zf_lang(A)))) -> (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> p1_s1_zf_lang(A))) # label(s1_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5503 $T # label(t13_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5504 $T # label(t3_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5505 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> -(r1_zf_lang(A,B) & r1_xreal_0(k3_finseq_1(B),k3_finseq_1(A))))))) # label(t81_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5506 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k2_zf_lang(A) = k1_nat_1(np__5,A))) # label(d2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5507 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v9_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (B = k25_zf_lang(A) <-> (exists C (k11_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))))))))) # label(d35_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5508 $T # label(t9_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5509 $T # label(t11_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5510 $T # label(t80_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5511 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_zf_lang(k28_zf_lang(A)) & m2_finseq_1(k28_zf_lang(A),k5_numbers))) # label(dt_k28_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5512 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> -r1_zf_lang(C,k4_zf_lang(A,B)))))))) # label(t69_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5513 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (k10_zf_lang(A,B) = k10_zf_lang(C,D) -> D = B & C = A))))))))) # label(t48_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5514 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> -r1_zf_lang(C,k5_zf_lang(A,B)))))))) # label(t70_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5515 $T # label(t68_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5516 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> -(r3_zf_lang(A,B) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> -r1_zf_lang(C,B)))))))) # label(t84_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5517 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> ((exists B ((exists C (v1_zf_lang(C) & k10_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers))) & m2_finseq_1(B,k5_numbers) & v1_zf_lang(B))) <-> v8_zf_lang(A)))) # label(d20_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5518 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v4_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (A = k6_zf_lang(B) <-> B = k20_zf_lang(A))))))) # label(d30_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5519 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v4_zf_lang(A) -> k2_xboole_0(k29_zf_lang(k20_zf_lang(A)),k1_tarski(A)) = k29_zf_lang(A)))) # label(t108_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5520 (all A all B (m1_subset_1(B,k1_zf_lang) & m1_subset_1(A,k1_zf_lang) -> m2_finseq_1(k4_zf_lang(A,B),k5_numbers))) # label(dt_k4_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5521 (all A all B all C all D (m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) & m1_finseq_1(D,k5_numbers) & v1_zf_lang(D) & m1_subset_1(C,k1_zf_lang) -> v1_zf_lang(k17_zf_lang(A,B,C,D)) & m2_finseq_1(k17_zf_lang(A,B,C,D),k5_numbers))) # label(dt_k17_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5522 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (k12_zf_lang(C,D) = k12_zf_lang(A,B) -> B = D & A = C))))))))) # label(t50_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5523 $T # label(t78_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5524 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v8_zf_lang(A) -> -((all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> A != k10_zf_lang(B,C))) & B = k21_zf_lang(A)) & ((exists C (m2_finseq_1(C,k5_numbers) & k10_zf_lang(B,C) = A & v1_zf_lang(C))) -> k21_zf_lang(A) = B) & -(B = k22_zf_lang(A) & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> A != k10_zf_lang(C,B)))) & ((exists C (m2_finseq_1(C,k5_numbers) & k10_zf_lang(C,B) = A & v1_zf_lang(C))) -> k22_zf_lang(A) = B)))))) # label(t57_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5525 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (A = B <-> r1_zf_lang(A,k6_zf_lang(B))))))) # label(t71_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5526 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v5_zf_lang(A) -> r3_zf_lang(k21_zf_lang(A),A) & r3_zf_lang(k22_zf_lang(A),A)))) # label(t95_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5527 (all A (m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) -> (k6_zf_lang(B) = k6_zf_lang(A) -> B = A))))) # label(t10_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5528 (all A all B (m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) -> m2_finseq_1(k5_zf_lang(A,B),k5_numbers))) # label(dt_k5_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5529 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k1_funct_1(k8_zf_lang(A,B),np__1) = np__4)))) # label(t34_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5530 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k6_zf_lang(k7_zf_lang(A,k6_zf_lang(B))) = k11_zf_lang(A,B))))) # label(d17_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5531 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (np__0 = k1_funct_1(A,np__1) -> v2_zf_lang(A)))) # label(t41_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5532 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r3_zf_lang(A,k6_zf_lang(B)) -> r2_zf_lang(A,B)))))) # label(t90_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5533 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v3_zf_lang(A) -> A = k5_zf_lang(k18_zf_lang(A),k19_zf_lang(A))))) # label(t54_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5534 (all A (m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (k8_zf_lang(C,A) = k8_zf_lang(D,B) -> B = A & D = C))))))))) # label(t12_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5535 (all A all B (v1_zf_lang(A) & m1_finseq_1(B,k5_numbers) & v1_zf_lang(B) & m1_finseq_1(A,k5_numbers) -> m2_finseq_1(k10_zf_lang(A,B),k5_numbers) & v1_zf_lang(k10_zf_lang(A,B)))) # label(dt_k10_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5536 (all A (m1_subset_1(A,k5_numbers) -> m2_subset_1(k2_zf_lang(A),k5_numbers,k1_zf_lang))) # label(dt_k2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 83.82/81.87 5537 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (k13_zf_lang(A,C) = k13_zf_lang(B,D) -> A = B & C = D))))))))) # label(t51_zf_lang) # label(axiom) # label(non_clause). [assumption]. 115.38/113.44 5538 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> k17_zf_lang(A,B,C,D) = k13_zf_lang(A,k15_zf_lang(B,C,D)))))))))) # label(d27_zf_lang) # label(axiom) # label(non_clause). [assumption]. 115.38/113.44 5539 $T # label(t24_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.44 5540 (all A (p1_s4_zf_model(A) -> p1_s4_zf_model(f3_s4_zf_model(A)))) & (all A all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (p1_s4_zf_model(A) -> p1_s4_zf_model(f5_s4_zf_model(B,A))))) & (all A all B (p1_s4_zf_model(B) & p1_s4_zf_model(A) -> p1_s4_zf_model(f4_s4_zf_model(A,B)))) & (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> p1_s4_zf_model(f1_s4_zf_model(A,B)) & p1_s4_zf_model(f2_s4_zf_model(A,B)))))) & (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (f6_s4_zf_model(A) = B <-> (exists C ((all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> r2_hidden(k4_tarski(k5_zf_lang(D,E),f2_s4_zf_model(D,E)),C) & r2_hidden(k4_tarski(k4_zf_lang(D,E),f1_s4_zf_model(D,E)),C))))) & (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (all E (r2_hidden(k4_tarski(D,E),C) -> (v2_zf_lang(D) -> E = f1_s4_zf_model(k18_zf_lang(D),k19_zf_lang(D))) & (v3_zf_lang(D) -> E = f2_s4_zf_model(k18_zf_lang(D),k19_zf_lang(D))) & -(v5_zf_lang(D) & (all F all G -(E = f4_s4_zf_model(F,G) & r2_hidden(k4_tarski(k21_zf_lang(D),F),C) & r2_hidden(k4_tarski(k22_zf_lang(D),G),C)))) & -(v6_zf_lang(D) & (all F -(r2_hidden(k4_tarski(k24_zf_lang(D),F),C) & f5_s4_zf_model(k23_zf_lang(D),F) = E))) & -((all F -(r2_hidden(k4_tarski(k20_zf_lang(D),F),C) & E = f3_s4_zf_model(F))) & v4_zf_lang(D)))))) & r2_hidden(k4_tarski(A,B),C))))))) -> p1_s4_zf_model(f6_s4_zf_model(f7_s4_zf_model)) # label(s4_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.44 5541 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k3_zf_model(A)))) # label(fc1_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.44 5542 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k1_zf_lang,A) & v1_funct_2(B,k1_zf_lang,A) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> ((all E (v1_funct_1(E) & m2_relset_1(E,k1_zf_lang,A) & v1_funct_2(E,k1_zf_lang,A) -> ((all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,B,F) -> F = D))) -> r1_zf_model(A,E,C)))) <-> r1_zf_model(A,B,k8_zf_lang(D,C))))))))))) # label(t16_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.44 5543 (exists A ((all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> r2_hidden(k4_tarski(k4_zf_lang(B,C),f1_s2_zf_model(B,C)),A) & r2_hidden(k4_tarski(k5_zf_lang(B,C),f2_s2_zf_model(B,C)),A))))) & r2_hidden(k4_tarski(f6_s2_zf_model,f8_s2_zf_model),A) & (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (r2_hidden(k4_tarski(B,C),A) -> (v2_zf_lang(B) -> f1_s2_zf_model(k18_zf_lang(B),k19_zf_lang(B)) = C) & (v3_zf_lang(B) -> f2_s2_zf_model(k18_zf_lang(B),k19_zf_lang(B)) = C) & -(v5_zf_lang(B) & (all D all E -(r2_hidden(k4_tarski(k22_zf_lang(B),E),A) & r2_hidden(k4_tarski(k21_zf_lang(B),D),A) & f4_s2_zf_model(D,E) = C))) & -((all D -(r2_hidden(k4_tarski(k24_zf_lang(B),D),A) & C = f5_s2_zf_model(k23_zf_lang(B),D))) & v6_zf_lang(B)) & -((all D -(C = f3_s2_zf_model(D) & r2_hidden(k4_tarski(k20_zf_lang(B),D),A))) & v4_zf_lang(B)))))))) & (exists A ((all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> r2_hidden(k4_tarski(k5_zf_lang(B,C),f2_s2_zf_model(B,C)),A) & r2_hidden(k4_tarski(k4_zf_lang(B,C),f1_s2_zf_model(B,C)),A))))) & (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (r2_hidden(k4_tarski(B,C),A) -> -((all D -(C = f3_s2_zf_model(D) & r2_hidden(k4_tarski(k20_zf_lang(B),D),A))) & v4_zf_lang(B)) & -(v5_zf_lang(B) & (all D all E -(r2_hidden(k4_tarski(k22_zf_lang(B),E),A) & r2_hidden(k4_tarski(k21_zf_lang(B),D),A) & f4_s2_zf_model(D,E) = C))) & -((all D -(C = f5_s2_zf_model(k23_zf_lang(B),D) & r2_hidden(k4_tarski(k24_zf_lang(B),D),A))) & v6_zf_lang(B)) & (v3_zf_lang(B) -> f2_s2_zf_model(k18_zf_lang(B),k19_zf_lang(B)) = C) & (v2_zf_lang(B) -> f1_s2_zf_model(k18_zf_lang(B),k19_zf_lang(B)) = C))))) & r2_hidden(k4_tarski(f6_s2_zf_model,f7_s2_zf_model),A))) -> f7_s2_zf_model = f8_s2_zf_model # label(s2_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5544 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k1_zf_lang,A) & v1_funct_2(B,k1_zf_lang,A) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (r1_zf_model(A,B,C) <-> -r1_zf_model(A,B,k6_zf_lang(C))))))))) # label(t14_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5545 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (m2_relset_1(D,k1_zf_lang,A) & v1_funct_2(D,k1_zf_lang,A) & v1_funct_1(D) -> (r2_hidden(D,k5_zf_model(k8_zf_lang(B,C),A)) <-> (all E (v1_funct_2(E,k1_zf_lang,A) & m2_relset_1(E,k1_zf_lang,A) & v1_funct_1(E) -> ((all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,D,F) -> B = F))) -> r2_hidden(E,k5_zf_model(C,A))))) & r2_hidden(D,k5_zf_model(C,A))))))))))) # label(t6_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5546 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> k11_zf_lang(k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(A,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))),k8_zf_lang(k2_zf_lang(np__1),k13_zf_lang(k2_zf_lang(np__2),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(k5_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__2)),k13_zf_lang(k2_zf_lang(np__3),k7_zf_lang(k5_zf_lang(k2_zf_lang(np__3),k2_zf_lang(np__1)),A))))))) = k11_zf_model(A))) # label(d11_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5547 (all A all B all C all D (m2_subset_1(C,k5_numbers,k1_zf_lang) & m2_subset_1(D,k5_numbers,k1_zf_lang) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_1_zf_model(B,C,D)) <-> (exists E (m1_subset_1(E,k3_zf_model(B)) & E = A & (all F (v1_funct_1(F) & m2_relset_1(F,k1_zf_lang,B) & v1_funct_2(F,k1_zf_lang,B) -> (E = F -> r2_hidden(k8_funct_2(k1_zf_lang,B,F,C),k8_funct_2(k1_zf_lang,B,F,D)))))))))) # label(fraenkel_a_3_1_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5548 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k1_zf_lang,A) & m2_relset_1(B,k1_zf_lang,A) & v1_funct_1(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> ((exists E ((all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k8_funct_2(k1_zf_lang,A,B,F) != k8_funct_2(k1_zf_lang,A,E,F) -> D = F))) & r1_zf_model(A,E,C) & m2_relset_1(E,k1_zf_lang,A) & v1_funct_2(E,k1_zf_lang,A) & v1_funct_1(E))) <-> r1_zf_model(A,B,k13_zf_lang(D,C))))))))))) # label(t20_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5549 (all A all B all C all D (-v1_xboole_0(B) & v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> ((exists E (m1_subset_1(E,k3_zf_model(B)) & E = A & (all F all G (m2_relset_1(G,k1_zf_lang,B) & v1_funct_2(G,k1_zf_lang,B) & v1_funct_1(G) -> (F = D & E = G -> (all H (v1_funct_2(H,k1_zf_lang,B) & m2_relset_1(H,k1_zf_lang,B) & v1_funct_1(H) -> ((all I (m2_subset_1(I,k5_numbers,k1_zf_lang) -> (k8_funct_2(k1_zf_lang,B,H,I) != k8_funct_2(k1_zf_lang,B,G,I) -> k23_zf_lang(C) = I))) -> r2_hidden(H,F)))) & r2_hidden(G,F)))))) <-> r2_hidden(A,a_3_2_zf_model(B,C,D))))) # label(fraenkel_a_3_2_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5550 (exists A exists B (r2_hidden(k4_tarski(f6_s1_zf_model,A),B) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (r2_hidden(k4_tarski(C,D),B) -> -(v4_zf_lang(C) & (all E -(f3_s1_zf_model(E) = D & r2_hidden(k4_tarski(k20_zf_lang(C),E),B)))) & -((all E -(f5_s1_zf_model(k23_zf_lang(C),E) = D & r2_hidden(k4_tarski(k24_zf_lang(C),E),B))) & v6_zf_lang(C)) & -((all E all F -(D = f4_s1_zf_model(E,F) & r2_hidden(k4_tarski(k22_zf_lang(C),F),B) & r2_hidden(k4_tarski(k21_zf_lang(C),E),B))) & v5_zf_lang(C)) & (v3_zf_lang(C) -> D = f2_s1_zf_model(k18_zf_lang(C),k19_zf_lang(C))) & (v2_zf_lang(C) -> D = f1_s1_zf_model(k18_zf_lang(C),k19_zf_lang(C))))))) & (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> r2_hidden(k4_tarski(k5_zf_lang(C,D),f2_s1_zf_model(C,D)),B) & r2_hidden(k4_tarski(k4_zf_lang(C,D),f1_s1_zf_model(C,D)),B))))))) # label(s1_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5551 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,k1_zf_lang,D) & m2_relset_1(E,k1_zf_lang,D) & v1_funct_1(E) -> (r1_zf_model(D,E,k15_zf_lang(B,C,A)) <-> (exists F ((all G (m2_subset_1(G,k5_numbers,k1_zf_lang) -> -(B != G & C != G & k8_funct_2(k1_zf_lang,D,E,G) != k8_funct_2(k1_zf_lang,D,F,G)))) & r1_zf_model(D,F,A) & m2_relset_1(F,k1_zf_lang,D) & v1_funct_2(F,k1_zf_lang,D) & v1_funct_1(F)))))))))))))) # label(t23_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5552 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k1_zf_lang,A) & m2_relset_1(B,k1_zf_lang,A) & v1_funct_1(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (r2_hidden(k8_funct_2(k1_zf_lang,A,B,C),k8_funct_2(k1_zf_lang,A,B,D)) <-> r1_zf_model(A,B,k5_zf_lang(C,D))))))))))) # label(t13_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5553 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k1_zf_lang,A) & v1_funct_2(B,k1_zf_lang,A) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m1_subset_1(D,A) -> (exists E (v1_funct_1(E) & v1_funct_2(E,k1_zf_lang,A) & m2_relset_1(E,k1_zf_lang,A) & D = k8_funct_2(k1_zf_lang,A,E,C) & (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (C != F -> k8_funct_2(k1_zf_lang,A,B,F) = k8_funct_2(k1_zf_lang,A,E,F)))))))))))))) # label(t21_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5554 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (-v1_xboole_0(B) -> (v2_zf_lang(A) -> (all C (v1_funct_2(C,k1_zf_lang,B) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_1(C) -> (r2_hidden(C,k5_zf_model(A,B)) <-> k8_funct_2(k1_zf_lang,B,C,k19_zf_lang(A)) = k8_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)))))))))) # label(t7_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5555 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (-v1_xboole_0(B) -> (v4_zf_lang(A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k1_zf_lang,B) & m2_relset_1(C,k1_zf_lang,B) -> (-r2_hidden(C,k5_zf_model(k20_zf_lang(A),B)) <-> r2_hidden(C,k5_zf_model(A,B)))))))))) # label(t9_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5556 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k1_zf_lang,A) & m2_relset_1(B,k1_zf_lang,A) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (r1_zf_model(A,B,k4_zf_lang(C,D)) <-> k8_funct_2(k1_zf_lang,A,B,C) = k8_funct_2(k1_zf_lang,A,B,D)))))))))) # label(t12_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5557 (all A all B all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_1_zf_model(B,C)) <-> (exists D (A = D & (all E (v1_funct_1(E) & v1_funct_2(E,k1_zf_lang,B) & m2_relset_1(E,k1_zf_lang,B) -> (E = D -> r2_hidden(k8_funct_2(k1_zf_lang,B,E,k18_zf_lang(C)),k8_funct_2(k1_zf_lang,B,E,k19_zf_lang(C)))))) & m1_subset_1(D,k3_zf_model(B))))))) # label(fraenkel_a_2_1_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5558 (all A (-v1_xboole_0(A) -> (all B (B = k3_zf_model(A) <-> (all C (r2_hidden(C,B) <-> v1_funct_1(C) & v1_funct_2(C,k1_zf_lang,A) & m2_relset_1(C,k1_zf_lang,A))))))) # label(d2_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.38/113.45 5559 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k1_zf_lang,A) & m2_relset_1(C,k1_zf_lang,A) -> (-r2_hidden(C,k5_zf_model(B,A)) <-> r2_hidden(C,k5_zf_model(k6_zf_lang(B),A))))))))) # label(t4_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.47/113.46 5560 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) & r2_zf_model(A,k7_zf_model) & r2_zf_model(A,k8_zf_model) & r2_zf_model(A,k9_zf_model) & (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(B)) -> r2_zf_model(A,k11_zf_model(B))))) & r2_zf_model(A,k10_zf_model) <-> v1_zf_model(A)))) # label(d12_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.47/113.46 5561 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (-v1_xboole_0(B) -> (v5_zf_lang(A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k1_zf_lang,B) & m2_relset_1(C,k1_zf_lang,B) -> (r2_hidden(C,k5_zf_model(A,B)) <-> r2_hidden(C,k5_zf_model(k22_zf_lang(A),B)) & r2_hidden(C,k5_zf_model(k21_zf_lang(A),B)))))))))) # label(t10_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.47/113.46 5562 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k1_zf_lang,A) & v1_funct_2(B,k1_zf_lang,A) & v1_funct_1(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (r1_zf_model(A,B,k11_zf_lang(C,D)) <-> (r1_zf_model(A,B,C) -> r1_zf_model(A,B,D))))))))))) # label(t18_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.47/113.46 5563 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k1_zf_lang,A) & m2_relset_1(B,k1_zf_lang,A) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (r1_zf_model(A,B,k12_zf_lang(C,D)) <-> (r1_zf_model(A,B,C) <-> r1_zf_model(A,B,D))))))))))) # label(t19_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.47/113.46 5564 (all A all B all C all D (m2_subset_1(D,k5_numbers,k1_zf_lang) & m2_subset_1(C,k5_numbers,k1_zf_lang) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_0_zf_model(B,C,D)) <-> (exists E (A = E & (all F (v1_funct_1(F) & m2_relset_1(F,k1_zf_lang,B) & v1_funct_2(F,k1_zf_lang,B) -> (F = E -> k8_funct_2(k1_zf_lang,B,F,C) = k8_funct_2(k1_zf_lang,B,F,D)))) & m1_subset_1(E,k3_zf_model(B))))))) # label(fraenkel_a_3_0_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.47/113.46 5565 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v2_zf_lang(A) -> k2_tarski(k18_zf_lang(A),k19_zf_lang(A)) = k2_zf_model(A)) & (v4_zf_lang(A) -> k2_zf_model(A) = k2_zf_model(k20_zf_lang(A))) & (v6_zf_lang(A) -> k2_zf_model(A) = k4_xboole_0(k2_zf_model(k24_zf_lang(A)),k1_tarski(k23_zf_lang(A)))) & (v5_zf_lang(A) -> k2_zf_model(A) = k4_subset_1(k1_zf_lang,k2_zf_model(k21_zf_lang(A)),k2_zf_model(k22_zf_lang(A)))) & (v3_zf_lang(A) -> k2_zf_model(A) = k2_tarski(k18_zf_lang(A),k19_zf_lang(A))))) # label(t1_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.47/113.46 5566 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,A) & m2_relset_1(D,k1_zf_lang,A) -> (r2_hidden(D,k5_zf_model(k4_zf_lang(B,C),A)) <-> k8_funct_2(k1_zf_lang,A,D,C) = k8_funct_2(k1_zf_lang,A,D,B)))))))))) # label(t2_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.47/113.46 5567 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k1_zf_lang,A) & m2_relset_1(B,k1_zf_lang,A) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (r1_zf_model(A,B,C) & r1_zf_model(A,B,D) <-> r1_zf_model(A,B,k7_zf_lang(C,D))))))))))) # label(t15_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.47/113.46 5568 $T # label(dt_k3_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.47/113.46 5569 $T # label(dt_k1_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.47/113.46 5570 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C ((exists D ((all E (v1_zf_lang(E) & m2_finseq_1(E,k5_numbers) -> (all F (r2_hidden(k4_tarski(E,F),D) -> (v2_zf_lang(E) -> F = a_2_0_zf_model(B,E)) & -((all G -(r2_hidden(k4_tarski(k20_zf_lang(E),G),D) & F = k4_xboole_0(k3_zf_model(B),k3_tarski(k1_tarski(G))))) & v4_zf_lang(E)) & -((all G -(a_3_2_zf_model(B,E,G) = F & r2_hidden(k4_tarski(k24_zf_lang(E),G),D))) & v6_zf_lang(E)) & -((all G all H -(k3_xboole_0(k3_tarski(k1_tarski(G)),k3_tarski(k1_tarski(H))) = F & r2_hidden(k4_tarski(k21_zf_lang(E),G),D) & r2_hidden(k4_tarski(k22_zf_lang(E),H),D))) & v5_zf_lang(E)) & (v3_zf_lang(E) -> a_2_1_zf_model(B,E) = F))))) & r2_hidden(k4_tarski(A,C),D) & (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> r2_hidden(k4_tarski(k5_zf_lang(E,F),a_3_1_zf_model(B,E,F)),D) & r2_hidden(k4_tarski(k4_zf_lang(E,F),a_3_0_zf_model(B,E,F)),D))))))) <-> k4_zf_model(A,B) = C)))))) # label(d3_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5571 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_relset_1(D,k1_zf_lang,A) & v1_funct_2(D,k1_zf_lang,A) & v1_funct_1(D) -> (r2_hidden(k8_funct_2(k1_zf_lang,A,D,B),k8_funct_2(k1_zf_lang,A,D,C)) <-> r2_hidden(D,k5_zf_model(k5_zf_lang(B,C),A))))))))))) # label(t3_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5572 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (v1_funct_2(D,k1_zf_lang,A) & m2_relset_1(D,k1_zf_lang,A) & v1_funct_1(D) -> (r2_hidden(D,k5_zf_model(k7_zf_lang(B,C),A)) <-> r2_hidden(D,k5_zf_model(B,A)) & r2_hidden(D,k5_zf_model(C,A))))))))))) # label(t5_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5573 (all A all B (v1_zf_lang(A) & -v1_xboole_0(B) & m1_finseq_1(A,k5_numbers) -> m1_subset_1(k5_zf_model(A,B),k1_zfmisc_1(k3_zf_model(B))))) # label(dt_k5_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5574 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k1_zf_lang,A) & v1_funct_2(B,k1_zf_lang,A) & v1_funct_1(B) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (r1_zf_model(A,B,k10_zf_lang(C,D)) <-> r1_zf_model(A,B,D) | r1_zf_model(A,B,C)))))))))) # label(t17_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5575 (all A all B all C (-v1_xboole_0(B) & v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> ((exists D (m1_subset_1(D,k3_zf_model(B)) & A = D & (all E (v1_funct_1(E) & v1_funct_2(E,k1_zf_lang,B) & m2_relset_1(E,k1_zf_lang,B) -> (D = E -> k8_funct_2(k1_zf_lang,B,E,k18_zf_lang(C)) = k8_funct_2(k1_zf_lang,B,E,k19_zf_lang(C))))))) <-> r2_hidden(A,a_2_0_zf_model(B,C))))) # label(fraenkel_a_2_0_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5576 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B ((exists C (r2_hidden(k4_tarski(A,B),C) & (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (all E (r2_hidden(k4_tarski(D,E),C) -> -(v4_zf_lang(D) & (all F -(f3_s3_zf_model(F) = E & r2_hidden(k4_tarski(k20_zf_lang(D),F),C)))) & -((all F all G -(f4_s3_zf_model(F,G) = E & r2_hidden(k4_tarski(k22_zf_lang(D),G),C) & r2_hidden(k4_tarski(k21_zf_lang(D),F),C))) & v5_zf_lang(D)) & -((all F -(E = f5_s3_zf_model(k23_zf_lang(D),F) & r2_hidden(k4_tarski(k24_zf_lang(D),F),C))) & v6_zf_lang(D)) & (v3_zf_lang(D) -> f2_s3_zf_model(k18_zf_lang(D),k19_zf_lang(D)) = E) & (v2_zf_lang(D) -> f1_s3_zf_model(k18_zf_lang(D),k19_zf_lang(D)) = E))))) & (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> r2_hidden(k4_tarski(k5_zf_lang(D,E),f2_s3_zf_model(D,E)),C) & r2_hidden(k4_tarski(k4_zf_lang(D,E),f1_s3_zf_model(D,E)),C))))))) <-> f7_s3_zf_model(A) = B)))) -> (v2_zf_lang(f6_s3_zf_model) -> f1_s3_zf_model(k18_zf_lang(f6_s3_zf_model),k19_zf_lang(f6_s3_zf_model)) = f7_s3_zf_model(f6_s3_zf_model)) & (v4_zf_lang(f6_s3_zf_model) -> f3_s3_zf_model(f7_s3_zf_model(k20_zf_lang(f6_s3_zf_model))) = f7_s3_zf_model(f6_s3_zf_model)) & (v6_zf_lang(f6_s3_zf_model) -> f5_s3_zf_model(k23_zf_lang(f6_s3_zf_model),f7_s3_zf_model(k24_zf_lang(f6_s3_zf_model))) = f7_s3_zf_model(f6_s3_zf_model)) & (v5_zf_lang(f6_s3_zf_model) -> (all A all B (B = f7_s3_zf_model(k22_zf_lang(f6_s3_zf_model)) & f7_s3_zf_model(k21_zf_lang(f6_s3_zf_model)) = A -> f4_s3_zf_model(A,B) = f7_s3_zf_model(f6_s3_zf_model)))) & (v3_zf_lang(f6_s3_zf_model) -> f7_s3_zf_model(f6_s3_zf_model) = f2_s3_zf_model(k18_zf_lang(f6_s3_zf_model),k19_zf_lang(f6_s3_zf_model))) # label(s3_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5577 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (-v1_xboole_0(B) -> (v6_zf_lang(A) -> (all C (v1_funct_2(C,k1_zf_lang,B) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_1(C) -> ((all D (v1_funct_2(D,k1_zf_lang,B) & m2_relset_1(D,k1_zf_lang,B) & v1_funct_1(D) -> ((all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (k8_funct_2(k1_zf_lang,B,C,E) != k8_funct_2(k1_zf_lang,B,D,E) -> k23_zf_lang(A) = E))) -> r2_hidden(D,k5_zf_model(k24_zf_lang(A),B))))) & r2_hidden(C,k5_zf_model(k24_zf_lang(A),B)) <-> r2_hidden(C,k5_zf_model(A,B)))))))))) # label(t11_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5578 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m1_subset_1(k2_zf_model(A),k1_zfmisc_1(k1_zf_lang)))) # label(dt_k2_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5579 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B ((exists C ((all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (all E (r2_hidden(k4_tarski(D,E),C) -> (v2_zf_lang(D) -> k2_tarski(k18_zf_lang(D),k19_zf_lang(D)) = E) & -((all F all G -(r2_hidden(k4_tarski(k22_zf_lang(D),G),C) & r2_hidden(k4_tarski(k21_zf_lang(D),F),C) & k3_tarski(k2_tarski(F,G)) = E)) & v5_zf_lang(D)) & -((all F -(r2_hidden(k4_tarski(k24_zf_lang(D),F),C) & E = k4_xboole_0(k3_tarski(k1_tarski(F)),k1_tarski(k23_zf_lang(D))))) & v6_zf_lang(D)) & -(v4_zf_lang(D) & (all F -(r2_hidden(k4_tarski(k20_zf_lang(D),F),C) & F = E))) & (v3_zf_lang(D) -> k2_tarski(k18_zf_lang(D),k19_zf_lang(D)) = E))))) & r2_hidden(k4_tarski(A,B),C) & (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> r2_hidden(k4_tarski(k4_zf_lang(D,E),k2_tarski(D,E)),C) & r2_hidden(k4_tarski(k5_zf_lang(D,E),k2_tarski(D,E)),C))))))) <-> B = k1_zf_model(A))))) # label(d1_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5580 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (-v1_xboole_0(B) -> (v3_zf_lang(A) -> (all C (v1_funct_2(C,k1_zf_lang,B) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_1(C) -> (r2_hidden(C,k5_zf_model(A,B)) <-> r2_hidden(k8_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)),k8_funct_2(k1_zf_lang,B,C,k19_zf_lang(A))))))))))) # label(t8_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5581 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> (r2_zf_model(C,A) <-> r2_zf_model(C,k8_zf_lang(B,A))))))))) # label(t25_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5582 (all A (-v1_xboole_0(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r2_zf_model(A,B) <-> (all C (v1_funct_2(C,k1_zf_lang,A) & m2_relset_1(C,k1_zf_lang,A) & v1_funct_1(C) -> r1_zf_model(A,C,B)))))))) # label(d5_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5583 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> v1_zf_lang(k11_zf_model(A)) & m2_finseq_1(k11_zf_model(A),k5_numbers))) # label(dt_k11_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5584 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k1_zf_lang,A) & m2_relset_1(B,k1_zf_lang,A) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r2_hidden(B,k5_zf_model(C,A)) <-> r1_zf_model(A,B,C)))))))) # label(d4_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5585 (all A all B (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) & -v1_xboole_0(B) -> k4_zf_model(A,B) = k5_zf_model(A,B))) # label(redefinition_k5_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5586 $T # label(dt_k4_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5587 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> k1_zf_model(A) = k2_zf_model(A))) # label(redefinition_k2_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5588 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k1_zf_lang,D) & v1_funct_2(E,k1_zf_lang,D) -> ((all F (v1_funct_2(F,k1_zf_lang,D) & m2_relset_1(F,k1_zf_lang,D) & v1_funct_1(F) -> ((all G (m2_subset_1(G,k5_numbers,k1_zf_lang) -> -(G != C & B != G & k8_funct_2(k1_zf_lang,D,E,G) != k8_funct_2(k1_zf_lang,D,F,G)))) -> r1_zf_model(D,F,A)))) <-> r1_zf_model(D,E,k14_zf_lang(B,C,A))))))))))))) # label(t22_zf_model) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5589 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (r2_hidden(B,k1_zf_colla(A,k1_xboole_0)) <-> (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))))) # label(t2_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5590 (all A (-v1_xboole_0(A) -> (all B (v3_ordinal1(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_hidden(D,k1_zf_colla(A,B)) & r2_hidden(C,D) -> r2_hidden(C,k1_zf_colla(A,B)) & (exists E (r2_hidden(C,k1_zf_colla(A,E)) & r2_hidden(E,B) & v3_ordinal1(E)))))))))))) # label(t6_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5591 (all A all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & r1_zf_colla(C,A,B))) <-> r2_zf_colla(A,B))) # label(d3_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5592 $T # label(dt_k1_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5593 (all A (-v1_xboole_0(A) -> (all B (v3_ordinal1(B) -> a_2_1_zf_colla(A,B) = k1_zf_colla(A,B))))) # label(t1_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5594 (all A all B all C all D (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v3_ordinal1(D) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_0_zf_colla(B,C,D)) <-> (exists E (m1_subset_1(E,B) & (all F (m1_subset_1(F,B) -> -(r2_hidden(F,E) & (all G (v3_ordinal1(G) -> -(r2_hidden(F,k3_tarski(k1_tarski(k1_funct_1(k2_ordinal1(C,D),G)))) & r2_hidden(G,k1_relat_1(k2_ordinal1(C,D))))))))) & A = E))))) # label(fraenkel_a_3_0_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5595 (all A all B all C (-v1_xboole_0(B) & v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) -> ((exists D (m1_subset_1(D,B) & (all E (m1_subset_1(E,B) -> -((all F (v3_ordinal1(F) -> -(r2_hidden(E,k3_tarski(k1_tarski(k1_funct_1(C,F)))) & r2_hidden(F,k1_relat_1(C))))) & r2_hidden(E,D)))) & A = D)) <-> r2_hidden(A,a_2_0_zf_colla(B,C))))) # label(fraenkel_a_2_0_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5596 (all A (-v1_xboole_0(A) -> (exists B (v1_relat_1(B) & v1_funct_1(B) & k1_relat_1(B) = A & (all C (m1_subset_1(C,A) -> k9_relat_1(B,C) = k1_funct_1(B,C))))))) # label(t9_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5597 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (exists C (v3_ordinal1(C) & r2_hidden(B,k1_zf_colla(A,C)))))))) # label(t5_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5598 (all A (-v1_xboole_0(A) -> (r2_zf_model(A,k6_zf_model) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) <-> r2_hidden(D,C)))) -> C = B)))))))) # label(t13_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5599 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (k1_relat_1(A) = B & C = k2_relat_1(A) & (all D all E (r2_hidden(D,B) & r2_hidden(E,B) -> -((exists F (E = F & r2_hidden(D,F))) & (all F -(F = k1_funct_1(A,E) & r2_hidden(k1_funct_1(A,D),F)))) & -((all F -(E = F & r2_hidden(D,F))) & (exists F (k1_funct_1(A,E) = F & r2_hidden(k1_funct_1(A,D),F)))))) & v2_funct_1(A) <-> r1_zf_colla(A,B,C))))) # label(d2_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5600 $T # label(t10_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5601 (all A (-v1_xboole_0(A) -> (all B (v3_ordinal1(B) -> (all C (m1_subset_1(C,A) -> (r2_hidden(C,k1_zf_colla(A,k1_ordinal1(B))) <-> r1_tarski(k3_xboole_0(C,A),k1_zf_colla(A,B))))))))) # label(t3_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.52 5602 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (m1_subset_1(C,A) -> k9_relat_1(B,C) = k1_funct_1(B,C))) & k1_relat_1(B) = A -> v1_ordinal1(k2_relat_1(B))))))) # label(t12_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5603 (all A (-v1_xboole_0(A) -> -(r2_zf_model(A,k6_zf_model) & (all B -(r2_zf_colla(A,B) & v1_ordinal1(B)))))) # label(t14_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5604 (all A (-v1_xboole_0(A) -> (all B (v3_ordinal1(B) -> (all C ((exists D (v1_funct_1(D) & v5_ordinal1(D) & B = k1_relat_1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(E,B) -> a_3_0_zf_colla(A,D,E) = k1_funct_1(D,E)))) & C = a_2_0_zf_colla(A,D) & v1_relat_1(D))) <-> k1_zf_colla(A,B) = C)))))) # label(d1_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5605 (all A (-v1_xboole_0(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(B,C) -> r1_tarski(k1_zf_colla(A,B),k1_zf_colla(A,C))))))))) # label(t4_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5606 $T # label(t11_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5607 (all A all B all C (v3_ordinal1(C) & -v1_xboole_0(B) -> ((exists D (m1_subset_1(D,B) & (all E (m1_subset_1(E,B) -> -(r2_hidden(E,D) & (all F (v3_ordinal1(F) -> -(r2_hidden(E,k1_zf_colla(B,F)) & r2_hidden(F,C))))))) & D = A)) <-> r2_hidden(A,a_2_1_zf_colla(B,C))))) # label(fraenkel_a_2_1_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5608 (all A (-v1_xboole_0(A) -> (exists B (k1_zf_colla(A,B) = A & v3_ordinal1(B))))) # label(t8_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5609 (all A (-v1_xboole_0(A) -> (all B (v3_ordinal1(B) -> r1_tarski(k1_zf_colla(A,B),A))))) # label(t7_zf_colla) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5610 $T # label(t26_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5611 (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]. 115.50/113.53 5612 (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]. 115.50/113.53 5613 $T # label(t83_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5614 (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]. 115.50/113.53 5615 $T # label(t15_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5616 (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]. 115.50/113.53 5617 $T # label(t39_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5618 $T # label(t40_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5619 $T # label(t11_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5620 $T # label(t168_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5621 $T # label(t32_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5622 (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]. 115.50/113.53 5623 $T # label(t101_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5624 $T # label(t27_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5625 (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]. 115.50/113.53 5626 (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]. 115.50/113.53 5627 (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]. 115.50/113.53 5628 $T # label(t81_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5629 (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]. 115.50/113.53 5630 $T # label(t74_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5631 $T # label(t24_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5632 (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]. 115.50/113.53 5633 $T # label(t90_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5634 (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]. 115.50/113.53 5635 $T # label(t57_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5636 $T # label(t50_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5637 $T # label(t102_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5638 (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]. 115.50/113.53 5639 $T # label(t56_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5640 (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]. 115.50/113.53 5641 $T # label(t75_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5642 (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]. 115.50/113.53 5643 $T # label(t79_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5644 $T # label(t76_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5645 $T # label(t82_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5646 $T # label(t53_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5647 (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]. 115.50/113.53 5648 (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]. 115.50/113.53 5649 $T # label(t145_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5650 (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]. 115.50/113.53 5651 $T # label(t72_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5652 $T # label(t154_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5653 (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]. 115.50/113.53 5654 $T # label(t63_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5655 $T # label(t34_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5656 (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]. 115.50/113.53 5657 $T # label(t20_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5658 $T # label(t144_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5659 $T # label(t43_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5660 (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]. 115.50/113.53 5661 (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]. 115.50/113.53 5662 $T # label(t153_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5663 (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]. 115.50/113.53 5664 (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]. 115.50/113.53 5665 $T # label(t103_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5666 $T # label(t22_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5667 (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]. 115.50/113.53 5668 (all A (v1_orders_1(k6_partfun1(A)) & v2_orders_1(k6_partfun1(A)))) # label(t120_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5669 (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]. 115.50/113.53 5670 $T # label(t116_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5671 (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]. 115.50/113.53 5672 (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]. 115.50/113.53 5673 (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]. 115.50/113.53 5674 $T # label(t55_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5675 $T # label(t147_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5676 $T # label(t23_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5677 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v1_orders_1(A)))) # label(t109_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5678 $T # label(t71_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5679 (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]. 115.50/113.53 5680 (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]. 115.50/113.53 5681 $T # label(t171_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5682 (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]. 115.50/113.53 5683 $T # label(t61_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5684 (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]. 115.50/113.53 5685 $T # label(t21_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5686 $T # label(t18_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5687 (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]. 115.50/113.53 5688 $T # label(t123_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5689 $T # label(t46_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5690 $T # label(t86_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5691 (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]. 115.50/113.53 5692 (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]. 115.50/113.53 5693 (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]. 115.50/113.53 5694 $T # label(t58_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5695 (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]. 115.50/113.53 5696 (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]. 115.50/113.53 5697 (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]. 115.50/113.53 5698 (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]. 115.50/113.53 5699 $T # label(t28_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5700 $T # label(t1_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5701 $T # label(t3_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5702 (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]. 115.50/113.53 5703 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_orders_1(A)))) # label(fc1_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5704 $T # label(t42_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5705 $T # label(t51_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5706 (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]. 115.50/113.53 5707 $T # label(t2_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5708 $T # label(t17_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5709 (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]. 115.50/113.53 5710 (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]. 115.50/113.53 5711 (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]. 115.50/113.53 5712 $T # label(t148_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5713 (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]. 115.50/113.53 5714 (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]. 115.50/113.53 5715 $T # label(t59_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5716 $T # label(t73_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5717 (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]. 115.50/113.53 5718 (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]. 115.50/113.53 5719 (all A (-v1_xboole_0(A) -> r2_hidden(A,k1_orders_1(A)))) # label(t7_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5720 (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]. 115.50/113.53 5721 (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]. 115.50/113.53 5722 (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]. 115.50/113.53 5723 (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]. 115.50/113.53 5724 $T # label(t155_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5725 (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]. 115.50/113.53 5726 $T # label(t118_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5727 $T # label(t29_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5728 $T # label(t37_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5729 (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]. 115.50/113.53 5730 (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]. 115.50/113.53 5731 (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]. 115.50/113.53 5732 (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]. 115.50/113.53 5733 $T # label(t8_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5734 (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]. 115.50/113.53 5735 (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]. 115.50/113.53 5736 $T # label(t30_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5737 $T # label(t38_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5738 $T # label(t49_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5739 $T # label(t117_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5740 $T # label(t85_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5741 (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]. 115.50/113.53 5742 $T # label(t78_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5743 (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]. 115.50/113.53 5744 $T # label(t172_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5745 (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]. 115.50/113.53 5746 $T # label(t16_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.50/113.53 5747 (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]. 115.56/113.57 5748 $T # label(t89_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5749 (all A (-v1_xboole_0(A) -> (exists B m1_orders_1(B,A)))) # label(existence_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5750 (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]. 115.56/113.57 5751 (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]. 115.56/113.57 5752 $T # label(t41_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5753 (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]. 115.56/113.57 5754 $T # label(dt_k1_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5755 $T # label(t52_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5756 $T # label(t80_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5757 (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]. 115.56/113.57 5758 $T # label(t10_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5759 $T # label(t77_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5760 (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]. 115.56/113.57 5761 (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]. 115.56/113.57 5762 (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]. 115.56/113.57 5763 (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]. 115.56/113.57 5764 (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]. 115.56/113.57 5765 $T # label(t60_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5766 $T # label(t47_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5767 $T # label(t169_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5768 $T # label(t88_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5769 $T # label(t87_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5770 (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]. 115.56/113.57 5771 $T # label(t36_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5772 $T # label(t9_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5773 $T # label(t19_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5774 $T # label(t167_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5775 $T # label(t33_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5776 $T # label(t170_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5777 $T # label(t66_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5778 (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]. 115.56/113.57 5779 $T # label(t35_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5780 (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]. 115.56/113.57 5781 $T # label(t45_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5782 (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]. 115.56/113.57 5783 $T # label(t25_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5784 (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]. 115.56/113.57 5785 (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]. 115.56/113.57 5786 (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]. 115.56/113.57 5787 $T # label(t67_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5788 $T # label(t44_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5789 (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]. 115.56/113.57 5790 $T # label(t70_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5791 $T # label(t64_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5792 (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]. 115.56/113.57 5793 (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]. 115.56/113.57 5794 $T # label(t156_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5795 (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]. 115.56/113.57 5796 (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]. 115.56/113.57 5797 $T # label(t31_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5798 (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]. 115.56/113.57 5799 (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]. 115.56/113.57 5800 (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]. 115.56/113.57 5801 $T # label(t122_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5802 (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]. 115.56/113.57 5803 $T # label(t84_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5804 $T # label(t65_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5805 $T # label(t54_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.56/113.57 5806 (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]. 115.62/113.61 5807 $T # label(t62_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5808 (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]. 115.62/113.61 5809 $T # label(t121_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5810 (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]. 115.62/113.61 5811 $T # label(t68_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5812 (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]. 115.62/113.61 5813 (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]. 115.62/113.61 5814 (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]. 115.62/113.61 5815 (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]. 115.62/113.61 5816 (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]. 115.62/113.61 5817 (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]. 115.62/113.61 5818 $T # label(t48_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5819 (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]. 115.62/113.61 5820 (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]. 115.62/113.61 5821 (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]. 115.62/113.61 5822 $T # label(t69_orders_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5823 (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]. 115.62/113.61 5824 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5825 (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]. 115.62/113.61 5826 (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]. 115.62/113.61 5827 (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]. 115.62/113.61 5828 (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]. 115.62/113.61 5829 (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]. 115.62/113.61 5830 (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]. 115.62/113.61 5831 (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]. 115.62/113.61 5832 (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]. 115.62/113.61 5833 (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]. 115.62/113.61 5834 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5835 (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]. 115.62/113.61 5836 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5837 (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]. 115.62/113.61 5838 (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]. 115.62/113.61 5839 (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]. 115.62/113.61 5840 (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]. 115.62/113.61 5841 (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]. 115.62/113.61 5842 (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]. 115.62/113.61 5843 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5844 (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]. 115.62/113.61 5845 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5846 (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]. 115.62/113.61 5847 (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]. 115.62/113.61 5848 (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]. 115.62/113.61 5849 (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]. 115.62/113.61 5850 (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]. 115.62/113.61 5851 (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]. 115.62/113.61 5852 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5853 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5854 (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]. 115.62/113.61 5855 (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]. 115.62/113.61 5856 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5857 (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]. 115.62/113.61 5858 (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]. 115.62/113.61 5859 (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]. 115.62/113.61 5860 (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]. 115.62/113.61 5861 (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]. 115.62/113.61 5862 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5863 (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]. 115.62/113.61 5864 (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]. 115.62/113.61 5865 (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]. 115.62/113.61 5866 (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]. 115.62/113.61 5867 (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]. 115.62/113.61 5868 (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]. 115.62/113.61 5869 (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]. 115.62/113.61 5870 (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]. 115.62/113.61 5871 (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]. 115.62/113.61 5872 (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]. 115.62/113.61 5873 (all A k2_zfmisc_1(A,A) = k1_eqrel_1(A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5874 (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]. 115.62/113.61 5875 (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]. 115.62/113.61 5876 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5877 (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]. 115.62/113.61 5878 (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]. 115.62/113.61 5879 (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]. 115.62/113.61 5880 (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]. 115.62/113.61 5881 (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]. 115.62/113.61 5882 (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]. 115.62/113.61 5883 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5884 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5885 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5886 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5887 (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]. 115.62/113.61 5888 (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]. 115.62/113.61 5889 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5890 (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]. 115.62/113.61 5891 (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]. 115.62/113.61 5892 (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]. 115.62/113.61 5893 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5894 (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]. 115.62/113.61 5895 (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]. 115.62/113.61 5896 (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]. 115.62/113.61 5897 (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]. 115.62/113.61 5898 (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]. 115.62/113.61 5899 (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]. 115.62/113.61 5900 (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]. 115.62/113.61 5901 (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]. 115.62/113.61 5902 (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]. 115.62/113.61 5903 (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]. 115.62/113.61 5904 (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]. 115.62/113.61 5905 (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]. 115.62/113.61 5906 (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]. 115.62/113.61 5907 (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]. 115.62/113.61 5908 (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]. 115.62/113.61 5909 (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]. 115.62/113.61 5910 (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]. 115.62/113.61 5911 (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]. 115.62/113.61 5912 (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]. 115.62/113.61 5913 $T # label(t22_funct_5) # label(axiom) # label(non_clause). [assumption]. 115.62/113.61 5914 (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]. 115.62/113.61 5915 (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]. 115.62/113.61 5916 (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]. 115.62/113.61 5917 (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]. 115.62/113.61 5918 (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]. 115.62/113.61 5919 (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]. 115.62/113.61 5920 (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]. 115.62/113.61 5921 (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]. 115.62/113.61 5922 (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]. 115.62/113.61 5923 (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]. 115.62/113.61 5924 (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]. 115.62/113.61 5925 (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]. 115.62/113.61 5926 (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]. 115.62/113.61 5927 (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]. 115.62/113.61 5928 (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]. 115.62/113.61 5929 (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]. 115.62/113.61 5930 (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]. 115.62/113.62 5931 $T # label(t24_funct_5) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5932 (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]. 115.62/113.62 5933 (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]. 115.62/113.62 5934 (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]. 115.62/113.62 5935 (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]. 115.62/113.62 5936 $T # label(t2_funct_5) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5937 (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]. 115.62/113.62 5938 (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]. 115.62/113.62 5939 (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]. 115.62/113.62 5940 (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]. 115.62/113.62 5941 $T # label(dt_k1_funct_5) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5942 (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]. 115.62/113.62 5943 (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]. 115.62/113.62 5944 (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]. 115.62/113.62 5945 (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]. 115.62/113.62 5946 (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]. 115.62/113.62 5947 (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]. 115.62/113.62 5948 (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]. 115.62/113.62 5949 (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]. 115.62/113.62 5950 (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]. 115.62/113.62 5951 (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]. 115.62/113.62 5952 (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]. 115.62/113.62 5953 (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]. 115.62/113.62 5954 (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]. 115.62/113.62 5955 (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]. 115.62/113.62 5956 (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]. 115.62/113.62 5957 (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]. 115.62/113.62 5958 $T # label(dt_k2_funct_5) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5959 (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]. 115.62/113.62 5960 (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]. 115.62/113.62 5961 (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]. 115.62/113.62 5962 (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]. 115.62/113.62 5963 (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]. 115.62/113.62 5964 $T # label(t25_funct_5) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5965 (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]. 115.62/113.62 5966 (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]. 115.62/113.62 5967 (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]. 115.62/113.62 5968 (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]. 115.62/113.62 5969 (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]. 115.62/113.62 5970 (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]. 115.62/113.62 5971 $T # label(t14_funct_5) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5972 $T # label(t23_funct_5) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5973 (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]. 115.62/113.62 5974 (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]. 115.62/113.62 5975 (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]. 115.62/113.62 5976 (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]. 115.62/113.62 5977 (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]. 115.62/113.62 5978 (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]. 115.62/113.62 5979 $T # label(t3_funct_5) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5980 (all A k1_funct_2(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t64_funct_5) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5981 (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]. 115.62/113.62 5982 (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]. 115.62/113.62 5983 (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]. 115.62/113.62 5984 (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]. 115.62/113.62 5985 (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]. 115.62/113.62 5986 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r1_xboole_0(A,B) -> k1_nat_1(k4_card_1(A),k4_card_1(B)) = k4_card_1(k2_xboole_0(A,B))))))) # label(t53_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5987 (all A all B all C (r2_wellord2(k2_zfmisc_1(k2_zfmisc_1(A,B),C),k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & k1_card_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C)) = k1_card_1(k2_zfmisc_1(A,k2_zfmisc_1(B,C))))) # label(t12_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5988 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k3_card_2(k1_card_2(A,B),np__2) = k1_card_2(k1_card_2(k2_card_2(A,A),k2_card_2(k2_card_2(np__2,A),B)),k2_card_2(B,B)))))) # label(t46_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5989 (all A all B (v1_card_1(A) & v1_card_1(B) -> v1_card_1(k1_card_2(A,B)))) # label(dt_k1_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5990 (all A (v1_card_1(A) -> np__0 = k2_card_2(A,np__0))) # label(t32_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5991 (all A all B r1_tarski(k1_card_1(k2_xboole_0(A,B)),k1_card_2(k1_card_1(A),k1_card_1(B)))) # label(t47_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5992 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k1_card_1(k14_ordinal2(A,B)) = k1_card_2(A,B))))) # label(d1_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5993 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> k4_card_1(k2_zfmisc_1(A,B)) = k2_nat_1(k4_card_1(A),k4_card_1(B)))))) # label(t65_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5994 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k1_card_1(k1_funct_2(B,A)) = k3_card_2(A,B))))) # label(d3_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5995 (all A all B all C all D (k1_card_1(k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))) = k1_card_1(k2_xboole_0(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C))) & r2_wellord2(k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)),k2_xboole_0(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C))))) # label(t27_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5996 (all A all B -(k4_xboole_0(B,A) = k1_xboole_0 & r2_hidden(k1_card_1(A),k1_card_1(B)))) # label(t4_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5997 (all A k3_card_2(np__2,k1_card_1(A)) = k1_card_1(k1_zfmisc_1(A))) # label(t44_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5998 (all A all B (r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(A,k1_card_1(B))) & r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(k1_card_1(A),k1_card_1(B))) & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(k1_card_1(A),k1_card_1(B))) & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(A,k1_card_1(B))) & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(k1_card_1(A),B)) & r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(k1_card_1(A),B)))) # label(t14_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 5999 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k2_card_2(k1_card_1(A),k1_card_1(B)) = k1_card_1(k15_ordinal2(A,B)))))) # label(t25_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6000 (all A (v1_card_1(A) -> k3_card_2(A,np__0) = np__1)) # label(t38_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6001 (all A (np__0 = k1_card_1(A) -> k1_xboole_0 = A)) # label(t59_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6002 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r2_hidden(k1_card_1(A),k1_card_1(B)) <-> -r1_xreal_0(k4_card_1(B),k4_card_1(A))))))) # label(t58_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6003 (all A all B all C all D all E all F all G r1_xreal_0(k4_card_1(k5_enumset1(A,B,C,D,E,F,G)),np__7)) # label(t74_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6004 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,A) -> k4_card_1(k4_xboole_0(A,B)) = k5_real_1(k4_card_1(A),k4_card_1(B))))))) # label(t63_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6005 $T # label(t55_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6006 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r1_xreal_0(k4_card_1(A),k4_card_1(B)) <-> r1_tarski(k1_card_1(A),k1_card_1(B))))))) # label(t57_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6007 (all A all B all C all D all E r1_xreal_0(k4_card_1(k3_enumset1(A,B,C,D,E)),np__5)) # label(t72_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6008 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k1_card_2(k1_card_1(A),k1_card_1(B)) = k1_card_1(k14_ordinal2(A,B)))))) # label(t24_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6009 (all A (v1_card_1(A) -> k2_card_2(np__2,A) = k1_card_2(A,A))) # label(t36_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6010 (all A all B (v1_card_1(A) & v1_card_1(B) -> v1_card_1(k2_card_2(A,B)))) # label(dt_k2_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6011 (all A all B (A != B -> np__2 = k4_card_1(k2_tarski(A,B)))) # label(t76_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6012 (all A (v1_finset_1(A) -> -((all B all C -(k2_tarski(B,C) = A & B != C)) & np__2 = k4_card_1(A)))) # label(t79_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6013 (all A all B (v1_finset_1(B) -> (-r2_hidden(A,B) -> k1_nat_1(k4_card_1(B),np__1) = k4_card_1(k2_xboole_0(B,k1_tarski(A)))))) # label(t54_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6014 (all A all B (v1_card_1(A) & v1_card_1(B) -> k2_card_2(A,B) = k2_card_2(B,A))) # label(commutativity_k2_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6015 (all A all B ((exists C (r1_tarski(A,k9_relat_1(C,B)) & v1_funct_1(C) & v1_relat_1(C))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t2_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6016 (all A all B r1_xreal_0(k4_card_1(k2_tarski(A,B)),np__2)) # label(t69_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6017 (all A all B all C all D all E all F all G all H r1_xreal_0(k4_card_1(k6_enumset1(A,B,C,D,E,F,G,H)),np__8)) # label(t75_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6018 $T # label(t66_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6019 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r2_wellord2(k15_ordinal2(A,B),k2_zfmisc_1(A,B)) & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k15_ordinal2(A,B)))))) # label(t18_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6020 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k1_card_1(k2_zfmisc_1(A,B)) = k2_card_2(A,B))))) # label(d2_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6021 $T # label(t56_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6022 (all A all B (v1_card_1(A) & v1_card_1(B) -> v1_card_1(k3_card_2(A,B)))) # label(dt_k3_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6023 (all A all B (v1_finset_1(B) -> -r2_hidden(k1_card_1(A),k1_card_1(B)) & -r1_tarski(k1_card_1(A),k1_card_1(B)) | v1_finset_1(A))) # label(t68_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6024 $T # label(t21_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6025 (all A all B (k1_card_1(k2_xboole_0(k2_zfmisc_1(B,k1_tarski(np__0)),k2_zfmisc_1(A,k1_tarski(np__1)))) = k1_card_1(k2_xboole_0(k2_zfmisc_1(A,k1_tarski(np__0)),k2_zfmisc_1(B,k1_tarski(np__1)))) & r2_wellord2(k2_xboole_0(k2_zfmisc_1(A,k1_tarski(np__0)),k2_zfmisc_1(B,k1_tarski(np__1))),k2_xboole_0(k2_zfmisc_1(B,k1_tarski(np__0)),k2_zfmisc_1(A,k1_tarski(np__1)))))) # label(t26_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6026 (all A ((all B all C -(-r1_tarski(B,C) & -r1_tarski(C,B) & r2_hidden(C,A) & r2_hidden(B,A))) & v1_finset_1(A) -> A = k1_xboole_0 | r2_hidden(k3_tarski(A),A))) # label(t81_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6027 (all A all B all C all D all E all F all G all H (r2_wellord2(A,B) & r2_wellord2(C,D) -> H = G | r2_wellord2(k2_xboole_0(k2_zfmisc_1(A,k1_tarski(E)),k2_zfmisc_1(C,k1_tarski(F))),k2_xboole_0(k2_zfmisc_1(B,k1_tarski(G)),k2_zfmisc_1(D,k1_tarski(H)))) & k1_card_1(k2_xboole_0(k2_zfmisc_1(A,k1_tarski(E)),k2_zfmisc_1(C,k1_tarski(F)))) = k1_card_1(k2_xboole_0(k2_zfmisc_1(B,k1_tarski(G)),k2_zfmisc_1(D,k1_tarski(H)))) | E = F)) # label(t23_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6028 (all A all B (v1_card_1(B) & v1_card_1(A) -> k1_card_2(B,A) = k1_card_2(A,B))) # label(commutativity_k1_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6029 (all A (v1_finset_1(A) -> r2_wellord2(A,k4_card_1(A)) & r2_wellord2(A,k2_finseq_1(k4_card_1(A))) & r2_wellord2(A,k1_card_1(k4_card_1(A))))) # label(t61_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6030 (all A all B all C all D all E all F r1_xreal_0(k4_card_1(k4_enumset1(A,B,C,D,E,F)),np__6)) # label(t73_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6031 (all A all B all C all D -(A != B & A != C & A != D & C != D & np__4 != k4_card_1(k2_enumset1(A,B,C,D)) & B != D & C != B)) # label(t78_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6032 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_card_1(k9_relat_1(B,A)),k1_card_1(A)))) # label(t3_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6033 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k14_ordinal2(A,B) = k1_nat_1(A,B))))) # label(t49_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6034 (all A (v1_card_1(A) -> (np__0 != A -> np__0 = k3_card_2(np__0,A)))) # label(t39_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6035 (all A all B (k1_card_1(A) = k1_card_1(k2_zfmisc_1(A,k1_tarski(B))) & r2_wellord2(A,k2_zfmisc_1(A,k1_tarski(B))))) # label(t13_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6036 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k2_card_2(k1_card_1(A),k1_card_1(B)) = k1_card_1(k2_nat_1(A,B)))))) # label(t52_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6037 (all A all B all C (r2_hidden(A,k1_funct_2(B,C)) -> k1_card_1(A) = k1_card_1(B) & r2_wellord2(A,B))) # label(t7_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6038 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> k1_card_2(k1_card_2(A,B),C) = k1_card_2(A,k1_card_2(B,C)))))))) # label(t31_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6039 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C all D (C != D -> r2_wellord2(k14_ordinal2(A,B),k2_xboole_0(k2_zfmisc_1(A,k1_tarski(C)),k2_zfmisc_1(B,k1_tarski(D)))) & k1_card_1(k14_ordinal2(A,B)) = k1_card_1(k2_xboole_0(k2_zfmisc_1(A,k1_tarski(C)),k2_zfmisc_1(B,k1_tarski(D)))))))))) # label(t16_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6040 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> k3_card_2(k3_card_2(A,B),C) = k3_card_2(A,k2_card_2(B,C)))))))) # label(t43_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6041 (all A (k1_card_1(k1_zfmisc_1(A)) = k1_card_1(k1_zfmisc_1(k1_card_1(A))) & r2_wellord2(k1_zfmisc_1(A),k1_zfmisc_1(k1_card_1(A))))) # label(t6_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6042 (all A all B all C all D (r2_wellord2(A,B) & r2_wellord2(C,D) -> r2_wellord2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) & k1_card_1(k2_zfmisc_1(A,C)) = k1_card_1(k2_zfmisc_1(B,D)))) # label(t15_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6043 $T # label(t1_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6044 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C all D (C != D -> k1_card_2(A,B) = k1_card_1(k2_xboole_0(k2_zfmisc_1(A,k1_tarski(C)),k2_zfmisc_1(B,k1_tarski(D)))) & r2_wellord2(k1_card_2(A,B),k2_xboole_0(k2_zfmisc_1(A,k1_tarski(C)),k2_zfmisc_1(B,k1_tarski(D)))))))))) # label(t17_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6045 $T # label(t30_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6046 (all A (v1_card_1(A) -> k2_card_2(A,A) = k3_card_2(A,np__2))) # label(t45_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6047 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> k3_card_2(A,k1_card_2(B,C)) = k2_card_2(k3_card_2(A,B),k3_card_2(A,C)))))))) # label(t41_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6048 (all A all B all C r1_xreal_0(k4_card_1(k1_enumset1(A,B,C)),np__3)) # label(t70_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6049 $T # label(t34_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6050 (all A all B all C -(C != B & k4_card_1(k1_enumset1(A,B,C)) != np__3 & A != C & A != B)) # label(t77_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6051 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> r1_xreal_0(k4_card_1(k2_xboole_0(A,B)),k1_nat_1(k4_card_1(A),k4_card_1(B))))))) # label(t62_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6052 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> k2_card_2(A,k2_card_2(B,C)) = k2_card_2(k2_card_2(A,B),C))))))) # label(t35_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6053 (all A (v1_card_1(A) -> np__1 = k3_card_2(np__1,A) & k3_card_2(A,np__1) = A)) # label(t40_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6054 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_ordinal1(k1_card_1(k2_relat_1(A)),k1_card_1(k1_relat_1(A))))) # label(t80_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6055 (all A (v1_card_1(A) -> k1_card_2(A,np__0) = A)) # label(t29_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6056 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> k3_card_2(k2_card_2(A,B),C) = k2_card_2(k3_card_2(A,C),k3_card_2(B,C)))))))) # label(t42_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6057 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k2_nat_1(A,B) = k15_ordinal2(A,B))))) # label(t50_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6058 (all A all B (r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(B,A)))) # label(t11_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6059 (all A all B all C (r2_hidden(A,B) & r2_wellord2(B,C) -> k1_xboole_0 != C & (exists D r2_hidden(D,C)))) # label(t5_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6060 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k1_card_2(k1_card_1(A),k1_card_1(B)) = k1_card_1(k1_nat_1(A,B)))))) # label(t51_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6061 (all A all B all C all D r1_xreal_0(k4_card_1(k2_enumset1(A,B,C,D)),np__4)) # label(t71_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6062 (all A (v1_card_1(A) -> A = k2_card_2(A,np__1))) # label(t33_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6063 (all A all B (r1_xboole_0(A,B) -> k1_card_1(k2_xboole_0(A,B)) = k1_card_2(k1_card_1(A),k1_card_1(B)))) # label(t48_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6064 (all A all B all C all D (A != B -> k1_card_1(k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B)))) = k1_card_2(k1_card_1(C),k1_card_1(D)))) # label(t28_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6065 (all A (np__1 = k1_card_1(A) <-> (exists B A = k1_tarski(B)))) # label(t60_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6066 $T # label(t8_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6067 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> k1_card_2(k2_card_2(A,B),k2_card_2(A,C)) = k2_card_2(A,k1_card_2(B,C)))))))) # label(t37_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6068 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r2_xboole_0(A,B) -> -r1_xreal_0(k4_card_1(B),k4_card_1(A)) & r2_hidden(k1_card_1(A),k1_card_1(B))))))) # label(t67_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6069 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> k4_card_1(k2_xboole_0(A,B)) = k5_real_1(k1_nat_1(k4_card_1(A),k4_card_1(B)),k4_card_1(k3_xboole_0(A,B))))))) # label(t64_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6070 $T # label(t10_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6071 $T # label(t9_card_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6072 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (exists B m1_trees_1(B,A)))) # label(existence_m1_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6073 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (m1_trees_1(B,A) -> -(B != k1_xboole_0 & r1_xreal_0(k6_trees_1(A),k6_trees_1(k4_trees_1(A,B)))))))) # label(t85_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6074 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> (all B (m2_trees_1(B,A) -> m1_trees_1(B,A))))) # label(dt_m2_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6075 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (m4_trees_1(B,A) -> v1_finset_1(B))))) # label(cc1_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6076 (all A all B (-v1_xboole_0(A) & v1_trees_1(A) & m1_finseq_1(B,k5_numbers) -> -v1_xboole_0(k4_trees_1(A,B)) & v1_trees_1(k4_trees_1(A,B)))) # label(dt_k4_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6077 $T # label(t18_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6078 $T # label(t22_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6079 $T # label(t12_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6080 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (v1_trees_1(B) & v1_finset_1(B) & -v1_xboole_0(B) -> -v1_xboole_0(k2_xboole_0(A,B)) & v1_finset_1(k2_xboole_0(A,B)) & v1_trees_1(k2_xboole_0(A,B)))))) # label(t52_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6081 $T # label(t29_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6082 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & B = k7_finseq_1(A,C) & v1_finseq_1(C)))))))) # label(t8_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6083 (all 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) -> -(k9_finseq_1(A) = k7_finseq_1(B,C) & -(k9_finseq_1(A) = C & B = k1_xboole_0) & -(k1_xboole_0 = C & B = k9_finseq_1(A))))))) # label(t6_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6084 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(-r1_xreal_0(A,C) & B = k12_finseq_1(k5_numbers,C)))) & B != k1_xboole_0 & r2_hidden(B,k2_trees_1(A))))))) # label(t57_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6085 (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) -> -(r2_xboole_0(B,A) & r2_xboole_0(A,B)))))) # label(t26_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6086 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (-r3_xboole_0(A,B) -> v2_trees_1(k2_tarski(A,B))))))) # label(t71_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6087 $T # label(d3_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6088 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> k4_trees_1(A,k6_finseq_1(k5_numbers)) = A)) # label(t60_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6089 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> k3_finseq_1(A) = k4_card_1(k1_trees_1(A)))) # label(t68_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6090 (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) -> (k3_finseq_1(B) = k3_finseq_1(A) & r1_tarski(A,B) -> A = B))))) # label(t15_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.62 6091 (all A (v1_finset_1(A) & v1_trees_1(A) & -v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B = k6_trees_1(A) <-> (exists C (m2_finseq_1(C,k5_numbers) & r2_hidden(C,A) & B = k3_finseq_1(C))) & (all C (m2_finseq_1(C,k5_numbers) -> (r2_hidden(C,A) -> r1_xreal_0(k3_finseq_1(C),B))))))))) # label(d15_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6092 $T # label(t10_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6093 (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) -> (-(A = k1_xboole_0 & -r2_xboole_0(k1_xboole_0,A)) -> r2_xboole_0(B,k7_finseq_1(B,A))))))) # label(t33_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6094 (all A (m2_finseq_1(A,k5_numbers) -> (all B (v1_trees_1(B) & -v1_xboole_0(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k7_finseq_1(A,C),B) -> r2_hidden(A,B)))))))) # label(t46_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6095 (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) -> ((exists C (k7_relat_1(B,k2_finseq_1(C)) = A & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r1_tarski(A,B)))))) # label(d1_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6096 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (k7_finseq_1(B,A) = A | A = k7_finseq_1(A,B) -> k1_xboole_0 = B))))) # label(t5_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6097 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k7_trees_1(k2_trees_1(k1_nat_1(A,np__1))) = k1_nat_1(A,np__1))) # label(t83_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6098 (all 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(B,C) -> r2_xboole_0(B,k7_finseq_1(C,k9_finseq_1(A)))))))) # label(t31_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6099 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (B = k1_trees_1(A) <-> (all C ((exists D (v1_finseq_1(D) & C = D & r2_xboole_0(D,A) & v1_funct_1(D) & v1_relat_1(D))) <-> r2_hidden(C,B))))))) # label(d4_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6100 (all A all B all C (m2_finseq_1(B,k5_numbers) & -v1_xboole_0(C) & v1_trees_1(C) -> (r2_hidden(A,a_2_1_trees_1(B,C)) <-> (exists D (m1_trees_1(D,C) & A = k8_finseq_1(k5_numbers,B,D) & D = D))))) # label(fraenkel_a_2_1_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6101 $T # label(t63_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6102 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (exists B m3_trees_1(B,A)))) # label(existence_m3_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6103 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> r2_hidden(k1_xboole_0,A) & r2_hidden(k6_finseq_1(k5_numbers),A))) # label(t47_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6104 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (r2_hidden(k7_finseq_1(B,C),k1_trees_1(A)) -> r2_hidden(B,k1_trees_1(A))))))))) # label(t38_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6105 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> (all B (m4_trees_1(B,A) -> v2_trees_1(B))))) # label(dt_m4_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6106 $T # label(t9_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6107 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> m1_subset_1(k3_trees_1(A),k1_zfmisc_1(A)))) # label(dt_k3_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6108 $T # label(t54_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6109 (all A (v1_finset_1(A) & v1_trees_1(A) & -v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B = k7_trees_1(A) <-> (exists C ((all D (m4_trees_1(D,A) -> r1_xreal_0(k4_card_1(D),k4_card_1(C)))) & k4_card_1(C) = B & m4_trees_1(C,A)))))))) # label(d16_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6110 (all A (r1_tarski(A,k13_finseq_1(k5_numbers)) & (all B (m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(D,C) & r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C)),A) -> r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,D)),A)))))))) & (all B (m2_finseq_1(B,k5_numbers) -> (r2_hidden(B,A) -> r1_tarski(k1_trees_1(B),A)))) <-> v1_trees_1(A))) # label(d5_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6111 (all A all B (r1_tarski(k9_finseq_1(A),k9_finseq_1(B)) <-> A = B)) # label(t16_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6112 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (r1_tarski(C,B) & r2_hidden(B,A) -> r2_hidden(C,A)))))))) # label(t45_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6113 (exists A (-v1_xboole_0(A) & v1_trees_1(A))) # label(rc1_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6114 (all A (m2_finseq_1(A,k5_numbers) -> (all B (v1_trees_1(B) & -v1_xboole_0(B) -> (all C (v1_trees_1(C) & -v1_xboole_0(C) -> (r2_hidden(A,B) -> k5_trees_1(B,A,C) = k2_xboole_0(a_2_0_trees_1(A,B),a_2_1_trees_1(A,C))))))))) # label(t64_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6115 (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_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (k7_relat_1(B,k2_finseq_1(A)) = C -> r1_xreal_0(k3_finseq_1(C),A)))))))) # label(t1_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6116 $T # label(t76_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6117 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> (all B (m2_finseq_1(B,k5_numbers) -> (all C (v1_trees_1(C) & -v1_xboole_0(C) -> (r2_hidden(B,A) -> (all D (-v1_xboole_0(D) & v1_trees_1(D) -> (k5_trees_1(A,B,C) = D <-> (all E (m2_finseq_1(E,k5_numbers) -> (r2_hidden(E,D) <-> -(-(r2_hidden(E,A) & -r2_xboole_0(B,E)) & (all F (m2_finseq_1(F,k5_numbers) -> -(r2_hidden(F,C) & k8_finseq_1(k5_numbers,B,F) = E))))))))))))))))) # label(d12_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6118 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (m1_subset_1(B,A) <-> m1_trees_1(B,A))))) # label(redefinition_m1_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6119 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> r1_xreal_0(np__1,k7_trees_1(A)))) # label(t78_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6120 $T # label(t65_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6121 $T # label(t43_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6122 (all A k1_xboole_0 != k9_finseq_1(A)) # label(t4_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6123 $T # label(dt_k1_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6124 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> (all B (m1_trees_1(B,A) -> m4_trees_1(k1_tarski(B),A))))) # label(t74_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6125 $T # label(d2_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6126 $T # label(t14_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6127 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (r1_tarski(k7_finseq_1(B,k9_finseq_1(A)),C) -> r2_xboole_0(B,C)))))) # label(t30_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6128 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> (k1_xboole_0 != k3_trees_1(A) -> (all B (m1_trees_1(B,A) -> (m2_trees_1(B,A) <-> r2_hidden(B,k3_trees_1(A)))))))) # label(d10_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6129 (all A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> m2_subset_1(k6_trees_1(A),k1_numbers,k5_numbers))) # label(dt_k6_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6130 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> -(r2_xboole_0(A,B) & r1_xreal_0(k4_card_1(B),k4_card_1(A))))))) # label(t24_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6131 $T # label(t61_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6132 $T # label(t77_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6133 (all A all B all C (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & m1_subset_1(B,A) & v1_trees_1(C) & v1_finset_1(C) & -v1_xboole_0(C) -> -v1_xboole_0(k5_trees_1(A,B,C)) & v1_trees_1(k5_trees_1(A,B,C)) & v1_finset_1(k5_trees_1(A,B,C)))) # label(fc2_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6134 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (v2_trees_1(B) -> (m4_trees_1(B,A) <-> r1_tarski(B,A)))))) # label(d14_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6135 $T # label(t13_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6136 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_trees_1(B) -> v1_trees_1(k3_xboole_0(A,B)) & -v1_xboole_0(k3_xboole_0(A,B)))))) # label(t50_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6137 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> -(r1_tarski(A,B) & r2_xboole_0(B,A)))))) # label(t28_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6138 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (exists B m4_trees_1(B,A)))) # label(existence_m4_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6139 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (exists B m2_trees_1(B,A)))) # label(existence_m2_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6140 (all A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> m2_subset_1(k7_trees_1(A),k1_numbers,k5_numbers))) # label(dt_k7_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6141 (all A all B all C (v1_trees_1(C) & -v1_xboole_0(C) & m2_finseq_1(B,k5_numbers) -> ((exists D (m1_trees_1(D,C) & D = A & -r2_xboole_0(B,D))) <-> r2_hidden(A,a_2_0_trees_1(B,C))))) # label(fraenkel_a_2_0_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6142 $T # label(t69_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6143 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k2_xboole_0(a_1_0_trees_1(A),k1_tarski(k1_xboole_0)) = k2_trees_1(A))) # label(d7_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6144 (all A k1_trees_1(k9_finseq_1(A)) = k1_tarski(k1_xboole_0)) # label(t40_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6145 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v2_trees_1(k1_tarski(A)))) # label(t70_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6146 (exists A v2_trees_1(A)) # label(rc3_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6147 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,a_1_0_trees_1(B)) <-> (exists C (-r1_xreal_0(B,C) & k12_finseq_1(k5_numbers,C) = A & m2_subset_1(C,k1_numbers,k5_numbers)))))) # label(fraenkel_a_1_0_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6148 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (m1_trees_1(B,A) -> (all C (m1_trees_1(C,A) -> (-r3_xboole_0(B,C) -> m4_trees_1(k2_tarski(B,C),A)))))))) # label(t75_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6149 (all A (m1_subset_1(A,k5_numbers) -> v1_trees_1(k2_trees_1(A)) & v1_finset_1(k2_trees_1(A)) & -v1_xboole_0(k2_trees_1(A)))) # label(dt_k2_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6150 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r2_hidden(A,k1_trees_1(B)) -> v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A)))) # label(t35_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6151 (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) -> (r1_tarski(A,B) -> r1_tarski(k1_trees_1(A),k1_trees_1(B))))))) # label(t41_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6152 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> m4_trees_1(k1_xboole_0,A) & m4_trees_1(k1_tarski(k1_xboole_0),A))) # label(t73_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6153 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_trees_1(A)) & r2_hidden(B,k1_trees_1(A)) -> r3_xboole_0(B,C)))))))) # label(t42_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6154 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(C) & v1_trees_1(C) & m1_finseq_1(B,k5_numbers) & v1_trees_1(A) -> v1_trees_1(k5_trees_1(A,B,C)) & -v1_xboole_0(k5_trees_1(A,B,C)))) # label(dt_k5_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6155 $T # label(t20_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6156 $T # label(t62_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6157 $T # label(d6_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6158 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> (all B (v1_trees_1(B) & v1_finset_1(B) & -v1_xboole_0(B) -> v1_trees_1(k3_xboole_0(A,B)) & v1_finset_1(k3_xboole_0(A,B)) & -v1_xboole_0(k3_xboole_0(A,B)) & v1_trees_1(k3_xboole_0(B,A)) & v1_finset_1(k3_xboole_0(B,A)) & -v1_xboole_0(k3_xboole_0(B,A)))))) # label(t53_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6159 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> (all B (m1_trees_1(B,A) -> m2_finseq_1(B,k5_numbers))))) # label(dt_m1_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6160 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> (np__0 = k6_trees_1(A) -> A = k2_trees_1(np__0)))) # label(t80_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6161 $T # label(t34_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6162 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k6_trees_1(k2_trees_1(k1_nat_1(A,np__1))) = np__1)) # label(t81_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6163 (all A ((all B (r2_hidden(B,A) -> v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B))) & (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> -(r2_hidden(C,A) & r3_xboole_0(B,C) & C != B & r2_hidden(B,A)))))) <-> v2_trees_1(A))) # label(d13_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6164 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (-(-(r2_xboole_0(B,C) & r2_xboole_0(A,B)) & -(r1_tarski(A,B) & r2_xboole_0(B,C)) & -(r1_tarski(B,C) & r2_xboole_0(A,B))) -> r2_xboole_0(A,C)))))))) # label(t27_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6165 $T # label(t7_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6166 (all A (m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) & v1_trees_1(B) -> (all C (v1_trees_1(C) & -v1_xboole_0(C) -> (r2_hidden(A,B) -> C = k4_trees_1(k5_trees_1(B,A,C),A)))))))) # label(t66_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6167 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_finset_1(k1_trees_1(A)))) # label(fc3_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6168 $T # label(t51_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6169 $T # label(t11_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6170 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -r2_xboole_0(B,k1_xboole_0) & -r2_xboole_0(B,k6_finseq_1(A)))))) # label(t25_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6171 $T # label(t21_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6172 (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_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> B != k7_finseq_1(C,D))) & k7_relat_1(B,k2_finseq_1(A)) = C))))))) # label(t3_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6173 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (m1_trees_1(B,A) -> r1_xreal_0(k6_trees_1(k4_trees_1(A,B)),k6_trees_1(A)))))) # label(t84_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6174 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (r2_xboole_0(B,k7_finseq_1(C,k9_finseq_1(A))) -> r1_tarski(B,C)))))) # label(t32_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6175 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (m3_trees_1(B,A) -> -v1_xboole_0(B) & v1_trees_1(B))))) # label(dt_m3_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6176 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (v1_trees_1(B) & -v1_xboole_0(B) -> v1_trees_1(k2_xboole_0(A,B)) & -v1_xboole_0(k2_xboole_0(A,B)))))) # label(t49_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6177 (exists A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A))) # label(rc2_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6178 (all A all B (v1_trees_1(B) & -v1_xboole_0(B) -> (r2_hidden(A,B) -> m2_finseq_1(A,k5_numbers)))) # label(t44_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6179 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (k4_card_1(B) = k4_card_1(A) & r3_xboole_0(A,B) -> A = B))))) # label(t19_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6180 (all A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k12_finseq_1(k5_numbers,B),A) -> p1_s1_trees_1(k4_trees_1(A,k12_finseq_1(k5_numbers,B)))))) -> p1_s1_trees_1(A)))) -> (all A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> p1_s1_trees_1(A))) # label(s1_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6181 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (v1_trees_1(B) & -v1_xboole_0(B) -> ((exists C (B = k4_trees_1(A,C) & m1_trees_1(C,A))) <-> m3_trees_1(B,A)))))) # label(d11_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6182 (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(k12_finseq_1(k5_numbers,A),k2_trees_1(B))))))) # label(t55_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6183 (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) -> (r2_hidden(A,k1_trees_1(B)) <-> r2_xboole_0(A,B)))))) # label(t36_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6184 $T # label(t58_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6185 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (k7_relat_1(B,k2_finseq_1(A)) = C -> r1_xreal_0(k3_finseq_1(C),k3_finseq_1(B))))))))) # label(t2_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6186 (all A all B (r3_xboole_0(k9_finseq_1(A),k9_finseq_1(B)) <-> B = A)) # label(t23_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6187 $T # label(t17_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6188 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (m2_finseq_1(B,k5_numbers) -> (r2_hidden(B,A) -> (all C (v1_trees_1(C) & -v1_xboole_0(C) -> ((all D (m2_finseq_1(D,k5_numbers) -> (r2_hidden(D,C) <-> r2_hidden(k8_finseq_1(k5_numbers,B,D),A)))) <-> C = k4_trees_1(A,B))))))))) # label(d9_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6189 $T # label(t72_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6190 $T # label(t59_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6191 (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) -> -(r2_hidden(A,k1_trees_1(B)) & r1_xreal_0(k3_finseq_1(B),k3_finseq_1(A))))))) # label(t37_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6192 (all A all B (m1_subset_1(B,A) & v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> v1_finset_1(k4_trees_1(A,B)) & v1_trees_1(k4_trees_1(A,B)) & -v1_xboole_0(k4_trees_1(A,B)))) # label(fc1_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6193 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (k3_trees_1(A) = B <-> (all C (m2_finseq_1(C,k5_numbers) -> (r2_hidden(C,A) & (all D (m2_finseq_1(D,k5_numbers) -> -(r2_hidden(D,A) & r2_xboole_0(C,D)))) <-> r2_hidden(C,B))))))))) # label(d8_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6194 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> r2_tarski(k1_trees_1(A),k4_finseq_1(A)))) # label(t67_trees_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6195 (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]. 115.62/113.63 6196 (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]. 115.62/113.63 6197 (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]. 115.62/113.63 6198 (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]. 115.62/113.63 6199 (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]. 115.62/113.63 6200 (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]. 115.62/113.63 6201 (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]. 115.62/113.63 6202 (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]. 115.62/113.63 6203 (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]. 115.62/113.63 6204 (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]. 115.62/113.63 6205 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]. 115.62/113.63 6206 (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]. 115.62/113.63 6207 (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]. 115.62/113.63 6208 (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]. 115.62/113.63 6209 (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]. 115.62/113.63 6210 (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]. 115.62/113.63 6211 (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]. 115.62/113.63 6212 (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]. 115.62/113.63 6213 (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]. 115.62/113.63 6214 (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]. 115.62/113.63 6215 (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]. 115.62/113.63 6216 (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]. 115.62/113.63 6217 (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]. 115.62/113.63 6218 (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]. 115.62/113.63 6219 (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]. 115.62/113.63 6220 (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]. 115.62/113.63 6221 (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]. 115.62/113.63 6222 (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]. 115.62/113.63 6223 (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]. 115.62/113.63 6224 (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]. 115.62/113.63 6225 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.63 6226 (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]. 115.62/113.63 6227 (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]. 115.62/113.63 6228 (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]. 115.62/113.63 6229 (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]. 115.62/113.64 6230 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6231 (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]. 115.62/113.64 6232 (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]. 115.62/113.64 6233 (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]. 115.62/113.64 6234 (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]. 115.62/113.64 6235 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6236 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6237 (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]. 115.62/113.64 6238 (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]. 115.62/113.64 6239 (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]. 115.62/113.64 6240 (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]. 115.62/113.64 6241 (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]. 115.62/113.64 6242 (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]. 115.62/113.64 6243 (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]. 115.62/113.64 6244 (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]. 115.62/113.64 6245 (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]. 115.62/113.64 6246 (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]. 115.62/113.64 6247 (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]. 115.62/113.64 6248 (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]. 115.62/113.64 6249 (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]. 115.62/113.64 6250 (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]. 115.62/113.64 6251 (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]. 115.62/113.64 6252 (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]. 115.62/113.64 6253 (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]. 115.62/113.64 6254 (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]. 115.62/113.64 6255 (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]. 115.62/113.64 6256 (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]. 115.62/113.64 6257 (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]. 115.62/113.64 6258 (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]. 115.62/113.64 6259 (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]. 115.62/113.64 6260 (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]. 115.62/113.64 6261 (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]. 115.62/113.64 6262 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6263 (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]. 115.62/113.64 6264 (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]. 115.62/113.64 6265 (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]. 115.62/113.64 6266 (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]. 115.62/113.64 6267 (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]. 115.62/113.64 6268 (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]. 115.62/113.64 6269 (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]. 115.62/113.64 6270 (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]. 115.62/113.64 6271 (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]. 115.62/113.64 6272 (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]. 115.62/113.64 6273 (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]. 115.62/113.64 6274 (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]. 115.62/113.64 6275 (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]. 115.62/113.64 6276 (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]. 115.62/113.64 6277 (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]. 115.62/113.64 6278 (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]. 115.62/113.64 6279 (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]. 115.62/113.64 6280 (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]. 115.62/113.64 6281 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 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,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]. 115.62/113.64 6283 (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]. 115.62/113.64 6284 (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]. 115.62/113.64 6285 (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]. 115.62/113.64 6286 (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]. 115.62/113.64 6287 (all A k10_finseq_1(A,A) = k2_finseq_2(np__2,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6288 (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]. 115.62/113.64 6289 (all A exists B (m1_finseq_2(B,A) & -v1_xboole_0(B))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6290 (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]. 115.62/113.64 6291 (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]. 115.62/113.64 6292 (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]. 115.62/113.64 6293 (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]. 115.62/113.64 6294 (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]. 115.62/113.64 6295 (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]. 115.62/113.64 6296 (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]. 115.62/113.64 6297 (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]. 115.62/113.64 6298 (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]. 115.62/113.64 6299 (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]. 115.62/113.64 6300 (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]. 115.62/113.64 6301 (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]. 115.62/113.64 6302 (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]. 115.62/113.64 6303 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6304 (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]. 115.62/113.64 6305 (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]. 115.62/113.64 6306 (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]. 115.62/113.64 6307 (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]. 115.62/113.64 6308 (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]. 115.62/113.64 6309 (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]. 115.62/113.64 6310 (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]. 115.62/113.64 6311 (all A k11_finseq_1(A,A,A) = k2_finseq_2(np__3,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6312 (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]. 115.62/113.64 6313 (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]. 115.62/113.64 6314 (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]. 115.62/113.64 6315 (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]. 115.62/113.64 6316 (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]. 115.62/113.64 6317 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6318 (all A k13_finseq_1(A) = k3_finseq_2(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6319 (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]. 115.62/113.64 6320 (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]. 115.62/113.64 6321 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6322 (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]. 115.62/113.64 6323 (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]. 115.62/113.64 6324 (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]. 115.62/113.64 6325 (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]. 115.62/113.64 6326 (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]. 115.62/113.64 6327 (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]. 115.62/113.64 6328 (all A (v4_ordinal2(A) -> A = k3_finseq_1(k1_finseq_2(A)))) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6329 (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]. 115.62/113.64 6330 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6331 (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]. 115.62/113.64 6332 (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]. 115.62/113.64 6333 (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]. 115.62/113.64 6334 (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]. 115.62/113.64 6335 (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]. 115.62/113.64 6336 (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]. 115.62/113.64 6337 (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]. 115.62/113.64 6338 (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]. 115.62/113.64 6339 (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]. 115.62/113.64 6340 (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]. 115.62/113.64 6341 (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]. 115.62/113.64 6342 (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]. 115.62/113.64 6343 (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]. 115.62/113.64 6344 (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]. 115.62/113.64 6345 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6346 (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]. 115.62/113.64 6347 (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]. 115.62/113.64 6348 (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]. 115.62/113.64 6349 (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]. 115.62/113.64 6350 (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]. 115.62/113.64 6351 (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]. 115.62/113.64 6352 (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]. 115.62/113.64 6353 (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]. 115.62/113.64 6354 (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]. 115.62/113.64 6355 (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]. 115.62/113.64 6356 (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]. 115.62/113.64 6357 (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]. 115.62/113.64 6358 (all A k2_finseq_2(np__1,A) = k9_finseq_1(A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6359 (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]. 115.62/113.64 6360 (all A k1_xboole_0 = k2_finseq_2(np__0,A)) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 115.62/113.64 6361 (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]. 115.62/113.64 6362 (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]. 115.62/113.64 6363 (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]. 115.62/113.64 6364 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> f3_s12_recdef_1(A,k8_funct_2(k5_numbers,f1_s12_recdef_1,f4_s12_recdef_1,A)) = k8_funct_2(k5_numbers,f1_s12_recdef_1,f4_s12_recdef_1,k1_nat_1(A,np__1)))) & k8_funct_2(k5_numbers,f1_s12_recdef_1,f5_s12_recdef_1,np__0) = f2_s12_recdef_1 & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> f3_s12_recdef_1(A,k8_funct_2(k5_numbers,f1_s12_recdef_1,f5_s12_recdef_1,A)) = k8_funct_2(k5_numbers,f1_s12_recdef_1,f5_s12_recdef_1,k1_nat_1(A,np__1)))) & f2_s12_recdef_1 = k8_funct_2(k5_numbers,f1_s12_recdef_1,f4_s12_recdef_1,np__0) -> f5_s12_recdef_1 = f4_s12_recdef_1 # label(s12_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.65 6365 (all A all B -((exists C (v1_relat_1(C) & v1_funct_1(C) & f1_s19_recdef_1 = k1_funct_1(C,np__0) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k1_funct_1(C,k1_nat_1(D,np__1)) = f3_s19_recdef_1(D,k1_funct_1(C,D)))) & k1_relat_1(C) = k5_numbers & A = k1_funct_1(C,f2_s19_recdef_1))) & B != A & (exists C (v1_funct_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> f3_s19_recdef_1(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_nat_1(D,np__1)))) & k1_funct_1(C,np__0) = f1_s19_recdef_1 & k5_numbers = k1_relat_1(C) & B = k1_funct_1(C,f2_s19_recdef_1) & v1_relat_1(C))))) # label(s19_recdef_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 115.62/113.65 6366 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & A = k1_funct_1(B,f2_s19_recdef_1) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k1_funct_1(B,k1_nat_1(C,np__1)) = f3_s19_recdef_1(C,k1_funct_1(B,C)))) & k1_funct_1(B,np__0) = f1_s19_recdef_1 & k5_numbers = k1_relat_1(B))) # label(s19_recdef_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 115.62/113.65 6367 k5_numbers = k1_relat_1(f3_s11_recdef_1) & f1_s11_recdef_1 = k1_funct_1(f3_s11_recdef_1,np__0) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_funct_1(f4_s11_recdef_1,k1_nat_1(A,np__1)) = f2_s11_recdef_1(A,k1_funct_1(f4_s11_recdef_1,A)))) & k1_funct_1(f4_s11_recdef_1,np__0) = f1_s11_recdef_1 & k5_numbers = k1_relat_1(f4_s11_recdef_1) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_funct_1(f3_s11_recdef_1,k1_nat_1(A,np__1)) = f2_s11_recdef_1(A,k1_funct_1(f3_s11_recdef_1,A)))) -> f3_s11_recdef_1 = f4_s11_recdef_1 # label(s11_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.65 6368 (exists A exists B (v1_relat_1(B) & k3_finseq_1(f1_s8_recdef_1) = k3_finseq_1(B) & k1_funct_1(f1_s8_recdef_1,np__1) = k1_funct_1(B,np__1) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) -> k1_funct_1(B,k1_nat_1(C,np__1)) = f2_s8_recdef_1(k1_funct_1(f1_s8_recdef_1,k1_nat_1(C,np__1)),k1_funct_1(B,C)) | r1_xreal_0(k3_finseq_1(f1_s8_recdef_1),C)))) & A = k1_funct_1(B,k3_finseq_1(B)) & v1_finseq_1(B) & v1_funct_1(B))) # label(s8_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.65 6369 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C all D all E (k1_funct_1(f1_s7_recdef_1,k1_nat_1(A,np__1)) = E & p1_s7_recdef_1(E,B,C) & p1_s7_recdef_1(E,B,D) & r1_xreal_0(np__1,A) -> r1_xreal_0(k3_finseq_1(f1_s7_recdef_1),A) | D = C)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B -(-r1_xreal_0(k3_finseq_1(f1_s7_recdef_1),A) & (all C -p1_s7_recdef_1(k1_funct_1(f1_s7_recdef_1,k1_nat_1(A,np__1)),B,C)) & r1_xreal_0(np__1,A))))) -> (exists A exists B (v1_relat_1(B) & v1_finseq_1(B) & k1_funct_1(B,k3_finseq_1(B)) = A & k1_funct_1(f1_s7_recdef_1,np__1) = k1_funct_1(B,np__1) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) -> p1_s7_recdef_1(k1_funct_1(f1_s7_recdef_1,k1_nat_1(C,np__1)),k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,np__1))) | r1_xreal_0(k3_finseq_1(f1_s7_recdef_1),C)))) & k3_finseq_1(B) = k3_finseq_1(f1_s7_recdef_1) & v1_funct_1(B))) # label(s7_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.65 6370 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,A) -> r1_xreal_0(f2_s14_recdef_1,A) | (all B all C all D (p1_s14_recdef_1(A,B,D) & p1_s14_recdef_1(A,B,C) -> C = D))))) & k3_finseq_1(f3_s14_recdef_1) = f2_s14_recdef_1 & (f2_s14_recdef_1 = np__0 | k1_funct_1(f3_s14_recdef_1,np__1) = f1_s14_recdef_1) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,A) -> r1_xreal_0(f2_s14_recdef_1,A) | p1_s14_recdef_1(A,k1_funct_1(f3_s14_recdef_1,A),k1_funct_1(f3_s14_recdef_1,k1_nat_1(A,np__1)))))) & f2_s14_recdef_1 = k3_finseq_1(f4_s14_recdef_1) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,A) -> r1_xreal_0(f2_s14_recdef_1,A) | p1_s14_recdef_1(A,k1_funct_1(f4_s14_recdef_1,A),k1_funct_1(f4_s14_recdef_1,k1_nat_1(A,np__1)))))) & (k1_funct_1(f4_s14_recdef_1,np__1) = f1_s14_recdef_1 | np__0 = f2_s14_recdef_1) -> f3_s14_recdef_1 = f4_s14_recdef_1 # label(s14_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.66 6371 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,f3_s13_recdef_1,k1_nat_1(A,np__1)) = f2_s13_recdef_1(A,k8_funct_2(k5_numbers,k1_numbers,f3_s13_recdef_1,A)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> f2_s13_recdef_1(A,k8_funct_2(k5_numbers,k1_numbers,f4_s13_recdef_1,A)) = k8_funct_2(k5_numbers,k1_numbers,f4_s13_recdef_1,k1_nat_1(A,np__1)))) & k8_funct_2(k5_numbers,k1_numbers,f4_s13_recdef_1,np__0) = f1_s13_recdef_1 & f1_s13_recdef_1 = k8_funct_2(k5_numbers,k1_numbers,f3_s13_recdef_1,np__0) -> f4_s13_recdef_1 = f3_s13_recdef_1 # label(s13_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.66 6372 (exists A ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,B) -> r1_xreal_0(k3_finseq_1(f1_s17_recdef_1),B) | f2_s17_recdef_1(k1_funct_1(f1_s17_recdef_1,k1_nat_1(B,np__1)),k1_funct_1(A,B)) = k1_funct_1(A,k1_nat_1(B,np__1))))) & k1_funct_1(f1_s17_recdef_1,np__1) = k1_funct_1(A,np__1) & k3_finseq_1(f1_s17_recdef_1) = k3_finseq_1(A) & k1_funct_1(A,k3_finseq_1(A)) = f3_s17_recdef_1 & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) & (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_funct_1(A,k3_finseq_1(A)) = f4_s17_recdef_1 & k1_funct_1(f1_s17_recdef_1,np__1) = k1_funct_1(A,np__1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,B) -> f2_s17_recdef_1(k1_funct_1(f1_s17_recdef_1,k1_nat_1(B,np__1)),k1_funct_1(A,B)) = k1_funct_1(A,k1_nat_1(B,np__1)) | r1_xreal_0(k3_finseq_1(f1_s17_recdef_1),B)))) & k3_finseq_1(f1_s17_recdef_1) = k3_finseq_1(A) & v1_finseq_1(A))) -> f4_s17_recdef_1 = f3_s17_recdef_1 # label(s17_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.66 6373 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> p1_s10_recdef_1(A,k8_funct_2(k5_numbers,f1_s10_recdef_1,f3_s10_recdef_1,A),k8_funct_2(k5_numbers,f1_s10_recdef_1,f3_s10_recdef_1,k1_nat_1(A,np__1))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> p1_s10_recdef_1(A,k8_funct_2(k5_numbers,f1_s10_recdef_1,f4_s10_recdef_1,A),k8_funct_2(k5_numbers,f1_s10_recdef_1,f4_s10_recdef_1,k1_nat_1(A,np__1))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_subset_1(B,f1_s10_recdef_1) -> (all C (m1_subset_1(C,f1_s10_recdef_1) -> (all D (m1_subset_1(D,f1_s10_recdef_1) -> (p1_s10_recdef_1(A,B,D) & p1_s10_recdef_1(A,B,C) -> D = C))))))))) & k8_funct_2(k5_numbers,f1_s10_recdef_1,f4_s10_recdef_1,np__0) = f2_s10_recdef_1 & f2_s10_recdef_1 = k8_funct_2(k5_numbers,f1_s10_recdef_1,f3_s10_recdef_1,np__0) -> f3_s10_recdef_1 = f4_s10_recdef_1 # label(s10_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.66 6374 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,A,k5_numbers) & m1_subset_1(C,A) -> k1_funct_1(B,C) = k1_recdef_1(A,B,C))) # label(redefinition_k1_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.66 6375 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_subset_1(B,f1_s2_recdef_1) -> (exists C (p1_s2_recdef_1(A,B,C) & m1_subset_1(C,f1_s2_recdef_1))))))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,f1_s2_recdef_1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> p1_s2_recdef_1(B,k8_funct_2(k5_numbers,f1_s2_recdef_1,A,B),k8_funct_2(k5_numbers,f1_s2_recdef_1,A,k1_nat_1(B,np__1))))) & f2_s2_recdef_1 = k8_funct_2(k5_numbers,f1_s2_recdef_1,A,np__0) & v1_funct_2(A,k5_numbers,f1_s2_recdef_1))) # label(s2_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.62/113.66 6376 (exists A exists B (v1_relat_1(B) & v1_finseq_1(B) & k3_finseq_1(B) = k3_finseq_1(f1_s23_recdef_1) & k1_funct_1(B,np__1) = k1_funct_1(f1_s23_recdef_1,np__1) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) -> r1_xreal_0(k3_finseq_1(f1_s23_recdef_1),C) | f2_s23_recdef_1(k1_funct_1(f1_s23_recdef_1,k1_nat_1(C,np__1)),k1_funct_1(B,C)) = k1_funct_1(B,k1_nat_1(C,np__1))))) & A = k1_funct_1(B,k3_finseq_1(B)) & v1_funct_1(B))) # label(s23_recdef_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 115.69/113.71 6377 (all A all B -((exists C (A = k1_funct_1(C,k3_finseq_1(C)) & k3_finseq_1(C) = k3_finseq_1(f1_s23_recdef_1) & k1_funct_1(C,np__1) = k1_funct_1(f1_s23_recdef_1,np__1) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,D) -> k1_funct_1(C,k1_nat_1(D,np__1)) = f2_s23_recdef_1(k1_funct_1(f1_s23_recdef_1,k1_nat_1(D,np__1)),k1_funct_1(C,D)) | r1_xreal_0(k3_finseq_1(f1_s23_recdef_1),D)))) & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))) & (exists C (v1_relat_1(C) & v1_finseq_1(C) & k1_funct_1(C,k3_finseq_1(C)) = B & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,D) -> f2_s23_recdef_1(k1_funct_1(f1_s23_recdef_1,k1_nat_1(D,np__1)),k1_funct_1(C,D)) = k1_funct_1(C,k1_nat_1(D,np__1)) | r1_xreal_0(k3_finseq_1(f1_s23_recdef_1),D)))) & k1_funct_1(C,np__1) = k1_funct_1(f1_s23_recdef_1,np__1) & k3_finseq_1(f1_s23_recdef_1) = k3_finseq_1(C) & v1_funct_1(C))) & B != A)) # label(s23_recdef_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 115.69/113.71 6378 (all A all B all C (m1_relset_1(B,A,k5_numbers) & m1_subset_1(C,A) & v1_funct_1(B) -> m2_subset_1(k1_recdef_1(A,B,C),k1_numbers,k5_numbers))) # label(dt_k1_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.71 6379 f1_s9_recdef_1 = k1_funct_1(f2_s9_recdef_1,np__0) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> p1_s9_recdef_1(A,k1_funct_1(f2_s9_recdef_1,A),k1_funct_1(f2_s9_recdef_1,k1_nat_1(A,np__1))))) & k5_numbers = k1_relat_1(f3_s9_recdef_1) & f1_s9_recdef_1 = k1_funct_1(f3_s9_recdef_1,np__0) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> p1_s9_recdef_1(A,k1_funct_1(f3_s9_recdef_1,A),k1_funct_1(f3_s9_recdef_1,k1_nat_1(A,np__1))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C all D (p1_s9_recdef_1(A,B,D) & p1_s9_recdef_1(A,B,C) -> D = C)))) & k1_relat_1(f2_s9_recdef_1) = k5_numbers -> f3_s9_recdef_1 = f2_s9_recdef_1 # label(s9_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.71 6380 (exists A (k1_relat_1(A) = k5_numbers & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k1_funct_1(A,k1_nat_1(B,np__1)) = f2_s3_recdef_1(B,k1_funct_1(A,B)))) & k1_funct_1(A,np__0) = f1_s3_recdef_1 & v1_funct_1(A) & v1_relat_1(A))) # label(s3_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.71 6381 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B -((all C -p1_s22_recdef_1(k1_funct_1(f1_s22_recdef_1,k1_nat_1(A,np__1)),B,C)) & -r1_xreal_0(k3_finseq_1(f1_s22_recdef_1),A) & r1_xreal_0(np__1,A))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C all D all E (E = k1_funct_1(f1_s22_recdef_1,k1_nat_1(A,np__1)) & p1_s22_recdef_1(E,B,C) & p1_s22_recdef_1(E,B,D) & r1_xreal_0(np__1,A) -> D = C | r1_xreal_0(k3_finseq_1(f1_s22_recdef_1),A))))) -> (all A all B -((exists C (k1_funct_1(C,np__1) = k1_funct_1(f1_s22_recdef_1,np__1) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,D) -> r1_xreal_0(k3_finseq_1(f1_s22_recdef_1),D) | p1_s22_recdef_1(k1_funct_1(f1_s22_recdef_1,k1_nat_1(D,np__1)),k1_funct_1(C,D),k1_funct_1(C,k1_nat_1(D,np__1)))))) & k3_finseq_1(f1_s22_recdef_1) = k3_finseq_1(C) & k1_funct_1(C,k3_finseq_1(C)) = A & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))) & (exists C (v1_relat_1(C) & k3_finseq_1(C) = k3_finseq_1(f1_s22_recdef_1) & k1_funct_1(C,np__1) = k1_funct_1(f1_s22_recdef_1,np__1) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,D) -> r1_xreal_0(k3_finseq_1(f1_s22_recdef_1),D) | p1_s22_recdef_1(k1_funct_1(f1_s22_recdef_1,k1_nat_1(D,np__1)),k1_funct_1(C,D),k1_funct_1(C,k1_nat_1(D,np__1)))))) & k1_funct_1(C,k3_finseq_1(C)) = B & v1_finseq_1(C) & v1_funct_1(C))) & B != A)) & (exists A exists B (v1_finseq_1(B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) -> p1_s22_recdef_1(k1_funct_1(f1_s22_recdef_1,k1_nat_1(C,np__1)),k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,np__1))) | r1_xreal_0(k3_finseq_1(f1_s22_recdef_1),C)))) & k1_funct_1(B,np__1) = k1_funct_1(f1_s22_recdef_1,np__1) & k3_finseq_1(f1_s22_recdef_1) = k3_finseq_1(B) & A = k1_funct_1(B,k3_finseq_1(B)) & v1_funct_1(B) & v1_relat_1(B))) # label(s22_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.73 6382 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B exists C p1_s1_recdef_1(A,B,C)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C all D (p1_s1_recdef_1(A,B,C) & p1_s1_recdef_1(A,B,D) -> C = D)))) -> (exists A (v1_funct_1(A) & k1_funct_1(A,np__0) = f1_s1_recdef_1 & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> p1_s1_recdef_1(B,k1_funct_1(A,B),k1_funct_1(A,k1_nat_1(B,np__1))))) & k5_numbers = k1_relat_1(A) & v1_relat_1(A))) # label(s1_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.73 6383 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,A) -> r1_xreal_0(f3_s6_recdef_1,A) | (all B (m1_subset_1(B,f1_s6_recdef_1) -> (exists C (p1_s6_recdef_1(A,B,C) & m1_subset_1(C,f1_s6_recdef_1)))))))) -> (exists A (m2_finseq_1(A,f1_s6_recdef_1) & k3_finseq_1(A) = f3_s6_recdef_1 & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,B) -> p1_s6_recdef_1(B,k1_funct_1(A,B),k1_funct_1(A,k1_nat_1(B,np__1))) | r1_xreal_0(f3_s6_recdef_1,B)))) & (np__0 = f3_s6_recdef_1 | k1_funct_1(A,np__1) = f2_s6_recdef_1))) # label(s6_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.73 6384 (exists A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,f1_s4_recdef_1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> f3_s4_recdef_1(B,k8_funct_2(k5_numbers,f1_s4_recdef_1,A,B)) = k8_funct_2(k5_numbers,f1_s4_recdef_1,A,k1_nat_1(B,np__1)))) & f2_s4_recdef_1 = k8_funct_2(k5_numbers,f1_s4_recdef_1,A,np__0) & v1_funct_2(A,k5_numbers,f1_s4_recdef_1))) # label(s4_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.73 6385 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,A) -> r1_xreal_0(f3_s15_recdef_1,A) | (all B (m1_subset_1(B,f1_s15_recdef_1) -> (all C (m1_subset_1(C,f1_s15_recdef_1) -> (all D (m1_subset_1(D,f1_s15_recdef_1) -> (p1_s15_recdef_1(A,B,D) & p1_s15_recdef_1(A,B,C) -> D = C)))))))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,A) -> p1_s15_recdef_1(A,k1_funct_1(f4_s15_recdef_1,A),k1_funct_1(f4_s15_recdef_1,k1_nat_1(A,np__1))) | r1_xreal_0(f3_s15_recdef_1,A)))) & k3_finseq_1(f5_s15_recdef_1) = f3_s15_recdef_1 & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,A) -> p1_s15_recdef_1(A,k1_funct_1(f5_s15_recdef_1,A),k1_funct_1(f5_s15_recdef_1,k1_nat_1(A,np__1))) | r1_xreal_0(f3_s15_recdef_1,A)))) & (k1_funct_1(f5_s15_recdef_1,np__1) = f2_s15_recdef_1 | f3_s15_recdef_1 = np__0) & (f3_s15_recdef_1 = np__0 | k1_funct_1(f4_s15_recdef_1,np__1) = f2_s15_recdef_1) & k3_finseq_1(f4_s15_recdef_1) = f3_s15_recdef_1 -> f4_s15_recdef_1 = f5_s15_recdef_1 # label(s15_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.73 6386 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C all D all E (E = k1_funct_1(f1_s16_recdef_1,k1_nat_1(A,np__1)) & p1_s16_recdef_1(E,B,D) & p1_s16_recdef_1(E,B,C) & r1_xreal_0(np__1,A) -> r1_xreal_0(k3_finseq_1(f1_s16_recdef_1),A) | D = C)))) & (exists A (v1_relat_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,B) -> r1_xreal_0(k3_finseq_1(f1_s16_recdef_1),B) | p1_s16_recdef_1(k1_funct_1(f1_s16_recdef_1,k1_nat_1(B,np__1)),k1_funct_1(A,B),k1_funct_1(A,k1_nat_1(B,np__1)))))) & k1_funct_1(A,np__1) = k1_funct_1(f1_s16_recdef_1,np__1) & k3_finseq_1(A) = k3_finseq_1(f1_s16_recdef_1) & f2_s16_recdef_1 = k1_funct_1(A,k3_finseq_1(A)) & v1_finseq_1(A) & v1_funct_1(A))) & (exists A (v1_funct_1(A) & k1_funct_1(A,np__1) = k1_funct_1(f1_s16_recdef_1,np__1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,B) -> p1_s16_recdef_1(k1_funct_1(f1_s16_recdef_1,k1_nat_1(B,np__1)),k1_funct_1(A,B),k1_funct_1(A,k1_nat_1(B,np__1))) | r1_xreal_0(k3_finseq_1(f1_s16_recdef_1),B)))) & k3_finseq_1(f1_s16_recdef_1) = k3_finseq_1(A) & f3_s16_recdef_1 = k1_funct_1(A,k3_finseq_1(A)) & v1_finseq_1(A) & v1_relat_1(A))) -> f2_s16_recdef_1 = f3_s16_recdef_1 # label(s16_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.73 6387 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,A) -> r1_xreal_0(f2_s5_recdef_1,A) | (all B all C all D (p1_s5_recdef_1(A,B,D) & p1_s5_recdef_1(A,B,C) -> C = D))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,A) -> (all B exists C p1_s5_recdef_1(A,B,C)) | r1_xreal_0(f2_s5_recdef_1,A)))) -> (exists A (v1_finseq_1(A) & (f2_s5_recdef_1 = np__0 | k1_funct_1(A,np__1) = f1_s5_recdef_1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,B) -> r1_xreal_0(f2_s5_recdef_1,B) | p1_s5_recdef_1(B,k1_funct_1(A,B),k1_funct_1(A,k1_nat_1(B,np__1)))))) & k3_finseq_1(A) = f2_s5_recdef_1 & v1_funct_1(A) & v1_relat_1(A))) # label(s5_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.73 6388 (all A (m1_subset_1(A,f1_s21_recdef_1) -> (all B (m1_subset_1(B,f1_s21_recdef_1) -> -((exists C (k8_funct_2(k5_numbers,f1_s21_recdef_1,C,np__0) = f2_s21_recdef_1 & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,f1_s21_recdef_1,C,k1_nat_1(D,np__1)) = f4_s21_recdef_1(D,k8_funct_2(k5_numbers,f1_s21_recdef_1,C,D)))) & B = k8_funct_2(k5_numbers,f1_s21_recdef_1,C,f3_s21_recdef_1) & m2_relset_1(C,k5_numbers,f1_s21_recdef_1) & v1_funct_2(C,k5_numbers,f1_s21_recdef_1) & v1_funct_1(C))) & A != B & (exists C (v1_funct_1(C) & v1_funct_2(C,k5_numbers,f1_s21_recdef_1) & m2_relset_1(C,k5_numbers,f1_s21_recdef_1) & A = k8_funct_2(k5_numbers,f1_s21_recdef_1,C,f3_s21_recdef_1) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,f1_s21_recdef_1,C,k1_nat_1(D,np__1)) = f4_s21_recdef_1(D,k8_funct_2(k5_numbers,f1_s21_recdef_1,C,D)))) & f2_s21_recdef_1 = k8_funct_2(k5_numbers,f1_s21_recdef_1,C,np__0)))))))) # label(s21_recdef_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 115.69/113.73 6389 (exists A (m1_subset_1(A,f1_s21_recdef_1) & (exists B (A = k8_funct_2(k5_numbers,f1_s21_recdef_1,B,f3_s21_recdef_1) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,f1_s21_recdef_1,B,k1_nat_1(C,np__1)) = f4_s21_recdef_1(C,k8_funct_2(k5_numbers,f1_s21_recdef_1,B,C)))) & k8_funct_2(k5_numbers,f1_s21_recdef_1,B,np__0) = f2_s21_recdef_1 & m2_relset_1(B,k5_numbers,f1_s21_recdef_1) & v1_funct_2(B,k5_numbers,f1_s21_recdef_1) & v1_funct_1(B))))) # label(s21_recdef_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 115.69/113.73 6390 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C all D (p1_s18_recdef_1(A,B,C) & p1_s18_recdef_1(A,B,D) -> D = C)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B exists C p1_s18_recdef_1(A,B,C)))) -> (exists A exists B (v1_funct_1(B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> p1_s18_recdef_1(C,k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,np__1))))) & k1_funct_1(B,np__0) = f1_s18_recdef_1 & k5_numbers = k1_relat_1(B) & A = k1_funct_1(B,f2_s18_recdef_1) & v1_relat_1(B))) & (all A all B -((exists C (v1_relat_1(C) & v1_funct_1(C) & k1_funct_1(C,f2_s18_recdef_1) = A & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> p1_s18_recdef_1(D,k1_funct_1(C,D),k1_funct_1(C,k1_nat_1(D,np__1))))) & f1_s18_recdef_1 = k1_funct_1(C,np__0) & k1_relat_1(C) = k5_numbers)) & B != A & (exists C (B = k1_funct_1(C,f2_s18_recdef_1) & k1_funct_1(C,np__0) = f1_s18_recdef_1 & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> p1_s18_recdef_1(D,k1_funct_1(C,D),k1_funct_1(C,k1_nat_1(D,np__1))))) & k1_relat_1(C) = k5_numbers & v1_funct_1(C) & v1_relat_1(C))))) # label(s18_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.73 6391 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_subset_1(B,f1_s20_recdef_1) -> (all C (m1_subset_1(C,f1_s20_recdef_1) -> (all D (m1_subset_1(D,f1_s20_recdef_1) -> (p1_s20_recdef_1(A,B,D) & p1_s20_recdef_1(A,B,C) -> D = C))))))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_subset_1(B,f1_s20_recdef_1) -> (exists C (m1_subset_1(C,f1_s20_recdef_1) & p1_s20_recdef_1(A,B,C))))))) -> (exists A ((exists B (m2_relset_1(B,k5_numbers,f1_s20_recdef_1) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> p1_s20_recdef_1(C,k8_funct_2(k5_numbers,f1_s20_recdef_1,B,C),k8_funct_2(k5_numbers,f1_s20_recdef_1,B,k1_nat_1(C,np__1))))) & f2_s20_recdef_1 = k8_funct_2(k5_numbers,f1_s20_recdef_1,B,np__0) & k8_funct_2(k5_numbers,f1_s20_recdef_1,B,f3_s20_recdef_1) = A & v1_funct_2(B,k5_numbers,f1_s20_recdef_1) & v1_funct_1(B))) & m1_subset_1(A,f1_s20_recdef_1))) & (all A (m1_subset_1(A,f1_s20_recdef_1) -> (all B (m1_subset_1(B,f1_s20_recdef_1) -> -(A != B & (exists C (v1_funct_1(C) & v1_funct_2(C,k5_numbers,f1_s20_recdef_1) & m2_relset_1(C,k5_numbers,f1_s20_recdef_1) & k8_funct_2(k5_numbers,f1_s20_recdef_1,C,np__0) = f2_s20_recdef_1 & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> p1_s20_recdef_1(D,k8_funct_2(k5_numbers,f1_s20_recdef_1,C,D),k8_funct_2(k5_numbers,f1_s20_recdef_1,C,k1_nat_1(D,np__1))))) & B = k8_funct_2(k5_numbers,f1_s20_recdef_1,C,f3_s20_recdef_1))) & (exists C (v1_funct_2(C,k5_numbers,f1_s20_recdef_1) & m2_relset_1(C,k5_numbers,f1_s20_recdef_1) & A = k8_funct_2(k5_numbers,f1_s20_recdef_1,C,f3_s20_recdef_1) & f2_s20_recdef_1 = k8_funct_2(k5_numbers,f1_s20_recdef_1,C,np__0) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> p1_s20_recdef_1(D,k8_funct_2(k5_numbers,f1_s20_recdef_1,C,D),k8_funct_2(k5_numbers,f1_s20_recdef_1,C,k1_nat_1(D,np__1))))) & v1_funct_1(C)))))))) # label(s20_recdef_1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6392 (all A all B all C (r1_tarski(C,A) & r2_hidden(A,k1_classes1(B)) -> r2_hidden(C,k1_classes1(B)))) # label(t6_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6393 (all A all B (v3_ordinal1(B) -> (all C ((exists D (v5_ordinal1(D) & k1_relat_1(D) = k1_ordinal1(B) & k1_tarski(A) = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k2_xboole_0(k2_xboole_0(a_3_0_classes1(A,D,E),a_3_1_classes1(A,D,E)),k3_xboole_0(k1_zfmisc_1(k1_funct_1(D,E)),k1_classes1(A)))))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_funct_1(D,E) = k3_xboole_0(k3_tarski(k2_relat_1(k2_ordinal1(D,E))),k1_classes1(A)) | E = k1_xboole_0))) & k1_ordinal2(D) = C & v1_funct_1(D) & v1_relat_1(D))) <-> k2_classes1(A,B) = C)))) # label(d5_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6394 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(k4_classes1(A),k4_classes1(B)) <-> r1_ordinal1(A,B)))))) # label(t43_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6395 (all A all B (r1_tarski(A,B) -> r1_ordinal1(k6_classes1(A),k6_classes1(B)))) # label(t75_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6396 (all A all B (v3_ordinal1(B) -> ((all C (r2_hidden(C,A) -> r2_hidden(k6_classes1(C),B))) <-> r1_ordinal1(k6_classes1(A),B)))) # label(t77_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6397 $T # label(dt_k4_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6398 (all A all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> -(r2_hidden(C,B) & (all D -(r1_ordinal1(C,k6_classes1(D)) & r2_hidden(D,A)))))) <-> r1_ordinal1(B,k6_classes1(A))))) # label(t78_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6399 (all A all B -(r2_hidden(A,k1_classes1(B)) & r2_tarski(A,k1_classes1(B)))) # label(t29_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6400 (all A r1_tarski(A,k5_classes1(A))) # label(t59_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6401 (all A k1_ordinal1(k6_classes1(A)) = k6_classes1(k1_zfmisc_1(A))) # label(t71_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6402 (all A all B (v3_ordinal1(B) -> m1_subset_1(k3_classes1(A,B),k1_zfmisc_1(k1_classes1(A))))) # label(dt_k3_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6403 (all A all B all C all D (v1_funct_1(C) & v5_ordinal1(C) & v3_ordinal1(D) & v1_relat_1(C) -> (r2_hidden(A,a_3_0_classes1(B,C,D)) <-> (exists E (m1_subset_1(E,k1_classes1(B)) & (exists F (m1_subset_1(F,k1_classes1(B)) & r1_tarski(E,F) & r2_hidden(F,k1_funct_1(C,D)))) & A = E))))) # label(fraenkel_a_3_0_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6404 (all A k5_classes1(A) = k5_classes1(k5_classes1(A))) # label(t66_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6405 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> (all B (r2_hidden(B,k4_classes1(A)) <-> (exists C (v3_ordinal1(C) & r2_hidden(C,A) & r2_hidden(B,k4_classes1(C)))))) | A = k1_xboole_0))) # label(t35_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6406 (all A all B all C all D (v1_relat_1(C) & v5_ordinal1(C) & v3_ordinal1(D) & v1_funct_1(C) -> ((exists E (m1_subset_1(E,k1_classes1(B)) & r2_hidden(E,k1_funct_1(C,D)) & k1_zfmisc_1(E) = A)) <-> r2_hidden(A,a_3_1_classes1(B,C,D))))) # label(fraenkel_a_3_1_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6407 (all A (v3_ordinal1(A) -> (all B (k4_classes1(A) = B <-> (exists C ((all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = k1_zfmisc_1(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) = k3_tarski(k2_relat_1(k2_ordinal1(C,D)))))) & k1_funct_1(C,k1_xboole_0) = k1_xboole_0 & k1_relat_1(C) = k1_ordinal1(A) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))))))) # label(d6_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6408 (all A all B all C (r2_hidden(C,k1_classes1(A)) & r2_hidden(B,k1_classes1(A)) -> r2_hidden(k1_tarski(B),k1_classes1(A)) & r2_hidden(k2_tarski(B,C),k1_classes1(A)))) # label(t30_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6409 (all A v3_ordinal1(k6_classes1(A))) # label(dt_k6_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6410 (all A (v1_ordinal1(A) -> v1_ordinal1(k1_classes1(A)))) # label(t27_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6411 (all A all B (v3_ordinal1(B) -> (k6_classes1(A) = B <-> (all C (v3_ordinal1(C) -> (r1_tarski(A,k4_classes1(C)) -> r1_ordinal1(B,C)))) & r1_tarski(A,k4_classes1(B))))) # label(d8_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6412 (all A -v1_xboole_0(k1_classes1(A))) # label(fc1_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6413 (all A all B all C (v3_ordinal1(C) -> (-((all D -((r1_tarski(A,D) | A = k1_zfmisc_1(D)) & r2_hidden(D,k3_classes1(B,C)))) & -(r2_hidden(A,k1_classes1(B)) & r1_tarski(A,k3_classes1(B,C)))) <-> r2_hidden(A,k3_classes1(B,k1_ordinal1(C)))))) # label(t13_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6414 (all A ((all B (r2_hidden(B,A) -> r2_hidden(k1_zfmisc_1(B),A))) & (all B -(-r2_hidden(B,A) & -r2_tarski(B,A) & r1_tarski(B,A))) & v1_classes1(A) <-> v2_classes1(A))) # label(d2_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6415 (all A all B (v3_ordinal1(B) -> k2_classes1(A,B) = k3_classes1(A,B))) # label(redefinition_k3_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6416 (all A all B -(A != B & (all C (v3_ordinal1(C) -> -(-r2_hidden(A,k3_classes1(B,C)) & r2_hidden(A,k3_classes1(B,k1_ordinal1(C)))))) & r2_hidden(A,k1_classes1(B)))) # label(t24_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6417 (all A all B (v3_ordinal1(B) -> (r2_hidden(k1_zfmisc_1(A),k4_classes1(k1_ordinal1(B))) <-> r2_hidden(A,k4_classes1(B))))) # label(t48_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6418 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,k3_classes1(B,C)) -> r2_hidden(k1_zfmisc_1(A),k3_classes1(B,k1_ordinal1(C)))))) # label(t15_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6419 (all A all B all C (v3_ordinal1(C) -> (r1_tarski(A,B) & r2_hidden(B,k4_classes1(C)) -> r2_hidden(A,k4_classes1(C))))) # label(t47_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6420 $T # label(t57_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6421 (all A all B (r1_classes1(A,B) <-> v2_classes1(B) & r2_hidden(A,B))) # label(d3_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6422 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,k4_classes1(B)) <-> r2_hidden(A,k4_classes1(k1_ordinal1(B)))))) # label(t36_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6423 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(B,k4_classes1(C)) & r2_hidden(A,k4_classes1(C)) <-> r2_hidden(k4_tarski(A,B),k4_classes1(k1_ordinal1(k1_ordinal1(C))))))) # label(t51_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6424 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,a_2_2_classes1(B,C)) <-> (exists D (D = A & (exists E (r2_hidden(D,k3_classes1(B,E)) & r2_hidden(E,C) & v3_ordinal1(E))) & m1_subset_1(D,k1_classes1(B))))))) # label(fraenkel_a_2_2_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6425 (all A all B (v3_ordinal1(B) -> -(k1_ordinal1(B) = k6_classes1(A) & (all C -(r2_hidden(C,A) & B = k6_classes1(C)))))) # label(t80_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6426 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) -> r2_hidden(k3_tarski(A),k4_classes1(B))))) # label(t41_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6427 (all A -(v1_ordinal1(A) & (all B (v3_ordinal1(B) -> -r1_tarski(k1_classes1(A),k4_classes1(B)))))) # label(t53_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6428 (all A all B (v1_ordinal1(A) & v1_ordinal1(B) -> v1_ordinal1(k3_xboole_0(A,B)))) # label(t56_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6429 (all A all B (v3_ordinal1(B) -> k2_xboole_0(k2_xboole_0(a_2_0_classes1(A,B),a_2_1_classes1(A,B)),k3_xboole_0(k1_zfmisc_1(k3_classes1(A,B)),k1_classes1(A))) = k3_classes1(A,k1_ordinal1(B)))) # label(t11_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6430 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r2_hidden(k4_classes1(A),k4_classes1(B))))))) # label(t42_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6431 (all A all B (B = k1_classes1(A) <-> r1_classes1(A,B) & (all C (r1_classes1(A,C) -> r1_tarski(B,C))))) # label(d4_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6432 (all A exists B (v3_ordinal1(B) & k3_classes1(A,B) = k1_classes1(A))) # label(t22_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6433 (all A (v3_ordinal1(A) -> r1_tarski(k3_tarski(k4_classes1(A)),k4_classes1(A)))) # label(t40_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6434 (all A exists B (k3_classes1(A,k1_ordinal1(B)) = k3_classes1(A,B) & v3_ordinal1(B))) # label(t20_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6435 (all A all B (r1_tarski(A,B) & v1_ordinal1(B) -> r1_tarski(k5_classes1(A),B))) # label(t60_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6436 (all A exists B (v3_ordinal1(B) & (all C (v3_ordinal1(C) -> -(k1_classes1(A) = k3_classes1(A,C) & r2_hidden(C,B)))) & k1_classes1(A) = k3_classes1(A,B))) # label(t23_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6437 (all A (k3_classes1(A,k1_xboole_0) != k3_classes1(A,k4_ordinal2) & r2_hidden(k3_classes1(A,k1_xboole_0),k3_classes1(A,k4_ordinal2)))) # label(t26_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6438 (all A all B all C (v3_ordinal1(C) -> (v4_ordinal1(C) -> C = k1_xboole_0 | ((exists D (v3_ordinal1(D) & r2_hidden(B,k3_classes1(A,D)) & r2_hidden(D,C))) <-> r2_hidden(B,k3_classes1(A,C)))))) # label(t16_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6439 (all A r2_hidden(A,k1_classes1(A))) # label(t5_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6440 (all A all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_zfmisc_1(A),k1_classes1(B)))) # label(t7_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6441 (all A all B (r1_tarski(A,B) & v1_ordinal1(B) & (all C (v1_ordinal1(C) & r1_tarski(A,C) -> r1_tarski(B,C))) -> B = k5_classes1(A))) # label(t61_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6442 (all A all B all C all D (v3_ordinal1(D) -> (r2_hidden(B,k3_classes1(C,D)) & r1_tarski(A,B) -> r2_hidden(A,k3_classes1(C,k1_ordinal1(D)))))) # label(t14_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6443 (all A all B (k5_classes1(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D (v1_relat_1(D) & (exists E (k1_funct_1(D,np__0) = A & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> k1_funct_1(D,k1_nat_1(F,np__1)) = k3_tarski(k1_funct_1(D,F)))) & k5_numbers = k1_relat_1(D) & r2_hidden(C,k1_funct_1(D,E)) & m2_subset_1(E,k1_numbers,k5_numbers))) & v1_funct_1(D))))))) # label(d7_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6444 (all A all B -(r1_tarski(A,k1_classes1(B)) & -r2_hidden(A,k1_classes1(B)) & -r2_tarski(A,k1_classes1(B)))) # label(t8_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6445 (all A all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(B,C) -> r1_tarski(k3_classes1(A,B),k3_classes1(A,C))))))) # label(t19_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6446 (all A all B (r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))) & r1_tarski(A,k1_classes1(B)) -> r2_hidden(A,k1_classes1(B)))) # label(t9_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6447 (all A ((all B all C (r2_hidden(B,A) & r1_tarski(C,B) -> r2_hidden(C,A))) <-> v1_classes1(A))) # label(d1_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6448 (all A (v3_ordinal1(A) -> r1_tarski(k4_classes1(A),k4_classes1(k1_ordinal1(A))))) # label(t39_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6449 (all A (v3_ordinal1(A) -> k4_classes1(k1_ordinal1(A)) = k1_zfmisc_1(k4_classes1(A)))) # label(t34_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6450 (all A (k1_xboole_0 = A <-> k6_classes1(A) = k1_xboole_0)) # label(t79_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6451 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,a_2_1_classes1(B,C)) <-> (exists D (k1_zfmisc_1(D) = A & r2_hidden(D,k3_classes1(B,C)) & m1_subset_1(D,k1_classes1(B))))))) # label(fraenkel_a_2_1_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6452 (all A all B all C (r2_hidden(C,k1_classes1(A)) & r2_hidden(B,k1_classes1(A)) -> r2_hidden(k4_tarski(B,C),k1_classes1(A)))) # label(t31_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6453 (all A all B all C (r1_tarski(A,k1_classes1(B)) & r1_tarski(C,k1_classes1(B)) -> r1_tarski(k2_zfmisc_1(A,C),k1_classes1(B)))) # label(t32_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6454 $T # label(t3_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6455 (all A all B (v3_ordinal1(B) -> (r2_hidden(k1_tarski(A),k4_classes1(k1_ordinal1(B))) <-> r2_hidden(A,k4_classes1(B))))) # label(t49_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6456 (all A all B (v3_ordinal1(B) -> (v4_ordinal1(B) -> B = k1_xboole_0 | a_2_2_classes1(A,B) = k3_classes1(A,B)))) # label(t12_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6457 (all A (v3_ordinal1(A) -> (all B (r2_hidden(B,k4_classes1(A)) -> -r2_tarski(B,k4_classes1(A)) & r2_hidden(k1_card_1(B),k1_card_1(k4_classes1(A))))))) # label(t45_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6458 $T # label(dt_k5_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6459 (all A all B (v3_ordinal1(B) -> (r1_ordinal1(k6_classes1(A),B) <-> r1_tarski(A,k4_classes1(B))))) # label(t73_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6460 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,k4_classes1(B)) <-> r1_tarski(k1_zfmisc_1(A),k4_classes1(k1_ordinal1(B)))))) # label(t46_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6461 $T # label(t4_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6462 (all A (v3_ordinal1(A) -> k6_classes1(A) = A)) # label(t81_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6463 (all A (v3_ordinal1(A) -> r1_tarski(A,k4_classes1(A)))) # label(t44_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6464 (all A all B all C all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(A,k3_classes1(B,D)) -> C != k1_zfmisc_1(A) & -r1_tarski(C,A) | r2_hidden(C,k3_classes1(B,D)) | k1_xboole_0 = D))) # label(t17_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6465 (all A exists B (r1_tarski(A,k4_classes1(B)) & v3_ordinal1(B))) # label(t69_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6466 $T # label(t70_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6467 (all A k1_tarski(A) = k3_classes1(A,k1_xboole_0)) # label(t10_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6468 (all A (v3_ordinal1(A) -> A = k5_classes1(A))) # label(t64_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6469 $T # label(dt_k2_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6470 (all A all B (r1_tarski(A,B) -> r1_tarski(k5_classes1(A),k5_classes1(B)))) # label(t65_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6471 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) -> r1_tarski(A,k4_classes1(B))))) # label(t38_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6472 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) <-> r2_hidden(k6_classes1(A),B)))) # label(t74_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6473 (all A all B (v3_ordinal1(B) -> (k3_classes1(A,B) = k3_classes1(A,k1_ordinal1(B)) -> k1_classes1(A) = k3_classes1(A,B)))) # label(t21_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6474 $T # label(t1_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6475 (all A (v1_ordinal1(A) -> r1_tarski(k3_tarski(A),A))) # label(t54_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6476 (all A (v3_ordinal1(A) -> k6_classes1(k4_classes1(A)) = A)) # label(t72_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6477 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,a_2_0_classes1(B,C)) <-> (exists D (A = D & (exists E (m1_subset_1(E,k1_classes1(B)) & r2_hidden(E,k3_classes1(B,C)) & r1_tarski(D,E))) & m1_subset_1(D,k1_classes1(B))))))) # label(fraenkel_a_2_0_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6478 (all A v1_ordinal1(k5_classes1(A))) # label(t58_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6479 (all A (v1_ordinal1(A) -> k5_classes1(A) = A)) # label(t62_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6480 (all A all B k5_classes1(k2_xboole_0(A,B)) = k2_xboole_0(k5_classes1(A),k5_classes1(B))) # label(t67_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6481 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(t37_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6482 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,k4_classes1(C)) & r2_hidden(B,k4_classes1(C)) <-> r2_hidden(k2_tarski(A,B),k4_classes1(k1_ordinal1(C)))))) # label(t50_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6483 (all A all B (v3_ordinal1(B) -> (k3_xboole_0(k4_classes1(k1_ordinal1(B)),k1_classes1(A)) = k3_xboole_0(k4_classes1(B),k1_classes1(A)) & v1_ordinal1(A) -> r1_tarski(k1_classes1(A),k4_classes1(B))))) # label(t52_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6484 (all A all B (v1_ordinal1(B) & v1_ordinal1(A) -> v1_ordinal1(k2_xboole_0(A,B)))) # label(t55_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6485 (all A (v4_ordinal1(k6_classes1(k1_classes1(A))) & k1_xboole_0 != k6_classes1(k1_classes1(A)))) # label(t82_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6486 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B != k1_xboole_0 -> v1_ordinal1(k3_classes1(A,B))))))) # label(t25_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6487 $T # label(dt_k1_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6488 (all A all B (r2_hidden(A,B) -> r2_hidden(k6_classes1(A),k6_classes1(B)))) # label(t76_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6489 (all A all B r1_tarski(k5_classes1(k3_xboole_0(A,B)),k3_xboole_0(k5_classes1(A),k5_classes1(B)))) # label(t68_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6490 (all A all B (v3_ordinal1(B) -> r1_tarski(k3_classes1(A,B),k3_classes1(A,k1_ordinal1(B))))) # label(t18_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6491 (all A (v2_classes1(A) <-> v1_classes1(A) & (all B (r2_hidden(B,A) -> r2_hidden(k1_zfmisc_1(B),A))) & (all B (r1_tarski(B,A) & r2_hidden(k1_card_1(B),k1_card_1(A)) -> r2_hidden(B,A))))) # label(t2_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6492 (all A all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))))) # label(t28_classes1) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6493 (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]. 115.69/113.74 6494 (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]. 115.69/113.74 6495 (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]. 115.69/113.74 6496 (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]. 115.69/113.74 6497 (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]. 115.69/113.74 6498 $T # label(dt_k4_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6499 (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]. 115.69/113.74 6500 (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]. 115.69/113.74 6501 (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]. 115.69/113.74 6502 (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]. 115.69/113.74 6503 (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]. 115.69/113.74 6504 (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]. 115.69/113.74 6505 (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]. 115.69/113.74 6506 (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]. 115.69/113.74 6507 $T # label(t6_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6508 (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]. 115.69/113.74 6509 (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]. 115.69/113.74 6510 (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]. 115.69/113.74 6511 (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]. 115.69/113.74 6512 (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]. 115.69/113.74 6513 (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]. 115.69/113.74 6514 (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]. 115.69/113.74 6515 (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]. 115.69/113.74 6516 (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]. 115.69/113.74 6517 (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]. 115.69/113.74 6518 $T # label(t2_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6519 $T # label(t5_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6520 (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]. 115.69/113.74 6521 (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]. 115.69/113.74 6522 (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]. 115.69/113.74 6523 (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]. 115.69/113.74 6524 (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]. 115.69/113.74 6525 (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]. 115.69/113.74 6526 (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]. 115.69/113.74 6527 $T # label(t4_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6528 (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]. 115.69/113.74 6529 (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]. 115.69/113.74 6530 (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]. 115.69/113.74 6531 (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]. 115.69/113.74 6532 (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]. 115.69/113.74 6533 (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]. 115.69/113.74 6534 (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]. 115.69/113.74 6535 (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]. 115.69/113.74 6536 (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]. 115.69/113.74 6537 (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]. 115.69/113.74 6538 (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]. 115.69/113.74 6539 $T # label(dt_k3_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6540 (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]. 115.69/113.74 6541 (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]. 115.69/113.74 6542 $T # label(t21_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6543 (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]. 115.69/113.74 6544 (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]. 115.69/113.74 6545 (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]. 115.69/113.74 6546 $T # label(dt_k5_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6547 (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]. 115.69/113.74 6548 (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]. 115.69/113.74 6549 (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]. 115.69/113.74 6550 (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]. 115.69/113.74 6551 $T # label(t41_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6552 (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]. 115.69/113.74 6553 $T # label(t23_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6554 (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]. 115.69/113.74 6555 $T # label(t42_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6556 (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]. 115.69/113.74 6557 $T # label(t7_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.74 6558 (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]. 115.69/113.75 6559 (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]. 115.69/113.75 6560 (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]. 115.69/113.75 6561 (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]. 115.69/113.75 6562 (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]. 115.69/113.75 6563 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A))) # label(rc1_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6564 (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]. 115.69/113.75 6565 (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]. 115.69/113.75 6566 (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]. 115.69/113.75 6567 (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]. 115.69/113.75 6568 (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]. 115.69/113.75 6569 (all A k5_card_3(A,k1_xboole_0) = k1_xboole_0) # label(t24_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6570 $T # label(t1_card_3) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6571 (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]. 115.69/113.75 6572 (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]. 115.69/113.75 6573 (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]. 115.69/113.75 6574 (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]. 115.69/113.75 6575 (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]. 115.69/113.75 6576 (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]. 115.69/113.75 6577 (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]. 115.69/113.75 6578 (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]. 115.69/113.75 6579 (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]. 115.69/113.75 6580 (all A (v1_classes2(A) -> v2_classes1(A) & v1_classes1(A) & v1_ordinal1(A))) # label(cc2_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6581 (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]. 115.69/113.75 6582 (all A (v1_classes2(k15_classes2(A)) & -v1_xboole_0(k15_classes2(A)))) # label(dt_k15_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6583 (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]. 115.69/113.75 6584 $T # label(t48_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6585 (all A (v2_classes1(A) -> r1_tarski(k4_classes1(k1_card_1(A)),A))) # label(t28_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6586 (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]. 115.69/113.75 6587 (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]. 115.69/113.75 6588 (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]. 115.69/113.75 6589 (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]. 115.69/113.75 6590 (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]. 115.69/113.75 6591 (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]. 115.69/113.75 6592 $T # label(t74_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6593 (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]. 115.69/113.75 6594 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v3_ordinal1(k2_ordinal2(A)))) # label(t50_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6595 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(fc7_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6596 (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]. 115.69/113.75 6597 (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]. 115.69/113.75 6598 (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]. 115.69/113.75 6599 (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]. 115.69/113.75 6600 $T # label(t2_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6601 (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]. 115.69/113.75 6602 (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]. 115.69/113.75 6603 (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]. 115.69/113.75 6604 (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]. 115.69/113.75 6605 (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]. 115.69/113.75 6606 $T # label(t60_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6607 (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]. 115.69/113.75 6608 $T # label(t68_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6609 (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]. 115.69/113.75 6610 (all A k1_card_1(k1_classes1(A)) = k2_ordinal2(k1_classes1(A))) # label(t11_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6611 (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]. 115.69/113.75 6612 (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]. 115.69/113.75 6613 (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]. 115.69/113.75 6614 (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]. 115.69/113.75 6615 (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]. 115.69/113.75 6616 (all A (v1_classes2(A) <-> v2_classes1(A) & v1_ordinal1(A))) # label(d1_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6617 (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]. 115.69/113.75 6618 (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]. 115.69/113.75 6619 (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]. 115.69/113.75 6620 (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]. 115.69/113.75 6621 (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]. 115.69/113.75 6622 (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]. 115.69/113.75 6623 (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]. 115.69/113.75 6624 (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]. 115.69/113.75 6625 $T # label(t73_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6626 (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]. 115.69/113.75 6627 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k1_xboole_0,A))) # label(t62_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6628 (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]. 115.69/113.75 6629 (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]. 115.69/113.75 6630 (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]. 115.69/113.75 6631 (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]. 115.69/113.75 6632 (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]. 115.69/113.75 6633 (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]. 115.69/113.75 6634 (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]. 115.69/113.75 6635 (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]. 115.69/113.75 6636 (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]. 115.69/113.75 6637 (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]. 115.69/113.75 6638 (all A (v2_classes1(A) -> k1_card_1(A) = k2_ordinal2(A))) # label(t10_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6639 $T # label(t47_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6640 (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]. 115.69/113.75 6641 (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]. 115.69/113.75 6642 (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]. 115.69/113.75 6643 (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]. 115.69/113.75 6644 (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]. 115.69/113.75 6645 $T # label(t49_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6646 (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]. 115.69/113.75 6647 (all A (v2_classes1(A) -> v1_classes1(A))) # label(cc1_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6648 (all A (v1_ordinal1(A) & v2_classes1(A) -> k4_classes1(k1_card_1(A)) = A)) # label(t32_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6649 (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]. 115.69/113.75 6650 (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]. 115.69/113.75 6651 (all A (v1_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t51_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6652 (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]. 115.69/113.75 6653 (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]. 115.69/113.75 6654 (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]. 115.69/113.75 6655 (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]. 115.69/113.75 6656 (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]. 115.69/113.75 6657 $T # label(dt_k16_classes2) # label(axiom) # label(non_clause). [assumption]. 115.69/113.75 6658 (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]. 115.69/113.75 6659 (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]. 115.69/113.75 6660 (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]. 115.69/113.75 6661 (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]. 115.69/113.75 6662 (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]. 115.69/113.75 6663 (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]. 115.78/113.75 6664 (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]. 115.78/113.75 6665 (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]. 115.78/113.75 6666 (all A v2_classes1(k4_classes1(k1_card_1(k1_classes1(A))))) # label(t40_classes2) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6667 $T # label(t72_classes2) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6668 (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]. 115.78/113.75 6669 (all A (v3_ordinal1(A) -> k1_classes1(k16_classes2(A)) = k16_classes2(k1_ordinal1(A)))) # label(t76_classes2) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6670 (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]. 115.78/113.75 6671 (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]. 115.78/113.75 6672 (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]. 115.78/113.75 6673 (all A (v3_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t53_classes2) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6674 (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]. 115.78/113.75 6675 (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]. 115.78/113.75 6676 (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]. 115.78/113.75 6677 (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]. 115.78/113.75 6678 (all A r1_tarski(k4_classes1(k1_card_1(k1_classes1(A))),k1_classes1(A))) # label(t29_classes2) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6679 (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]. 115.78/113.75 6680 (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]. 115.78/113.75 6681 (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]. 115.78/113.75 6682 (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]. 115.78/113.75 6683 (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]. 115.78/113.75 6684 (all A (-v1_xboole_0(A) & v1_classes2(A) -> k4_classes1(k2_ordinal2(A)) = A)) # label(t54_classes2) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6685 (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]. 115.78/113.75 6686 (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]. 115.78/113.75 6687 (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]. 115.78/113.75 6688 (all A (v1_ordinal1(A) & v2_classes1(A) -> v1_classes2(A))) # label(cc3_classes2) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6689 (all A (v2_classes1(A) -> v2_classes1(k4_classes1(k1_card_1(A))))) # label(t39_classes2) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6690 (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]. 115.78/113.75 6691 (all A (v2_classes1(A) -> v4_ordinal1(k1_card_1(A)))) # label(t20_classes2) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6692 (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]. 115.78/113.75 6693 (all A v1_ordinal1(k5_classes1(A))) # label(fc5_classes2) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6694 (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]. 115.78/113.75 6695 (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]. 115.78/113.75 6696 (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]. 115.78/113.75 6697 (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]. 115.78/113.75 6698 (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]. 115.78/113.75 6699 (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]. 115.78/113.75 6700 (all A all B (v1_classes2(A) & m1_ordinal4(B,A) & -v1_xboole_0(A) -> k1_ordinal1(B) = k6_ordinal4(A,B))) # label(redefinition_k6_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6701 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v3_ordinal1(B) -> (m1_ordinal4(B,A) <-> r2_hidden(B,A)))))) # label(d2_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6702 (all A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) -> (v2_ordinal2(A) -> v5_ordinal1(k5_relat_1(A,B)) & v1_ordinal2(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B))))))) # label(t12_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6703 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(k16_ordinal2(A,B) = k1_xboole_0 & k1_xboole_0 != A))))) # label(t22_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6704 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k16_ordinal2(A,C),k16_ordinal2(B,C))))))))) # label(t28_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6705 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> -(v2_ordinal2(A) & (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> -(v2_ordinal2(C) & k5_relat_1(B,A) = C))) & v2_ordinal2(B)))))) # label(t13_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6706 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) -> (all D (v1_relat_1(D) & v1_ordinal2(D) & v5_ordinal1(D) & v1_funct_1(D) -> (k1_relat_1(A) = k1_relat_1(D) & r1_ordinal2(B,C) & r1_ordinal2(B,D) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_relat_1(A)) -> r1_ordinal1(k1_funct_1(A,E),k1_funct_1(D,E)) & r1_ordinal1(k1_funct_1(C,E),k1_funct_1(A,E))))) & k1_relat_1(C) = k1_relat_1(A) -> r1_ordinal2(B,A)))))))))) # label(t7_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6707 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r1_ordinal2(C,A) & r1_ordinal2(D,B) & k1_relat_1(B) = k1_relat_1(A) -> (exists E (v3_ordinal1(E) & -r2_hidden(k1_funct_1(A,E),k1_funct_1(B,E)) & r2_hidden(E,k1_relat_1(A)))) & (exists E (-r1_ordinal1(k1_funct_1(A,E),k1_funct_1(B,E)) & r2_hidden(E,k1_relat_1(A)) & v3_ordinal1(E))) | r1_ordinal1(C,D)))))))))) # label(t6_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6708 (all A all B all C (-v1_xboole_0(A) & m2_ordinal4(C,A) & m2_ordinal4(B,A) & v1_classes2(A) -> k5_relat_1(B,C) = k5_ordinal4(A,B,C))) # label(redefinition_k5_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6709 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k3_ordinal4(A)) & m1_ordinal4(k3_ordinal4(A),A))) # label(dt_k3_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6710 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k2_ordinal4(A) = k1_xboole_0 & k3_ordinal4(A) = k4_ordinal2)) # label(t35_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6711 (all A all B all C (m1_ordinal4(C,A) & m1_ordinal4(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k8_ordinal4(A,B,C) = k15_ordinal2(B,C))) # label(redefinition_k8_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6712 (all A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(k1_relat_1(A),B) & r1_tarski(k2_relat_1(A),B) -> r2_hidden(k8_ordinal2(A),B)))))) # label(t37_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6713 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (k1_relat_1(A) = k1_ordinal1(B) -> r1_ordinal2(k1_ordinal2(A),A) & k12_ordinal2(A) = k1_ordinal2(A)))))) # label(t1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6714 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k4_ordinal2,A) -> r2_hidden(k16_ordinal2(A,B),k16_ordinal2(A,k1_ordinal1(B)))))))) # label(t23_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6715 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (exists B m2_ordinal4(B,A)))) # label(existence_m2_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6716 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> r2_hidden(B,k1_relat_1(C)))))))) # label(t36_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6717 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v5_ordinal1(D) & v1_ordinal2(D) & v1_funct_1(D) & v1_relat_1(D) -> (v2_ordinal2(C) & k5_relat_1(C,D) = A & k7_ordinal2(k2_relat_1(C)) = k1_relat_1(D) & r1_ordinal2(B,D) -> r1_ordinal2(B,A)))))))))) # label(t14_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.75 6718 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) & r1_ordinal1(B,C) & v2_ordinal2(A) -> r1_ordinal1(k1_funct_1(A,B),k1_funct_1(A,C))))))))) # label(t9_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6719 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k2_ordinal2(A) & r1_tarski(k2_relat_1(B),k2_ordinal2(A)) <-> m2_ordinal4(B,A)))))) # label(d3_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6720 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (v2_ordinal2(A) & r2_hidden(B,k1_relat_1(A)) -> r1_ordinal1(B,k1_funct_1(A,B))))))) # label(t10_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6721 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k16_ordinal2(A,k15_ordinal2(C,B)) = k16_ordinal2(k16_ordinal2(A,B),C))))))) # label(t31_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6722 (all A all B all C (-v1_xboole_0(A) & m2_ordinal4(B,A) & m2_ordinal4(C,A) & v1_classes2(A) -> m2_ordinal4(k5_ordinal4(A,B,C),A))) # label(dt_k5_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6723 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (v2_ordinal2(A) -> v3_ordinal1(k10_relat_1(A,B))))))) # label(t11_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6724 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> (v3_ordinal2(A) & v3_ordinal2(B) & C = k5_relat_1(A,B) & v2_ordinal2(A) -> v3_ordinal2(C)))))))) # label(t17_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6725 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> v3_ordinal1(k1_ordinal2(A)) & v2_ordinal1(k1_ordinal2(A)) & v1_ordinal1(k1_ordinal2(A)))) # label(fc1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6726 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (exists B m1_ordinal4(B,A)))) # label(existence_m1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6727 (all A all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_ordinal4(A,B)) & v5_ordinal1(k1_ordinal4(A,B)) & v1_funct_1(k1_ordinal4(A,B)))) # label(dt_k1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6728 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k16_ordinal2(A,k14_ordinal2(B,C)) = k15_ordinal2(k16_ordinal2(A,C),k16_ordinal2(A,B)))))))) # label(t30_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6729 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> r2_hidden(f1_s1_ordinal4(A),f1_s1_ordinal4(B))))))) & (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(B) -> B = k1_xboole_0 | (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> (B = k1_relat_1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,B) -> f1_s1_ordinal4(D) = k1_funct_1(C,D)))) -> r1_ordinal2(f1_s1_ordinal4(B),C))))))))) -> (exists A (f1_s1_ordinal4(A) = A & v3_ordinal1(A))) # label(s1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6730 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> (v2_ordinal2(A) & v4_ordinal1(k1_relat_1(A)) -> r1_ordinal2(k8_ordinal2(A),A) & k12_ordinal2(A) = k8_ordinal2(A) | k1_relat_1(A) = k1_xboole_0))) # label(t8_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6731 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k4_ordinal2,A) -> r1_ordinal1(B,k16_ordinal2(A,B))))))) # label(t32_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6732 (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(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k15_ordinal2(C,B)))) -> v2_ordinal2(A) | B = k1_xboole_0))))) # label(t19_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6733 $T # label(t34_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6734 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k4_ordinal2,A) & v4_ordinal1(B) -> (all C (v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C) -> (B = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,B) -> k1_funct_1(C,D) = k16_ordinal2(A,D)))) -> k8_ordinal2(C) = k16_ordinal2(A,B)))) | k1_xboole_0 = B))))) # label(t26_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6735 (all A (-v1_xboole_0(A) & v1_classes2(A) -> k2_ordinal4(A) = k1_xboole_0)) # label(d4_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6736 (all A all B all C (v1_classes2(A) & m1_ordinal4(C,A) & m2_ordinal4(B,A) & -v1_xboole_0(A) -> m1_ordinal4(k4_ordinal4(A,B,C),A))) # label(dt_k4_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6737 $T # label(t2_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6738 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m2_ordinal4(B,A) -> v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B))))) # label(dt_m2_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6739 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) & v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v5_ordinal1(A) -> v1_relat_1(k1_ordinal4(A,B)) & v1_funct_1(k1_ordinal4(A,B)) & v1_ordinal2(k1_ordinal4(A,B)) & v5_ordinal1(k1_ordinal4(A,B)))) # label(fc2_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6740 (all A all B all C (-v1_xboole_0(A) & m1_ordinal4(C,A) & m1_ordinal4(B,A) & v1_classes2(A) -> m1_ordinal4(k7_ordinal4(A,B,C),A))) # label(dt_k7_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6741 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k4_ordinal2 = k3_ordinal4(A))) # label(d5_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6742 $T # label(t33_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6743 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k4_ordinal2,A) -> k1_xboole_0 = B | r2_hidden(k4_ordinal2,k16_ordinal2(A,B))))))) # label(t29_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6744 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal2(C,A) -> r1_ordinal2(C,k1_ordinal4(B,A))))))))) # label(t3_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6745 (exists A ((all B (m1_ordinal4(B,f1_s2_ordinal4) -> k1_funct_1(A,B) = f2_s2_ordinal4(B))) & m2_ordinal4(A,f1_s2_ordinal4))) # label(s2_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6746 (all A (-v1_xboole_0(A) & v1_classes2(A) -> m1_ordinal4(k2_ordinal4(A),A))) # label(dt_k2_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6747 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> v3_ordinal1(B))))) # label(dt_m1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6748 (all A all B all C (-v1_xboole_0(A) & m1_ordinal4(C,A) & m1_ordinal4(B,A) & v1_classes2(A) -> k14_ordinal2(B,C) = k7_ordinal4(A,B,C))) # label(redefinition_k7_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6749 (all A all B all C (m1_ordinal4(C,A) & m1_ordinal4(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_ordinal4(k8_ordinal4(A,B,C),A))) # label(dt_k8_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6750 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (exists B (v2_ordinal1(B) & v3_ordinal1(B) & -v1_xboole_0(B) & v1_ordinal1(B) & m1_ordinal4(B,A))))) # label(rc1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6751 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) & r2_hidden(k4_ordinal2,A) -> r2_hidden(k16_ordinal2(A,B),k16_ordinal2(A,C))))))))) # label(t24_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6752 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal2(B,A) -> r1_ordinal2(k15_ordinal2(B,C),k4_ordinal3(C,A))))))))) # label(t5_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6753 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k14_ordinal2(B,C)))) -> v2_ordinal2(A)))))) # label(t18_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6754 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(B,C) -> r1_ordinal1(k16_ordinal2(A,B),k16_ordinal2(A,C)) | A = k1_xboole_0))))))) # label(t27_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6755 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m2_ordinal4(B,A) -> -(v2_ordinal2(B) & (all C (v3_ordinal1(C) -> -(C = k1_funct_1(B,C) & r2_hidden(C,k1_relat_1(B))))) & r2_hidden(k5_ordinal2,A) & v3_ordinal2(B)))))) # label(t38_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6756 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k16_ordinal2(B,C)))) & r2_hidden(k4_ordinal2,B) -> v2_ordinal2(A)))))) # label(t25_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6757 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> (v2_ordinal2(A) & v4_ordinal1(k1_relat_1(A)) -> v4_ordinal1(k8_ordinal2(A))))) # label(t16_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6758 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k16_ordinal2(B,D) = k1_funct_1(C,D)))) -> r1_ordinal2(k16_ordinal2(B,A),C))))))))) # label(t21_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6759 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) -> (C = k1_ordinal4(A,B) <-> k14_ordinal2(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(A,D) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,k14_ordinal2(k1_relat_1(A),D)))))))))))) # label(d1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6760 (all A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> (v2_ordinal2(A) -> v2_ordinal2(k2_ordinal1(A,B))))))) # label(t15_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6761 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & m1_ordinal4(B,A) -> m1_ordinal4(k6_ordinal4(A,B),A) & -v1_xboole_0(k6_ordinal4(A,B)))) # label(dt_k6_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6762 (all A (v3_ordinal1(A) -> (A != k1_xboole_0 -> k1_xboole_0 = k16_ordinal2(k1_xboole_0,A)))) # label(t20_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6763 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal2(B,A) -> r1_ordinal2(k14_ordinal2(C,B),k1_ordinal3(C,A))))))))) # label(t4_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6764 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m2_ordinal4(B,A) & m1_ordinal4(C,A) -> k4_ordinal4(A,B,C) = k1_funct_1(B,C))) # label(redefinition_k4_ordinal4) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6765 (all A all B all C all D all E all F (-v1_xboole_0(A) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_finseq_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(C) & -v1_xboole_0(B) -> m2_finseq_1(k2_finseqop(A,B,C,D,E,F),C))) # label(dt_k2_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6766 (all A all B all C all D all E all F (-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) & m1_finseq_1(F,B) & m1_subset_1(E,A) & v1_funct_1(D) & -v1_xboole_0(A) -> m2_finseq_1(k3_finseqop(A,B,C,D,E,F),C))) # label(dt_k3_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6767 (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) -> (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,A,A) & v1_funct_2(E,A,A) & v1_funct_1(E) -> (E = k8_funcop_1(A,A,C,B,k6_partfun1(A)) & r6_binop_1(A,C,D) -> r7_binop_1(A,E,D)))))))))))) # label(t55_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6768 (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) -> v1_funct_2(k6_finseqop(A,B),A,A) & m2_relset_1(k6_finseqop(A,B),A,A) & v1_funct_1(k6_finseqop(A,B)))) # label(dt_k6_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6769 (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,C) & m2_relset_1(D,A,C) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,C,B) & v1_funct_2(F,C,B) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(C,C),C) & m2_relset_1(G,k2_zfmisc_1(C,C),C) -> (all H (v1_funct_2(H,k2_zfmisc_1(B,B),B) & m2_relset_1(H,k2_zfmisc_1(B,B),B) & v1_funct_1(H) -> ((all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,C) -> k2_binop_1(B,B,B,H,k8_funct_2(C,B,F,I),k8_funct_2(C,B,F,J)) = k8_funct_2(C,B,F,k2_binop_1(C,C,C,G,I,J)))))) -> k7_funct_2(A,C,B,k6_funcop_1(C,A,G,D,E),F) = k6_funcop_1(B,A,H,k7_funct_2(A,C,B,D,F),k7_funct_2(A,C,B,E,F))))))))))))))))))) # label(t38_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6770 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_finseq_2(C,A,k4_finseq_2(B,A)) -> (all D (m2_finseq_2(D,A,k4_finseq_2(B,A)) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_2(E,k2_zfmisc_1(A,A),A) -> (v2_binop_1(E,A) & v1_setwiseo(E,A) & k1_finseqop(A,A,A,E,C,D) = k4_finseqop(A,B,k3_binop_1(A,E)) & v1_finseqop(E,A) -> k5_finseqop(A,A,D,k6_finseqop(A,E)) = C & D = k5_finseqop(A,A,C,k6_finseqop(A,E))))))))))))) # label(t78_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6771 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m2_finseq_2(E,B,k4_finseq_2(C,B)) -> (all F (m2_finseq_2(F,B,k4_finseq_2(C,B)) -> (all G (v1_funct_1(G) & m2_relset_1(G,k2_zfmisc_1(B,B),B) & v1_funct_2(G,k2_zfmisc_1(B,B),B) -> (all H (m2_relset_1(H,k2_zfmisc_1(A,A),A) & v1_funct_2(H,k2_zfmisc_1(A,A),A) & v1_funct_1(H) -> ((all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,B) -> k8_funct_2(B,A,D,k2_binop_1(B,B,B,G,I,J)) = k2_binop_1(A,A,A,H,k8_funct_2(B,A,D,I),k8_funct_2(B,A,D,J)))))) -> k5_finseqop(B,A,k1_finseqop(B,B,B,G,E,F),D) = k1_finseqop(A,A,A,H,k5_finseqop(B,A,E,D),k5_finseqop(B,A,F,D))))))))))))))))))) # label(t49_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6772 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_finseq_2(D,A,k4_finseq_2(C,A)) -> (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_2(F,A,A) & m2_relset_1(F,A,A) & v1_funct_1(F) -> (r7_binop_1(A,F,E) -> k5_finseqop(A,A,k2_finseqop(A,A,A,E,D,B),F) = k2_finseqop(A,A,A,E,k5_finseqop(A,A,D,F),k8_funct_2(A,A,F,B))))))))))))))) # label(t54_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6773 (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 (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,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> (v2_binop_1(B,A) & k6_finseqop(A,B) = D & v1_setwiseo(C,A) & r6_binop_1(A,C,B) & v1_finseqop(B,A) & v1_setwiseo(B,A) -> D = k8_funcop_1(A,A,C,k8_funct_2(A,A,D,k3_binop_1(A,C)),k6_partfun1(A))))))))))) # label(t72_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6774 $T # label(t3_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6775 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(k7_finseqop(C,D,E))) -> k1_binop_1(k7_finseqop(C,D,E),A,B) = k1_binop_1(C,k1_funct_1(D,A),k1_funct_1(E,B))))))))) # label(t83_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6776 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,C) -> (all E (m1_subset_1(E,A) -> (all F (m2_relset_1(F,k2_zfmisc_1(C,A),B) & v1_funct_2(F,k2_zfmisc_1(C,A),B) & v1_funct_1(F) -> (all G (m2_finseq_1(G,C) -> k8_finseq_1(B,k2_finseqop(C,A,B,F,G,E),k12_finseq_1(B,k2_binop_1(C,A,B,F,D,E))) = k2_finseqop(C,A,B,F,k8_finseq_1(C,G,k12_finseq_1(C,D)),E))))))))))))))) # label(t15_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6777 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,C) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,C,B) & v1_funct_2(F,C,B) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(C,C),C) & m2_relset_1(G,k2_zfmisc_1(C,C),C) -> (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) -> ((all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,C) -> k2_binop_1(B,B,B,H,k8_funct_2(C,B,F,I),k8_funct_2(C,B,F,J)) = k8_funct_2(C,B,F,k2_binop_1(C,C,C,G,I,J)))))) -> k7_funcop_1(B,A,H,k7_funct_2(A,C,B,E,F),k8_funct_2(C,B,F,D)) = k7_funct_2(A,C,B,k7_funcop_1(C,A,G,E,D),F)))))))))))))))))) # label(t40_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6778 (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) -> ((exists C (v1_funct_1(C) & v1_funct_2(C,A,A) & r1_finseqop(A,C,B) & m2_relset_1(C,A,A))) <-> v1_finseqop(B,A)))))) # label(d2_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6779 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_finseq_2(C,A,k4_finseq_2(B,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) -> (v1_setwiseo(D,A) -> k2_finseqop(A,A,A,D,C,k3_binop_1(A,D)) = C))))))))) # label(t59_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6780 (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_subset_1(F,k1_numbers,k5_numbers) -> (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) -> k3_finseqop(A,B,C,G,D,k4_finseqop(B,F,E)) = k4_finseqop(C,F,k2_binop_1(A,B,C,G,D,E)))))))))))))))) # label(t19_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6781 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_finseq_2(C,A,k4_finseq_2(B,A)) -> (all D (m2_finseq_2(D,A,k4_finseq_2(B,A)) -> (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) & m2_relset_1(F,A,A) & v1_funct_2(F,A,A) -> k1_finseqop(A,A,A,E,C,k5_finseqop(A,A,D,F)) = k1_finseqop(A,A,A,k8_finseqop(A,E,k6_partfun1(A),F),C,D))))))))))))) # label(t89_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6782 (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) -> (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) -> (v2_binop_1(E,A) & v1_finseqop(E,A) & v1_setwiseo(E,A) -> C = D | k2_binop_1(A,A,A,E,B,C) != k2_binop_1(A,A,A,E,B,D) & k2_binop_1(A,A,A,E,C,B) != k2_binop_1(A,A,A,E,D,B)))))))))))) # label(t68_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6783 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (v1_setwiseo(B,A) & v2_binop_1(B,A) & v1_binop_1(B,A) & v1_finseqop(B,A) -> r7_binop_1(A,k6_finseqop(A,B),B)))))) # label(t67_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6784 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,C) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(C,A),B) & v1_funct_2(F,k2_zfmisc_1(C,A),B) -> (all G (m2_finseq_2(G,C,k4_finseq_2(E,C)) -> k4_funcop_1(F,G,D) = k5_relat_1(G,k4_funcop_1(F,k6_partfun1(C),D)))))))))))))))) # label(t24_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6785 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (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,B,B) & m2_relset_1(F,B,B) -> (r7_binop_1(B,F,E) -> k7_funct_2(A,B,B,k7_funcop_1(B,A,E,D,C),F) = k7_funcop_1(B,A,E,k7_funct_2(A,B,B,D,F),k8_funct_2(B,B,F,C))))))))))))))) # label(t43_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6786 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (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,k2_zfmisc_1(B,B),B) & v1_funct_2(E,k2_zfmisc_1(B,B),B) -> (all F (v1_funct_1(F) & v1_funct_2(F,B,B) & m2_relset_1(F,B,B) -> k6_funcop_1(B,A,k8_finseqop(B,E,k6_partfun1(B),F),C,D) = k6_funcop_1(B,A,E,C,k7_funct_2(A,B,B,D,F)))))))))))))) # label(t88_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6787 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_finseq_2(C,A,k4_finseq_2(B,A)) -> (all D (m2_finseq_2(D,A,k4_finseq_2(B,A)) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_2(E,k2_zfmisc_1(A,A),A) -> (all F (m2_relset_1(F,A,A) & v1_funct_2(F,A,A) & v1_funct_1(F) -> (r7_binop_1(A,F,E) -> k5_finseqop(A,A,k1_finseqop(A,A,A,E,C,D),F) = k1_finseqop(A,A,A,E,k5_finseqop(A,A,C,F),k5_finseqop(A,A,D,F))))))))))))))) # label(t52_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6788 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D (r2_hidden(k4_tarski(C,D),k1_relat_1(A)) -> k2_funcop_1(B,k1_funct_1(A,k4_tarski(C,D))) = k3_funcop_1(A,k2_funcop_1(B,C),k2_funcop_1(B,D)))))) # label(t8_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6789 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (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,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(B,B),B) & m2_relset_1(G,k2_zfmisc_1(B,B),B) -> (r6_binop_1(B,F,G) -> k6_funcop_1(B,A,G,k8_funcop_1(B,A,F,C,E),k8_funcop_1(B,A,F,D,E)) = k8_funcop_1(B,A,F,k2_binop_1(B,B,B,G,C,D),E)))))))))))))))) # label(t36_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6790 (all A all B all C all D (m1_finseq_1(C,A) & v1_funct_1(D) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k5_finseqop(A,B,C,D) = k5_relat_1(C,D))) # label(redefinition_k5_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6791 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,A) & m2_relset_1(E,A,A) & v1_funct_1(E) -> (v2_binop_1(D,A) & v1_setwiseo(D,A) & k6_finseqop(A,D) = E & v1_finseqop(D,A) & v1_binop_1(D,A) -> k8_funct_2(A,A,E,k2_binop_1(A,A,A,k8_finseqop(A,D,E,k6_partfun1(A)),B,C)) = k2_binop_1(A,A,A,k8_finseqop(A,D,k6_partfun1(A),E),B,C) & k2_binop_1(A,A,A,k8_finseqop(A,D,E,k6_partfun1(A)),B,C) = k8_funct_2(A,A,E,k2_binop_1(A,A,A,k8_finseqop(A,D,k6_partfun1(A),E),B,C))))))))))))) # label(t90_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6792 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,C) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> (all F (v1_funct_1(F) & m2_relset_1(F,C,B) & v1_funct_2(F,C,B) -> (all G (m2_relset_1(G,k2_zfmisc_1(C,C),C) & v1_funct_2(G,k2_zfmisc_1(C,C),C) & 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) -> ((all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,C) -> k8_funct_2(C,B,F,k2_binop_1(C,C,C,G,I,J)) = k2_binop_1(B,B,B,H,k8_funct_2(C,B,F,I),k8_funct_2(C,B,F,J)))))) -> k7_funct_2(A,C,B,k8_funcop_1(C,A,G,D,E),F) = k8_funcop_1(B,A,H,k8_funct_2(C,B,F,D),k7_funct_2(A,C,B,E,F))))))))))))))))))) # label(t39_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6793 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_finseq_2(D,A,k4_finseq_2(C,A)) -> (all E (m2_finseq_2(E,A,k4_finseq_2(C,A)) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,A),A) & v1_funct_2(F,k2_zfmisc_1(A,A),A) -> (v2_binop_1(F,A) -> k1_finseqop(A,A,A,F,k2_finseqop(A,A,A,F,D,B),E) = k1_finseqop(A,A,A,F,D,k3_finseqop(A,A,A,F,B,E))))))))))))))) # label(t31_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6794 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,k5_numbers) & -v1_xboole_0(A) -> m2_finseq_2(k4_finseqop(A,B,C),A,k4_finseq_2(B,A)))) # label(dt_k4_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6795 (all A all B all C k13_funct_3(k2_funcop_1(A,B),k2_funcop_1(A,C)) = k2_funcop_1(A,k4_tarski(B,C))) # label(t7_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6796 (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 (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 (v1_funct_2(G,D,A) & m2_relset_1(G,D,A) & v1_funct_1(G) -> (all H (v1_funct_1(H) & v1_funct_2(H,E,B) & m2_relset_1(H,E,B) -> v1_funct_1(k7_finseqop(F,G,H)) & m2_relset_1(k7_finseqop(F,G,H),k2_zfmisc_1(D,E),C) & v1_funct_2(k7_finseqop(F,G,H),k2_zfmisc_1(D,E),C))))))))))))))))) # label(t84_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6797 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,B,A) & m2_relset_1(C,B,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) & v1_funct_2(E,k2_zfmisc_1(A,A),A) & m2_relset_1(E,k2_zfmisc_1(A,A),A) -> (v2_binop_1(E,A) & v1_setwiseo(E,A) & k2_funcop_1(B,k3_binop_1(A,E)) = k6_funcop_1(A,B,E,C,D) & v1_finseqop(E,A) -> k7_funct_2(B,A,A,D,k6_finseqop(A,E)) = C & D = k7_funct_2(B,A,A,C,k6_finseqop(A,E))))))))))))) # label(t76_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6798 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,k2_zfmisc_1(B,B),B) & v1_funct_2(G,k2_zfmisc_1(B,B),B) -> (r6_binop_1(B,F,G) -> k6_funcop_1(B,A,G,k7_funcop_1(B,A,F,E,C),k7_funcop_1(B,A,F,E,D)) = k7_funcop_1(B,A,F,E,k2_binop_1(B,B,B,G,C,D))))))))))))))))) # label(t37_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6799 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_finseq_2(C,A,k4_finseq_2(B,A)) -> (all D (m2_finseq_2(D,A,k4_finseq_2(B,A)) -> (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) -> (v1_binop_1(E,A) -> k1_finseqop(A,A,A,E,C,D) = k1_finseqop(A,A,A,E,D,C)))))))))))) # label(t34_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6800 (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(E,A) & m1_finseq_1(F,B) & v1_funct_1(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k5_funcop_1(D,E,F) = k3_finseqop(A,B,C,D,E,F))) # label(redefinition_k3_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6801 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) -> (v2_binop_1(F,B) -> k7_funct_2(A,B,B,k6_funcop_1(B,A,F,D,E),k8_funcop_1(B,B,F,C,k6_partfun1(B))) = k6_funcop_1(B,A,F,k7_funct_2(A,B,B,D,k8_funcop_1(B,B,F,C,k6_partfun1(B))),E)))))))))))))) # label(t25_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6802 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,C),A) & m2_relset_1(F,k2_zfmisc_1(B,C),A) -> (all G (m2_finseq_2(G,B,k4_finseq_2(D,B)) -> (all H (m2_finseq_2(H,C,k4_finseq_2(D,C)) -> (all I (m2_finseq_2(I,B,k4_finseq_2(E,B)) -> (all J (m2_finseq_2(J,C,k4_finseq_2(E,C)) -> k1_finseqop(B,C,A,F,k8_finseq_1(B,G,I),k8_finseq_1(C,H,J)) = k8_finseq_1(A,k1_finseqop(B,C,A,F,G,H),k1_finseqop(B,C,A,F,I,J)))))))))))))))))))))) # label(t12_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6803 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_finseq_2(D,A,k4_finseq_2(C,A)) -> (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 (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,A),A) & v1_funct_2(F,k2_zfmisc_1(A,A),A) -> (r6_binop_1(A,F,E) & v1_finseqop(E,A) & B = k3_binop_1(A,E) & v1_setwiseo(E,A) & v2_binop_1(E,A) -> k4_finseqop(A,C,B) = k3_finseqop(A,A,A,F,B,D)))))))))))))) # label(t80_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6804 (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,C) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,C),B) & m2_relset_1(F,k2_zfmisc_1(A,C),B) & v1_funct_1(F) -> (all G (m2_finseq_1(G,C) -> k8_finseq_1(B,k3_finseqop(A,C,B,F,D,G),k12_finseq_1(B,k2_binop_1(A,C,B,F,D,E))) = k3_finseqop(A,C,B,F,D,k8_finseq_1(C,G,k12_finseq_1(C,E))))))))))))))))) # label(t13_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6805 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_finseq_2(E,A,k4_finseq_2(D,A)) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,A),A) & m2_relset_1(F,k2_zfmisc_1(A,A),A) & v1_funct_1(F) -> (v2_binop_1(F,A) -> k2_finseqop(A,A,A,F,k2_finseqop(A,A,A,F,E,B),C) = k2_finseqop(A,A,A,F,E,k2_binop_1(A,A,A,F,B,C))))))))))))))) # label(t33_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6806 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (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(A,A),A) & m2_relset_1(F,k2_zfmisc_1(A,A),A) -> (v1_finseqop(E,A) & r6_binop_1(A,F,E) & C = k3_binop_1(A,E) & v1_setwiseo(E,A) & v2_binop_1(E,A) -> k2_funcop_1(B,C) = k8_funcop_1(A,B,F,C,D)))))))))))))) # label(t79_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6807 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(k7_finseqop(C,D,E))) -> k1_funct_1(k7_finseqop(C,D,E),k4_tarski(A,B)) = k1_funct_1(C,k4_tarski(k1_funct_1(D,A),k1_funct_1(E,B)))))))))) # label(t82_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6808 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (all F (m2_finseq_2(F,B,k4_finseq_2(D,B)) -> (all G (v1_funct_2(G,k2_zfmisc_1(B,B),B) & m2_relset_1(G,k2_zfmisc_1(B,B),B) & v1_funct_1(G) -> (all H (v1_funct_2(H,k2_zfmisc_1(A,A),A) & m2_relset_1(H,k2_zfmisc_1(A,A),A) & v1_funct_1(H) -> ((all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,B) -> k2_binop_1(A,A,A,H,k8_funct_2(B,A,E,I),k8_funct_2(B,A,E,J)) = k8_funct_2(B,A,E,k2_binop_1(B,B,B,G,I,J)))))) -> k3_finseqop(A,A,A,H,k8_funct_2(B,A,E,C),k5_finseqop(B,A,F,E)) = k5_finseqop(B,A,k3_finseqop(B,B,B,G,C,F),E)))))))))))))))))) # label(t50_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6809 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (all F (m2_finseq_2(F,B,k4_finseq_2(D,B)) -> (all G (m2_relset_1(G,k2_zfmisc_1(B,B),B) & v1_funct_2(G,k2_zfmisc_1(B,B),B) & v1_funct_1(G) -> (all H (m2_relset_1(H,k2_zfmisc_1(A,A),A) & v1_funct_2(H,k2_zfmisc_1(A,A),A) & v1_funct_1(H) -> ((all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,B) -> k2_binop_1(A,A,A,H,k8_funct_2(B,A,E,I),k8_funct_2(B,A,E,J)) = k8_funct_2(B,A,E,k2_binop_1(B,B,B,G,I,J)))))) -> k5_finseqop(B,A,k2_finseqop(B,B,B,G,F,C),E) = k2_finseqop(A,A,A,H,k5_finseqop(B,A,F,E),k8_funct_2(B,A,E,C))))))))))))))))))) # label(t51_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6810 (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) & v1_funct_1(D) & m1_relset_1(D,A,A) & v1_funct_2(D,A,A) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> k8_finseqop(A,B,C,D) = k7_finseqop(B,C,D))) # label(redefinition_k8_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6811 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_finseq_2(E,A,k4_finseq_2(D,A)) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,A),A) & m2_relset_1(F,k2_zfmisc_1(A,A),A) -> (all G (m2_relset_1(G,k2_zfmisc_1(A,A),A) & v1_funct_2(G,k2_zfmisc_1(A,A),A) & v1_funct_1(G) -> (r6_binop_1(A,F,G) -> k2_finseqop(A,A,A,F,E,k2_binop_1(A,A,A,G,B,C)) = k1_finseqop(A,A,A,G,k2_finseqop(A,A,A,F,E,B),k2_finseqop(A,A,A,F,E,C))))))))))))))))) # label(t48_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6812 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_finseq_2(D,A,k4_finseq_2(C,A)) -> (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) -> (v1_binop_1(E,A) -> k3_finseqop(A,A,A,E,B,D) = k2_finseqop(A,A,A,E,D,B)))))))))))) # label(t35_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6813 (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_subset_1(F,k1_numbers,k5_numbers) -> (all G (v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) -> k2_finseqop(A,B,C,G,k4_finseqop(A,F,D),E) = k4_finseqop(C,F,k2_binop_1(A,B,C,G,D,E)))))))))))))))) # label(t20_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6814 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,B,A) & v1_funct_2(C,B,A) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v1_setwiseo(D,A) -> k3_funcop_1(D,k2_funcop_1(B,k3_binop_1(A,D)),C) = C & k3_funcop_1(D,C,k2_funcop_1(B,k3_binop_1(A,D))) = C))))))))) # label(t44_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.76 6815 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,C) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m2_relset_1(F,k2_zfmisc_1(C,A),B) & v1_funct_2(F,k2_zfmisc_1(C,A),B) & v1_funct_1(F) -> (all G (m2_finseq_2(G,C,k4_finseq_2(E,C)) -> k4_funcop_1(F,G,D) = k3_funcop_1(F,G,k4_finseqop(C,E,D)))))))))))))))) # label(t22_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6816 (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_subset_1(F,k1_numbers,k5_numbers) -> (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) -> k1_finseqop(A,B,C,G,k4_finseqop(A,F,D),k4_finseqop(B,F,E)) = k4_finseqop(C,F,k2_binop_1(A,B,C,G,D,E)))))))))))))))) # label(t18_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6817 (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) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (v2_binop_1(C,A) & v1_setwiseo(C,A) & k3_binop_1(A,C) = B & r6_binop_1(A,D,C) & v1_finseqop(C,A) -> (all E (m1_subset_1(E,A) -> B = k2_binop_1(A,A,A,D,B,E) & B = k2_binop_1(A,A,A,D,E,B)))))))))))) # label(t70_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6818 $T # label(t60_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6819 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k1_xboole_0 = k5_funcop_1(B,A,k1_xboole_0))) # label(t6_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6820 (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 (m1_subset_1(E,C) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(B,C),A) & m2_relset_1(G,k2_zfmisc_1(B,C),A) -> (all H (m2_finseq_2(H,B,k4_finseq_2(F,B)) -> (all I (m2_finseq_2(I,C,k4_finseq_2(F,C)) -> k8_finseq_1(A,k1_finseqop(B,C,A,G,H,I),k12_finseq_1(A,k2_binop_1(B,C,A,G,D,E))) = k1_finseqop(B,C,A,G,k8_finseq_1(B,H,k12_finseq_1(B,D)),k8_finseq_1(C,I,k12_finseq_1(C,E))))))))))))))))))))) # label(t11_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6821 (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) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (v2_binop_1(C,A) & v1_setwiseo(C,A) & r6_binop_1(A,D,C) & v1_finseqop(C,A) -> k8_funct_2(A,A,k7_funcop_1(A,A,D,k6_partfun1(A),B),k3_binop_1(A,C)) = k3_binop_1(A,C)))))))))) # label(t74_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6822 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_2(E,k2_zfmisc_1(A,A),A) & v1_funct_1(E) -> (all F (m2_relset_1(F,A,A) & v1_funct_2(F,A,A) & v1_funct_1(F) -> (v1_setwiseo(D,A) & v2_binop_1(D,A) & v1_finseqop(D,A) & r6_binop_1(A,E,D) & k6_finseqop(A,D) = F -> k8_funct_2(A,A,F,k2_binop_1(A,A,A,E,B,C)) = k2_binop_1(A,A,A,E,B,k8_funct_2(A,A,F,C)) & k2_binop_1(A,A,A,E,k8_funct_2(A,A,F,B),C) = k8_funct_2(A,A,F,k2_binop_1(A,A,A,E,B,C))))))))))))))) # label(t71_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6823 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_finseq_2(C,A,k4_finseq_2(B,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) -> (v1_setwiseo(D,A) & v1_finseqop(D,A) & v2_binop_1(D,A) -> k1_finseqop(A,A,A,D,k5_finseqop(A,A,C,k6_finseqop(A,D)),C) = k4_finseqop(A,B,k3_binop_1(A,D)) & k1_finseqop(A,A,A,D,C,k5_finseqop(A,A,C,k6_finseqop(A,D))) = k4_finseqop(A,B,k3_binop_1(A,D))))))))))) # label(t77_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6824 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (v1_finseqop(B,A) & v2_binop_1(B,A) & v1_setwiseo(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (r1_finseqop(A,C,B) <-> k6_finseqop(A,B) = C)))))))) # label(d3_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6825 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v1_setwiseo(B,A) & v1_finseqop(B,A) & v2_binop_1(B,A) -> k3_binop_1(A,B) = k8_funct_2(A,A,k6_finseqop(A,B),k3_binop_1(A,B))))))) # label(t65_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6826 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(C,A),B) & v1_funct_2(E,k2_zfmisc_1(C,A),B) -> (all F (m2_finseq_1(F,C) -> (all G (m2_finseq_1(G,C) -> k8_finseq_1(B,k2_finseqop(C,A,B,E,F,D),k2_finseqop(C,A,B,E,G,D)) = k2_finseqop(C,A,B,E,k8_finseq_1(C,F,G),D))))))))))))))) # label(t16_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6827 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(D) & v1_funct_2(D,A,A) & m1_relset_1(D,A,A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v1_funct_1(k8_finseqop(A,B,C,D)) & m2_relset_1(k8_finseqop(A,B,C,D),k2_zfmisc_1(A,A),A) & v1_funct_2(k8_finseqop(A,B,C,D),k2_zfmisc_1(A,A),A))) # label(dt_k8_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6828 (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_2(E,k2_zfmisc_1(A,C),B) & m2_relset_1(E,k2_zfmisc_1(A,C),B) & v1_funct_1(E) -> (all F (m2_finseq_1(F,C) -> (all G (m2_finseq_1(G,C) -> k3_finseqop(A,C,B,E,D,k8_finseq_1(C,F,G)) = k8_finseq_1(B,k3_finseqop(A,C,B,E,D,F),k3_finseqop(A,C,B,E,D,G)))))))))))))))) # label(t14_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6829 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> m2_relset_1(k7_finseqop(B,C,D),k2_zfmisc_1(A,A),A) & v1_funct_2(k7_finseqop(B,C,D),k2_zfmisc_1(A,A),A) & v1_funct_1(k7_finseqop(B,C,D)))))))))) # label(t85_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6830 (all A all B all C all D all E all F (-v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_finseq_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(A) -> k2_finseqop(A,B,C,D,E,F) = k4_funcop_1(D,E,F))) # label(redefinition_k2_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6831 $T # label(t62_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6832 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> (v1_setwiseo(C,A) & v1_finseqop(C,A) & D = k6_finseqop(A,C) & v2_binop_1(C,A) -> k2_binop_1(A,A,A,k8_finseqop(A,C,k6_partfun1(A),D),k3_binop_1(A,C),B) = k8_funct_2(A,A,D,B)))))))))) # label(t93_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6833 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(C) & v1_funct_1(D) & m1_finseq_1(F,B) & m1_finseq_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(B) -> k1_finseqop(A,B,C,D,E,F) = k3_funcop_1(D,E,F))) # label(redefinition_k1_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6834 (all A all B all C all D (m1_finseq_1(C,A) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) -> m2_finseq_1(k5_finseqop(A,B,C,D),B))) # label(dt_k5_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6835 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_finseq_1(D,A) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> k8_finseq_1(B,k5_finseqop(A,B,D,E),k12_finseq_1(B,k8_funct_2(A,B,E,C))) = k5_finseqop(A,B,k8_finseq_1(A,D,k12_finseq_1(A,C)),E))))))))))) # label(t9_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6836 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k1_xboole_0 = k3_funcop_1(A,k1_xboole_0,B) & k3_funcop_1(A,B,k1_xboole_0) = k1_xboole_0)))) # label(t4_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6837 (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) -> (v2_binop_1(C,A) & v1_finseqop(C,A) & v1_setwiseo(C,A) -> k8_funct_2(A,A,k6_finseqop(A,C),k8_funct_2(A,A,k6_finseqop(A,C),B)) = B))))))) # label(t66_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6838 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(D) & m1_finseq_1(E,A) & m1_finseq_1(F,B) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(C) & -v1_xboole_0(A) -> m2_finseq_1(k1_finseqop(A,B,C,D,E,F),C))) # label(dt_k1_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6839 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v2_binop_1(C,A) & v1_finseqop(C,A) & v1_setwiseo(C,A) -> k3_binop_1(A,C) = k2_binop_1(A,A,A,k8_finseqop(A,C,k6_partfun1(A),k6_finseqop(A,C)),B,B)))))))) # label(t91_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6840 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_finseq_2(E,A,k4_finseq_2(D,A)) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,A),A) & m2_relset_1(F,k2_zfmisc_1(A,A),A) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,A),A) & m2_relset_1(G,k2_zfmisc_1(A,A),A) -> (r6_binop_1(A,F,G) -> k3_finseqop(A,A,A,F,k2_binop_1(A,A,A,G,B,C),E) = k1_finseqop(A,A,A,G,k3_finseqop(A,A,A,F,B,E),k3_finseqop(A,A,A,F,C,E))))))))))))))))) # label(t47_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6841 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,B,A) & m2_relset_1(C,B,A) & v1_funct_1(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v1_finseqop(D,A) & v2_binop_1(D,A) & v1_setwiseo(D,A) -> k2_funcop_1(B,k3_binop_1(A,D)) = k6_funcop_1(A,B,D,C,k7_funct_2(B,A,A,C,k6_finseqop(A,D))) & k6_funcop_1(A,B,D,k7_funct_2(B,A,A,C,k6_finseqop(A,D)),C) = k2_funcop_1(B,k3_binop_1(A,D))))))))))) # label(t75_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6842 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,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) -> (v2_binop_1(F,B) -> k6_funcop_1(B,A,F,D,k7_funct_2(A,B,B,E,k7_funcop_1(B,B,F,k6_partfun1(B),C))) = k7_funct_2(A,B,B,k6_funcop_1(B,A,F,D,E),k7_funcop_1(B,B,F,k6_partfun1(B),C))))))))))))))) # label(t26_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6843 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_finseq_2(D,A,k4_finseq_2(C,A)) -> (all E (m2_finseq_2(E,A,k4_finseq_2(C,A)) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,A),A) & m2_relset_1(F,k2_zfmisc_1(A,A),A) & v1_funct_1(F) -> (v2_binop_1(F,A) -> k1_finseqop(A,A,A,F,D,k5_finseqop(A,A,E,k7_funcop_1(A,A,F,k6_partfun1(A),B))) = k5_finseqop(A,A,k1_finseqop(A,A,A,F,D,E),k7_funcop_1(A,A,F,k6_partfun1(A),B))))))))))))))) # label(t28_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6844 (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 (m1_subset_1(F,D) -> (all G (m1_subset_1(G,E) -> (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 (v1_funct_2(I,D,A) & m2_relset_1(I,D,A) & v1_funct_1(I) -> (all J (v1_funct_1(J) & v1_funct_2(J,E,B) & m2_relset_1(J,E,B) -> k1_binop_1(k7_finseqop(H,I,J),F,G) = k2_binop_1(A,B,C,H,k8_funct_2(D,A,I,F),k8_funct_2(E,B,J,G)))))))))))))))))))))) # label(t86_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6845 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v2_binop_1(C,A) & v1_setwiseo(C,A) & v1_finseqop(C,A) & r6_binop_1(A,D,C) -> k3_binop_1(A,C) = k8_funct_2(A,A,k8_funcop_1(A,A,D,B,k6_partfun1(A)),k3_binop_1(A,C))))))))))) # label(t73_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6846 (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) -> (v1_setwiseo(C,A) & v1_finseqop(C,A) & v2_binop_1(C,A) -> k2_binop_1(A,A,A,k8_finseqop(A,C,k6_partfun1(A),k6_finseqop(A,C)),B,k3_binop_1(A,C)) = B))))))) # label(t92_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6847 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_finseq_2(D,A,k4_finseq_2(C,A)) -> (all E (m2_finseq_2(E,A,k4_finseq_2(C,A)) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,A),A) & v1_funct_2(F,k2_zfmisc_1(A,A),A) -> (v2_binop_1(F,A) -> k5_finseqop(A,A,k1_finseqop(A,A,A,F,D,E),k8_funcop_1(A,A,F,B,k6_partfun1(A))) = k1_finseqop(A,A,A,F,k5_finseqop(A,A,D,k8_funcop_1(A,A,F,B,k6_partfun1(A))),E)))))))))))))) # label(t27_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6848 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,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,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,B,B) & v1_funct_2(F,B,B) & v1_funct_1(F) -> (r7_binop_1(B,F,E) -> k7_funct_2(A,B,B,k8_funcop_1(B,A,E,C,D),F) = k8_funcop_1(B,A,E,k8_funct_2(B,B,F,C),k7_funct_2(A,B,B,D,F))))))))))))))) # label(t42_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6849 (all A (-v1_xboole_0(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 (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,A) & m2_relset_1(E,A,A) -> (k7_funcop_1(A,A,C,k6_partfun1(A),B) = E & r6_binop_1(A,C,D) -> r7_binop_1(A,E,D)))))))))))) # label(t56_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6850 (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(B,A) & v1_setwiseo(B,A) & v1_finseqop(B,A) & k8_finseqop(A,B,k6_partfun1(A),k6_finseqop(A,B)) = C & v2_binop_1(B,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) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,F),k2_binop_1(A,A,A,B,E,G)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,F,G))))))))))))))))) # label(t94_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6851 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (v1_setwiseo(D,A) & v2_binop_1(D,A) & k3_binop_1(A,D) = k2_binop_1(A,A,A,D,B,C) & v1_finseqop(D,A) -> k8_funct_2(A,A,k6_finseqop(A,D),C) = B & C = k8_funct_2(A,A,k6_finseqop(A,D),B)))))))))) # label(t64_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6852 (all A (v1_funct_1(A) & v1_relat_1(A) -> k15_funct_3(k1_xboole_0,A) = k1_xboole_0 & k1_xboole_0 = k15_funct_3(A,k1_xboole_0))) # label(t2_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6853 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,k5_numbers) & -v1_xboole_0(A) -> k2_finseq_2(B,C) = k4_finseqop(A,B,C))) # label(redefinition_k4_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6854 (all A (v1_relat_1(A) & v1_funct_1(A) -> k13_funct_3(k1_xboole_0,A) = k1_xboole_0 & k1_xboole_0 = k13_funct_3(A,k1_xboole_0))) # label(t1_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6855 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_finseq_2(C,A,k4_finseq_2(B,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) -> (v1_setwiseo(D,A) -> C = k1_finseqop(A,A,A,D,C,k4_finseqop(A,B,k3_binop_1(A,D))) & C = k1_finseqop(A,A,A,D,k4_finseqop(A,B,k3_binop_1(A,D)),C)))))))))) # label(t57_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6856 (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(k15_funct_3(B,C),A) = k7_finseqop(A,B,C))))))) # label(d4_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6857 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> k5_finseqop(A,B,k4_finseqop(A,D,C),E) = k4_finseqop(B,D,k8_funct_2(A,B,E,C)))))))))))) # label(t17_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6858 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (v2_binop_1(D,A) & v1_finseqop(D,A) & v1_setwiseo(D,A) -> k3_binop_1(A,D) = B | k2_binop_1(A,A,A,D,B,C) != C & k2_binop_1(A,A,A,D,C,B) != C))))))))) # label(t69_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6859 $T # label(t81_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6860 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k1_xboole_0 = k4_funcop_1(B,k1_xboole_0,A))) # label(t5_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6861 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_finseq_2(C,A,k4_finseq_2(B,A)) -> (all D (m2_finseq_2(D,A,k4_finseq_2(B,A)) -> (all E (m2_finseq_2(E,A,k4_finseq_2(B,A)) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,A),A) & v1_funct_2(F,k2_zfmisc_1(A,A),A) -> (v2_binop_1(F,A) -> k1_finseqop(A,A,A,F,k1_finseqop(A,A,A,F,C,D),E) = k1_finseqop(A,A,A,F,C,k1_finseqop(A,A,A,F,D,E))))))))))))))) # label(t29_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6862 (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) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (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,B,B) & m2_relset_1(F,B,B) -> (r7_binop_1(B,F,E) -> k6_funcop_1(B,A,E,k7_funct_2(A,B,B,C,F),k7_funct_2(A,B,B,D,F)) = k7_funct_2(A,B,B,k6_funcop_1(B,A,E,C,D),F)))))))))))))) # label(t41_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6863 (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_2(D,k2_zfmisc_1(B,B),B) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (v1_setwiseo(D,B) -> k8_funcop_1(B,A,D,k3_binop_1(B,D),C) = C))))))))) # label(t45_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6864 (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_subset_1(E,k1_numbers,k5_numbers) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,C),B) & m2_relset_1(F,k2_zfmisc_1(A,C),B) & v1_funct_1(F) -> (all G (m2_finseq_2(G,C,k4_finseq_2(E,C)) -> k1_finseqop(A,C,B,F,k4_finseqop(A,E,D),G) = k3_finseqop(A,C,B,F,D,G))))))))))))))) # label(t21_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6865 (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_subset_1(E,k1_numbers,k5_numbers) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,C),B) & v1_funct_2(F,k2_zfmisc_1(A,C),B) -> (all G (m2_finseq_2(G,C,k4_finseq_2(E,C)) -> k3_finseqop(A,C,B,F,D,G) = k5_relat_1(G,k5_funcop_1(F,D,k6_partfun1(C))))))))))))))))) # label(t23_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6866 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_finseq_2(D,A,k4_finseq_2(C,A)) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_2(E,k2_zfmisc_1(A,A),A) -> (all F (m2_relset_1(F,A,A) & v1_funct_2(F,A,A) & v1_funct_1(F) -> (r7_binop_1(A,F,E) -> k5_finseqop(A,A,k3_finseqop(A,A,A,E,B,D),F) = k3_finseqop(A,A,A,E,k8_funct_2(A,A,F,B),k5_finseqop(A,A,D,F))))))))))))))) # label(t53_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6867 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_finseq_2(E,A,k4_finseq_2(D,A)) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,A),A) & v1_funct_2(F,k2_zfmisc_1(A,A),A) & v1_funct_1(F) -> (v2_binop_1(F,A) -> k3_finseqop(A,A,A,F,B,k2_finseqop(A,A,A,F,E,C)) = k2_finseqop(A,A,A,F,k3_finseqop(A,A,A,F,B,E),C)))))))))))))) # label(t30_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6868 $T # label(t61_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6869 (all A all B all C (v1_funct_1(A) & v1_funct_1(B) & v1_funct_1(C) & v1_relat_1(C) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k7_finseqop(A,B,C)) & v1_relat_1(k7_finseqop(A,B,C)))) # label(dt_k7_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6870 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_2(D,k2_zfmisc_1(B,B),B) -> (v1_setwiseo(D,B) -> C = k7_funcop_1(B,A,D,C,k3_binop_1(B,D))))))))))) # label(t46_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6871 (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) -> (v2_binop_1(C,A) & v1_finseqop(C,A) & v1_setwiseo(C,A) -> k3_binop_1(A,C) = k2_binop_1(A,A,A,C,B,k8_funct_2(A,A,k6_finseqop(A,C),B)) & k3_binop_1(A,C) = k2_binop_1(A,A,A,C,k8_funct_2(A,A,k6_finseqop(A,C),B),B)))))))) # label(t63_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6872 (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) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r1_finseqop(A,B,C) <-> (all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,C,D,k8_funct_2(A,A,B,D)) = k3_binop_1(A,C) & k3_binop_1(A,C) = k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),D)))))))))) # label(d1_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6873 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,A) & m2_relset_1(E,A,A) & v1_funct_1(E) -> k2_binop_1(A,A,A,D,k8_funct_2(A,A,E,B),C) = k2_binop_1(A,A,A,k8_finseqop(A,D,E,k6_partfun1(A)),B,C) & k2_binop_1(A,A,A,D,B,k8_funct_2(A,A,E,C)) = k2_binop_1(A,A,A,k8_finseqop(A,D,k6_partfun1(A),E),B,C))))))))))) # label(t87_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6874 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_finseq_2(C,A,k4_finseq_2(B,A)) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v1_setwiseo(D,A) -> k3_finseqop(A,A,A,D,k3_binop_1(A,D),C) = C))))))))) # label(t58_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6875 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,A) -> (all D (m2_finseq_1(D,A) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> k8_finseq_1(B,k5_finseqop(A,B,C,E),k5_finseqop(A,B,D,E)) = k5_finseqop(A,B,k8_finseq_1(A,C,D),E))))))))))) # label(t10_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6876 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_finseq_2(E,A,k4_finseq_2(D,A)) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,A),A) & v1_funct_2(F,k2_zfmisc_1(A,A),A) -> (v2_binop_1(F,A) -> k3_finseqop(A,A,A,F,B,k3_finseqop(A,A,A,F,C,E)) = k3_finseqop(A,A,A,F,k2_binop_1(A,A,A,F,B,C),E)))))))))))))) # label(t32_finseqop) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6877 $T # label(t35_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6878 (all A (v4_ordinal2(A) -> k1_finseq_2(A) = k14_finseq_1(k2_finseq_1(A)))) # label(t54_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6879 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k2_relat_1(A)) -> r2_hidden(np__1,k4_finseq_1(A)))))) # label(t33_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6880 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> k1_finseq_2(A) = k7_relat_1(k1_finseq_2(k2_xcmplx_0(A,B)),k2_finseq_1(A)))))) # label(t56_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6881 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (k2_relat_1(k1_finseq_3(A,B)) = k2_relat_1(A) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t74_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6882 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C k7_finseq_1(k1_finseq_3(A,C),k1_finseq_3(B,C)) = k1_finseq_3(k7_finseq_1(A,B),C)))))) # label(t80_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6883 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (r2_hidden(A,k4_finseq_1(B)) -> k1_funct_1(B,A) = k1_funct_1(k7_finseq_1(k9_finseq_1(C),B),k2_xcmplx_0(A,np__1)))))))) # label(t112_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6884 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v2_funct_1(A) & k2_relat_1(A) = k2_tarski(B,C) -> B = C | k3_finseq_1(A) = np__2)))) # label(t107_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6885 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k2_relat_1(A) = k1_tarski(B) & v2_funct_1(A) -> k3_finseq_1(A) = np__1)))) # label(t105_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6886 (all A (v4_ordinal2(A) -> k1_tarski(k2_xcmplx_0(A,np__1)) = k6_subset_1(k5_numbers,k2_finseq_1(k2_xcmplx_0(A,np__1)),k2_finseq_1(A)))) # label(t16_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6887 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k1_nat_1(C,np__1) = D & r2_hidden(B,k2_finseq_1(D)) & r2_hidden(A,k2_finseq_1(C)) -> (r1_xreal_0(B,A) & r1_xreal_0(A,C) -> k1_nat_1(A,np__1) = k1_funct_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(D),k1_tarski(B))),A)) & (r1_xreal_0(np__1,A) -> A = k1_funct_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(D),k1_tarski(B))),A) | r1_xreal_0(B,A))))))))))) # label(t117_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6888 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(B,A) <-> k1_finseq_2(B) = k7_relat_1(k1_finseq_2(A),k2_finseq_1(B))))))) # label(t57_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6889 (all A (v4_ordinal2(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_finseq_1(A)) -> k4_card_1(B) = k3_finseq_1(k14_finseq_1(B))))))) # label(t44_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6890 $T # label(t21_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6891 (all A all B all C (r2_hidden(A,B) -> k1_finseq_3(k10_finseq_1(A,C),B) = k9_finseq_1(C) | r2_hidden(C,B))) # label(t85_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6892 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (-r2_hidden(A,k4_finseq_1(B)) -> k2_finseq_3(A,B) = B) & -(r2_hidden(A,k4_finseq_1(B)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(k1_nat_1(C,np__1) = k3_finseq_1(B) & C = k3_finseq_1(k2_finseq_3(A,B)))))))))) # label(t113_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6893 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B all C (m2_finseq_1(A,B) -> m2_finseq_1(k1_finseq_3(A,C),B))))) # label(t93_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6894 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k2_finseq_3(A,B) = k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(B),k1_tarski(A))),B))))) # label(d2_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6895 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B r1_tarski(k4_finseq_1(k1_finseq_3(A,B)),k4_finseq_1(A))))) # label(t70_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6896 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k4_finseq_1(A)) -> m2_subset_1(B,k1_numbers,k5_numbers))))) # label(t25_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6897 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B all C all D (k1_enumset1(B,C,D) = k2_relat_1(A) & v2_funct_1(k11_finseq_1(B,C,D)) & v2_funct_1(A) -> np__3 = k3_finseq_1(A))))) # label(t109_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6898 $T # label(t101_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6899 (all A k1_finseq_3(k1_xboole_0,A) = k1_xboole_0) # label(t81_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6900 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(B,A) -> r2_hidden(k2_xcmplx_0(A,np__1),k2_finseq_1(B))))))) # label(t12_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6901 (all A (v4_ordinal2(A) -> k2_finseq_1(k2_xcmplx_0(A,np__1)) != k2_finseq_1(A))) # label(t17_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6902 (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 all D (v4_ordinal2(D) -> (k2_xcmplx_0(D,np__1) = k3_finseq_1(A) & B = k7_relat_1(A,k2_finseq_1(D)) -> (k1_finseq_3(A,C) = k7_finseq_1(k1_finseq_3(B,C),k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(D,np__1)))) <-> -r2_hidden(k1_funct_1(A,k2_xcmplx_0(D,np__1)),C))))))))) # label(t91_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6903 (all A v2_funct_1(k9_finseq_1(A))) # label(t102_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6904 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v4_ordinal2(B) -> (m2_subset_1(k6_xcmplx_0(B,np__1),k1_numbers,k5_numbers) & m2_subset_1(k6_xcmplx_0(k3_finseq_1(A),B),k1_numbers,k5_numbers) <-> r2_hidden(B,k4_finseq_1(A))))))) # label(t28_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6905 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (k3_finseq_1(A) = k3_finseq_1(k1_finseq_3(A,B)) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t68_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6906 (all A (v4_ordinal2(A) -> (A != np__0 -> k14_finseq_1(k1_tarski(A)) = k9_finseq_1(A)))) # label(t50_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6907 (all A all B all C (-r2_hidden(B,C) & -r2_hidden(A,C) <-> k10_finseq_1(A,B) = k1_finseq_3(k10_finseq_1(A,B),C))) # label(t89_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6908 (all A (v4_ordinal2(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_finseq_1(A)) -> k2_finseq_1(k4_card_1(B)) = k4_finseq_1(k14_finseq_1(B))))))) # label(t45_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6909 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v4_ordinal2(C) -> (C = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B))) -> k2_finseq_1(C) = k4_finseq_1(k1_finseq_3(A,B))))))) # label(t69_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6910 (all A all B k4_finseq_1(k10_finseq_1(A,B)) = k2_finseq_1(np__2)) # label(t29_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6911 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> k1_xboole_0 = k1_finseq_3(A,k2_relat_1(A)))) # label(t79_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6912 (all A all B all C k1_xboole_0 != k11_finseq_1(A,B,C)) # label(t39_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6913 (all A all B (k9_finseq_1(A) = k1_finseq_3(k9_finseq_1(A),B) <-> -r2_hidden(A,B))) # label(t82_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6914 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v2_funct_1(A) -> v2_funct_1(k1_finseq_3(A,B)))))) # label(t94_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6915 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C k4_card_1(k10_relat_1(k7_finseq_1(A,B),C)) = k1_nat_1(k4_card_1(k10_relat_1(A,C)),k4_card_1(k10_relat_1(B,C)))))))) # label(t63_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6916 (all A all B (k1_finseq_3(k9_finseq_1(A),B) = k1_xboole_0 <-> r2_hidden(A,B))) # label(t83_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6917 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r3_xboole_0(k2_finseq_1(A),k2_finseq_1(B)))))) # label(t20_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6918 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(k2_xcmplx_0(A,B),k2_finseq_1(A)) -> np__0 = B))))) # label(t11_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6919 (all A (v4_ordinal2(A) -> v2_funct_1(k1_finseq_2(A)))) # label(t100_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6920 (all A all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(-r1_xreal_0(D,C) & D = k1_funct_1(k14_finseq_1(A),E) & r1_xreal_0(E,F) & k1_funct_1(k14_finseq_1(A),F) = C & r1_xreal_0(F,k3_finseq_1(k14_finseq_1(A))) & r1_xreal_0(np__1,E) & r1_tarski(A,k2_finseq_1(B))))))))))))) # label(t46_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6921 (all A (v4_ordinal2(A) -> A = k3_finseq_1(k14_finseq_1(k2_finseq_1(A))))) # label(t52_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6922 (all A (v4_ordinal2(A) -> (-r2_hidden(A,k2_finseq_1(A)) <-> k2_finseq_1(A) = k1_xboole_0))) # label(t7_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6923 $T # label(t36_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6924 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v4_ordinal2(C) -> (k3_finseq_1(A) = k2_xcmplx_0(C,np__1) & k7_relat_1(A,k2_finseq_1(C)) = B -> k7_finseq_1(B,k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(C,np__1)))) = A))))))) # label(t61_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6925 (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 (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (k3_finseq_1(A) = k2_xcmplx_0(C,D) & k7_relat_1(A,k2_finseq_1(C)) = B -> k2_finseq_1(C) = k4_finseq_1(B)))))))))) # label(t60_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6926 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) & v2_funct_1(A) -> k9_finseq_1(B) = A)))) # label(t106_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6927 (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 all D (v4_ordinal2(D) -> (k2_xcmplx_0(D,np__1) = k3_finseq_1(A) & k7_relat_1(A,k2_finseq_1(D)) = B -> (k1_finseq_3(A,C) = k1_finseq_3(B,C) <-> r2_hidden(k1_funct_1(A,k2_xcmplx_0(D,np__1)),C))))))))) # label(t90_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.77 6928 $T # label(t8_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6929 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (k1_xboole_0 = k1_finseq_3(A,B) <-> r1_tarski(k2_relat_1(A),B))))) # label(t75_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6930 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (r1_xboole_0(B,k2_relat_1(A)) <-> k1_finseq_3(A,B) = A)))) # label(t76_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6931 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B r1_xreal_0(k3_finseq_1(k1_finseq_3(A,B)),k3_finseq_1(A))))) # label(t67_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6932 (all A all B all C (k1_finseq_3(k10_finseq_1(A,B),C) = k9_finseq_1(A) -> B = A | -r2_hidden(A,C) & r2_hidden(B,C))) # label(t88_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6933 (all A all B (v2_funct_1(k10_finseq_1(A,B)) <-> B != A)) # label(t103_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6934 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k2_finseq_1(k2_xcmplx_0(A,B)) -> B = np__0))))) # label(t18_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6935 (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) -> (k4_finseq_1(B) = k4_finseq_1(A) <-> k3_finseq_1(B) = k3_finseq_1(A)))))) # label(t31_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6936 (all A all B (v4_ordinal2(B) -> (r1_tarski(A,k2_finseq_1(B)) -> v2_funct_1(k14_finseq_1(A))))) # label(t99_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6937 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(A),k10_relat_1(A,B))),A) = k1_finseq_3(A,B)))) # label(d1_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6938 (all A all B all C all D k9_finseq_1(A) != k11_finseq_1(B,C,D)) # label(t41_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6939 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) <-> k7_relat_1(k1_finseq_2(A),k2_finseq_1(B)) = k1_finseq_2(A)))))) # label(t58_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6940 (all A all B all C k4_finseq_1(k11_finseq_1(A,B,C)) = k2_finseq_1(np__3)) # label(t30_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6941 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(B,k4_finseq_1(A)) <-> r1_xreal_0(np__1,B) & r1_xreal_0(B,k3_finseq_1(A))))))) # label(t27_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6942 (all A all B all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (r1_tarski(A,k2_finseq_1(C)) & r1_tarski(B,k2_finseq_1(D)) -> (k8_finseq_1(k5_numbers,k14_finseq_1(A),k14_finseq_1(B)) = k14_finseq_1(k2_xboole_0(A,B)) <-> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> -(r2_hidden(F,B) & r1_xreal_0(F,E) & r2_hidden(E,A)))))))))))) # label(t48_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6943 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> A = k1_finseq_3(A,k1_xboole_0))) # label(t78_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6944 (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 r1_tarski(k10_relat_1(A,C),k10_relat_1(k7_finseq_1(A,B),C))))))) # label(t64_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6945 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(B,D) = k1_funct_1(A,D)))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(C)) -> k1_funct_1(C,D) = k1_funct_1(A,k1_nat_1(k3_finseq_1(B),D))))) & k3_finseq_1(A) = k1_nat_1(k3_finseq_1(B),k3_finseq_1(C)) -> A = k7_finseq_1(B,C)))))))) # label(t43_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6946 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (k7_relat_1(A,k2_finseq_1(C)) = B & k3_finseq_1(A) = k2_xcmplx_0(C,D) -> k3_finseq_1(B) = C))))))))) # label(t59_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6947 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B ((exists C (k3_xboole_0(B,k4_finseq_1(A)) = k2_finseq_1(C) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> v1_funct_1(k7_relat_1(A,B)) & v1_finseq_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))))) # label(t62_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6948 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k1_nat_1(C,np__1) = k3_finseq_1(A) -> r1_xreal_0(B,D) | k1_funct_1(k2_finseq_3(B,A),D) = k1_funct_1(A,D)))))))))) # label(t119_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6949 $T # label(t65_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6950 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (r1_tarski(k4_finseq_1(A),k4_finseq_1(B)) <-> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t32_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6951 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k2_relat_1(A)) & v2_funct_1(A) -> k6_xcmplx_0(k3_finseq_1(A),np__1) = k3_finseq_1(k1_finseq_3(A,k1_tarski(B))))))) # label(t97_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6952 (all A all B all C k10_finseq_1(B,C) != k9_finseq_1(A)) # label(t40_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6953 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (A != np__0 -> r2_hidden(A,k2_finseq_1(k2_xcmplx_0(A,B)))))))) # label(t10_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6954 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(k2_finseq_3(A,C),B))))))) # label(t114_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6955 (all A all B all C all D all E k11_finseq_1(C,D,E) != k10_finseq_1(A,B)) # label(t42_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6956 (all A all B all C (k1_finseq_3(k10_finseq_1(A,B),C) = k9_finseq_1(B) -> A = B | -r2_hidden(B,C) & r2_hidden(A,C))) # label(t86_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6957 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(A,k2_finseq_1(B)) -> r1_xreal_0(A,C) | r2_hidden(k6_xcmplx_0(A,C),k2_finseq_1(B))))))))) # label(t13_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6958 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_relat_1(A)) & v2_funct_1(A) -> k6_xcmplx_0(k3_finseq_1(A),k4_card_1(B)) = k3_finseq_1(k1_finseq_3(A,B))))))) # label(t96_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6959 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B)))))) # label(t66_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6960 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k2_finseq_3(A,B)),k2_relat_1(B)))))) # label(t115_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6961 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B r1_tarski(k2_relat_1(k1_finseq_3(A,B)),k2_relat_1(A))))) # label(t73_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6962 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v2_funct_1(A) -> k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k3_xboole_0(B,k2_relat_1(A)))))))) # label(t95_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6963 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (k1_xboole_0 != k2_relat_1(A) -> r2_hidden(np__1,k4_finseq_1(A))))) # label(t34_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6964 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B -(r2_hidden(B,k4_finseq_1(A)) & np__0 = B)))) # label(t26_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6965 (all A all B k10_finseq_1(A,B) != k1_xboole_0) # label(t38_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6966 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> v1_finseq_1(k1_finseq_3(A,B)) & v1_funct_1(k1_finseq_3(A,B)) & v1_relat_1(k1_finseq_3(A,B)))) # label(dt_k1_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6967 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> k14_finseq_1(k2_finseq_1(A)) = k7_relat_1(k14_finseq_1(k2_finseq_1(k2_xcmplx_0(A,B))),k2_finseq_1(A)))))) # label(t53_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6968 (all A (v4_ordinal2(A) -> r1_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t15_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6969 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(B,k4_finseq_1(A)) & k2_xcmplx_0(C,np__1) = k3_finseq_1(A) -> C = k3_finseq_1(k2_finseq_3(B,A))))))))) # label(t118_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6970 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (A = k1_finseq_3(A,k1_tarski(B)) <-> -r2_hidden(B,k2_relat_1(A)))))) # label(t77_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6971 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (k2_xcmplx_0(B,np__1) = A & r2_hidden(C,k2_finseq_1(A)) -> B = k3_finseq_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(A),k1_tarski(C))))))))))) # label(t116_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6972 (all A all B all C (v2_funct_1(k11_finseq_1(A,B,C)) <-> B != C & C != A & A != B)) # label(t104_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6973 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B all C all D (k1_enumset1(B,C,D) = k2_relat_1(A) & v2_funct_1(A) -> B = C | D = C | np__3 = k3_finseq_1(A) | B = D)))) # label(t110_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6974 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r1_tarski(k2_finseq_1(A),k2_finseq_1(k2_xcmplx_0(A,B))))))) # label(t19_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6975 (all A all B all C (r2_hidden(C,B) -> r2_hidden(A,B) | k1_finseq_3(k10_finseq_1(A,C),B) = k9_finseq_1(A))) # label(t87_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6976 (all A all B all C (k1_xboole_0 = k1_finseq_3(k10_finseq_1(A,B),C) <-> r2_hidden(A,C) & r2_hidden(B,C))) # label(t84_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6977 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v4_ordinal2(C) -> (r2_hidden(C,k4_finseq_1(A)) -> (all D (v1_finset_1(D) -> -(D = a_3_0_finseq_3(A,B,C) & -r2_hidden(k1_funct_1(A,C),B) & k1_funct_1(A,C) != k1_funct_1(k1_finseq_3(A,B),k6_xcmplx_0(C,k4_card_1(D))))))))))) # label(t92_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6978 (all A all B (v4_ordinal2(B) -> (k1_tarski(A) = k2_finseq_1(B) -> A = np__1 & np__1 = B))) # label(t22_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6979 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B k2_relat_1(k1_finseq_3(A,B)) = k4_xboole_0(k2_relat_1(A),B)))) # label(t72_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6980 (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) -> (v2_funct_1(B) & v2_funct_1(A) & r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) <-> v2_funct_1(k7_finseq_1(A,B))))))) # label(t98_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6981 (all A all B all C (v4_ordinal2(C) -> (k2_finseq_1(C) = k2_tarski(A,B) -> A = B | k2_tarski(A,B) = k2_tarski(np__1,np__2) & C = np__2))) # label(t23_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6982 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v4_ordinal2(B) -> (A = k7_relat_1(A,k2_finseq_1(B)) <-> r1_xreal_0(k3_finseq_1(A),B)))))) # label(t55_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6983 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (k4_finseq_1(k1_finseq_3(A,B)) = k4_finseq_1(A) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t71_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6984 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B all C -(k2_tarski(B,C) = k2_relat_1(A) & B != C & k10_finseq_1(B,C) != A & A != k10_finseq_1(C,B) & v2_funct_1(A))))) # label(t108_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6985 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v4_ordinal2(A) -> v1_finseq_1(k2_finseq_3(A,B)) & v1_funct_1(k2_finseq_3(A,B)) & v1_relat_1(k2_finseq_3(A,B)))) # label(dt_k2_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6986 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(A,B) <-> r2_hidden(k6_xcmplx_0(A,B),k2_finseq_1(A))))))) # label(t14_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6987 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k1_nat_1(C,np__1) = k3_finseq_1(A) & r2_hidden(B,k4_finseq_1(A)) & r1_xreal_0(D,C) & r1_xreal_0(B,D) -> k1_funct_1(A,k1_nat_1(D,np__1)) = k1_funct_1(k2_finseq_3(B,A),D)))))))))) # label(t120_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6988 (all A all B all C all D (v1_funct_1(B) & v4_ordinal2(D) & v1_finseq_1(B) & v1_relat_1(B) -> (r2_hidden(A,a_3_0_finseq_3(B,C,D)) <-> (exists E (m2_subset_1(E,k1_numbers,k5_numbers) & E = A & r2_hidden(k1_funct_1(B,E),C) & r1_xreal_0(E,D) & r2_hidden(E,k4_finseq_1(B))))))) # label(fraenkel_a_3_0_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6989 $T # label(t37_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6990 (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 (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))))))))) # label(t24_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6991 (all A (v4_ordinal2(A) -> (all B all C (m2_finseq_1(C,B) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(D,A) -> k1_funct_1(k16_finseq_1(B,C,A),D) = k1_funct_1(C,D)))))))) # label(t121_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6992 (all A (v4_ordinal2(A) -> -r2_hidden(k2_xcmplx_0(A,np__1),k2_finseq_1(A)))) # label(t9_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6993 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(k10_finseq_1(A,B) != k14_finseq_1(k2_tarski(A,B)) & -r1_xreal_0(B,A) & -r1_xreal_0(A,np__0)))))) # label(t51_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6994 $T # label(t47_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6995 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> -(-v1_xboole_0(B) & (all C (m1_subset_1(C,A) -> (all D (m2_finseq_1(D,A) -> -(B = k8_finseq_1(A,k12_finseq_1(A,C),D) & C = k1_funct_1(B,np__1))))))))))) # label(t111_finseq_3) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6996 $T # label(t15_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.78/113.78 6997 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> ((all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(B)) -> r2_zf_model(A,k11_zf_model(B))))) <-> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (v1_funct_1(C) & m2_relset_1(C,k1_zf_lang,A) & v1_funct_2(C,k1_zf_lang,A) -> (r1_zf_model(A,C,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0))))))) & r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(B)) -> (all D (m1_subset_1(D,A) -> r2_hidden(k2_funct_2(A,A,k1_zfmodel1(B,A,C),D),A)))))))))))) # label(t19_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 6998 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k2_tarski(B,C),A))))) <-> r2_zf_model(A,k7_zf_model))))) # label(t2_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 6999 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k2_tarski(B,C),A))))) & (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k1_zf_lang,A) & m2_relset_1(C,k1_zf_lang,A) -> (r1_zf_model(A,C,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0))))))) & r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(B)) -> (all D (m1_subset_1(D,A) -> r2_hidden(k2_funct_2(A,A,k1_zfmodel1(B,A,C),D),A)))))))) & (all B (m1_subset_1(B,A) -> r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A))) & (all B (m1_subset_1(B,A) -> r2_hidden(k3_tarski(B),A))) & v1_ordinal1(A) -> (all B (m1_subset_1(B,A) -> -((all C (m1_subset_1(C,A) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,A) -> -(r2_xboole_0(C,D) & r2_hidden(D,B))))))) & B != k1_xboole_0))) | v1_zf_model(A)))) # label(t22_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7000 (all A all B (-v1_xboole_0(B) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_funct_1(k2_zfmodel1(A,B)) & v1_funct_2(k2_zfmodel1(A,B),B,B) & m2_relset_1(k2_zfmodel1(A,B),B,B))) # label(dt_k2_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7001 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (-v1_xboole_0(B) -> ((exists C (m2_finseq_1(C,k5_numbers) & (exists D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,B) & r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(C)) & r1_zf_model(B,D,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(C,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0))))))) & k1_zfmodel1(C,B,D) = A & m2_relset_1(D,k1_zf_lang,B))) & v1_zf_lang(C))) <-> r2_zfmodel1(A,B)))))) # label(d4_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7002 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_zfmodel1(B,A) -> r2_zfmodel1(B,A)))))) # label(t18_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7003 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k1_zf_lang,D) & v1_funct_2(E,k1_zf_lang,D) & v1_funct_1(E) -> (r1_xboole_0(k2_tarski(A,B),k2_zf_model(C)) & r1_zf_model(D,E,C) -> r1_zf_model(D,E,k14_zf_lang(A,B,C))))))))))))) # label(t11_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7004 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> (r2_zf_model(A,k7_zf_model) <-> (all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k2_tarski(B,C),A))))))) # label(t3_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7005 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k1_zf_lang,B) & m2_relset_1(C,k1_zf_lang,B) -> (r1_zf_model(B,C,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(A,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0))))))) -> (all D (m2_relset_1(D,B,B) & v1_funct_2(D,B,B) & v1_funct_1(D) -> ((all E (m2_relset_1(E,k1_zf_lang,B) & v1_funct_2(E,k1_zf_lang,B) & v1_funct_1(E) -> ((all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> -(k2_zf_lang(np__3) != F & F != k2_zf_lang(np__4) & k2_zf_lang(np__0) != F & k8_funct_2(k1_zf_lang,B,E,F) != k8_funct_2(k1_zf_lang,B,C,F)))) -> (r1_zf_model(B,E,A) <-> k8_funct_2(k1_zf_lang,B,E,k2_zf_lang(np__4)) = k8_funct_2(B,B,D,k8_funct_2(k1_zf_lang,B,E,k2_zf_lang(np__3))))))) <-> k1_zfmodel1(A,B,C) = D))) | r2_hidden(k2_zf_lang(np__0),k2_zf_model(A))))))))) # label(d1_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7006 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_zf_lang,B) & m1_relset_1(C,k1_zf_lang,B) & -v1_xboole_0(B) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m2_relset_1(k1_zfmodel1(A,B,C),B,B) & v1_funct_2(k1_zfmodel1(A,B,C),B,B) & v1_funct_1(k1_zfmodel1(A,B,C)))) # label(dt_k1_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7007 $T # label(t13_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7008 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> (r2_zf_model(A,k8_zf_model) <-> (all B (m1_subset_1(B,A) -> r2_hidden(k3_tarski(B),A))))))) # label(t4_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7009 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (r2_zf_model(B,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(A,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0))))))) & r1_tarski(k2_zf_model(A),k2_tarski(k2_zf_lang(np__3),k2_zf_lang(np__4))) -> (all C (v1_funct_1(C) & m2_relset_1(C,B,B) & v1_funct_2(C,B,B) -> ((all D (m2_relset_1(D,k1_zf_lang,B) & v1_funct_2(D,k1_zf_lang,B) & v1_funct_1(D) -> (r1_zf_model(B,D,A) <-> k8_funct_2(B,B,C,k8_funct_2(k1_zf_lang,B,D,k2_zf_lang(np__3))) = k8_funct_2(k1_zf_lang,B,D,k2_zf_lang(np__4))))) <-> k2_zfmodel1(A,B) = C)))))))) # label(d2_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7010 $T # label(t17_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7011 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> (r2_zf_model(A,k9_zf_model) <-> (exists B ((all C (m1_subset_1(C,A) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,A) -> -(r2_hidden(D,B) & r2_xboole_0(C,D))))))) & k1_xboole_0 != B & m1_subset_1(B,A))))))) # label(t6_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7012 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) -> (r1_zf_model(C,D,B) -> r2_hidden(A,k2_zf_model(B)) | r1_zf_model(C,D,k8_zf_lang(A,B))))))))))) # label(t10_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7013 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> (r2_zf_model(A,k10_zf_model) <-> (all B (r2_hidden(B,A) -> r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A))))))) # label(t9_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7014 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> (r2_zf_model(A,k8_zf_model) <-> (all B (r2_hidden(B,A) -> r2_hidden(k3_tarski(B),A))))))) # label(t5_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7015 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (-v1_xboole_0(B) -> (r1_zfmodel1(A,B) <-> (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & A = k2_zfmodel1(C,B) & r2_zf_model(B,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(C,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0))))))) & r1_tarski(k2_zf_model(C),k2_tarski(k2_zf_lang(np__3),k2_zf_lang(np__4)))))))))) # label(d3_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7016 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> r2_zf_model(A,k6_zf_model)))) # label(t1_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7017 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> ((exists B (B != k1_xboole_0 & (all C -((all D -(r2_xboole_0(C,D) & r2_hidden(D,B))) & r2_hidden(C,B))) & r2_hidden(B,A))) <-> r2_zf_model(A,k9_zf_model))))) # label(t7_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7018 (all A (-v1_xboole_0(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_relset_1(C,k1_zf_lang,A) & v1_funct_2(C,k1_zf_lang,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_zf_lang,A) & v1_funct_2(D,k1_zf_lang,A) -> (r1_zf_model(A,C,B) & (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> -(r2_hidden(E,k2_zf_model(B)) & k8_funct_2(k1_zf_lang,A,D,E) != k8_funct_2(k1_zf_lang,A,C,E)))) -> r1_zf_model(A,D,B)))))))))) # label(t14_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7019 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> ((all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(B)) -> r2_zf_model(A,k11_zf_model(B))))) <-> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_zfmodel1(B,A) -> (all C (r2_hidden(C,A) -> r2_hidden(k9_relat_1(B,C),A)))))))))) # label(t20_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7020 (all A (-v1_xboole_0(A) -> (v1_zf_model(A) -> v1_ordinal1(A) & (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k2_tarski(B,C),A))))) & (all B (m1_subset_1(B,A) -> r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A))) & (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_relset_1(C,k1_zf_lang,A) & v1_funct_2(C,k1_zf_lang,A) & v1_funct_1(C) -> (r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(B)) & r1_zf_model(A,C,k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0))))))) -> (all D (m1_subset_1(D,A) -> r2_hidden(k2_funct_2(A,A,k1_zfmodel1(B,A,C),D),A)))))))) & (exists B (k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,A) -> -(r2_hidden(D,B) & r2_xboole_0(C,D))))))) & m1_subset_1(B,A))) & (all B (m1_subset_1(B,A) -> r2_hidden(k3_tarski(B),A))) & (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) <-> r2_hidden(D,C)))) -> C = B)))))))) # label(t21_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7021 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> (r2_zf_model(A,k10_zf_model) <-> (all B (m1_subset_1(B,A) -> r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A))))))) # label(t8_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7022 $T # label(t16_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7023 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (all E (-v1_xboole_0(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,k1_zf_lang,E) & v1_funct_2(F,k1_zf_lang,E) -> (r1_zf_model(E,F,D) & r1_xboole_0(k1_enumset1(A,B,C),k2_zf_model(D)) -> r1_zf_model(E,F,k16_zf_lang(A,B,C,D))))))))))))))) # label(t12_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7024 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v9_zf_lang(A) -> v5_zf_lang(k20_zf_lang(A)) & v4_zf_lang(k22_zf_lang(k20_zf_lang(A))) & v4_zf_lang(A)))) # label(t39_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7025 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,k1_zf_lang,C) & v1_funct_2(D,k1_zf_lang,C) & v1_funct_1(D) -> ((all E (m1_subset_1(E,C) -> r1_zf_model(C,k1_zf_lang1(C,D,B,E),A))) <-> r1_zf_model(C,D,k8_zf_lang(B,A))))))))))) # label(t80_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7026 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (-(-(r1_zf_lang(B,C) & r3_zf_lang(A,B)) & -(r3_zf_lang(B,C) & r1_zf_lang(A,B)) & -(r1_zf_lang(A,B) & r2_zf_lang(B,C)) & -(r2_zf_lang(A,B) & r1_zf_lang(B,C)) & -(r2_zf_lang(A,B) & r3_zf_lang(B,C)) & -(r2_zf_lang(B,C) & r3_zf_lang(A,B))) -> r3_zf_lang(A,C)))))))) # label(t44_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7027 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_zf_lang,C) & v1_funct_2(D,k1_zf_lang,C) -> r2_zf_model(C,k11_zf_lang(A,k10_zf_lang(B,A))) & r1_zf_model(C,D,k11_zf_lang(A,k10_zf_lang(B,A))))))))))) # label(t124_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7028 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> A = k24_zf_lang(k8_zf_lang(B,A)) & k23_zf_lang(k8_zf_lang(B,A)) = B)))) # label(t8_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7029 $T # label(t132_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7030 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k1_zf_lang,D) & v1_funct_2(E,k1_zf_lang,D) & v1_funct_1(E) -> r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(C,B),k11_zf_lang(k10_zf_lang(A,C),B)))) & r1_zf_model(D,E,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(C,B),k11_zf_lang(k10_zf_lang(A,C),B)))))))))))))) # label(t127_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7031 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (-v1_xboole_0(D) -> (r2_zf_model(D,k11_zf_lang(B,C)) & r2_zf_model(D,k11_zf_lang(A,B)) -> r2_zf_model(D,k11_zf_lang(A,C))))))))))) # label(t114_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7032 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_zf_lang,C) & v1_funct_2(D,k1_zf_lang,C) -> r2_zf_model(C,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(A,B))) & r1_zf_model(C,D,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(A,B))))))))))) # label(t110_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7033 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k16_zf_lang(C,D,E,A) = k8_zf_lang(F,B) -> B = k14_zf_lang(D,E,A) & C = F))))))))))))) # label(t18_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7034 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> k16_zf_lang(B,C,D,A) = k8_zf_lang(B,k8_zf_lang(C,k8_zf_lang(D,A))) & k14_zf_lang(B,C,k8_zf_lang(D,A)) = k16_zf_lang(B,C,D,A))))))))) # label(t15_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7035 (all A all B all C (m1_subset_1(B,k1_zf_lang) & m1_subset_1(C,k1_zf_lang) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> k5_zf_lang1(A,B,C) = k6_zf_lang1(A,B,C))) # label(redefinition_k6_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7036 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> k2_zf_model(k16_zf_lang(B,C,D,A)) = k4_xboole_0(k2_zf_model(A),k1_enumset1(B,C,D)))))))))) # label(t73_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7037 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (all G (m2_subset_1(G,k5_numbers,k1_zf_lang) -> (k14_zf_lang(F,G,B) = k16_zf_lang(C,D,E,A) -> F = C & D = G & k8_zf_lang(E,A) = B))))))))))))))) # label(t19_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7038 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (k13_zf_lang(E,B) = k15_zf_lang(C,D,A) -> C = E & k13_zf_lang(D,A) = B))))))))))) # label(t12_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7039 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,k1_zf_lang,C) & v1_funct_2(D,k1_zf_lang,C) & v1_funct_1(D) -> r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(A,B),B)) & r2_zf_model(C,k11_zf_lang(k7_zf_lang(A,B),B)))))))))) # label(t119_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7040 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (-v1_xboole_0(B) -> r2_zf_model(B,k4_zf_lang(A,A)))))) # label(t90_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7041 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> -v1_xboole_0(k4_zf_lang1(A)) & m1_subset_1(k4_zf_lang1(A),k1_zfmisc_1(k1_zf_lang)))) # label(dt_k4_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7042 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> r1_tarski(k2_zf_model(A),k3_zf_lang1(A)))) # label(t164_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7043 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> k2_xboole_0(k3_zf_lang1(A),k1_enumset1(B,C,D)) = k3_zf_lang1(k16_zf_lang(B,C,D,A)))))))))) # label(t162_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7044 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (-v1_xboole_0(E) -> (r2_zf_model(E,k16_zf_lang(B,C,D,A)) <-> r2_zf_model(E,A)))))))))))) # label(t108_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7045 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> r3_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k10_zf_lang(A,B)) & r3_zf_lang(A,k10_zf_lang(A,B)) & r3_zf_lang(B,k10_zf_lang(A,B)) & r3_zf_lang(k6_zf_lang(B),k10_zf_lang(A,B)) & r3_zf_lang(k6_zf_lang(A),k10_zf_lang(A,B)))))) # label(t55_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7046 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k20_zf_lang(k13_zf_lang(B,A)) = k8_zf_lang(B,k6_zf_lang(A)))))) # label(t37_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7047 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k2_zf_model(k10_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)))))) # label(t68_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7048 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,C) -> (all E (m1_subset_1(E,C) -> (all F (v1_funct_2(F,k1_zf_lang,C) & m2_relset_1(F,k1_zf_lang,C) & v1_funct_1(F) -> (A != B -> k1_zf_lang1(C,k1_zf_lang1(C,F,A,D),B,E) = k1_zf_lang1(C,k1_zf_lang1(C,F,B,E),A,D)))))))))))))) # label(t79_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7049 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (k5_zf_lang1(B,C,D) = A <-> k6_zf_lang(A) = k5_zf_lang1(k6_zf_lang(B),C,D)))))))))) # label(t170_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7050 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r2_zf_lang(A,B) -> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t43_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7051 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (all G (m2_subset_1(G,k5_numbers,k1_zf_lang) -> (all H (m2_subset_1(H,k5_numbers,k1_zf_lang) -> (k17_zf_lang(F,G,H,B) = k17_zf_lang(C,D,E,A) -> C = F & G = D & E = H & A = B))))))))))))))))) # label(t22_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7052 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> k3_zf_lang1(k17_zf_lang(B,C,D,A)) = k2_xboole_0(k3_zf_lang1(A),k1_enumset1(B,C,D)))))))))) # label(t163_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7053 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k1_zf_lang,A) & v1_funct_2(B,k1_zf_lang,A) & v1_funct_1(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m1_subset_1(D,A) -> (all E (v1_funct_2(E,k1_zf_lang,A) & m2_relset_1(E,k1_zf_lang,A) & v1_funct_1(E) -> ((all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k8_funct_2(k1_zf_lang,A,B,F) != k8_funct_2(k1_zf_lang,A,E,F) -> C = F))) & k8_funct_2(k1_zf_lang,A,E,C) = D <-> k1_zf_lang1(A,B,C,D) = E))))))))))) # label(d1_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7054 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (-v1_xboole_0(D) -> (r2_zf_model(D,k11_zf_lang(A,k8_zf_lang(C,B))) -> r2_zf_model(D,k11_zf_lang(A,B))))))))))) # label(t144_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7055 $T # label(t76_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7056 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (B = k6_zf_lang1(D,E,F) & A = k6_zf_lang1(C,E,F) <-> k10_zf_lang(A,B) = k6_zf_lang1(k10_zf_lang(C,D),E,F)))))))))))))) # label(t175_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7057 (all A all B all C (m1_finseq_1(A,k5_numbers) & m1_subset_1(C,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) & v1_zf_lang(A) -> v1_funct_1(k5_zf_lang1(A,B,C)) & v1_relat_1(k5_zf_lang1(A,B,C)))) # label(dt_k5_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7058 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v10_zf_lang(A) -> v9_zf_lang(k21_zf_lang(A)) & v9_zf_lang(k22_zf_lang(A)) & v5_zf_lang(A)))) # label(t40_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7059 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> B = k22_zf_lang(k7_zf_lang(A,B)) & k21_zf_lang(k7_zf_lang(A,B)) = A)))) # label(t4_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7060 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) = k3_zf_lang1(k7_zf_lang(A,B)))))) # label(t154_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7061 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> k2_zf_model(k15_zf_lang(B,C,A)) = k4_xboole_0(k2_zf_model(A),k2_tarski(B,C)))))))) # label(t74_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7062 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,k1_zf_lang,B) & m2_relset_1(D,k1_zf_lang,B) & v1_funct_1(D) -> (r1_zf_model(B,C,A) & (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (r2_hidden(E,k2_zf_model(A)) -> k8_funct_2(k1_zf_lang,B,C,E) = k8_funct_2(k1_zf_lang,B,D,E)))) -> r1_zf_model(B,D,A)))))))))) # label(t84_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7063 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k17_zf_lang(C,D,E,A) = k13_zf_lang(F,B) -> k15_zf_lang(D,E,A) = B & F = C))))))))))))) # label(t23_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7064 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) -> r1_zf_model(C,D,k11_zf_lang(k6_zf_lang(k7_zf_lang(A,B)),k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B)))) & r2_zf_model(C,k11_zf_lang(k6_zf_lang(k7_zf_lang(A,B)),k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B)))))))))))) # label(t134_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7065 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> r2_zf_model(C,k11_zf_lang(A,k13_zf_lang(B,A))))))))) # label(t139_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7066 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) -> (v9_zf_lang(A) -> ((r1_zf_model(B,C,k25_zf_lang(A)) -> r1_zf_model(B,C,k26_zf_lang(A))) <-> r1_zf_model(B,C,A))))))))) # label(t101_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7067 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v3_zf_lang(A) <-> v3_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t181_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7068 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) = k2_zf_model(k11_zf_lang(A,B)))))) # label(t69_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7069 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> -r2_hidden(A,k3_enumset1(np__0,np__1,np__2,np__3,np__4)))) # label(t149_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7070 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) -> r2_zf_model(C,k11_zf_lang(A,k10_zf_lang(A,B))) & r1_zf_model(C,D,k11_zf_lang(A,k10_zf_lang(A,B))))))))))) # label(t123_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7071 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> -(r1_zf_lang(B,A) & r2_zf_lang(A,B)))))) # label(t49_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7072 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> r2_hidden(A,k29_zf_lang(A)))) # label(t59_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7073 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k1_zf_lang,D) & v1_funct_2(E,k1_zf_lang,D) -> (r1_zf_model(D,E,k11_zf_lang(A,B)) & r1_zf_model(D,E,k11_zf_lang(B,C)) -> r1_zf_model(D,E,k11_zf_lang(A,C))))))))))))) # label(t113_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7074 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) -> r1_zf_model(C,D,k11_zf_lang(k6_zf_lang(k10_zf_lang(A,B)),k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)))) & r2_zf_model(C,k11_zf_lang(k6_zf_lang(k10_zf_lang(A,B)),k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)))))))))))) # label(t136_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7075 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> r1_tarski(k4_zf_lang1(k6_zf_lang1(A,B,C)),k2_xboole_0(k4_xboole_0(k4_zf_lang1(A),k1_tarski(B)),k1_tarski(C))))))))) # label(t201_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7076 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> -(r3_zf_lang(A,B) & r3_zf_lang(B,A)))))) # label(t48_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7077 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> ((all D (v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) & v1_funct_1(D) -> (exists E (m1_subset_1(E,C) & r1_zf_model(C,k1_zf_lang1(C,D,B,E),A))))) <-> r2_zf_model(C,k13_zf_lang(B,A))))))))) # label(t104_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7078 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> k13_zf_lang(C,A) = k24_zf_lang(k15_zf_lang(B,C,A)) & B = k23_zf_lang(k15_zf_lang(B,C,A)) & v11_zf_lang(k15_zf_lang(B,C,A)))))))) # label(t14_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7079 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k1_zf_lang,B) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_1(C) -> (v4_zf_lang(A) -> (-r1_zf_model(B,C,k20_zf_lang(A)) <-> r1_zf_model(B,C,A))))))))) # label(t97_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7080 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> B = k23_zf_lang(k16_zf_lang(B,C,D,A)) & k24_zf_lang(k16_zf_lang(B,C,D,A)) = k14_zf_lang(C,D,A) & v6_zf_lang(k16_zf_lang(B,C,D,A)))))))))) # label(t25_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7081 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k19_zf_lang(k5_zf_lang(A,B)) = B & A = k18_zf_lang(k5_zf_lang(A,B)))))) # label(t2_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7082 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k2_tarski(A,B) = k2_zf_model(k4_zf_lang(A,B)))))) # label(t63_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7083 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (k13_zf_lang(C,A) = k6_zf_lang1(k13_zf_lang(D,B),D,C) <-> k6_zf_lang1(B,D,C) = A))))))))) # label(t179_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7084 (all A all B all C (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) & m1_subset_1(B,k1_zf_lang) & m1_subset_1(C,k1_zf_lang) -> m2_finseq_1(k6_zf_lang1(A,B,C),k5_numbers) & v1_zf_lang(k6_zf_lang1(A,B,C)))) # label(dt_k6_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7085 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (-r2_hidden(B,k4_zf_lang1(A)) -> A = k6_zf_lang1(A,B,C)))))))) # label(t196_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7086 $T # label(t147_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7087 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (A = k6_zf_lang1(C,E,F) & B = k6_zf_lang1(D,E,F) <-> k11_zf_lang(A,B) = k6_zf_lang1(k11_zf_lang(C,D),E,F)))))))))))))) # label(t176_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7088 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_finset_1(k2_zf_model(A)))) # label(t85_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.80 7089 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) = k2_zf_model(k12_zf_lang(A,B)))))) # label(t70_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7090 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> r3_zf_lang(k6_zf_lang(A),k13_zf_lang(B,A)) & r3_zf_lang(k8_zf_lang(B,k6_zf_lang(A)),k13_zf_lang(B,A)))))) # label(t56_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7091 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (C != B -> k6_zf_lang1(k6_zf_lang1(A,B,C),B,D) = k6_zf_lang1(A,B,C)))))))))) # label(t200_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7092 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k4_xboole_0(k2_zf_model(A),k1_tarski(B)) = k2_zf_model(k8_zf_lang(B,A)))))) # label(t67_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7093 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> A = k18_zf_lang(k4_zf_lang(A,B)) & B = k19_zf_lang(k4_zf_lang(A,B)))))) # label(t1_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7094 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,k1_zf_lang,C) & v1_funct_2(D,k1_zf_lang,C) & v1_funct_1(D) -> r2_zf_model(C,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,k6_zf_lang(B))),k6_zf_lang(A))) & r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,k6_zf_lang(B))),k6_zf_lang(A))))))))))) # label(t131_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7095 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k14_zf_lang(E,F,B) = k14_zf_lang(C,D,A) -> B = A & F = D & C = E))))))))))))) # label(t16_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7096 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k29_zf_lang(k11_zf_lang(A,B)) = k2_xboole_0(k2_xboole_0(k29_zf_lang(A),k29_zf_lang(B)),k1_enumset1(k6_zf_lang(B),k7_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(A,B))))))) # label(t60_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7097 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k1_zf_lang,D) & v1_funct_2(E,k1_zf_lang,D) & v1_funct_1(E) -> r2_zf_model(D,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(C,B)),k11_zf_lang(k10_zf_lang(A,C),B))) & r1_zf_model(D,E,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(C,B)),k11_zf_lang(k10_zf_lang(A,C),B))))))))))))) # label(t128_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7098 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v5_zf_lang(k6_zf_lang1(A,B,C)) <-> v5_zf_lang(A)))))))) # label(t183_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7099 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k3_zf_lang1(k4_zf_lang(A,B)) = k2_tarski(A,B))))) # label(t151_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7100 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k3_zf_lang1(k10_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)))))) # label(t156_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7101 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v4_zf_lang(A) <-> v4_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t182_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7102 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r2_zf_lang(k7_zf_lang(A,B),C) -> r3_zf_lang(A,C) & r3_zf_lang(B,C)))))))) # label(t52_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7103 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k1_zf_lang,B) & m2_relset_1(C,k1_zf_lang,B) -> r1_zf_model(B,C,k4_zf_lang(A,A)))))))) # label(t89_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7104 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) = k2_zf_model(k7_zf_lang(A,B)))))) # label(t66_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7105 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> r3_zf_lang(k7_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(A,B)) & r3_zf_lang(A,k11_zf_lang(A,B)) & r3_zf_lang(k6_zf_lang(B),k11_zf_lang(A,B)) & r3_zf_lang(B,k11_zf_lang(A,B)))))) # label(t54_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7106 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v9_zf_lang(k6_zf_lang1(A,B,C)) <-> v9_zf_lang(A)))))))) # label(t189_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7107 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (all G (m2_subset_1(G,k5_numbers,k1_zf_lang) -> (k17_zf_lang(C,D,E,A) = k15_zf_lang(F,G,B) -> F = C & B = k13_zf_lang(E,A) & D = G))))))))))))))) # label(t24_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7108 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (all G (m2_subset_1(G,k5_numbers,k1_zf_lang) -> (all H (m2_subset_1(H,k5_numbers,k1_zf_lang) -> (k16_zf_lang(F,G,H,B) = k16_zf_lang(C,D,E,A) -> C = F & A = B & H = E & G = D))))))))))))))))) # label(t17_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7109 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v10_zf_lang(A) -> v10_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t190_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7110 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) & v1_funct_1(C) -> -r1_zf_model(B,C,k5_zf_lang(A,A)))))))) # label(t91_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7111 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) -> r2_zf_model(B,k11_zf_lang(A,k7_zf_lang(A,A))) & r1_zf_model(B,C,k11_zf_lang(A,k7_zf_lang(A,A))))))))) # label(t121_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7112 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> np__1 != A & np__2 != A & np__4 != A & np__3 != A & np__0 != A)) # label(t148_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7113 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k1_zf_lang,D) & m2_relset_1(E,k1_zf_lang,D) -> r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,k11_zf_lang(B,C)),k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,C)))) & r1_zf_model(D,E,k11_zf_lang(k11_zf_lang(A,k11_zf_lang(B,C)),k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(A,C)))))))))))))) # label(t117_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7114 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) & v1_funct_1(D) -> ((exists E (r1_zf_model(C,k1_zf_lang1(C,D,B,E),A) & m1_subset_1(E,C))) <-> r1_zf_model(C,D,k13_zf_lang(B,A))))))))))) # label(t82_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7115 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v6_zf_lang(A) -> k6_zf_lang1(k24_zf_lang(A),B,C) = k24_zf_lang(k6_zf_lang1(A,B,C)) & (k23_zf_lang(A) != B -> k23_zf_lang(k6_zf_lang1(A,B,C)) = k23_zf_lang(A)) & (B = k23_zf_lang(A) -> C = k23_zf_lang(k6_zf_lang1(A,B,C)))))))))) # label(t187_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7116 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k2_tarski(A,B) = k2_zf_model(k5_zf_lang(A,B)))))) # label(t64_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7117 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k2_zf_lang(A) = k2_zf_lang(B) -> B = A))))) # label(t86_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7118 $T # label(t45_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7119 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (-v1_xboole_0(C) -> (r2_zf_model(C,k11_zf_lang(A,B)) & r2_zf_model(C,A) -> r2_zf_model(C,B)))))))) # label(t133_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7120 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> ((all E (r2_hidden(E,k4_finseq_1(A)) -> (k1_funct_1(A,E) = B -> k1_funct_1(D,E) = C) & (B != k1_funct_1(A,E) -> k1_funct_1(A,E) = k1_funct_1(D,E)))) & k4_finseq_1(A) = k1_relat_1(D) <-> k5_zf_lang1(A,B,C) = D))))))))) # label(d4_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7121 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v2_zf_lang(k6_zf_lang1(A,B,C)) <-> v2_zf_lang(A)))))))) # label(t180_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7122 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k20_zf_lang(k11_zf_lang(A,B)) = k7_zf_lang(A,k6_zf_lang(B)))))) # label(t35_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7123 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) & v1_funct_1(C) -> r1_zf_model(B,C,k11_zf_lang(A,k10_zf_lang(A,A))) & r2_zf_model(B,k11_zf_lang(A,k10_zf_lang(A,A))))))))) # label(t126_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7124 $T # label(t77_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7125 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> (r2_zf_model(C,k6_zf_lang(k5_zf_lang(A,B))) <-> B = A | (all D (r2_hidden(D,C) -> r1_xboole_0(D,C)))))))))) # label(t94_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7126 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (r2_hidden(B,k4_zf_lang1(A)) -> r2_hidden(C,k4_zf_lang1(k6_zf_lang1(A,B,C)))))))))) # label(t199_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7127 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> -(r3_zf_lang(A,B) & r2_zf_lang(B,A)))))) # label(t47_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7128 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> k3_zf_lang1(k14_zf_lang(B,C,A)) = k2_xboole_0(k3_zf_lang1(A),k2_tarski(B,C)))))))) # label(t160_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7129 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,C) -> (all E (v1_funct_2(E,k1_zf_lang,C) & m2_relset_1(E,k1_zf_lang,C) & v1_funct_1(E) -> (r1_zf_model(C,k1_zf_lang1(C,E,B,D),k13_zf_lang(B,A)) <-> r1_zf_model(C,E,k13_zf_lang(B,A))))))))))))) # label(t83_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7130 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (-v1_xboole_0(D) -> (r2_zf_model(D,k11_zf_lang(B,A)) -> r2_hidden(C,k2_zf_model(A)) | r2_zf_model(D,k11_zf_lang(k13_zf_lang(C,B),A))))))))))) # label(t143_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7131 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) -> (v3_zf_lang(A) -> (r1_zf_model(B,C,A) <-> r2_hidden(k8_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)),k8_funct_2(k1_zf_lang,B,C,k19_zf_lang(A))))))))))) # label(t96_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7132 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k1_zf_lang,B) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_1(C) -> (v2_zf_lang(A) -> (k8_funct_2(k1_zf_lang,B,C,k19_zf_lang(A)) = k8_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)) <-> r1_zf_model(B,C,A))))))))) # label(t95_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7133 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k4_xboole_0(k2_zf_model(A),k1_tarski(B)) = k2_zf_model(k13_zf_lang(B,A)))))) # label(t71_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7134 (all A all B all C all D (m1_subset_1(C,k1_zf_lang) & m1_subset_1(D,A) & m1_relset_1(B,k1_zf_lang,A) & v1_funct_2(B,k1_zf_lang,A) & v1_funct_1(B) & -v1_xboole_0(A) -> v1_funct_1(k1_zf_lang1(A,B,C,D)) & m2_relset_1(k1_zf_lang1(A,B,C,D),k1_zf_lang,A) & v1_funct_2(k1_zf_lang1(A,B,C,D),k1_zf_lang,A))) # label(dt_k1_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7135 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) & v1_funct_1(D) -> r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k10_zf_lang(A,B)))) & r2_zf_model(C,k11_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k10_zf_lang(A,B)))))))))))) # label(t137_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7136 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k1_zf_lang,B) & m2_relset_1(C,k1_zf_lang,B) -> (v8_zf_lang(A) -> (r1_zf_model(B,C,k22_zf_lang(A)) | r1_zf_model(B,C,k21_zf_lang(A)) <-> r1_zf_model(B,C,A))))))))) # label(t100_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7137 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) -> r1_zf_model(C,D,k11_zf_lang(A,k11_zf_lang(B,A))) & r2_zf_model(C,k11_zf_lang(A,k11_zf_lang(B,A))))))))))) # label(t116_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7138 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> (r2_zf_model(C,A) -> r2_zf_model(C,k13_zf_lang(B,A))))))))) # label(t105_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7139 $T # label(t88_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7140 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (-v1_xboole_0(D) -> (-r2_hidden(C,k2_zf_model(A)) -> r2_zf_model(D,k11_zf_lang(k8_zf_lang(C,k11_zf_lang(A,B)),k11_zf_lang(A,k8_zf_lang(C,B))))))))))))) # label(t140_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7141 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) -> r2_zf_model(C,k11_zf_lang(k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k7_zf_lang(A,B)))) & r1_zf_model(C,D,k11_zf_lang(k10_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k6_zf_lang(k7_zf_lang(A,B)))))))))))) # label(t135_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7142 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (k6_zf_lang1(k8_zf_lang(D,B),D,C) = k8_zf_lang(C,A) <-> k6_zf_lang1(B,D,C) = A))))))))) # label(t174_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7143 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (exists E ((exists F (k5_zf_lang(E,F) = k5_zf_lang1(k5_zf_lang(A,B),C,D) & m2_subset_1(F,k5_numbers,k1_zf_lang))) & m2_subset_1(E,k5_numbers,k1_zf_lang))))))))))) # label(t169_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7144 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> r2_hidden(k5_zf_lang1(A,B,C),k9_zf_lang))))))) # label(t171_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7145 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (r2_zf_lang(k8_zf_lang(C,A),B) -> r3_zf_lang(A,B)))))))) # label(t53_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7146 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> A = k21_zf_lang(k10_zf_lang(A,B)) & B = k22_zf_lang(k10_zf_lang(A,B)))))) # label(t5_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7147 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v11_zf_lang(A) <-> v11_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t191_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7148 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (k8_zf_lang(E,B) = k14_zf_lang(C,D,A) -> E = C & B = k8_zf_lang(D,A)))))))))))) # label(t11_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7149 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v4_zf_lang(A) -> k20_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k20_zf_lang(A),B,C)))))))) # label(t185_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7150 $T # label(t165_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7151 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k4_zf_lang(E,F) = k5_zf_lang1(k4_zf_lang(A,B),C,D) <-> -(-(C = A & B != C & E = D & F = B) & -(A != C & B = C & F = D & A = E) & -(A = C & D = E & D = F & B = C) & -(B != C & B = F & E = A & A != C))))))))))))))) # label(t166_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7152 $T # label(dt_k3_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7153 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v8_zf_lang(A) -> v4_zf_lang(k21_zf_lang(k20_zf_lang(A))) & v4_zf_lang(k22_zf_lang(k20_zf_lang(A))) & v5_zf_lang(k20_zf_lang(A)) & v4_zf_lang(A) & v9_zf_lang(A)))) # label(t38_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7154 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> k2_zf_model(k6_zf_lang(A)) = k2_zf_model(A))) # label(t65_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7155 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v8_zf_lang(A) -> k6_zf_lang1(k22_zf_lang(A),B,C) = k22_zf_lang(k6_zf_lang1(A,B,C)) & k6_zf_lang1(k21_zf_lang(A),B,C) = k21_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t192_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7156 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v10_zf_lang(A) -> k27_zf_lang(A) = k25_zf_lang(k21_zf_lang(A)) & k27_zf_lang(A) = k26_zf_lang(k22_zf_lang(A))))) # label(t31_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7157 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (-v1_xboole_0(D) -> (r2_zf_model(D,k11_zf_lang(k13_zf_lang(C,A),B)) -> r2_zf_model(D,k11_zf_lang(A,B))))))))))) # label(t145_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7158 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> v11_zf_lang(k17_zf_lang(B,C,D,A)) & k15_zf_lang(C,D,A) = k24_zf_lang(k17_zf_lang(B,C,D,A)) & B = k23_zf_lang(k17_zf_lang(B,C,D,A)))))))))) # label(t26_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7159 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> k3_zf_lang1(A) = k3_zf_lang1(k6_zf_lang(A)))) # label(t153_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7160 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k3_zf_lang1(k13_zf_lang(B,A)) = k2_xboole_0(k3_zf_lang1(A),k1_tarski(B)))))) # label(t159_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7161 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_finset_1(k1_zf_model(A)))) # label(fc1_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7162 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> k4_xboole_0(k2_zf_model(A),k1_enumset1(B,C,D)) = k2_zf_model(k17_zf_lang(B,C,D,A)))))))))) # label(t75_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7163 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> -(-(-v6_zf_lang(A) & -v5_zf_lang(A) & -v4_zf_lang(A) & -v3_zf_lang(A)) & v2_zf_lang(A)) & -(v3_zf_lang(A) & -(-v5_zf_lang(A) & -v6_zf_lang(A) & -v4_zf_lang(A))) & -((v6_zf_lang(A) | v5_zf_lang(A)) & v4_zf_lang(A)) & -(v6_zf_lang(A) & v5_zf_lang(A)))) # label(t42_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7164 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k27_zf_lang(k12_zf_lang(A,B)) = A & B = k28_zf_lang(k12_zf_lang(A,B)))))) # label(t7_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7165 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> -(B != C & r2_hidden(B,k4_zf_lang1(k6_zf_lang1(A,B,C)))))))))) # label(t198_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7166 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k1_zf_lang,B) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_1(C) -> (v5_zf_lang(A) -> (r1_zf_model(B,C,k22_zf_lang(A)) & r1_zf_model(B,C,k21_zf_lang(A)) <-> r1_zf_model(B,C,A))))))))) # label(t98_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7167 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) = k3_zf_lang1(k12_zf_lang(A,B)))))) # label(t158_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7168 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k1_zf_lang,D) & v1_funct_2(E,k1_zf_lang,D) & v1_funct_1(E) -> r2_zf_model(D,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,C)),k11_zf_lang(A,C))) & r1_zf_model(D,E,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,C)),k11_zf_lang(A,C))))))))))))) # label(t115_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7169 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (-v1_xboole_0(E) -> (r2_zf_model(E,A) -> r2_zf_model(E,k17_zf_lang(B,C,D,A))))))))))))) # label(t109_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7170 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> k8_zf_lang(C,A) = k24_zf_lang(k14_zf_lang(B,C,A)) & B = k23_zf_lang(k14_zf_lang(B,C,A)) & v6_zf_lang(k14_zf_lang(B,C,A)))))))) # label(t13_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7171 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (r2_hidden(B,k3_zf_lang1(A)) -> B != np__2 & np__3 != B & B != np__4 & B != np__1 & np__0 != B)))) # label(t150_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7172 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -r1_zf_lang(A,A))) # label(t46_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7173 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v9_zf_lang(A) -> k25_zf_lang(A) = k21_zf_lang(k20_zf_lang(A))))) # label(t29_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7174 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k2_xboole_0(k2_xboole_0(k29_zf_lang(A),k29_zf_lang(B)),k5_enumset1(k6_zf_lang(B),k7_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(A,B),k6_zf_lang(A),k7_zf_lang(B,k6_zf_lang(A)),k11_zf_lang(B,A),k12_zf_lang(A,B))) = k29_zf_lang(k12_zf_lang(A,B)))))) # label(t62_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7175 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r2_hidden(A,k29_zf_lang(B)) <-> r2_zf_lang(A,B)))))) # label(t57_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7176 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (r2_hidden(A,k29_zf_lang(B)) -> r1_tarski(k29_zf_lang(A),k29_zf_lang(B))))))) # label(t58_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7177 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k15_zf_lang(C,D,A) = k15_zf_lang(E,F,B) -> E = C & D = F & A = B))))))))))))) # label(t20_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7178 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v9_zf_lang(A) -> k25_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k25_zf_lang(A),B,C) & k26_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k26_zf_lang(A),B,C)))))))) # label(t193_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7179 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) = k3_zf_lang1(k11_zf_lang(A,B)))))) # label(t157_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7180 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) -> (v10_zf_lang(A) -> (r1_zf_model(B,C,A) <-> (r1_zf_model(B,C,k28_zf_lang(A)) <-> r1_zf_model(B,C,k27_zf_lang(A))))))))))) # label(t102_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7181 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (-v1_xboole_0(D) -> (r2_zf_model(D,A) <-> r2_zf_model(D,k14_zf_lang(B,C,A))))))))))) # label(t106_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7182 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,k1_zf_lang,C) & v1_funct_2(D,k1_zf_lang,C) & v1_funct_1(D) -> r2_zf_model(C,k11_zf_lang(k7_zf_lang(A,B),k7_zf_lang(B,A))) & r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(A,B),k7_zf_lang(B,A))))))))))) # label(t120_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7183 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v11_zf_lang(A) -> k24_zf_lang(A) = k20_zf_lang(k24_zf_lang(k20_zf_lang(A))) & k23_zf_lang(A) = k23_zf_lang(k20_zf_lang(A))))) # label(t33_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7184 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k3_zf_lang1(k8_zf_lang(B,A)) = k2_xboole_0(k3_zf_lang1(A),k1_tarski(B)))))) # label(t155_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7185 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k11_zf_lang(k6_zf_lang(A),B) = k10_zf_lang(A,B))))) # label(t10_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7186 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) -> r2_zf_model(C,k11_zf_lang(k7_zf_lang(A,B),A)) & r1_zf_model(C,D,k11_zf_lang(k7_zf_lang(A,B),A)))))))))) # label(t118_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7187 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (C != D -> (k6_zf_lang1(B,D,E) = A <-> k6_zf_lang1(k13_zf_lang(C,B),D,E) = k13_zf_lang(C,A))))))))))))) # label(t178_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7188 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> k15_zf_lang(B,C,k13_zf_lang(D,A)) = k17_zf_lang(B,C,D,A) & k13_zf_lang(B,k13_zf_lang(C,k13_zf_lang(D,A))) = k17_zf_lang(B,C,D,A))))))))) # label(t21_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7189 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (-v1_xboole_0(D) -> (-r2_hidden(C,k2_zf_model(A)) -> r2_zf_model(D,k11_zf_lang(k8_zf_lang(C,k11_zf_lang(B,A)),k11_zf_lang(k13_zf_lang(C,B),A)))))))))))) # label(t142_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7190 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> k2_xboole_0(k3_zf_lang1(A),k2_tarski(B,C)) = k3_zf_lang1(k15_zf_lang(B,C,A)))))))) # label(t161_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7191 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k3_zf_lang1(k5_zf_lang(A,B)) = k2_tarski(A,B))))) # label(t152_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7192 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (-v1_xboole_0(D) -> (r2_zf_model(D,k11_zf_lang(A,B)) -> r2_zf_model(D,k11_zf_lang(A,k8_zf_lang(C,B))) | r2_hidden(C,k2_zf_model(A))))))))))) # label(t141_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7193 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v8_zf_lang(A) <-> v8_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t188_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7194 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) & v1_funct_1(D) -> r1_zf_model(C,D,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(B,A))) & r2_zf_model(C,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(B,A))))))))))) # label(t111_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7195 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v11_zf_lang(A) -> v4_zf_lang(A) & v6_zf_lang(k20_zf_lang(A)) & v4_zf_lang(k24_zf_lang(k20_zf_lang(A)))))) # label(t41_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7196 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v10_zf_lang(A) -> k26_zf_lang(k21_zf_lang(A)) = k28_zf_lang(A) & k25_zf_lang(k22_zf_lang(A)) = k28_zf_lang(A)))) # label(t32_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7197 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> (r2_zf_model(C,k4_zf_lang(A,B)) <-> -((all D C != k1_tarski(D)) & A != B)))))))) # label(t93_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7198 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (-v1_xboole_0(D) -> (r2_zf_model(D,A) -> r2_zf_model(D,k15_zf_lang(B,C,A))))))))))) # label(t107_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7199 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (-v1_xboole_0(B) -> -r2_zf_model(B,k5_zf_lang(A,A)) & r2_zf_model(B,k6_zf_lang(k5_zf_lang(A,A))))))) # label(t92_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7200 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> k2_zf_model(k14_zf_lang(B,C,A)) = k4_xboole_0(k2_zf_model(A),k2_tarski(B,C)))))))) # label(t72_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7201 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k1_zf_lang,D) & m2_relset_1(E,k1_zf_lang,D) -> r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(A,C),k11_zf_lang(A,k7_zf_lang(B,C))))) & r1_zf_model(D,E,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(A,C),k11_zf_lang(A,k7_zf_lang(B,C))))))))))))))) # label(t122_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.82/113.81 7202 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k7_zf_lang(A,B) = k6_zf_lang1(k7_zf_lang(C,D),E,F) <-> k6_zf_lang1(C,E,F) = A & k6_zf_lang1(D,E,F) = B))))))))))))) # label(t172_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7203 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_zf_lang,C) & v1_funct_2(D,k1_zf_lang,C) -> r2_zf_model(C,k11_zf_lang(k6_zf_lang(A),k11_zf_lang(A,B))) & r1_zf_model(C,D,k11_zf_lang(k6_zf_lang(A),k11_zf_lang(A,B))))))))))) # label(t130_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7204 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_2(E,k1_zf_lang,B) & m2_relset_1(E,k1_zf_lang,B) & v1_funct_1(E) -> E = k1_zf_lang1(B,E,A,k8_funct_2(k1_zf_lang,B,E,A)) & k1_zf_lang1(B,E,A,D) = k1_zf_lang1(B,k1_zf_lang1(B,E,A,C),A,D))))))))))) # label(t78_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7205 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> k4_zf_lang1(A) = k3_zf_lang1(A))) # label(redefinition_k4_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7206 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> k3_zf_lang1(A) = k4_xboole_0(k2_relat_1(A),k3_enumset1(np__0,np__1,np__2,np__3,np__4)))) # label(d3_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7207 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> r2_zf_model(C,k11_zf_lang(k8_zf_lang(B,A),A)))))))) # label(t138_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7208 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (p1_s1_zf_lang1(A) & p1_s1_zf_lang1(B) -> p1_s1_zf_lang1(k7_zf_lang(A,B))))))) & (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (p1_s1_zf_lang1(A) -> p1_s1_zf_lang1(k8_zf_lang(B,A))))))) & (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (p1_s1_zf_lang1(A) -> p1_s1_zf_lang1(k6_zf_lang(A))))) & (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> p1_s1_zf_lang1(k4_zf_lang(A,B)) & p1_s1_zf_lang1(k5_zf_lang(A,B)))))) -> (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> p1_s1_zf_lang1(A))) # label(s1_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7209 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,C) -> (all E (v1_funct_1(E) & v1_funct_2(E,k1_zf_lang,C) & m2_relset_1(E,k1_zf_lang,C) -> (r1_zf_model(C,k1_zf_lang1(C,E,B,D),k8_zf_lang(B,A)) <-> r1_zf_model(C,E,k8_zf_lang(B,A))))))))))))) # label(t81_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7210 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v8_zf_lang(A) -> k21_zf_lang(A) = k20_zf_lang(k21_zf_lang(k20_zf_lang(A)))))) # label(t27_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7211 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (D != C -> (k6_zf_lang1(k8_zf_lang(C,B),D,E) = k8_zf_lang(C,A) <-> A = k6_zf_lang1(B,D,E))))))))))))) # label(t173_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7212 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) & -v1_xboole_0(C) -> v1_funct_1(k2_zf_lang1(A,B,C,D)) & m2_relset_1(k2_zf_lang1(A,B,C,D),A,C) & v1_funct_2(k2_zf_lang1(A,B,C,D),A,C))) # label(dt_k2_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7213 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) -> (v11_zf_lang(A) -> (r1_zf_model(B,C,A) <-> (exists D (m1_subset_1(D,B) & r1_zf_model(B,k1_zf_lang1(B,C,k23_zf_lang(A),D),k24_zf_lang(A)))))))))))) # label(t103_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7214 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v8_zf_lang(A) -> k20_zf_lang(k22_zf_lang(k20_zf_lang(A))) = k22_zf_lang(A)))) # label(t28_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7215 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> A = k20_zf_lang(k6_zf_lang(A)))) # label(t3_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7216 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v11_zf_lang(A) -> (B = k23_zf_lang(A) -> C = k23_zf_lang(k6_zf_lang1(A,B,C))) & (k23_zf_lang(A) != B -> k23_zf_lang(A) = k23_zf_lang(k6_zf_lang1(A,B,C))) & k6_zf_lang1(k24_zf_lang(A),B,C) = k24_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t195_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7217 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k11_zf_lang(A,B) = k21_zf_lang(k12_zf_lang(A,B)) & k22_zf_lang(k12_zf_lang(A,B)) = k11_zf_lang(B,A))))) # label(t36_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7218 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k2_xboole_0(k2_xboole_0(k29_zf_lang(A),k29_zf_lang(B)),k2_enumset1(k6_zf_lang(B),k6_zf_lang(A),k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k10_zf_lang(A,B))) = k29_zf_lang(k10_zf_lang(A,B)))))) # label(t61_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7219 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> -(r3_zf_lang(A,B) & r1_zf_lang(B,A)))))) # label(t50_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7220 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (exists E (m2_subset_1(E,k5_numbers,k1_zf_lang) & (exists F (m2_subset_1(F,k5_numbers,k1_zf_lang) & k4_zf_lang(E,F) = k5_zf_lang1(k4_zf_lang(A,B),C,D))))))))))))) # label(t167_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7221 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v5_zf_lang(A) -> k22_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k22_zf_lang(A),B,C) & k6_zf_lang1(k21_zf_lang(A),B,C) = k21_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t186_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7222 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (-(-(A != C & C != B & F = B & A = E) & -(F = B & E = D & B != C & A = C) & -(A != C & A = E & D = F & B = C) & -(F = D & D = E & B = C & C = A)) <-> k5_zf_lang(E,F) = k5_zf_lang1(k5_zf_lang(A,B),C,D)))))))))))))) # label(t168_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7223 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> B = k26_zf_lang(k11_zf_lang(A,B)) & k25_zf_lang(k11_zf_lang(A,B)) = A)))) # label(t6_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7224 (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) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> D = k2_zf_lang1(A,B,C,D)))))))))) # label(d2_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7225 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) -> r2_zf_model(C,k11_zf_lang(k11_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(B,k6_zf_lang(A)))) & r1_zf_model(C,D,k11_zf_lang(k11_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(B,k6_zf_lang(A)))))))))))) # label(t129_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7226 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k6_zf_lang1(k12_zf_lang(C,D),E,F) = k12_zf_lang(A,B) <-> A = k6_zf_lang1(C,E,F) & B = k6_zf_lang1(D,E,F)))))))))))))) # label(t177_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7227 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k6_zf_lang1(A,B,B) = A)))) # label(t197_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7228 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (-v1_xboole_0(D) -> r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,B),k11_zf_lang(k11_zf_lang(B,C),k11_zf_lang(A,C)))))))))))) # label(t112_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7229 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v10_zf_lang(A) -> k6_zf_lang1(k27_zf_lang(A),B,C) = k27_zf_lang(k6_zf_lang1(A,B,C)) & k6_zf_lang1(k28_zf_lang(A),B,C) = k28_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t194_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7230 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r2_zf_lang(k6_zf_lang(A),B) -> r3_zf_lang(A,B)))))) # label(t51_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7231 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) & v1_funct_1(C) -> (v6_zf_lang(A) -> (r1_zf_model(B,C,A) <-> (all D (m1_subset_1(D,B) -> r1_zf_model(B,k1_zf_lang1(B,C,k23_zf_lang(A),D),k24_zf_lang(A)))))))))))) # label(t99_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7232 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) -> r1_zf_model(C,D,k11_zf_lang(k10_zf_lang(A,B),k10_zf_lang(B,A))) & r2_zf_model(C,k11_zf_lang(k10_zf_lang(A,B),k10_zf_lang(B,A))))))))))) # label(t125_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7233 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k20_zf_lang(k10_zf_lang(A,B)) = k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)) & k6_zf_lang(A) = k25_zf_lang(k10_zf_lang(A,B)) & B = k26_zf_lang(k10_zf_lang(A,B)))))) # label(t34_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7234 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (exists B (A = k2_zf_lang(B) & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(t87_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7235 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> A = k24_zf_lang(k13_zf_lang(B,A)) & k23_zf_lang(k13_zf_lang(B,A)) = B)))) # label(t9_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7236 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v9_zf_lang(A) -> k20_zf_lang(k22_zf_lang(k20_zf_lang(A))) = k26_zf_lang(A)))) # label(t30_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7237 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (v6_zf_lang(A) <-> v6_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t184_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7238 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(B)) -> r2_zf_model(A,k11_zf_model(B))))))) # label(t6_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7239 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) -> (all B (v3_ordinal1(B) -> v1_funct_1(k7_relat_1(A,k4_classes1(B))) & v5_ordinal1(k7_relat_1(A,k4_classes1(B))) & v1_ordinal2(k7_relat_1(A,k4_classes1(B))) & v1_relat_1(k7_relat_1(A,k4_classes1(B))))))) # label(t11_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7240 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal1(B,A) -> (k1_relat_1(B) = k2_ordinal2(A) <-> v1_zf_refle(B,A)))))) # label(d5_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7241 $T # label(t20_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7242 (all A (m1_subset_1(A,f2_s2_zf_refle) -> (exists B (m1_ordinal4(B,f1_s2_zf_refle) & p1_s2_zf_refle(A,B))))) -> (exists A (k1_relat_1(A) = f2_s2_zf_refle & (all B (m1_subset_1(B,f2_s2_zf_refle) -> (exists C (m1_ordinal4(C,f1_s2_zf_refle) & (all D (m1_ordinal4(D,f1_s2_zf_refle) -> (p1_s2_zf_refle(B,D) -> r1_tarski(C,D)))) & p1_s2_zf_refle(B,C) & C = k1_funct_1(A,B))))) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7243 $T # label(t26_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7244 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (r2_hidden(k5_ordinal2,A) -> r2_zf_model(A,k9_zf_model)))) # label(t4_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7245 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> (all C (v2_relat_1(C) & v1_zf_refle(C,A) & m1_ordinal1(C,A) -> r2_hidden(B,k1_relat_1(C)))))))) # label(t23_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7246 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> (all C (m1_ordinal4(C,B) -> k1_zf_refle(A,B,C) = k3_card_3(k8_relat_1(B,k7_relat_1(A,k4_classes1(C)))))))))) # label(d2_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7247 (all A all B all C (v2_relat_1(B) & m1_ordinal4(C,A) & m1_ordinal1(B,A) & v1_zf_refle(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k5_zf_refle(A,B,C)) & m1_subset_1(k5_zf_refle(A,B,C),A))) # label(dt_k5_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7248 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> (all C (v2_relat_1(C) & v1_zf_refle(C,A) & m1_ordinal1(C,A) -> r1_tarski(k5_zf_refle(A,C,B),k4_zf_refle(A,C)))))))) # label(t24_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7249 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (exists B (m1_subset_1(B,A) & -v1_xboole_0(B))))) # label(rc1_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7250 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_ordinal4(B,A) & m1_ordinal4(C,A) -> k3_zf_refle(A,C,B) = k3_zf_refle(A,B,C))) # label(commutativity_k3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7251 $T # label(t19_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7252 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) -> v3_ordinal1(k3_card_3(A)))) # label(t12_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7253 $T # label(t16_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7254 $T # label(t1_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7255 (all A all B all C (-v1_xboole_0(A) & m1_ordinal4(B,A) & m1_ordinal4(C,A) & v1_classes2(A) -> m1_ordinal4(k3_zf_refle(A,B,C),A))) # label(dt_k3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7256 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r2_zf_model(A,k7_zf_model))) # label(t2_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7257 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) <-> r2_hidden(B,k2_ordinal2(A)))))) # label(t8_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7258 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_ordinal4(C,A) & m1_ordinal1(B,A) & v1_zf_refle(B,A) & v2_relat_1(B) -> k1_funct_1(B,C) = k5_zf_refle(A,B,C))) # label(redefinition_k5_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7259 (all A (m1_ordinal4(A,f1_s3_zf_refle) -> (exists B (m1_ordinal4(B,f1_s3_zf_refle) & p1_s3_zf_refle(A,B))))) & (all A (m1_ordinal4(A,f1_s3_zf_refle) -> (all B (m1_ordinal4(B,f1_s3_zf_refle) -> (all C (m1_ordinal4(C,f1_s3_zf_refle) -> (p1_s3_zf_refle(A,B) & p1_s3_zf_refle(A,C) -> B = C))))))) -> (exists A (m2_ordinal4(A,f1_s3_zf_refle) & (all B (m1_ordinal4(B,f1_s3_zf_refle) -> p1_s3_zf_refle(B,k4_ordinal4(f1_s3_zf_refle,A,B)))))) # label(s3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7260 (all A all B all C (v1_classes2(A) & m1_ordinal4(C,A) & m1_ordinal4(B,A) & -v1_xboole_0(A) -> k2_xboole_0(B,C) = k3_zf_refle(A,B,C))) # label(redefinition_k3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7261 $T # label(d3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7262 $T # label(t9_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7263 $T # label(t18_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7264 (all A (v3_ordinal1(A) -> k2_ordinal2(k4_classes1(A)) = A)) # label(t14_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7265 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_ordinal4(C,A) & m1_ordinal4(B,A) -> B = k3_zf_refle(A,B,B))) # label(idempotence_k3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7266 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (r2_hidden(B,A) -> r2_hidden(k7_ordinal2(B),A))))) # label(t28_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7267 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) -> k2_ordinal1(B,A) = k7_relat_1(B,k4_classes1(A)))))) # label(t15_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7268 (exists A (m2_ordinal4(A,f1_s4_zf_refle) & (all B (m1_ordinal4(B,f1_s4_zf_refle) -> f3_s4_zf_refle(B,k4_ordinal4(f1_s4_zf_refle,A,B)) = k4_ordinal4(f1_s4_zf_refle,A,k6_ordinal4(f1_s4_zf_refle,B)))) & (all B (m1_ordinal4(B,f1_s4_zf_refle) -> (v4_ordinal1(B) -> B = k2_ordinal4(f1_s4_zf_refle) | f4_s4_zf_refle(B,k2_ordinal1(A,B)) = k4_ordinal4(f1_s4_zf_refle,A,B)))) & k4_ordinal4(f1_s4_zf_refle,A,k2_ordinal4(f1_s4_zf_refle)) = f2_s4_zf_refle)) # label(s4_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7269 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> k2_zf_refle(k2_ordinal1(C,B),A,B) = k3_card_3(k2_ordinal1(C,B)) & k2_zf_refle(C,A,B) = k3_card_3(k2_ordinal1(C,B)))))))) # label(t17_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7270 (all A all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> v3_ordinal1(k3_card_3(k8_relat_1(A,B))))) # label(t13_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7271 $T # label(d4_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7272 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> v1_relat_1(k7_relat_1(A,k4_classes1(B))) & v5_ordinal1(k7_relat_1(A,k4_classes1(B))) & v1_funct_1(k7_relat_1(A,k4_classes1(B))))))) # label(t10_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7273 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(A,B) <-> (all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d1_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7274 (all A all B (v2_relat_1(B) & m1_ordinal1(B,A) & v1_zf_refle(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k3_card_3(B) = k4_zf_refle(A,B))) # label(redefinition_k4_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.84 7275 p1_s5_zf_refle(k2_ordinal4(f1_s5_zf_refle)) & (all A (m1_ordinal4(A,f1_s5_zf_refle) -> (p1_s5_zf_refle(A) -> p1_s5_zf_refle(k6_ordinal4(f1_s5_zf_refle,A))))) & (all A (m1_ordinal4(A,f1_s5_zf_refle) -> ((all B (m1_ordinal4(B,f1_s5_zf_refle) -> (r2_hidden(B,A) -> p1_s5_zf_refle(B)))) & v4_ordinal1(A) -> k2_ordinal4(f1_s5_zf_refle) = A | p1_s5_zf_refle(A)))) -> (all A (m1_ordinal4(A,f1_s5_zf_refle) -> p1_s5_zf_refle(A))) # label(s5_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7276 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & -v1_xboole_0(B) & m1_ordinal4(C,B) & v1_classes2(B) -> m1_ordinal4(k2_zf_refle(A,B,C),B))) # label(dt_k2_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7277 $T # label(t21_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7278 $T # label(dt_k1_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7279 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r2_zf_model(A,k8_zf_model))) # label(t3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7280 (all A all B (-v1_xboole_0(A) & m1_ordinal1(B,A) & v1_zf_refle(B,A) & v2_relat_1(B) & v1_classes2(A) -> m1_subset_1(k4_zf_refle(A,B),k1_zfmisc_1(A)) & -v1_xboole_0(k4_zf_refle(A,B)))) # label(dt_k4_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7281 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal1(B,A) & v1_zf_refle(B,A) & v2_relat_1(B) -> (r2_hidden(k5_ordinal2,A) & (all C (m1_ordinal4(C,A) -> (all D (m1_ordinal4(D,A) -> (r2_hidden(C,D) -> r1_tarski(k5_zf_refle(A,B,C),k5_zf_refle(A,B,D))))))) & (all C (m1_ordinal4(C,A) -> (v4_ordinal1(C) -> k5_zf_refle(A,B,C) = k3_card_3(k2_ordinal1(B,C)) | C = k1_xboole_0))) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (exists D (v2_ordinal2(D) & (all E (m1_ordinal4(E,A) -> (E = k4_ordinal4(A,D,E) -> (all F (m2_relset_1(F,k1_zf_lang,k5_zf_refle(A,B,E)) & v1_funct_2(F,k1_zf_lang,k5_zf_refle(A,B,E)) & v1_funct_1(F) -> (r1_zf_model(k4_zf_refle(A,B),k2_zf_lang1(k1_zf_lang,k5_zf_refle(A,B,E),k4_zf_refle(A,B),F),C) <-> r1_zf_model(k5_zf_refle(A,B,E),F,C)))) | E = k1_xboole_0))) & v3_ordinal2(D) & m2_ordinal4(D,A)))))))))) # label(t29_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7282 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (exists B (m1_ordinal1(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_zf_refle(B,A) & v5_ordinal1(B) & v1_funct_1(B))))) # label(rc2_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7283 (all A r1_tarski(k7_ordinal2(A),k1_ordinal1(k3_tarski(k2_ordinal2(A))))) # label(t27_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7284 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (r2_hidden(k5_ordinal2,A) -> v1_zf_model(A)))) # label(t7_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7285 (all A (m1_subset_1(A,f1_s1_zf_refle) -> (exists B (p1_s1_zf_refle(A,B) & v3_ordinal1(B))))) -> (exists A (v1_relat_1(A) & (all B (m1_subset_1(B,f1_s1_zf_refle) -> (exists C ((all D (v3_ordinal1(D) -> (p1_s1_zf_refle(B,D) -> r1_tarski(C,D)))) & p1_s1_zf_refle(B,C) & C = k1_funct_1(A,B) & v3_ordinal1(C))))) & k1_relat_1(A) = f1_s1_zf_refle & v1_funct_1(A))) # label(s1_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7286 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_zf_model(A,k10_zf_model))) # label(t5_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7287 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & -v1_xboole_0(B) & m1_ordinal4(C,B) & v1_classes2(B) & v1_ordinal2(A) -> k1_zf_refle(A,B,C) = k2_zf_refle(A,B,C))) # label(redefinition_k2_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7288 $T # label(t22_zf_refle) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7289 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(B,C) <-> r1_zfrefle1(A,C)))) <-> r2_zfrefle1(A,B)))))) # label(t8_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7290 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_zfrefle1(A,B) -> r2_zfrefle1(B,A)))) # label(symmetry_r2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7291 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,B) & r1_zfrefle1(A,C) -> r1_zfrefle1(A,k4_subset_1(k9_zf_lang,B,C))))))))) # label(t3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7292 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r4_zfrefle1(A,A))) # label(reflexivity_r4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7293 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) -> (v3_ordinal2(B) & v2_ordinal2(B) -> v3_ordinal2(k1_ordinal3(A,B))))))) # label(t17_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7294 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> r2_zfrefle1(A,A))) # label(reflexivity_r2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7295 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(A),k8_ordinal2(A)))) # label(t20_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7296 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> -(r2_hidden(k5_ordinal2,A) & v2_ordinal2(C) & (all D (m1_ordinal4(D,A) -> -(D = k4_ordinal4(A,C,D) & r2_hidden(B,D)))) & v3_ordinal2(C)))))))) # label(t30_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7297 $T # label(t18_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7298 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_zfrefle1(A,B) & v1_ordinal1(B) & v1_zf_model(A) -> v1_zf_model(B)))))) # label(t10_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7299 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v1_zf_refle(B,A) & m1_ordinal1(B,A) & v2_relat_1(B) -> -(r2_hidden(k5_ordinal2,A) & (all C (m2_ordinal4(C,A) -> -(v2_ordinal2(C) & (all D (m1_ordinal4(D,A) -> (D = k4_ordinal4(A,C,D) -> r2_zfrefle1(k5_zf_refle(A,B,D),k4_zf_refle(A,B)) | k1_xboole_0 = D))) & v3_ordinal2(C)))) & (all C (m1_ordinal4(C,A) -> (v4_ordinal1(C) -> k5_zf_refle(A,B,C) = k3_card_3(k2_ordinal1(B,C)) | k1_xboole_0 = C))) & (all C (m1_ordinal4(C,A) -> (all D (m1_ordinal4(D,A) -> (r2_hidden(C,D) -> r1_tarski(k5_zf_refle(A,B,C),k5_zf_refle(A,B,D)))))))))))) # label(t38_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7300 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & v1_ordinal2(C) & r1_tarski(k2_relat_1(C),A) & k8_ordinal2(C) = A & v2_ordinal2(C) & B = k1_relat_1(C) & v5_ordinal1(C)))))))) # label(d5_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7301 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> r3_zfrefle1(A,A))) # label(reflexivity_r3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7302 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -((all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(k4_classes1(B) = C & v1_zf_model(C) & r4_zfrefle1(B,k5_ordinal2)))))) & r2_hidden(k5_ordinal2,A)))) # label(t42_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7303 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> r2_hidden(k4_classes1(B),A))))) # label(t33_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7304 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) & v1_funct_2(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) -> -(r2_hidden(k1_card_1(B),k1_card_1(A)) & (all D (m2_ordinal4(D,A) -> -(v2_ordinal2(D) & (all E (m1_ordinal4(E,A) -> (v4_ordinal1(E) -> k8_ordinal2(k2_ordinal1(D,E)) = k4_ordinal4(A,D,E) | k2_ordinal4(A) = E))) & (all E (m1_ordinal4(E,A) -> k4_ordinal4(A,D,k6_ordinal4(A,E)) = k7_ordinal2(k2_xboole_0(k1_tarski(k4_ordinal4(A,D,E)),k9_relat_1(k4_funct_5(C),k2_zfmisc_1(B,k1_tarski(k6_ordinal4(A,E)))))))) & k4_ordinal4(A,D,k2_ordinal4(A)) = k2_ordinal4(A) & v3_ordinal2(D))))))))))) # label(t14_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7305 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> -r4_zfrefle1(k2_ordinal2(A),B))))) # label(t29_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.85 7306 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> ((all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r2_zf_model(B,C) <-> r2_zf_model(A,C)))) <-> r2_zfrefle1(A,B)))))) # label(t7_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7307 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> -(r2_hidden(k5_ordinal2,A) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> -(r3_zfrefle1(D,A) & D = k4_classes1(C) & r2_hidden(B,C))))))))))) # label(t36_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7308 (all A (-v1_xboole_0(A) -> r1_zfrefle1(A,k1_subset_1(k9_zf_lang)))) # label(t1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7309 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(r4_zfrefle1(A,k1_ordinal1(B)) & (all C (v3_ordinal1(C) -> A != k1_ordinal1(C)))))))) # label(t26_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7310 (all A -(r2_hidden(A,f1_s1_zfrefle1) & (all B -p1_s1_zfrefle1(A,B)))) -> (exists A (f1_s1_zfrefle1 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s1_zfrefle1) -> p1_s1_zfrefle1(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7311 (all A (v3_ordinal1(A) -> r4_zfrefle1(k1_ordinal1(A),k4_ordinal2))) # label(t25_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7312 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,B) <-> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (r2_hidden(C,B) -> r2_zf_model(A,C))))))))) # label(d1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7313 (all A all B (r2_wellord2(A,B) | k1_card_1(A) = k1_card_1(B) -> k1_card_1(k1_zfmisc_1(B)) = k1_card_1(k1_zfmisc_1(A)) & r2_wellord2(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t13_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7314 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal1(B,A) & v1_zf_refle(B,A) & v2_relat_1(B) -> -(r2_hidden(k5_ordinal2,A) & (all C (m1_ordinal4(C,A) -> (all D (m1_ordinal4(D,A) -> (r2_hidden(C,D) -> r1_tarski(k5_zf_refle(A,B,C),k5_zf_refle(A,B,D))))))) & (all C (m1_ordinal4(C,A) -> (v4_ordinal1(C) -> k5_zf_refle(A,B,C) = k3_card_3(k2_ordinal1(B,C)) | C = k1_xboole_0))) & (all C (m2_ordinal4(C,A) -> -(v3_ordinal2(C) & (all D (m1_ordinal4(D,A) -> (D = k4_ordinal4(A,C,D) -> r3_zfrefle1(k5_zf_refle(A,B,D),k4_zf_refle(A,B)) | D = k1_xboole_0))) & v2_ordinal2(C))))))))) # label(t32_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7315 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> -(r2_hidden(k5_ordinal2,B) & r2_hidden(A,B) & (all C (-v1_xboole_0(C) -> -(v1_zf_model(C) & r2_hidden(C,B) & r2_hidden(A,C))))))) # label(t43_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7316 $T # label(t11_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7317 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) -> (v4_ordinal1(A) <-> v4_ordinal1(B))))))) # label(t27_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7318 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) & r1_zfrefle1(A,k2_zfrefle1) -> v1_zf_model(A)))) # label(t5_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7319 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> -(v2_ordinal2(C) & v3_ordinal2(C) & (all D (m1_ordinal4(D,A) -> -(r4_zfrefle1(D,k5_ordinal2) & k4_ordinal4(A,C,D) = D & r2_hidden(B,D)))) & r2_hidden(k5_ordinal2,A)))))))) # label(t31_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7320 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(k4_classes1(B) = C & r2_zfrefle1(C,A) & r4_zfrefle1(B,k5_ordinal2)))))) & r2_hidden(k5_ordinal2,A)))) # label(t41_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7321 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (exists B (v1_zf_lang(B) & k2_zf_model(B) = k1_xboole_0 & (all C (-v1_xboole_0(C) -> (r2_zf_model(C,A) <-> r2_zf_model(C,B)))) & m2_finseq_1(B,k5_numbers))))) # label(t6_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7322 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> (v4_ordinal1(k1_relat_1(B)) & r1_ordinal2(A,B) & v2_ordinal2(B) -> r4_zfrefle1(A,k1_relat_1(B)) | k1_relat_1(B) = k1_xboole_0))))) # label(t24_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7323 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(k1_relat_1(A),B) & r1_tarski(k2_relat_1(A),B) -> r2_hidden(k2_relat_1(A),B)))))) # label(t12_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7324 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r3_zfrefle1(A,B) -> r2_zfrefle1(A,B)))))) # label(t9_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7325 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) -> r1_tarski(B,A)))))) # label(t22_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7326 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C) -> k2_ordinal1(k1_ordinal3(A,C),B) = k1_ordinal3(A,k2_ordinal1(C,B)))))))) # label(t16_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7327 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_zfrefle1(A,B) & r4_zfrefle1(B,C) -> r4_zfrefle1(A,C)))))))) # label(t21_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7328 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(C = k4_classes1(B) & r3_zfrefle1(C,A) & r4_zfrefle1(B,k5_ordinal2)))))) & r2_hidden(k5_ordinal2,A)))) # label(t37_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7329 (all A (v3_ordinal1(A) -> (r4_zfrefle1(A,k1_xboole_0) -> A = k1_xboole_0))) # label(t28_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7330 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_zfrefle1(A,B) <-> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (k1_xboole_0 = k2_zf_model(C) -> (r2_zf_model(B,C) <-> r2_zf_model(A,C)))))))))) # label(d2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7331 (all A ((all B (-(k8_zf_model != B & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> -(r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(C)) & k11_zf_model(C) = B))) & B != k10_zf_model & B != k9_zf_model & k7_zf_model != B & B != k6_zf_model) & r2_hidden(B,k9_zf_lang) <-> r2_hidden(B,A))) <-> k1_zfrefle1 = A)) # label(d4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7332 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) & r4_zfrefle1(B,A) -> B = A))))) # label(t23_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7333 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,C) & r1_tarski(B,C) -> r1_zfrefle1(A,B)))))))) # label(t2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7334 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> -(r2_hidden(k5_ordinal2,A) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> -(k4_classes1(C) = D & r2_zfrefle1(D,A) & r2_hidden(B,C))))))))))) # label(t40_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7335 $T # label(dt_k1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7336 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> (k1_xboole_0 != B -> m1_subset_1(k4_classes1(B),A) & -v1_xboole_0(k4_classes1(B))))))) # label(t34_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7337 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> (v2_ordinal2(B) -> v2_ordinal2(k1_ordinal3(A,B))))))) # label(t15_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7338 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -(r2_hidden(k5_ordinal2,A) & (all B (m2_ordinal4(B,A) -> -(v3_ordinal2(B) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> (k4_classes1(C) = D & C = k4_ordinal4(A,B,C) -> C = k1_xboole_0 | r2_zfrefle1(D,A)))))) & v2_ordinal2(B))))))) # label(t39_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7339 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m2_ordinal4(B,A) -> -(v2_ordinal2(B) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> (D = k4_classes1(C) & C = k4_ordinal4(A,B,C) -> k1_xboole_0 = C | r3_zfrefle1(D,A)))))) & v3_ordinal2(B)))) & r2_hidden(k5_ordinal2,A)))) # label(t35_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7340 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> ((all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,A) & m2_relset_1(D,k1_zf_lang,A) -> (r1_zf_model(A,D,C) <-> r1_zf_model(B,k2_zf_lang1(k1_zf_lang,A,B,D),C)))))) & r1_tarski(A,B) <-> r3_zfrefle1(A,B)))))) # label(d3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7341 (all A (-v1_xboole_0(A) -> (v1_zf_model(A) -> r1_zfrefle1(A,k2_zfrefle1)))) # label(t4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7342 (all A all B (v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) -> v3_ordinal1(A)))) # label(t19_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7343 $T # label(t5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7344 $T # label(t7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7345 (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]. 115.88/113.86 7346 (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]. 115.88/113.86 7347 (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]. 115.88/113.86 7348 (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]. 115.88/113.86 7349 (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]. 115.88/113.86 7350 (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]. 115.88/113.86 7351 (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]. 115.88/113.86 7352 (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]. 115.88/113.86 7353 (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]. 115.88/113.86 7354 (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]. 115.88/113.86 7355 $T # label(t42_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7356 $T # label(t11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7357 (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]. 115.88/113.86 7358 (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]. 115.88/113.86 7359 (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]. 115.88/113.86 7360 $T # label(t20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7361 (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]. 115.88/113.86 7362 (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]. 115.88/113.86 7363 $T # label(t26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7364 $T # label(t38_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7365 (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]. 115.88/113.86 7366 (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]. 115.88/113.86 7367 (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]. 115.88/113.86 7368 $T # label(t16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7369 $T # label(t24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7370 (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]. 115.88/113.86 7371 (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]. 115.88/113.86 7372 $T # label(t32_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7373 $T # label(t40_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7374 $T # label(t14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7375 (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]. 115.88/113.86 7376 (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]. 115.88/113.86 7377 $T # label(t41_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7378 $T # label(t28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7379 $T # label(t3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7380 $T # label(t17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7381 $T # label(dt_k1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7382 $T # label(t27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7383 (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]. 115.88/113.86 7384 $T # label(t30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7385 (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]. 115.88/113.86 7386 (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]. 115.88/113.86 7387 (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]. 115.88/113.86 7388 (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]. 115.88/113.86 7389 (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]. 115.88/113.86 7390 (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]. 115.88/113.86 7391 $T # label(t19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7392 (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]. 115.88/113.86 7393 $T # label(t43_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7394 (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]. 115.88/113.86 7395 (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]. 115.88/113.86 7396 (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]. 115.88/113.86 7397 (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]. 115.88/113.86 7398 $T # label(t44_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7399 (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]. 115.88/113.86 7400 $T # label(t12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7401 (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]. 115.88/113.86 7402 $T # label(t18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7403 $T # label(t15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7404 (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]. 115.88/113.86 7405 (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]. 115.88/113.86 7406 (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]. 115.88/113.86 7407 (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]. 115.88/113.86 7408 $T # label(t29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7409 (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]. 115.88/113.86 7410 (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]. 115.88/113.86 7411 (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]. 115.88/113.86 7412 (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]. 115.88/113.86 7413 $T # label(t39_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.86 7414 (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]. 115.88/113.87 7415 $T # label(t6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.87 7416 (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]. 115.88/113.87 7417 (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]. 115.88/113.87 7418 (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]. 115.88/113.87 7419 $T # label(t25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.87 7420 (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]. 115.88/113.87 7421 (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]. 115.88/113.87 7422 $T # label(t31_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.87 7423 (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]. 115.88/113.87 7424 $T # label(t8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.87 7425 (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]. 115.88/113.87 7426 (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]. 115.88/113.87 7427 (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]. 115.88/113.87 7428 (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]. 115.88/113.87 7429 (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]. 115.88/113.87 7430 $T # label(t13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.87 7431 $T # label(t9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.87 7432 (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]. 115.88/113.87 7433 $T # label(t22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.87 7434 (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]. 115.88/113.87 7435 (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]. 115.88/113.87 7436 $T # label(dt_k5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.87 7437 (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]. 115.88/113.88 7438 (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]. 115.88/113.88 7439 (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]. 115.88/113.88 7440 (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]. 115.88/113.88 7441 (all A (m1_subset_1(A,k8_qc_lang1) -> A = k10_qc_lang1(A))) # label(d12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7442 (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]. 115.88/113.88 7443 (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]. 115.88/113.88 7444 (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]. 115.88/113.88 7445 (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]. 115.88/113.88 7446 (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]. 115.88/113.88 7447 (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]. 115.88/113.88 7448 (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]. 115.88/113.88 7449 (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]. 115.88/113.88 7450 (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]. 115.88/113.88 7451 (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]. 115.88/113.88 7452 (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]. 115.88/113.88 7453 (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]. 115.88/113.88 7454 (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]. 115.88/113.88 7455 (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]. 115.88/113.88 7456 (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]. 115.88/113.88 7457 (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]. 115.88/113.88 7458 (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]. 115.88/113.88 7459 (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]. 115.88/113.88 7460 $T # label(t57_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7461 (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]. 115.88/113.88 7462 (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]. 115.88/113.88 7463 (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]. 115.88/113.88 7464 (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]. 115.88/113.88 7465 $T # label(t43_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7466 $T # label(t70_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7467 (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]. 115.88/113.88 7468 (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]. 115.88/113.88 7469 (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]. 115.88/113.88 7470 (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]. 115.88/113.88 7471 (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]. 115.88/113.88 7472 (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]. 115.88/113.88 7473 (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]. 115.88/113.88 7474 (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]. 115.88/113.88 7475 (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]. 115.88/113.88 7476 (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]. 115.88/113.88 7477 (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]. 115.88/113.88 7478 (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]. 115.88/113.88 7479 (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]. 115.88/113.88 7480 (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]. 115.88/113.88 7481 (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]. 115.88/113.88 7482 (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]. 115.88/113.88 7483 (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]. 115.88/113.88 7484 $T # label(t41_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7485 (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]. 115.88/113.88 7486 (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]. 115.88/113.88 7487 $T # label(dt_k15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7488 (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]. 115.88/113.88 7489 (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]. 115.88/113.88 7490 $T # label(t44_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7491 (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]. 115.88/113.88 7492 (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]. 115.88/113.88 7493 (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]. 115.88/113.88 7494 (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]. 115.88/113.88 7495 $T # label(t102_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7496 $T # label(t40_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7497 (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]. 115.88/113.88 7498 (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]. 115.88/113.88 7499 (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]. 115.88/113.88 7500 (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]. 115.88/113.88 7501 (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]. 115.88/113.88 7502 (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]. 115.88/113.88 7503 (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]. 115.88/113.88 7504 (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]. 115.88/113.88 7505 (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]. 115.88/113.88 7506 (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]. 115.88/113.88 7507 $T # label(t68_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7508 (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]. 115.88/113.88 7509 (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]. 115.88/113.88 7510 (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]. 115.88/113.88 7511 (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]. 115.88/113.88 7512 (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]. 115.88/113.88 7513 (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]. 115.88/113.88 7514 (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]. 115.88/113.88 7515 $T # label(t11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7516 (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]. 115.88/113.88 7517 (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]. 115.88/113.88 7518 (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]. 115.88/113.88 7519 (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]. 115.88/113.88 7520 $T # label(t34_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7521 (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]. 115.88/113.88 7522 (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]. 115.88/113.88 7523 (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]. 115.88/113.88 7524 (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]. 115.88/113.88 7525 (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]. 115.88/113.88 7526 $T # label(t12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7527 $T # label(t15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7528 (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]. 115.88/113.88 7529 (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]. 115.88/113.88 7530 (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]. 115.88/113.88 7531 $T # label(t35_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7532 (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]. 115.88/113.88 7533 (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]. 115.88/113.88 7534 (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]. 115.88/113.88 7535 $T # label(t69_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.88 7536 (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]. 115.88/113.89 7537 (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]. 115.88/113.89 7538 $T # label(t36_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7539 (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]. 115.88/113.89 7540 (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]. 115.88/113.89 7541 $T # label(t106_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7542 (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]. 115.88/113.89 7543 (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]. 115.88/113.89 7544 (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]. 115.88/113.89 7545 (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]. 115.88/113.89 7546 (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]. 115.88/113.89 7547 (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]. 115.88/113.89 7548 (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]. 115.88/113.89 7549 (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]. 115.88/113.89 7550 (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]. 115.88/113.89 7551 $T # label(t10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7552 (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]. 115.88/113.89 7553 (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]. 115.88/113.89 7554 $T # label(t9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7555 (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]. 115.88/113.89 7556 (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]. 115.88/113.89 7557 (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]. 115.88/113.89 7558 (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]. 115.88/113.89 7559 $T # label(d17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7560 $T # label(t37_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7561 (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]. 115.88/113.89 7562 (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]. 115.88/113.89 7563 (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]. 115.88/113.89 7564 (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]. 115.88/113.89 7565 (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]. 115.88/113.89 7566 (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]. 115.88/113.89 7567 (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]. 115.88/113.89 7568 (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]. 115.88/113.89 7569 (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]. 115.88/113.89 7570 (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]. 115.88/113.89 7571 (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]. 115.88/113.89 7572 (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]. 115.88/113.89 7573 (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]. 115.88/113.89 7574 (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]. 115.88/113.89 7575 (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]. 115.88/113.89 7576 (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]. 115.88/113.89 7577 (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]. 115.88/113.89 7578 $T # label(t39_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7579 (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]. 115.88/113.89 7580 (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]. 115.88/113.89 7581 (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]. 115.88/113.89 7582 (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]. 115.88/113.89 7583 (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]. 115.88/113.89 7584 (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]. 115.88/113.89 7585 (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]. 115.88/113.89 7586 (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]. 115.88/113.89 7587 (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]. 115.88/113.89 7588 (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]. 115.88/113.89 7589 (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]. 115.88/113.89 7590 (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]. 115.88/113.89 7591 (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]. 115.88/113.89 7592 (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]. 115.88/113.89 7593 (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]. 115.88/113.89 7594 (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]. 115.88/113.89 7595 (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]. 115.88/113.89 7596 (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]. 115.88/113.89 7597 $T # label(t42_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7598 (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]. 115.88/113.89 7599 (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]. 115.88/113.89 7600 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) -> (v3_qc_lang1(A) -> k4_qc_lang3(B,A) = k4_qc_lang3(B,k17_qc_lang1(A))))))) # label(t49_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7601 (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) -> k6_qc_lang3(k9_qc_lang1(B,C)) = a_2_3_qc_lang3(A,C))))))) # label(t77_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7602 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) & m1_finseq_1(A,k1_qc_lang1) -> m1_subset_1(k1_qc_lang3(A,B),k1_zfmisc_1(B)))) # label(dt_k1_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7603 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k5_qc_lang3(B) = k5_qc_lang3(k14_qc_lang1(A,B)))))) # label(t70_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7604 (all A all B all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) & m1_subset_1(B,k8_qc_lang1) -> (r2_hidden(A,a_2_1_qc_lang3(B,C)) <-> (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & k1_funct_1(k16_qc_lang1(B),D) = A & r1_xreal_0(D,k3_finseq_1(k16_qc_lang1(B))) & r2_hidden(k1_funct_1(k16_qc_lang1(B),D),C) & r1_xreal_0(np__1,D)))))) # label(fraenkel_a_2_1_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7605 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> k6_subset_1(k2_qc_lang1,k24_qc_lang1(k21_qc_lang1(A)),k23_qc_lang1(k20_qc_lang1(A))) = k24_qc_lang1(A)))) # label(t15_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.89 7606 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k24_qc_lang1(k4_qc_lang2(A,B)) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(A),k24_qc_lang1(B)))))) # label(t22_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7607 (all A (m2_subset_1(A,k1_qc_lang1,k4_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> B != A)))) # label(t42_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7608 $T # label(t75_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7609 (all A (m1_subset_1(A,k8_qc_lang1) -> k4_qc_lang3(k3_qc_lang1,A) = k6_qc_lang3(A))) # label(d7_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7610 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v6_qc_lang1(k2_qc_lang2(A,B)) <-> v6_qc_lang1(B) & v6_qc_lang1(A)))))) # label(t30_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7611 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,f1_s3_qc_lang3) -> ((exists C (v1_funct_1(C) & v1_funct_2(C,k8_qc_lang1,f1_s3_qc_lang3) & (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,f1_s3_qc_lang3) -> (all F (m1_subset_1(F,f1_s3_qc_lang3) -> (k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k21_qc_lang1(D)) = E & v5_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f7_s3_qc_lang3(D,E)) & (k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k18_qc_lang1(D)) = E & F = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k19_qc_lang1(D)) & v4_qc_lang1(D) -> f6_s3_qc_lang3(E,F) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D)) & (E = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k17_qc_lang1(D)) & v3_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f5_s3_qc_lang3(E)) & (v2_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f4_s3_qc_lang3(D)) & (D = k11_qc_lang1 -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f3_s3_qc_lang3))))))) & B = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,A) & m2_relset_1(C,k8_qc_lang1,f1_s3_qc_lang3))) <-> f2_s3_qc_lang3(A) = B))))) -> f3_s3_qc_lang3 = f2_s3_qc_lang3(k11_qc_lang1) # label(s3_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7612 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k4_subset_1(k2_qc_lang1,k24_qc_lang1(A),k24_qc_lang1(B)) = k24_qc_lang1(k2_qc_lang2(A,B)))))) # label(t20_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7613 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k4_subset_1(k2_qc_lang1,k24_qc_lang1(A),k24_qc_lang1(B)) = k24_qc_lang1(k13_qc_lang1(A,B)))))) # label(t14_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7614 $T # label(t43_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7615 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(B) -> (v4_qc_lang2(A) -> k4_qc_lang3(B,k17_qc_lang1(k21_qc_lang1(k17_qc_lang1(A)))) = k4_qc_lang3(B,A)))))) # label(t62_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7616 (all A (m1_subset_1(A,k8_qc_lang1) -> k4_qc_lang3(k4_qc_lang1,A) = k5_qc_lang3(A))) # label(d6_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7617 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> k24_qc_lang1(A) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(k10_qc_lang2(A)),k24_qc_lang1(k11_qc_lang2(A)))))) # label(t17_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7618 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k4_subset_1(k4_qc_lang1,k5_qc_lang3(A),k5_qc_lang3(B)) = k5_qc_lang3(k13_qc_lang1(A,B)))))) # label(t69_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7619 (all A all B all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) & m2_finseq_1(B,k1_qc_lang1) -> ((exists D (m2_subset_1(D,k1_numbers,k5_numbers) & r2_hidden(k1_funct_1(B,D),C) & r1_xreal_0(D,k3_finseq_1(B)) & r1_xreal_0(np__1,D) & k1_funct_1(B,D) = A)) <-> r2_hidden(A,a_2_0_qc_lang3(B,C))))) # label(fraenkel_a_2_0_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7620 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k3_qc_lang3(A) = k4_tarski(np__6,A))) # label(d4_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 115.88/113.91 7621 (all A (m2_subset_1(A,k1_qc_lang1,k3_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> B != A)))) # label(t41_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.75 7622 $T # label(t37_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.75 7623 (exists A ((exists B (v1_funct_2(B,k8_qc_lang1,f1_s2_qc_lang3) & m2_relset_1(B,k8_qc_lang1,f1_s2_qc_lang3) & (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,f1_s2_qc_lang3) -> (all E (m1_subset_1(E,f1_s2_qc_lang3) -> (C = k11_qc_lang1 -> f2_s2_qc_lang3 = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,C)) & (v5_qc_lang1(C) & D = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,k21_qc_lang1(C)) -> k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,C) = f7_s2_qc_lang3(C,D)) & (k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,k19_qc_lang1(C)) = E & D = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,k18_qc_lang1(C)) & v4_qc_lang1(C) -> k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,C) = f6_s2_qc_lang3(D,E)) & (v3_qc_lang1(C) & k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,k17_qc_lang1(C)) = D -> f5_s2_qc_lang3(D) = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,C)) & (v2_qc_lang1(C) -> f4_s2_qc_lang3(C) = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,C)))))))) & k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,B,f3_s2_qc_lang3) = A & v1_funct_1(B))) & m1_subset_1(A,f1_s2_qc_lang3))) # label(s2_qc_lang3_AndLHS) # label(axiom) # label(non_clause). [assumption]. 266.79/264.75 7624 (all A (m1_subset_1(A,f1_s2_qc_lang3) -> (all B (m1_subset_1(B,f1_s2_qc_lang3) -> -((exists C (m2_relset_1(C,k8_qc_lang1,f1_s2_qc_lang3) & A = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,f3_s2_qc_lang3) & (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,f1_s2_qc_lang3) -> (all F (m1_subset_1(F,f1_s2_qc_lang3) -> (D = k11_qc_lang1 -> k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f2_s2_qc_lang3) & (v2_qc_lang1(D) -> f4_s2_qc_lang3(D) = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D)) & (v3_qc_lang1(D) & E = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k17_qc_lang1(D)) -> f5_s2_qc_lang3(E) = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D)) & (v4_qc_lang1(D) & F = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k19_qc_lang1(D)) & E = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k18_qc_lang1(D)) -> f6_s2_qc_lang3(E,F) = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D)) & (k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k21_qc_lang1(D)) = E & v5_qc_lang1(D) -> f7_s2_qc_lang3(D,E) = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D)))))))) & v1_funct_2(C,k8_qc_lang1,f1_s2_qc_lang3) & v1_funct_1(C))) & (exists C (v1_funct_1(C) & m2_relset_1(C,k8_qc_lang1,f1_s2_qc_lang3) & (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,f1_s2_qc_lang3) -> (all F (m1_subset_1(F,f1_s2_qc_lang3) -> (k11_qc_lang1 = D -> f2_s2_qc_lang3 = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D)) & (F = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k19_qc_lang1(D)) & k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k18_qc_lang1(D)) = E & v4_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f6_s2_qc_lang3(E,F)) & (E = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k21_qc_lang1(D)) & v5_qc_lang1(D) -> f7_s2_qc_lang3(D,E) = k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D)) & (k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,k17_qc_lang1(D)) = E & v3_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f5_s2_qc_lang3(E)) & (v2_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,D) = f4_s2_qc_lang3(D)))))))) & k8_funct_2(k8_qc_lang1,f1_s2_qc_lang3,C,f3_s2_qc_lang3) = B & v1_funct_2(C,k8_qc_lang1,f1_s2_qc_lang3))) & B != A))))) # label(s2_qc_lang3_AndRHS) # label(axiom) # label(non_clause). [assumption]. 266.79/264.75 7625 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k6_qc_lang3(k13_qc_lang1(A,B)) = k4_subset_1(k3_qc_lang1,k6_qc_lang3(A),k6_qc_lang3(B)))))) # label(t80_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.75 7626 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k5_qc_lang3(k4_qc_lang2(A,B)) = k4_subset_1(k4_qc_lang1,k5_qc_lang3(A),k5_qc_lang3(B)))))) # label(t73_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.75 7627 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k4_subset_1(k3_qc_lang1,k6_qc_lang3(A),k6_qc_lang3(B)) = k6_qc_lang3(k4_qc_lang2(A,B)))))) # label(t84_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7628 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(B) -> (v5_qc_lang1(A) -> k4_qc_lang3(B,k21_qc_lang1(A)) = k4_qc_lang3(B,A)))))) # label(t54_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7629 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) -> (v4_qc_lang1(A) -> k4_subset_1(B,k4_qc_lang3(B,k18_qc_lang1(A)),k4_qc_lang3(B,k19_qc_lang1(A))) = k4_qc_lang3(B,A)))))) # label(t52_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7630 (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,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(C) -> k4_qc_lang3(C,B) = k4_qc_lang3(C,k14_qc_lang1(A,B)))))))) # label(t55_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7631 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k2_qc_lang3(A) = k2_qc_lang3(B) -> B = A))))) # label(t35_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7632 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) -> k4_subset_1(k2_qc_lang1,k24_qc_lang1(k12_qc_lang2(A)),k24_qc_lang1(k11_qc_lang2(A))) = k24_qc_lang1(A)))) # label(t19_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7633 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k4_subset_1(k4_qc_lang1,k5_qc_lang3(A),k5_qc_lang3(B)) = k5_qc_lang3(k2_qc_lang2(A,B)))))) # label(t72_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7634 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) -> k4_subset_1(C,k4_qc_lang3(C,A),k4_qc_lang3(C,B)) = k4_qc_lang3(C,k3_qc_lang2(A,B)))))))) # label(t57_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7635 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> k24_qc_lang1(A) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(k13_qc_lang2(A)),k24_qc_lang1(k14_qc_lang2(A)))))) # label(t21_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7636 v2_qc_lang1(f4_s4_qc_lang3) & (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,f1_s4_qc_lang3) -> (B = f3_s4_qc_lang3(A) <-> (exists C (m2_relset_1(C,k8_qc_lang1,f1_s4_qc_lang3) & (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,f1_s4_qc_lang3) -> (all F (m1_subset_1(F,f1_s4_qc_lang3) -> (D = k11_qc_lang1 -> f2_s4_qc_lang3 = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D)) & (v3_qc_lang1(D) & E = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k17_qc_lang1(D)) -> f6_s4_qc_lang3(E) = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D)) & (v4_qc_lang1(D) & E = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k18_qc_lang1(D)) & F = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k19_qc_lang1(D)) -> k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D) = f7_s4_qc_lang3(E,F)) & (v5_qc_lang1(D) & E = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k21_qc_lang1(D)) -> f8_s4_qc_lang3(D,E) = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D)) & (v2_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D) = f5_s4_qc_lang3(D)))))))) & B = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,A) & v1_funct_2(C,k8_qc_lang1,f1_s4_qc_lang3) & v1_funct_1(C)))))))) -> f5_s4_qc_lang3(f4_s4_qc_lang3) = f3_s4_qc_lang3(f4_s4_qc_lang3) # label(s4_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7637 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(A) -> m1_subset_1(k4_qc_lang3(A,B),k1_zfmisc_1(A)))) # label(dt_k4_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7638 (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) -> a_2_2_qc_lang3(A,C) = k5_qc_lang3(k9_qc_lang1(B,C)))))))) # label(t66_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7639 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k4_tarski(np__4,A) = k2_qc_lang3(A))) # label(d3_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7640 (all A (m2_subset_1(A,k1_qc_lang1,k4_qc_lang1) -> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & A = k3_qc_lang3(B))))) # label(t39_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7641 (all A all B all C (m1_qc_lang1(C,B) & m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,a_2_2_qc_lang3(B,C)) <-> (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(D,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,D),k4_qc_lang1) & r1_xreal_0(np__1,D) & k1_funct_1(C,D) = A))))) # label(fraenkel_a_2_2_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7642 $T # label(t34_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7643 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(B) -> (v2_qc_lang2(A) -> k4_subset_1(B,k4_qc_lang3(B,k12_qc_lang2(A)),k4_qc_lang3(B,k11_qc_lang2(A))) = k4_qc_lang3(B,A)))))) # label(t58_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7644 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v6_qc_lang1(k13_qc_lang1(A,B)) <-> v6_qc_lang1(B) & v6_qc_lang1(A)))))) # label(t26_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7645 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> k24_qc_lang1(A) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(k18_qc_lang1(A)),k24_qc_lang1(k19_qc_lang1(A)))))) # label(t13_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7646 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v6_qc_lang1(k14_qc_lang1(A,B)) <-> r1_tarski(k24_qc_lang1(B),k23_qc_lang1(A))))))) # label(t27_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7647 $T # label(t2_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7648 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k3_qc_lang3(B) = k3_qc_lang3(A) -> A = B))))) # label(t38_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7649 (all A (m2_subset_1(A,k1_qc_lang1,k3_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k4_qc_lang1) -> B != A)))) # label(t40_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7650 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k5_qc_lang3(k5_qc_lang2(A,B)) = k5_qc_lang3(B))))) # label(t74_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7651 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v6_qc_lang1(B) & v6_qc_lang1(A) <-> v6_qc_lang1(k3_qc_lang2(A,B))))))) # label(t29_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7652 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(B) -> (v3_qc_lang2(A) -> k4_qc_lang3(B,A) = k4_subset_1(B,k4_qc_lang3(B,k13_qc_lang2(A)),k4_qc_lang3(B,k14_qc_lang2(A)))))))) # label(t60_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7653 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k6_qc_lang3(k2_qc_lang2(A,B)) = k4_subset_1(k3_qc_lang1,k6_qc_lang3(A),k6_qc_lang3(B)))))) # label(t83_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7654 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v6_qc_lang1(B) -> v6_qc_lang1(k5_qc_lang2(A,B))))))) # label(t33_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7655 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) -> k4_qc_lang3(B,k12_qc_lang1(A)) = k4_qc_lang3(B,A))))) # label(t50_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7656 (all A (m1_subset_1(A,k5_qc_lang1) -> m2_subset_1(A,k5_qc_lang1,k7_qc_lang1(k6_qc_lang1(A))))) # label(t3_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7657 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(B) -> (v2_qc_lang1(A) -> k4_qc_lang3(B,A) = k1_qc_lang3(k16_qc_lang1(A),B) & k4_qc_lang3(B,A) = a_2_1_qc_lang3(A,B)))))) # label(t47_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7658 (all A (m1_subset_1(A,k8_qc_lang1) -> k5_qc_lang3(k12_qc_lang1(A)) = k5_qc_lang3(A))) # label(t67_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7659 (all A (m1_subset_1(A,k8_qc_lang1) -> (v6_qc_lang1(A) <-> v6_qc_lang1(k12_qc_lang1(A))))) # label(t25_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7660 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(B) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A)) -> (all D (m1_qc_lang1(D,A) -> k4_qc_lang3(B,k9_qc_lang1(C,D)) = a_3_0_qc_lang3(A,B,D) & k1_qc_lang3(D,B) = k4_qc_lang3(B,k9_qc_lang1(C,D)))))))))) # label(t48_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7661 (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) -> k22_qc_lang1(C) = k24_qc_lang1(k9_qc_lang1(B,C)))))))) # label(t9_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7662 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k24_qc_lang1(k3_qc_lang2(A,B)) = k4_subset_1(k2_qc_lang1,k24_qc_lang1(A),k24_qc_lang1(B)))))) # label(t18_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7663 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k6_qc_lang3(k14_qc_lang1(A,B)) = k6_qc_lang3(B))))) # label(t81_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7664 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v6_qc_lang1(B) -> v6_qc_lang1(k14_qc_lang1(A,B))))))) # label(t28_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7665 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & A = k2_qc_lang3(B))))) # label(t36_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7666 (all A (m1_subset_1(A,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(A) -> k1_xboole_0 = k4_qc_lang3(A,k1_qc_lang2))) # label(t51_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7667 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(C) -> k4_subset_1(C,k4_qc_lang3(C,A),k4_qc_lang3(C,B)) = k4_qc_lang3(C,k4_qc_lang2(A,B)))))))) # label(t61_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7668 (all A all B all C (m2_subset_1(B,k1_numbers,k5_numbers) & m1_qc_lang1(C,B) -> ((exists 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) & k1_funct_1(C,D) = A & m2_subset_1(D,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_2_3_qc_lang3(B,C))))) # label(fraenkel_a_2_3_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7669 $T # label(d1_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7670 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k4_subset_1(k4_qc_lang1,k5_qc_lang3(A),k5_qc_lang3(B)) = k5_qc_lang3(k3_qc_lang2(A,B)))))) # label(t71_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7671 (all A all B all C all D (-v1_xboole_0(C) & m1_qc_lang1(D,B) & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) & m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists E (m2_subset_1(E,k1_numbers,k5_numbers) & k1_funct_1(D,E) = A & r1_xreal_0(np__1,E) & r2_hidden(k1_funct_1(D,E),C) & r1_xreal_0(E,k3_finseq_1(D)))) <-> r2_hidden(A,a_3_0_qc_lang3(B,C,D))))) # label(fraenkel_a_3_0_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7672 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) -> k4_qc_lang3(C,B) = k4_qc_lang3(C,k5_qc_lang2(A,B)))))))) # label(t63_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7673 (all A (m1_subset_1(A,k8_qc_lang1) -> k6_qc_lang3(k12_qc_lang1(A)) = k6_qc_lang3(A))) # label(t78_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 266.79/264.78 7674 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_langCputime limit exceeded (core dumped) 300.01/297.99 EOF