0.03/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n028.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 07:46:40 EDT 2022 0.13/0.34 % CPUTime : 59.37/56.95 ============================== Prover9 =============================== 59.37/56.95 Prover9 (32) version 2009-11A, November 2009. 59.37/56.95 Process 28760 was started by sandbox2 on n028.cluster.edu, 59.37/56.95 Tue Aug 9 07:47:25 2022 59.37/56.95 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_28596_n028.cluster.edu". 59.37/56.95 ============================== end of head =========================== 59.37/56.95 59.37/56.95 ============================== INPUT ================================= 59.37/56.95 59.37/56.95 % Reading from file /tmp/Prover9_28596_n028.cluster.edu 59.37/56.95 59.37/56.95 set(prolog_style_variables). 59.37/56.95 set(auto2). 59.37/56.95 % set(auto2) -> set(auto). 59.37/56.95 % set(auto) -> set(auto_inference). 59.37/56.95 % set(auto) -> set(auto_setup). 59.37/56.95 % set(auto_setup) -> set(predicate_elim). 59.37/56.95 % set(auto_setup) -> assign(eq_defs, unfold). 59.37/56.95 % set(auto) -> set(auto_limits). 59.37/56.95 % set(auto_limits) -> assign(max_weight, "100.000"). 59.37/56.95 % set(auto_limits) -> assign(sos_limit, 20000). 59.37/56.95 % set(auto) -> set(auto_denials). 59.37/56.95 % set(auto) -> set(auto_process). 59.37/56.95 % set(auto2) -> assign(new_constants, 1). 59.37/56.95 % set(auto2) -> assign(fold_denial_max, 3). 59.37/56.95 % set(auto2) -> assign(max_weight, "200.000"). 59.37/56.95 % set(auto2) -> assign(max_hours, 1). 59.37/56.95 % assign(max_hours, 1) -> assign(max_seconds, 3600). 59.37/56.95 % set(auto2) -> assign(max_seconds, 0). 59.37/56.95 % set(auto2) -> assign(max_minutes, 5). 59.37/56.95 % assign(max_minutes, 5) -> assign(max_seconds, 300). 59.37/56.95 % set(auto2) -> set(sort_initial_sos). 59.37/56.95 % set(auto2) -> assign(sos_limit, -1). 59.37/56.95 % set(auto2) -> assign(lrs_ticks, 3000). 59.37/56.95 % set(auto2) -> assign(max_megs, 400). 59.37/56.95 % set(auto2) -> assign(stats, some). 59.37/56.95 % set(auto2) -> clear(echo_input). 59.37/56.95 % set(auto2) -> set(quiet). 59.37/56.95 % set(auto2) -> clear(print_initial_clauses). 59.37/56.95 % set(auto2) -> clear(print_given). 59.37/56.95 assign(lrs_ticks,-1). 59.37/56.95 assign(sos_limit,10000). 59.37/56.95 assign(order,kbo). 59.37/56.95 set(lex_order_vars). 59.37/56.95 clear(print_given). 59.37/56.95 59.37/56.95 % formulas(sos). % not echoed (37475 formulas) 59.37/56.95 59.37/56.95 ============================== end of input ========================== 59.37/56.95 59.37/56.95 % From the command line: assign(max_seconds, 960). 59.37/56.95 59.37/56.95 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 59.37/56.95 59.37/56.95 % Formulas that are not ordinary clauses: 59.37/56.95 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 2 (all A all B (r1_tarski(A,B) <-> (all C (r2_hidden(C,A) -> r2_hidden(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 3 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 4 (all A all B -(r2_hidden(A,B) & (all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & r2_hidden(D,C))))))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 5 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 6 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 7 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 8 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 9 (all A all B all C (p1_s1_tarski(A,B) & p1_s1_tarski(A,C) -> B = C)) -> (exists A all B (r2_hidden(B,A) <-> (exists C (r2_hidden(C,f1_s1_tarski) & p1_s1_tarski(C,B))))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 10 (all A all B all C (k2_tarski(A,B) = C <-> (all D (r2_hidden(D,C) <-> D = B | D = A)))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 11 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 12 (all A exists B ((all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & (all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & (all E (r1_tarski(E,C) -> r2_hidden(E,D))))))) & (all C -(-r2_hidden(C,B) & -r2_tarski(C,B) & r1_tarski(C,B))) & r2_hidden(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 13 (all A all B k2_tarski(A,B) = k2_tarski(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 14 (all A all B k2_tarski(k2_tarski(A,B),k1_tarski(A)) = k4_tarski(A,B)) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 15 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 16 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 17 (all A all B (r2_tarski(A,B) <-> (exists C ((all D all E all F all G (r2_hidden(k4_tarski(F,G),C) & r2_hidden(k4_tarski(D,E),C) -> (E = G <-> F = D))) & (all D -((all E -(r2_hidden(k4_tarski(E,D),C) & r2_hidden(E,A))) & r2_hidden(D,B))) & (all D -(r2_hidden(D,A) & (all E -(r2_hidden(k4_tarski(D,E),C) & r2_hidden(E,B))))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 18 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 19 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 20 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 21 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 22 (all A all B ((all C (r2_hidden(C,B) <-> (exists D (r2_hidden(D,A) & r2_hidden(C,D))))) <-> k3_tarski(A) = B)) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 23 (all A all B ((all C (r2_hidden(C,B) <-> A = C)) <-> B = k1_tarski(A))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 24 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 25 (all A all B (r1_xboole_0(A,B) <-> k3_xboole_0(A,B) = k1_xboole_0)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 26 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 27 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 28 (all A all B all C ((all D (r2_hidden(D,C) <-> r2_hidden(D,A) & -r2_hidden(D,B))) <-> k4_xboole_0(A,B) = C)) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 29 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 30 (all A all B A = k2_xboole_0(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 31 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 32 (all A all B (r3_xboole_0(A,B) <-> r1_tarski(B,A) | r1_tarski(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 33 (all A all B all C ((all D (r2_hidden(D,A) & r2_hidden(D,B) <-> r2_hidden(D,C))) <-> C = k3_xboole_0(A,B))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 34 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f1_s2_xboole_0))) & (all A (r2_hidden(A,f2_s2_xboole_0) <-> p1_s2_xboole_0(A))) -> f1_s2_xboole_0 = f2_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 35 (all A all B ((all C (r2_hidden(C,A) <-> p1_s3_xboole_0(C))) & (all C (r2_hidden(C,B) <-> p1_s3_xboole_0(C))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 36 (all A all B all C (C = k2_xboole_0(A,B) <-> (all D (r2_hidden(D,A) | r2_hidden(D,B) <-> r2_hidden(D,C))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 37 (all A all B k5_xboole_0(A,B) = k5_xboole_0(B,A)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 38 (all A all B (r2_xboole_0(A,B) -> -r2_xboole_0(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 39 (all A all B k3_xboole_0(B,A) = k3_xboole_0(A,B)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 40 (all A all B (r1_xboole_0(A,B) -> r1_xboole_0(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 41 (all A all B k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 42 (all A all B (B = A <-> r1_tarski(A,B) & r1_tarski(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 43 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 44 (all A ((all B -r2_hidden(B,A)) <-> k1_xboole_0 = A)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 45 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 46 (all A all B all C -(r2_hidden(C,k2_xboole_0(A,B)) & -(r2_hidden(C,A) & -r2_hidden(C,B)) & -(r2_hidden(C,B) & -r2_hidden(C,A)) & r1_xboole_0(A,B))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 47 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 48 (all A all B (-((all C -(r2_hidden(C,B) & r2_hidden(C,A))) & -r1_xboole_0(A,B)) & -((exists C (r2_hidden(C,B) & r2_hidden(C,A))) & r1_xboole_0(A,B)))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 49 (all A all B (r2_xboole_0(A,B) <-> r1_tarski(A,B) & B != A)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 50 (all A all B k2_xboole_0(B,A) = k2_xboole_0(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 51 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 52 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 53 (all A all B all C ((all D ((r2_hidden(D,C) <-> r2_hidden(D,B)) <-> -r2_hidden(D,A))) -> A = k5_xboole_0(B,C))) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 54 (all A all B (-((all C -r2_hidden(C,k3_xboole_0(A,B))) & -r1_xboole_0(A,B)) & -((exists C r2_hidden(C,k3_xboole_0(A,B))) & r1_xboole_0(A,B)))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 55 (all A (A = k1_xboole_0 <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 56 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 57 (all A all B (r3_xboole_0(A,B) -> r3_xboole_0(B,A))) # label(symmetry_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 58 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 59 (exists A all B (p1_s1_xboole_0(B) & r2_hidden(B,f1_s1_xboole_0) <-> r2_hidden(B,A))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 60 (all A all B all C (r2_hidden(A,k5_xboole_0(B,C)) <-> -(r2_hidden(A,B) <-> r2_hidden(A,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 61 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 62 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 63 (all A A = k4_xboole_0(A,k1_xboole_0)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 64 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 65 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 66 (all A all B -(v1_xboole_0(B) & r2_hidden(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 67 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 68 (all A all B -(v1_xboole_0(A) & B != A & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 69 (all A all B k2_xboole_0(A,B) = k2_xboole_0(A,k4_xboole_0(B,A))) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 70 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(k4_xboole_0(A,B),C))) # label(t43_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 71 (all A all B all C k5_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B)) = k3_xboole_0(k5_xboole_0(A,C),B)) # label(t112_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 72 (all A all B all C r1_tarski(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)),k2_xboole_0(B,C))) # label(t31_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 73 (all A all B all C (r2_xboole_0(A,B) & r1_tarski(B,C) -> r2_xboole_0(A,C))) # label(t58_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 74 (all A all B (r1_xboole_0(A,B) -> A = k4_xboole_0(k2_xboole_0(A,B),B))) # label(t88_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 75 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 76 (all A all B all C (r1_xboole_0(B,C) & r1_tarski(A,C) & r1_tarski(A,B) -> A = k1_xboole_0)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 77 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 78 (all A all B r1_tarski(k4_xboole_0(A,B),k5_xboole_0(A,B))) # label(t96_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 79 (all A all B k4_xboole_0(A,k3_xboole_0(A,B)) = k4_xboole_0(A,B)) # label(t47_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 80 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C))) # label(t4_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 81 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) -> r1_tarski(A,k2_xboole_0(B,C)))) # label(t44_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 82 (all A all B k4_xboole_0(A,k2_xboole_0(A,B)) = k1_xboole_0) # label(t46_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 83 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k5_xboole_0(A,B)) # label(t101_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 84 (all A all B all C -(-r1_xboole_0(A,k3_xboole_0(B,C)) & r1_xboole_0(A,B))) # label(t74_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 85 (all A all B all C (r1_tarski(C,B) & r1_tarski(A,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 86 (all A all B all C k4_xboole_0(k4_xboole_0(A,B),C) = k4_xboole_0(A,k2_xboole_0(B,C))) # label(t41_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 87 (all A all B all C -(r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)) & -r1_xboole_0(A,B))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 88 (all A all B all C k4_xboole_0(k5_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C)))) # label(t99_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 89 (all A all B (r1_tarski(A,B) <-> k4_xboole_0(A,B) = k1_xboole_0)) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 90 (all A all B k2_xboole_0(A,B) = k5_xboole_0(A,k4_xboole_0(B,A))) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 91 (all A all B k3_xboole_0(A,k2_xboole_0(A,B)) = A) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 92 (all A all B all C k2_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C))) # label(t24_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 93 (all A all B all C (r1_tarski(A,k3_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t18_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 94 (all A all B -(r2_xboole_0(A,B) & k1_xboole_0 = k4_xboole_0(B,A))) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 95 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 96 (all A all B k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) = k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B))) # label(t55_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 97 (all A all B all C (-v1_xboole_0(C) -> -(r1_tarski(C,A) & r1_tarski(C,B) & r1_xboole_0(A,B)))) # label(t68_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 98 (all A all B all C all D (k2_xboole_0(A,B) = k2_xboole_0(C,D) & r1_xboole_0(D,B) & r1_xboole_0(C,A) -> B = C)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 99 (all A all B r1_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t82_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 100 (all A all B all C (r2_xboole_0(B,C) & r1_tarski(A,B) -> r2_xboole_0(A,C))) # label(t59_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 101 (all A all B k4_xboole_0(A,B) = k5_xboole_0(A,k3_xboole_0(A,B))) # label(t100_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 102 (all A all B all C k2_xboole_0(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(B,C)),k3_xboole_0(C,A)) = k3_xboole_0(k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(B,C)),k2_xboole_0(C,A))) # label(t25_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 103 (all A all B (k4_xboole_0(A,B) = k4_xboole_0(B,A) -> B = A)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 104 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 105 (all A all B k3_xboole_0(A,B) = k4_xboole_0(A,k4_xboole_0(A,B))) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 106 (all A all B (A = k4_xboole_0(A,B) <-> r1_xboole_0(A,B))) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 107 (all A all B (r1_tarski(A,B) -> k3_xboole_0(A,B) = A)) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 108 (all A all B all C k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t23_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 109 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 110 (all A all B all C ((all D (r1_tarski(A,D) & r1_tarski(C,D) -> r1_tarski(B,D))) & r1_tarski(C,B) & r1_tarski(A,B) -> k2_xboole_0(A,C) = B)) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 111 (all A all B all C (r2_xboole_0(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t56_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 112 (all A (-(k1_xboole_0 = A & -r1_xboole_0(A,A)) & -(r1_xboole_0(A,A) & k1_xboole_0 != A))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 113 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 114 (all A all B (r1_tarski(A,k4_xboole_0(B,A)) -> A = k1_xboole_0)) # label(t38_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 115 (all A all B k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A) # label(t51_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 116 (all A all B all C (r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,k2_xboole_0(B,C)) <-> r1_tarski(A,k5_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 117 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 118 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 119 (all A all B all C (k2_xboole_0(C,B) = k2_xboole_0(A,B) & r1_xboole_0(C,B) & r1_xboole_0(A,B) -> C = A)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 120 (all A all B k2_xboole_0(A,k2_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t6_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 121 (all A all B (-v1_xboole_0(B) -> -(r1_tarski(B,A) & r1_xboole_0(B,A)))) # label(t69_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 122 (all A all B all C (r1_tarski(A,B) & (all D (r1_tarski(D,B) & r1_tarski(D,C) -> r1_tarski(D,A))) & r1_tarski(A,C) -> A = k3_xboole_0(B,C))) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 123 (all A all B all C (r1_xboole_0(A,B) -> k4_xboole_0(k2_xboole_0(C,B),A) = k2_xboole_0(k4_xboole_0(C,A),B))) # label(t87_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 124 (all A all B (k1_xboole_0 = k2_xboole_0(A,B) -> A = k1_xboole_0)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 125 (all A all B all C k4_xboole_0(A,k3_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C))) # label(t54_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 126 (all A all B all C (r1_tarski(k2_xboole_0(A,B),C) -> r1_tarski(A,C))) # label(t11_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 127 (all A all B all C r1_tarski(k3_xboole_0(A,B),k2_xboole_0(A,C))) # label(t29_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 128 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,B))) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 129 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),B))) # label(t108_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 130 (all A all B r1_xboole_0(k3_xboole_0(A,B),k5_xboole_0(A,B))) # label(t103_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 131 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 132 (all A all B r1_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t89_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 133 (all A all B A = k2_xboole_0(A,k3_xboole_0(A,B))) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 134 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,B) -> r1_tarski(A,k4_xboole_0(B,C)))) # label(t86_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 135 (all A all B -(r1_tarski(A,B) & r2_xboole_0(B,A))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 136 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,k4_xboole_0(B,A)) = B)) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 137 (all A all B all C (r1_tarski(A,B) -> r1_tarski(A,k2_xboole_0(C,B)))) # label(t10_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 138 (all A all B all C (r1_tarski(A,B) & r1_tarski(B,C) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 139 (all A all B all C all D k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D) = k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D))) # label(t113_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 140 (all A all B all C k3_xboole_0(k4_xboole_0(A,C),B) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B))) # label(t111_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 141 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 142 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)))) # label(t34_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 143 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 144 (all A all B all C (r1_tarski(A,B) -> k2_xboole_0(A,k3_xboole_0(C,B)) = k3_xboole_0(k2_xboole_0(A,C),B))) # label(t30_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 145 (all A all B all C k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C))) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 146 (all A all B all C k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C)) = k4_xboole_0(A,k5_xboole_0(B,C))) # label(t102_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 147 (all A all B (-(-r2_xboole_0(A,B) & A != B & -r2_xboole_0(B,A)) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 148 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k2_xboole_0(A,C),B))) # label(t8_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 149 (all A (A != k1_xboole_0 -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 150 (all A all B all C all D (r1_xboole_0(A,D) & r1_xboole_0(B,D) & r1_xboole_0(C,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 151 (all A all B all C (r1_tarski(A,k4_xboole_0(B,C)) -> r1_xboole_0(A,C) & r1_tarski(A,B))) # label(t106_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 152 (all A all B k2_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t94_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 153 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(k3_xboole_0(C,A),k3_xboole_0(C,B)))) # label(t76_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 154 (all A all B all C (r1_tarski(A,B) -> r1_xboole_0(A,k4_xboole_0(C,B)))) # label(t85_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 155 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t80_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 156 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 157 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),B))) # label(t109_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 158 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 159 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)))) # label(t9_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 160 (all A all B k4_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 161 (all A all B k3_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k2_xboole_0(A,B))) # label(t95_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 162 (all A all B -(-r1_xboole_0(A,B) & r1_xboole_0(k3_xboole_0(A,B),B))) # label(t75_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 163 (all A all B all C k5_xboole_0(k5_xboole_0(A,B),C) = k5_xboole_0(A,k5_xboole_0(B,C))) # label(t91_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 164 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)))) # label(t33_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 165 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,k2_xboole_0(B,C)) = k3_xboole_0(A,C))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 166 (all A all B all C -(r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,C) & -r1_xboole_0(A,B))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 167 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k4_xboole_0(B,C))) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 168 (all A all B r1_xboole_0(k4_xboole_0(A,k3_xboole_0(A,B)),B)) # label(t90_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 169 (all A all B k2_xboole_0(A,B) = k2_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B))) # label(t93_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 170 (all A all B all C k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C))) # label(t42_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 171 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) = k3_xboole_0(A,k4_xboole_0(B,C))) # label(t50_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 172 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) & r1_tarski(k4_xboole_0(B,A),C) -> r1_tarski(k5_xboole_0(A,B),C))) # label(t97_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 173 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)))) # label(t26_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 174 (all A all B all C (r1_tarski(A,B) & r1_tarski(A,C) -> r1_tarski(A,k3_xboole_0(B,C)))) # label(t19_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 175 (all A all B all C (r1_xboole_0(A,k4_xboole_0(B,C)) -> r1_xboole_0(B,k4_xboole_0(A,C)))) # label(t81_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 176 (all A all B all C all D (r1_xboole_0(B,D) & r1_tarski(C,D) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t64_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 177 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C)) = k4_xboole_0(A,k4_xboole_0(B,C))) # label(t52_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 178 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(B,C) -> r1_xboole_0(A,C))) # label(t63_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 179 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 180 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k2_xboole_0(A,C),k2_xboole_0(B,C))) # label(t5_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 181 (all A all B all C (-(-(r1_xboole_0(A,C) & r1_xboole_0(A,B)) & r1_xboole_0(A,k2_xboole_0(B,C))) & -(-r1_xboole_0(A,k2_xboole_0(B,C)) & r1_xboole_0(A,C) & r1_xboole_0(A,B)))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 182 (all A all B all C k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k2_xboole_0(B,C))) # label(t53_xboole_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 183 (all A all B all C k1_enumset1(A,B,C) = k6_enumset1(A,A,A,A,A,A,B,C)) # label(t93_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 184 (all A all B all C k1_enumset1(A,B,C) = k4_enumset1(A,A,A,A,B,C)) # label(t84_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 185 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k6_enumset1(A,A,A,A,B,C,D,E)) # label(t86_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 186 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,A,D,C)) # label(t109_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 187 (all A all B k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B)) # label(t41_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 188 (all A all B all C k2_enumset1(A,A,B,C) = k1_enumset1(A,B,C)) # label(t71_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 189 (all A k3_enumset1(A,A,A,A,A) = k1_tarski(A)) # label(t87_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 190 $T # label(dt_k5_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 191 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k1_enumset1(A,B,C),k2_enumset1(D,E,F,G))) # label(t58_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 192 $T # label(dt_k4_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 193 (all A all B all C all D all E k2_xboole_0(k2_enumset1(A,B,C,D),k1_tarski(E)) = k3_enumset1(A,B,C,D,E)) # label(t50_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 194 (all A all B all C all D all E all F all G all H k2_xboole_0(k5_enumset1(A,B,C,D,E,F,G),k1_tarski(H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t68_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 195 (all A all B all C all D all E all F k2_xboole_0(k1_tarski(A),k3_enumset1(B,C,D,E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t51_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 196 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k1_tarski(A),k5_enumset1(B,C,D,E,F,G,H))) # label(t62_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 197 (all A all B all C all D all E all F all G k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t59_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 198 (all A all B all C all D all E k5_enumset1(A,A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E)) # label(t80_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 199 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k1_enumset1(A,B,C),k3_enumset1(D,E,F,G,H))) # label(t64_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 200 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k2_tarski(A,B),k4_enumset1(C,D,E,F,G,H))) # label(t63_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 201 (all A all B all C k1_enumset1(B,A,C) = k1_enumset1(A,B,C)) # label(t99_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 202 (all A all B all C all D all E all F all G k6_enumset1(A,A,B,C,D,E,F,G) = k5_enumset1(A,B,C,D,E,F,G)) # label(t75_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 203 $T # label(t23_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 204 $T # label(t115_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 205 (all A all B all C all D k2_enumset1(C,D,A,B) = k2_enumset1(A,B,C,D)) # label(t118_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 206 (all A all B all C all D k6_enumset1(A,A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t90_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 207 $T # label(t20_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 208 (all A all B all C k3_enumset1(A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t78_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 209 (all A all B all C all D all E all F ((all G (r2_hidden(G,F) <-> -(A != G & G != B & D != G & G != E & C != G))) <-> F = k3_enumset1(A,B,C,D,E))) # label(d3_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 210 $T # label(t14_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 211 $T # label(t39_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 212 $T # label(t24_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 213 (all A k1_tarski(A) = k6_enumset1(A,A,A,A,A,A,A,A)) # label(t96_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 214 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,D,C,A)) # label(t113_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 215 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k5_enumset1(A,A,B,C,D,E,F)) # label(t74_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 216 $T # label(t120_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 217 $T # label(t7_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 218 $T # label(t101_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 219 (all A all B all C all D all E all F k2_xboole_0(k2_enumset1(A,B,C,D),k2_tarski(E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t54_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 220 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(D,C,B,A)) # label(t125_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 221 $T # label(t114_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 222 (all A all B all C all D k2_enumset1(C,B,A,D) = k2_enumset1(A,B,C,D)) # label(t116_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 223 $T # label(t22_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 224 (all A all B all C all D all E all F all G all H all I (I = k6_enumset1(A,B,C,D,E,F,G,H) <-> (all J (r2_hidden(J,I) <-> -(E != J & J != H & J != G & F != J & D != J & C != J & J != B & J != A))))) # label(d6_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 225 $T # label(t26_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 226 $T # label(t8_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 227 (all A all B all C all D k2_enumset1(A,C,D,B) = k2_enumset1(A,B,C,D)) # label(t105_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 228 $T # label(t9_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 229 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,C,A,D)) # label(t110_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 230 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 231 $T # label(t15_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 232 (all A all B all C all D k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(A,B,C,D)) # label(t45_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 233 (all A all B k2_tarski(A,B) = k6_enumset1(A,A,A,A,A,A,A,B)) # label(t95_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 234 $T # label(t121_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 235 $T # label(t21_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 236 $T # label(t5_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 237 $T # label(t25_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 238 (all A all B all C all D ((all E (-(E != A & B != E & C != E) <-> r2_hidden(E,D))) <-> D = k1_enumset1(A,B,C))) # label(d1_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 239 (all A k1_tarski(A) = k2_tarski(A,A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 240 (all A all B k2_tarski(A,B) = k5_enumset1(A,A,A,A,A,A,B)) # label(t92_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 241 (all A k1_tarski(A) = k4_enumset1(A,A,A,A,A,A)) # label(t91_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 242 (all A all B all C k1_enumset1(A,C,B) = k1_enumset1(A,B,C)) # label(t98_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 243 (all A all B k3_enumset1(A,A,A,A,B) = k2_tarski(A,B)) # label(t83_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 244 $T # label(t13_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 245 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_enumset1(F,G,H))) # label(t66_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 246 $T # label(t38_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 247 $T # label(t33_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 248 $T # label(t40_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 249 $T # label(t10_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 250 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,C,D,A)) # label(t111_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 251 (all A all B all C all D all E all F k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_tarski(F)) = k4_enumset1(A,B,C,D,E,F)) # label(t55_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 252 $T # label(t6_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 253 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,B,D,C)) # label(t103_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 254 (all A all B all C k1_enumset1(B,C,A) = k1_enumset1(A,B,C)) # label(t100_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 255 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(D,B,C,A)) # label(t123_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 256 $T # label(t19_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 257 $T # label(t122_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 258 $T # label(dt_k3_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 259 (all A all B all C k1_enumset1(A,B,C) = k5_enumset1(A,A,A,A,A,B,C)) # label(t89_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 260 (all A all B all C all D all E all F all G k2_xboole_0(k2_tarski(A,B),k3_enumset1(C,D,E,F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t57_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 261 (all A all B k2_tarski(A,B) = k2_enumset1(A,A,A,B)) # label(t77_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 262 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k2_tarski(G,H))) # label(t67_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 263 $T # label(t97_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 264 $T # label(t12_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 265 (all A all B all C all D k2_enumset1(C,B,D,A) = k2_enumset1(A,B,C,D)) # label(t117_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 266 $T # label(t34_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 267 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,D,C,B)) # label(t107_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 268 $T # label(dt_k2_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 269 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_tarski(A,B),k2_enumset1(C,D,E,F))) # label(t52_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 270 $T # label(t106_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 271 (all A all B all C all D all E all F all G k2_xboole_0(k1_tarski(A),k4_enumset1(B,C,D,E,F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t56_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 272 $T # label(t4_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 273 $T # label(t27_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 274 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,D,A,C)) # label(t112_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 275 (all A all B k2_tarski(A,B) = k1_enumset1(A,A,B)) # label(t70_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 276 (all A all B all C all D all E k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E)) = k3_enumset1(A,B,C,D,E)) # label(t49_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 277 $T # label(t16_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 278 $T # label(t36_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 279 (all A all B all C all D all E all F k2_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t53_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 280 $T # label(t28_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 281 (all A all B all C all D k2_enumset1(A,B,C,D) = k3_enumset1(A,A,B,C,D)) # label(t72_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 282 (all A all B all C all D k2_enumset1(C,D,B,A) = k2_enumset1(A,B,C,D)) # label(t119_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 283 $T # label(t30_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 284 $T # label(t37_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 285 (all A k1_enumset1(A,A,A) = k1_tarski(A)) # label(t76_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 286 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k6_enumset1(A,A,A,B,C,D,E,F)) # label(t81_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 287 $T # label(t3_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 288 (all A all B all C all D all E all F all G (k4_enumset1(A,B,C,D,E,F) = G <-> (all H (r2_hidden(H,G) <-> -(H != C & D != H & F != H & E != H & H != B & H != A))))) # label(d4_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 289 $T # label(t17_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 290 (all A all B all C k1_enumset1(A,B,C) = k2_xboole_0(k2_tarski(A,B),k1_tarski(C))) # label(t43_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 291 $T # label(t35_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 292 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k1_enumset1(A,B,C),k1_tarski(D))) # label(t46_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 293 $T # label(t32_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 294 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_tarski(F,G))) # label(t60_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 295 (all A all B all C all D all E ((all F (-(F != A & B != F & F != C & D != F) <-> r2_hidden(F,E))) <-> k2_enumset1(A,B,C,D) = E)) # label(d2_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 296 (all A all B all C all D all E all F all G k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t61_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 297 (all A all B k4_enumset1(A,A,A,A,A,B) = k2_tarski(A,B)) # label(t88_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 298 $T # label(dt_k6_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.95 299 (all A k5_enumset1(A,A,A,A,A,A,A) = k1_tarski(A)) # label(t94_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 300 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,A,C,D)) # label(t108_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 301 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,C,B,D)) # label(t104_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 302 $T # label(t31_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 303 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k2_enumset1(A,B,C,D),k2_enumset1(E,F,G,H))) # label(t65_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 304 $T # label(t29_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 305 (all A all B all C all D all E k4_enumset1(A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E)) # label(t73_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 306 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_tarski(A),k2_enumset1(B,C,D,E))) # label(t47_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 307 (all A k2_enumset1(A,A,A,A) = k1_tarski(A)) # label(t82_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 308 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_tarski(A,B),k1_enumset1(C,D,E))) # label(t48_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 309 $T # label(t11_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 310 (all A all B all C all D k5_enumset1(A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t85_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 311 (all A all B all C all D k2_xboole_0(k1_tarski(A),k1_enumset1(B,C,D)) = k2_enumset1(A,B,C,D)) # label(t44_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 312 (all A all B all C all D all E all F all G all H ((all I (r2_hidden(I,H) <-> -(I != A & C != I & I != G & F != I & E != I & I != D & I != B))) <-> H = k5_enumset1(A,B,C,D,E,F,G))) # label(d5_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 313 (all A all B all C all D k4_enumset1(A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t79_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 314 $T # label(t2_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 315 $T # label(t18_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 316 (all A all B all C k1_enumset1(A,B,C) = k2_xboole_0(k1_tarski(A),k2_tarski(B,C))) # label(t42_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 317 $T # label(t1_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 318 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(C,B,A)) # label(t102_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 319 $T # label(t124_enumset1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 320 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 321 (all A all B k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B))) # label(t96_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 322 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> A = k1_xboole_0)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 323 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> k2_xboole_0(k2_tarski(A,C),B) = B)) # label(t48_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 324 (all A all B ((all C all D (r2_hidden(D,k2_xboole_0(A,B)) & r2_hidden(C,k2_xboole_0(A,B)) -> r1_xboole_0(C,D) | C = D)) -> k3_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k3_xboole_0(A,B)))) # label(t101_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 325 (all A all B (r2_hidden(A,B) <-> k4_xboole_0(k1_tarski(A),B) = k1_xboole_0)) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 326 (all A all B all C all D (r2_hidden(A,C) & r2_hidden(B,D) <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 327 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)),k1_zfmisc_1(k2_xboole_0(A,B)))) # label(t81_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 328 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 329 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(C,B))) -> r1_tarski(k3_tarski(A),B))) # label(t94_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 330 (all A all B r1_tarski(k1_zfmisc_1(k4_xboole_0(A,B)),k2_xboole_0(k1_tarski(k1_xboole_0),k4_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B))))) # label(t84_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 331 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))) <-> B = D & A = C)) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 332 (all A all B all C (r1_tarski(k2_xboole_0(k2_tarski(A,B),C),C) -> r2_hidden(A,C))) # label(t47_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 333 (all A all B k1_tarski(k4_tarski(A,B)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 334 (all A all B -(k4_xboole_0(A,k1_tarski(B)) = k1_xboole_0 & k1_tarski(B) != A & A != k1_xboole_0)) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 335 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 336 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> A = C)) # label(t26_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 337 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 338 (all A all B all C -(k2_xboole_0(B,C) = k1_tarski(A) & C != B & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 339 (all A all B all C all D (k4_tarski(A,B) = k4_tarski(C,D) -> C = A & D = B)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 340 (all A all B (A != B <-> k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A))) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 341 (all A all B all C (-(k2_tarski(B,C) != A & k1_tarski(C) != A & A != k1_tarski(B) & A != k1_xboole_0) <-> k1_xboole_0 = k4_xboole_0(A,k2_tarski(B,C)))) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 342 (all A all B (r1_tarski(A,B) -> r1_tarski(k3_tarski(A),k3_tarski(B)))) # label(t95_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 343 (all A all B k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k3_xboole_0(A,B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 344 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)) <-> A = C & r2_hidden(B,D))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 345 (all A all B all C all D -(k2_tarski(C,D) = k2_tarski(A,B) & A != C & D != A)) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 346 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 347 (all A all B all C (k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k4_tarski(A,B),k4_tarski(A,C)) & k2_tarski(k4_tarski(A,C),k4_tarski(B,C)) = k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 348 (all A all B all C -(r2_hidden(A,C) & r1_xboole_0(k2_tarski(A,B),C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 349 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t79_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 350 (all A all B (k1_xboole_0 = k2_zfmisc_1(A,B) <-> A = k1_xboole_0 | k1_xboole_0 = B)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 351 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(D,E)) & r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))))) # label(t137_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 352 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C))) # label(t124_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 353 (all A all B all C all D -(r1_tarski(A,k2_zfmisc_1(B,C)) & r2_hidden(D,A) & (all E all F -(r2_hidden(E,B) & D = k4_tarski(E,F) & r2_hidden(F,C))))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 354 (all A all B all C (r2_hidden(A,k4_xboole_0(B,k1_tarski(C))) <-> C != A & r2_hidden(A,B))) # label(t64_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 355 (all A all B r1_tarski(k3_tarski(k3_xboole_0(A,B)),k3_xboole_0(k3_tarski(A),k3_tarski(B)))) # label(t97_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 356 (all A all B all C all D k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 357 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> k3_xboole_0(k2_tarski(A,C),B) = k2_tarski(A,C))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 358 (all A all B all C -(A != k1_xboole_0 & (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A))) & -r1_tarski(B,C))) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 359 (all A all B r1_tarski(k2_zfmisc_1(A,B),k1_zfmisc_1(k1_zfmisc_1(k2_xboole_0(A,B))))) # label(t105_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 360 (all A all B k1_tarski(A) = k3_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 361 (all A all B (r2_hidden(A,B) -> k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 362 (all A all B k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B)) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 363 (all A all B (r2_hidden(A,B) -> k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A))) # label(t52_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 364 (all A all B (A = k1_tarski(B) | A = k1_xboole_0 <-> r1_tarski(A,k1_tarski(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 365 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 366 (all A all B k1_xboole_0 = k4_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 367 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 368 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 369 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> C = B)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 370 (all A all B (r1_tarski(A,k2_zfmisc_1(A,B)) | r1_tarski(A,k2_zfmisc_1(B,A)) -> A = k1_xboole_0)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 371 (all A all B all C -(k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C) & k2_tarski(A,B) != k4_xboole_0(k2_tarski(A,B),C) & k1_xboole_0 != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 372 (all A k1_zfmisc_1(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A))) # label(t30_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 373 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 374 (all A all B all C (r1_tarski(A,B) -> r2_hidden(C,A) | r1_tarski(A,k4_xboole_0(B,k1_tarski(C))))) # label(t40_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 375 (all A all B all C -(k3_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) & r2_hidden(B,C) & B != A)) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 376 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 377 (all A all B all C all D (r1_tarski(A,k2_zfmisc_1(B,C)) & (all E all F (r2_hidden(k4_tarski(E,F),A) -> r2_hidden(k4_tarski(E,F),D))) -> r1_tarski(A,D))) # label(t109_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 378 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 379 (all A k3_tarski(k1_tarski(A)) = A) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 380 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 381 (all A all B all C (r2_hidden(B,C) & r2_hidden(A,C) <-> k1_xboole_0 = k4_xboole_0(k2_tarski(A,B),C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 382 (all A all B (A != B -> k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 383 (all A all B all C (-r2_hidden(A,C) & -r2_hidden(B,C) <-> k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 384 (all A all B all C all D k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D))) = k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))) # label(t126_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 385 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_tarski(A) <-> -r2_hidden(A,B))) # label(t67_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 386 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) & (all C -(r2_hidden(C,A) & (all D all E C != k4_tarski(D,E)))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 387 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),B) | k4_xboole_0(k1_tarski(A),B) = k1_tarski(A))) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 388 (all A all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> r1_tarski(A,C) & r1_tarski(B,D) | k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 389 (all A all B (k1_tarski(A) = k3_xboole_0(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 390 (all A all B (k2_zfmisc_1(B,B) = k2_zfmisc_1(A,A) -> A = B)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 391 (all A all B (r1_tarski(k2_xboole_0(k1_tarski(A),B),B) -> r2_hidden(A,B))) # label(t45_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 392 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 393 (all A all B (k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> B = A)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 394 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 395 (all A all B all C (k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) -> r2_hidden(A,C))) # label(t63_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 396 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k1_tarski(A),B))) # label(t46_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 397 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 398 (all A all B all C all D (r2_hidden(A,C) & D = B <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))))) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 399 (all A all B -(r1_xboole_0(k1_tarski(A),k1_tarski(B)) & A = B)) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 400 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t118_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 401 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 402 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 403 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 404 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 405 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 406 (all A all B all C all D all E -(r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))) & (all F all G -(k4_tarski(F,G) = A & r2_hidden(G,k3_xboole_0(C,E)) & r2_hidden(F,k3_xboole_0(B,D)))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 407 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 408 (all A all B (k4_xboole_0(A,k1_tarski(B)) = A <-> -r2_hidden(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 409 (all A all B -(A != k1_tarski(B) & (all C -(r2_hidden(C,A) & C != B)) & k1_xboole_0 != A)) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 410 (all A exists B (r2_hidden(A,B) & (all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & (all C -(-r2_hidden(C,B) & -r2_tarski(C,B) & r1_tarski(C,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 411 (all A all B all C all D (r1_xboole_0(C,D) | r1_xboole_0(A,B) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 412 (all A all B all C all D -(r1_tarski(k2_tarski(A,B),k2_tarski(C,D)) & A != C & A != D)) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 413 (all A all B all C -(r2_hidden(A,k2_zfmisc_1(B,C)) & (all D all E k4_tarski(D,E) != A))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 414 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 415 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 416 (all A all B all C all D k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D))) # label(t123_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 417 (all A all B (B = k1_zfmisc_1(A) <-> (all C (r1_tarski(C,A) <-> r2_hidden(C,B))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 418 (all A all B (A != B -> k2_tarski(A,B) = k5_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t29_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 419 (all A all B r1_tarski(k2_xboole_0(k1_zfmisc_1(k4_xboole_0(A,B)),k1_zfmisc_1(k4_xboole_0(B,A))),k1_zfmisc_1(k5_xboole_0(A,B)))) # label(t86_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 420 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 421 (all A all B all C (k2_zfmisc_1(k4_xboole_0(A,B),C) = k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k4_xboole_0(A,B)))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 422 (all A all B ((all C (r2_hidden(C,A) -> r1_xboole_0(C,B))) -> r1_xboole_0(k3_tarski(A),B))) # label(t98_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 423 (all A all B all C all D (A != B -> r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) & r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D)))) # label(t131_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 424 (all A all B (-r2_hidden(A,B) -> k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t141_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 425 (all A all B all C (k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k2_xboole_0(A,B)) & k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 426 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 427 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(A != k1_tarski(B) & k1_tarski(C) != A & A != k2_tarski(B,C) & k1_xboole_0 != A))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 428 (all A all B all C all D ((all E all F (r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B)) <-> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(C,D)))) -> k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B))) # label(t108_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 429 (all A all B ((all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,A))) & (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A))) & (all C -(r2_hidden(C,B) & (all D all E C != k4_tarski(D,E)))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 430 (all A all B all C all D k2_zfmisc_1(k3_zfmisc_1(A,B,C),D) = k4_zfmisc_1(A,B,C,D)) # label(d4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 431 (all A all B all C (C = k2_zfmisc_1(A,B) <-> (all D (r2_hidden(D,C) <-> (exists E exists F (D = k4_tarski(E,F) & r2_hidden(F,B) & r2_hidden(E,A))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 432 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 433 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 434 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 435 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) -> r2_hidden(k4_tarski(B,A),k2_zfmisc_1(D,C)))) # label(t107_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 436 (all A all B (k3_xboole_0(A,k1_tarski(B)) = k1_tarski(B) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 437 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 438 (all A all B (B != A -> r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t17_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 439 (all A all B (-r2_hidden(A,B) -> r1_xboole_0(k1_tarski(A),B))) # label(t56_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 440 (all A all B -(r2_hidden(A,B) & r1_xboole_0(k1_tarski(A),B))) # label(t54_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 441 (all A all B (k1_zfmisc_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) -> r3_xboole_0(A,B))) # label(t82_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 442 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 443 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 444 (all A all B all C -(B != A & C != A & r1_tarski(k1_tarski(A),k2_tarski(B,C)))) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 445 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 446 (all A all B k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B)) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 447 (all A all B all C (r2_hidden(A,B) -> k3_xboole_0(k2_tarski(A,C),B) = k1_tarski(A) | A != C & r2_hidden(C,B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 448 (all A all B all C (-r2_hidden(A,C) & (B = A | r2_hidden(B,C)) <-> k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 449 (all A all B all C all D all E all F ((all G all H (r2_hidden(k4_tarski(G,H),A) <-> r2_hidden(k4_tarski(G,H),D))) & r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> A = D)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 450 (all A all B all C k2_xboole_0(k2_tarski(A,B),C) != k1_xboole_0) # label(t50_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 451 (all A all B all C k3_zfmisc_1(A,B,C) = k2_zfmisc_1(k2_zfmisc_1(A,B),C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 452 (all A all B all C (k2_zfmisc_1(C,k2_tarski(A,B)) = k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) & k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)) = k2_zfmisc_1(k2_tarski(A,B),C))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 453 (all A all B all C all D (k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D) -> k1_xboole_0 = B | C = A & B = D | A = k1_xboole_0)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 454 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 455 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> B = A)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 456 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> k1_tarski(C) = k2_tarski(A,B))) # label(t27_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 457 (all A all B (k2_zfmisc_1(B,A) = k2_zfmisc_1(A,B) -> k1_xboole_0 = A | A = B | k1_xboole_0 = B)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 458 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 459 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 460 (all A all B k2_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k2_tarski(A,B)) # label(t14_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 461 (all A all B all C -(-r2_hidden(C,B) & -r1_xboole_0(k2_tarski(A,C),B) & -r2_hidden(A,B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 462 (all A all B all C -(k1_tarski(A) = k2_xboole_0(B,C) & -(k1_tarski(A) = C & B = k1_tarski(A)) & -(k1_tarski(A) = C & B = k1_xboole_0) & -(B = k1_tarski(A) & C = k1_xboole_0))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 463 (all A all B (k1_tarski(A) = k3_xboole_0(k1_tarski(A),B) | r1_xboole_0(k1_tarski(A),B))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 464 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 465 (all A all B all C (k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k3_xboole_0(A,B)) & k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 466 (all A all B (A != k1_xboole_0 -> k1_xboole_0 != k2_zfmisc_1(A,k1_tarski(B)) & k2_zfmisc_1(k1_tarski(B),A) != k1_xboole_0)) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 467 (all A all B all C (r1_tarski(k2_tarski(A,B),C) <-> r2_hidden(A,C) & r2_hidden(B,C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 468 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 469 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 470 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 471 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 472 (all A (A != k1_xboole_0 -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,A) -> (-r2_hidden(C,B) -> r2_hidden(C,k3_subset_1(A,B))))))))) # label(t50_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 473 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 474 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = k5_subset_1(A,B,k3_subset_1(A,C)))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 475 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> B = k5_subset_1(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 476 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 477 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 478 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 479 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k4_subset_1(A,B,C)) = k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 480 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k7_subset_1(A,C,B))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 481 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,C) | r2_hidden(E,D)))) -> k4_subset_1(A,C,D) = B))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 482 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) -> r2_subset_1(B,A)))) # label(symmetry_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 483 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 484 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) -> r1_tarski(C,k3_subset_1(A,B))))))) # label(t35_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 485 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k2_xboole_0(B,C) = k4_subset_1(A,B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 486 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 487 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 488 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),C) -> r1_tarski(k3_subset_1(A,C),B)))))) # label(t36_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 489 (all A all B (m1_subset_1(B,A) -> (A != k1_xboole_0 -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 490 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(A))))))))) # label(t57_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 491 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (A != k1_xboole_0 -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 492 (all A k1_xboole_0 = k1_subset_1(A)) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 493 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> r1_xboole_0(B,k3_subset_1(A,B)))) # label(t26_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 494 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k5_subset_1(A,B,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 495 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> ((all C (m1_subset_1(C,A) -> r2_hidden(C,B))) -> A = B))) # label(t49_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 496 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 497 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = k4_xboole_0(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 498 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,B) -> r2_hidden(D,C))) -> r1_tarski(B,C)))))) # label(t48_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 499 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k3_subset_1(A,k3_subset_1(A,B)))) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 500 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_tarski(B,k3_subset_1(A,C)) -> B = k1_xboole_0))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 501 (all A (-$T -> (all B (m1_subset_1(B,A) -> B = k8_subset_1(A))))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 502 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r1_subset_1(A,A))) # label(irreflexivity_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 503 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) -> r2_hidden(D,C)))) -> r1_tarski(B,C)))))) # label(t7_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 504 (all A k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A))) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 505 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,B) <-> m2_subset_1(C,A,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 506 (all A (m1_subset_1(A,k1_zfmisc_1(f1_s2_subset_1)) -> (all B (m1_subset_1(B,k1_zfmisc_1(f1_s2_subset_1)) -> ((all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,B)))) & (all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,A)))) -> A = B))))) # label(s2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 507 (exists A ((all B (r2_hidden(B,A) <-> p1_s1_subset_1(B) & r2_hidden(B,f1_s1_subset_1))) & m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 508 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 509 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(B) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 510 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) <-> r1_tarski(B,k3_subset_1(A,C))))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 511 (all A all B ((-v1_xboole_0(A) -> (r2_hidden(B,A) <-> m1_subset_1(B,A))) & (v1_xboole_0(A) -> (v1_xboole_0(B) <-> m1_subset_1(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 512 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 513 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (A != k1_xboole_0 -> m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A))))))))))))))) # label(t60_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 514 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k6_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),C))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 515 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,B)) <-> B = k1_subset_1(A)))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 516 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 517 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 518 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f2_s4_subset_1) <-> p1_s4_subset_1(A)))) & (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f3_s4_subset_1) <-> p1_s4_subset_1(A)))) -> f2_s4_subset_1 = f3_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 519 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 520 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 521 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) <-> r1_xboole_0(B,k3_subset_1(A,C))))))) # label(t44_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 522 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 523 (all A all B (r2_hidden(A,B) -> m1_subset_1(k1_tarski(A),k1_zfmisc_1(B)))) # label(t63_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 524 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -r2_subset_1(A,A))) # label(irreflexivity_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 525 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k2_subset_1(A) = k4_subset_1(A,B,k3_subset_1(A,B)))) # label(t25_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 526 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> -(r2_hidden(B,C) & r2_hidden(B,k3_subset_1(A,C))))) # label(t54_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 527 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 528 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,D) & r2_hidden(E,C)))) -> k5_subset_1(A,C,D) = B))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 529 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -r2_hidden(E,D) & r2_hidden(E,C)))) -> k6_subset_1(A,C,D) = B))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 530 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),B) <-> B = k2_subset_1(A)))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 531 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(D) & -v1_xboole_0(B) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 532 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 533 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k7_subset_1(A,B,C)) = k4_subset_1(A,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))))))) # label(t34_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 534 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 535 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 536 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 537 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 538 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k2_subset_1(A) = k4_subset_1(A,B,k2_subset_1(A)))) # label(t28_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 539 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 540 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_xboole_0(D,C) & r1_tarski(B,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 541 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (k1_xboole_0 != A -> m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A))))))) # label(t56_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 542 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 543 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,B),k3_subset_1(A,k5_subset_1(A,B,C))))))) # label(t42_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 544 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 545 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 546 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -((all C (m1_subset_1(C,A) -> -r2_hidden(C,B))) & B != k1_xboole_0))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 547 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 548 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> -r2_hidden(D,B)))) -> B = k3_subset_1(A,C)))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 549 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 550 (all A exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 551 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r1_tarski(k3_subset_1(A,k4_subset_1(A,B,C)),k3_subset_1(A,B)))))) # label(t41_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 552 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 553 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,A) -> (k1_xboole_0 != A -> m1_subset_1(k6_enumset1(B,C,D,E,F,G,H,I),k1_zfmisc_1(A))))))))))))))))))) # label(t62_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 554 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 555 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_xboole_0(B,C) = k7_subset_1(A,B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 556 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 557 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 558 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 559 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) <-> -r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t51_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 560 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) <-> r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B))))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 561 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 562 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 563 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (A != k1_xboole_0 -> m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A))))))))))))) # label(t59_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 564 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 565 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k5_subset_1(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 566 (exists A ((all B (m1_subset_1(B,f1_s3_subset_1) -> (r2_hidden(B,A) <-> p1_s3_subset_1(B)))) & m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1)))) # label(s3_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 567 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k4_subset_1(A,C,B))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 568 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_subset_1(A,B) -> r1_subset_1(B,A)))) # label(symmetry_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 569 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 570 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 571 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) & r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) -> B = k3_subset_1(A,C)))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 572 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (-(r2_hidden(E,D) <-> r2_hidden(E,C)) <-> r2_hidden(E,B)))) -> k7_subset_1(A,C,D) = B))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 573 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 574 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 575 (all A (m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)) & v1_xboole_0(k1_subset_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 576 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 577 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (A != k1_xboole_0 -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 578 (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,k7_setfam_1(A,C)) <-> r1_tarski(k7_setfam_1(A,B),C)))))) # label(t52_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 579 (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]. 59.37/56.96 580 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_tarski(A) = B -> k1_tarski(k1_xboole_0) = k7_setfam_1(A,B)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 581 (exists A (v1_setfam_1(A) & -v1_xboole_0(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 582 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 583 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> B = k7_setfam_1(A,k7_setfam_1(A,B)))) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.96 584 (all A all B all C (r1_setfam_1(C,k2_tarski(A,B)) -> (all D -(-r1_tarski(D,B) & -r1_tarski(D,A) & r2_hidden(D,C))))) # label(t25_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 585 (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]. 59.37/56.97 586 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 587 (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]. 59.37/56.97 588 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 589 (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]. 59.37/56.97 590 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 591 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k5_setfam_1(A,k7_setfam_1(A,B)) = k6_subset_1(A,k2_subset_1(A),k6_setfam_1(A,B))))) # label(t48_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 592 (all A all B -(B != k1_xboole_0 & -r1_tarski(k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B)),k1_setfam_1(k2_setfam_1(A,B))) & k1_xboole_0 != A)) # label(t40_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 593 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 594 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 595 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 596 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 597 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 598 (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]. 59.37/56.97 599 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 600 (all A all B all C (r1_xboole_0(A,C) & r2_hidden(A,B) -> r1_xboole_0(k1_setfam_1(B),C))) # label(t9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 601 (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]. 59.37/56.97 602 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k3_tarski(B) = k5_setfam_1(A,B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 603 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 604 (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]. 59.37/56.97 605 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_tarski(A)) & v1_setfam_1(k1_tarski(A)))) # label(fc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 606 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 607 (all A all B ((k1_xboole_0 != A -> ((all C (r2_hidden(C,B) <-> (all D (r2_hidden(D,A) -> r2_hidden(C,D))))) <-> B = k1_setfam_1(A))) & (A = k1_xboole_0 -> (B = k1_setfam_1(A) <-> B = k1_xboole_0)))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 608 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 = B -> k8_setfam_1(A,B) = A) & (k1_xboole_0 != B -> k8_setfam_1(A,B) = k6_setfam_1(A,B)))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 609 (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]. 59.37/56.97 610 (all A all B (r1_tarski(A,B) -> k1_xboole_0 = A | r1_tarski(k1_setfam_1(B),k1_setfam_1(A)))) # label(t7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 611 (all A all B (r2_setfam_1(B,A) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | k1_xboole_0 = A)) # label(t19_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 612 (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]. 59.37/56.97 613 (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]. 59.37/56.97 614 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 615 (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]. 59.37/56.97 616 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> k7_setfam_1(A,k4_subset_1(k1_zfmisc_1(A),B,C)) = k4_subset_1(k1_zfmisc_1(A),k7_setfam_1(A,B),k7_setfam_1(A,C)))))) # label(t54_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 617 (all A all B all C (k3_setfam_1(A,B) = C <-> (all D ((exists E exists F (r2_hidden(E,A) & D = k3_xboole_0(E,F) & r2_hidden(F,B))) <-> r2_hidden(D,C))))) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 618 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 619 (all A (v1_setfam_1(A) <-> -r2_hidden(k1_xboole_0,A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 620 (all A all B k3_xboole_0(A,B) = k1_setfam_1(k2_tarski(A,B))) # label(t12_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 621 (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]. 59.37/56.97 622 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & k2_xboole_0(E,F) = D & r2_hidden(F,B))))) <-> k2_setfam_1(A,B) = C)) # label(d4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 623 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 624 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 625 (all A all B all C (r1_setfam_1(A,B) & r1_setfam_1(B,C) -> r1_setfam_1(A,C))) # label(t23_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 626 (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]. 59.37/56.97 627 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k6_setfam_1(A,k7_setfam_1(A,B)) = k6_subset_1(A,k2_subset_1(A),k5_setfam_1(A,B))))) # label(t47_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 628 (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]. 59.37/56.97 629 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 630 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & r2_hidden(F,B) & D = k4_xboole_0(E,F))))) <-> C = k4_setfam_1(A,B))) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 631 (all A all B (r2_setfam_1(A,B) <-> (all C -((all D -(r1_tarski(D,C) & r2_hidden(D,A))) & r2_hidden(C,B))))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 632 (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)))) -> B = C))))) # label(t44_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 633 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.37/56.97 634 (all A (-v2_setfam_1(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,A))))) # label(rc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 635 (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]. 59.46/56.97 636 (all A (r1_setfam_1(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 637 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 638 (all A all B all C (r1_tarski(A,C) & r2_hidden(A,B) -> r1_tarski(k1_setfam_1(B),C))) # label(t8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 639 (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) = k7_setfam_1(A,C) -> B = C))))) # label(t53_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 640 (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))) -> (C = k7_setfam_1(A,B) <-> (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]. 59.46/56.97 641 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) <-> r2_hidden(k3_subset_1(A,C),k7_setfam_1(A,B))))))) # label(t49_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 642 (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]. 59.46/56.97 643 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 644 (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]. 59.46/56.97 645 (all A k1_setfam_1(k1_tarski(A)) = A) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 646 (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]. 59.46/56.97 647 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 648 (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]. 59.46/56.97 649 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 650 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 651 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(B,C))) -> k1_xboole_0 = A | r1_tarski(B,k1_setfam_1(A)))) # label(t6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 652 (all A all B -(k1_xboole_0 != B & k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) & k1_xboole_0 != A)) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 653 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 654 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 655 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(k7_setfam_1(A,B) = k1_xboole_0 & B != k1_xboole_0))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 656 (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]. 59.46/56.97 657 (all A all B ((all C -((all D -(r1_tarski(C,D) & r2_hidden(D,B))) & r2_hidden(C,A))) <-> r1_setfam_1(A,B))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 658 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 659 (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]. 59.46/56.97 660 (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]. 59.46/56.97 661 (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]. 59.46/56.97 662 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 663 (all A all B k3_tarski(k3_setfam_1(k1_tarski(A),B)) = k3_xboole_0(A,k3_tarski(B))) # label(t36_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 664 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 665 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 666 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 667 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k1_setfam_1(B) = k6_setfam_1(A,B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 668 (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]. 59.46/56.97 669 (all A all B (B != k1_xboole_0 -> k4_xboole_0(A,k1_setfam_1(B)) = k3_tarski(k4_setfam_1(k1_tarski(A),B)))) # label(t38_setfam_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 670 (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]. 59.46/56.97 671 (all A all B all C (r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 672 (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]. 59.46/56.97 673 (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]. 59.46/56.97 674 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 675 (all A all B all C -(m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) & r2_hidden(A,B))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 676 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k7_relat_1(B,A) <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 677 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 678 (all A (v1_relat_1(A) -> k3_relat_1(k4_relat_1(A)) = k3_relat_1(A))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 679 (all A (v1_relat_1(A) -> k1_relat_1(A) = k2_relat_1(k4_relat_1(A)) & k2_relat_1(A) = k1_relat_1(k4_relat_1(A)))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 680 (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]. 59.46/56.97 681 (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]. 59.46/56.97 682 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(k5_relat_1(B,C),A) = k10_relat_1(B,k10_relat_1(C,A)))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 683 (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]. 59.46/56.97 684 (all A all B (v1_relat_1(B) -> -(A != k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & k1_xboole_0 = k9_relat_1(B,A)))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 685 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 686 (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]. 59.46/56.97 687 (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]. 59.46/56.97 688 (all A all B (v1_relat_1(B) -> -((all C -r2_hidden(C,k1_relat_1(B))) & r2_hidden(A,k2_relat_1(B))))) # label(t19_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 689 (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]. 59.46/56.97 690 (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]. 59.46/56.97 691 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k8_relat_1(A,C),B) = k8_relat_1(A,k7_relat_1(C,B)))) # label(t140_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 692 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 693 (exists A ((all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(C,f2_s1_relat_1) & p1_s1_relat_1(B,C) & r2_hidden(B,f1_s1_relat_1))) & v1_relat_1(A))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 694 (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]. 59.46/56.97 695 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 696 (all A (v1_relat_1(A) -> (all B all C ((all D ((exists E (r2_hidden(k4_tarski(E,D),A) & r2_hidden(E,B))) <-> r2_hidden(D,C))) <-> k9_relat_1(A,B) = C)))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 697 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 698 (all A k1_xboole_0 = k10_relat_1(k1_xboole_0,A)) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 699 (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]. 59.46/56.97 700 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 701 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 702 (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]. 59.46/56.97 703 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> (C = k7_relat_1(A,B) <-> (all D all E (r2_hidden(k4_tarski(D,E),A) & r2_hidden(D,B) <-> r2_hidden(k4_tarski(D,E),C)))))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 704 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t134_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 705 (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]. 59.46/56.97 706 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 707 (all A all B (v1_relat_1(B) -> k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)) = k10_relat_1(B,A))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 708 (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]. 59.46/56.97 709 (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]. 59.46/56.97 710 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 711 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 712 (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]. 59.46/56.97 713 (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]. 59.46/56.97 714 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k5_relat_1(A,B)) = k5_relat_1(k4_relat_1(B),k4_relat_1(A)))))) # label(t54_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 715 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(A),k1_relat_1(B)) -> k1_relat_1(A) = k1_relat_1(k5_relat_1(A,B))))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 716 (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]. 59.46/56.97 717 (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]. 59.46/56.97 718 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 719 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 720 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> B = A))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 721 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 722 (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]. 59.46/56.97 723 (all A (v1_relat_1(A) -> (k2_relat_1(A) = k1_xboole_0 | k1_relat_1(A) = k1_xboole_0 -> A = k1_xboole_0))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 724 (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]. 59.46/56.97 725 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 726 (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]. 59.46/56.97 727 (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]. 59.46/56.97 728 (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]. 59.46/56.97 729 (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]. 59.46/56.97 730 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k2_xboole_0(A,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 731 (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]. 59.46/56.97 732 (all A (v1_relat_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A))) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 733 (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]. 59.46/56.97 734 (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]. 59.46/56.97 735 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 736 (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]. 59.46/56.97 737 (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]. 59.46/56.97 738 (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]. 59.46/56.97 739 (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]. 59.46/56.97 740 (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]. 59.46/56.97 741 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 742 (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]. 59.46/56.97 743 (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]. 59.46/56.97 744 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k8_relat_1(A,k8_relat_1(A,B)))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 745 (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]. 59.46/56.97 746 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> k1_relat_1(k7_relat_1(B,A)) = A))) # label(t91_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 747 (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]. 59.46/56.97 748 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 749 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(C)) & r2_hidden(A,B) <-> r2_hidden(A,k2_relat_1(k8_relat_1(B,C)))))) # label(t115_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 750 (all A (k2_relat_1(k6_relat_1(A)) = A & k1_relat_1(k6_relat_1(A)) = A)) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 751 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,B) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k7_relat_1(C,B)))))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 752 (all A all B (v1_relat_1(B) -> -(r1_tarski(A,k2_relat_1(B)) & k10_relat_1(B,A) = k1_xboole_0 & k1_xboole_0 != A))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 753 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(D,C),A))) <-> B = k4_relat_1(A)))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 754 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 755 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 756 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 757 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 758 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 759 (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]. 59.46/56.97 760 (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]. 59.46/56.97 761 (all A (v1_relat_1(A) -> k4_relat_1(k4_relat_1(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 762 (all A k6_relat_1(A) = k4_relat_1(k6_relat_1(A))) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 763 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 764 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 765 (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]. 59.46/56.97 766 (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]. 59.46/56.97 767 (all A k9_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 768 (all A (v1_relat_1(A) -> A = k7_relat_1(A,k1_relat_1(A)))) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 769 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),D) & r2_hidden(B,C) <-> r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C)))))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 770 (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]. 59.46/56.97 771 (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]. 59.46/56.97 772 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k1_tarski(B) = k2_relat_1(C) & k1_relat_1(C) = k1_tarski(A)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 773 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 774 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 775 (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]. 59.46/56.97 776 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 777 (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]. 59.46/56.97 778 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(k2_xboole_0(A,B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 779 (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]. 59.46/56.97 780 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 781 (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]. 59.46/56.97 782 (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]. 59.46/56.97 783 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k2_relat_1(C)) & r2_hidden(A,k1_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 784 (exists A (v1_relat_1(A) & v3_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 785 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 786 (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]. 59.46/56.97 787 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 788 (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]. 59.46/56.97 789 (exists A (v1_relat_1(A) & v1_xboole_0(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 790 (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]. 59.46/56.97 791 (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]. 59.46/56.97 792 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,C) = k7_relat_1(A,C) & k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(B,k2_xboole_0(C,D)) = k7_relat_1(A,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 793 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (r1_tarski(C,D) & k7_relat_1(B,D) = k7_relat_1(A,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 794 (all A (v1_relat_1(A) -> r1_tarski(k1_relat_1(A),k3_relat_1(A)) & r1_tarski(k2_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 795 (all A all B (v1_relat_1(B) -> (B = k6_relat_1(A) <-> (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(C,A) & C = D))))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 796 (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]. 59.46/56.97 797 (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]. 59.46/56.97 798 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 799 (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]. 59.46/56.97 800 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k9_relat_1(B,A) <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 801 (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]. 59.46/56.97 802 (all A (v1_relat_1(A) -> k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))) = A)) # label(t22_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 803 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(D,k2_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(A,D),C))) <-> r2_hidden(A,k10_relat_1(C,B))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 804 (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]. 59.46/56.97 805 (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]. 59.46/56.97 806 (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]. 59.46/56.97 807 (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]. 59.46/56.97 808 (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]. 59.46/56.97 809 (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]. 59.46/56.97 810 (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]. 59.46/56.97 811 (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]. 59.46/56.97 812 (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]. 59.46/56.97 813 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k2_xboole_0(A,B)))))) # label(t40_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 814 (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]. 59.46/56.97 815 (all A all B (v1_relat_1(B) -> -(v3_relat_1(B) & -v3_relat_1(k7_relat_1(B,A))))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 816 (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]. 59.46/56.97 817 (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]. 59.46/56.97 818 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k6_relat_1(k1_relat_1(D)) = k5_relat_1(C,B) & k6_relat_1(A) = k5_relat_1(B,D) & r1_tarski(k2_relat_1(C),A) & A = k1_relat_1(B) -> C = D))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 819 (all A (v1_xboole_0(A) -> v1_relat_1(k4_relat_1(A)) & v1_xboole_0(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 820 (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]. 59.46/56.97 821 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 822 (all A all B all C all D all E (v1_relat_1(E) -> (k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) = E -> k2_tarski(B,D) = k2_relat_1(E) & k2_tarski(A,C) = k1_relat_1(E)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 823 (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]. 59.46/56.97 824 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 825 (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]. 59.46/56.97 826 (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]. 59.46/56.97 827 (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]. 59.46/56.97 828 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 829 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 830 (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]. 59.46/56.97 831 (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]. 59.46/56.97 832 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)) & v1_xboole_0(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 833 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(D,k1_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(D,A),C))) <-> r2_hidden(A,k9_relat_1(C,B))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 834 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 835 (all A (v1_relat_1(A) -> (r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0)) <-> v3_relat_1(A)))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 836 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> k2_relat_1(A) = B)))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 837 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 838 (all A (v1_relat_1(A) -> k1_relat_1(A) = k10_relat_1(A,k2_relat_1(A)))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 839 (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]. 59.46/56.97 840 (all A (v1_xboole_0(A) -> v1_relat_1(k2_relat_1(A)) & v1_xboole_0(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 841 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 842 (all A (v1_relat_1(A) -> (all B all C (C = k10_relat_1(A,B) <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),A))))))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 843 (all A all B (v3_relat_1(A) & v1_relat_1(A) -> v3_relat_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 844 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 845 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 846 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 847 (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]. 59.46/56.97 848 (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]. 59.46/56.97 849 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k2_tarski(A,B) = k3_relat_1(C)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 850 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 851 (all A all B (v1_relat_1(B) -> r1_tarski(k5_relat_1(B,k6_relat_1(A)),B) & r1_tarski(k5_relat_1(k6_relat_1(A),B),B))) # label(t76_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 852 (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]. 59.46/56.97 853 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 854 (all A all B all C (v1_relat_1(C) -> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 855 (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]. 59.46/56.97 856 (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]. 59.46/56.97 857 (all A (v1_relat_1(A) -> k1_xboole_0 = k5_relat_1(k1_xboole_0,A) & k5_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 858 (all A (v1_relat_1(A) -> ((all B (r2_hidden(B,k2_relat_1(A)) -> B = k1_xboole_0)) <-> v3_relat_1(A)))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.97 859 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> A = k1_xboole_0))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 860 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 861 (all A all B (v1_relat_1(B) -> k7_relat_1(k7_relat_1(B,A),A) = k7_relat_1(B,A))) # label(t101_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 862 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,k5_relat_1(B,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 863 (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]. 59.46/56.98 864 (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]. 59.46/56.98 865 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 866 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 867 (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]. 59.46/56.98 868 (all A (v1_relat_1(A) <-> (all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 869 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 870 (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]. 59.46/56.98 871 (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]. 59.46/56.98 872 (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]. 59.46/56.98 873 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 874 (all A k8_relat_1(A,k1_xboole_0) = k1_xboole_0) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 875 (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]. 59.46/56.98 876 (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]. 59.46/56.98 877 (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]. 59.46/56.98 878 (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]. 59.46/56.98 879 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 880 (all A (v1_relat_1(A) -> (k2_relat_1(A) = k1_xboole_0 <-> k1_relat_1(A) = k1_xboole_0))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 881 (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]. 59.46/56.98 882 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(C,B) & r1_tarski(k1_relat_1(C),A) -> r1_tarski(C,k7_relat_1(B,A))))))) # label(t186_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 883 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k3_xboole_0(A,B),C) = k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t135_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 884 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 885 (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]. 59.46/56.98 886 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k5_relat_1(k6_relat_1(A),B)))) # label(t77_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 887 (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]. 59.46/56.98 888 (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]. 59.46/56.98 889 (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]. 59.46/56.98 890 (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]. 59.46/56.98 891 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> r2_hidden(E,A) & r2_hidden(k4_tarski(D,E),B))) <-> C = k8_relat_1(A,B)))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 892 (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]. 59.46/56.98 893 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> B = k8_relat_1(A,B)))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 894 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E ((exists F (r2_hidden(k4_tarski(F,E),B) & r2_hidden(k4_tarski(D,F),A))) <-> r2_hidden(k4_tarski(D,E),C))) <-> k5_relat_1(A,B) = C))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 895 (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]. 59.46/56.98 896 (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]. 59.46/56.98 897 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 898 (all A (v1_relat_1(A) -> A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t80_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 899 (all A (v1_relat_1(A) -> (all B ((all C ((exists D r2_hidden(k4_tarski(C,D),A)) <-> r2_hidden(C,B))) <-> B = k1_relat_1(A))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 900 (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]. 59.46/56.98 901 (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]. 59.46/56.98 902 (all A all B (v1_relat_1(B) -> k2_relat_1(k8_relat_1(A,B)) = k3_xboole_0(k2_relat_1(B),A))) # label(t119_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 903 (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]. 59.46/56.98 904 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B))))))) # label(t106_relat_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 905 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A)))) <-> r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A)))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 906 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 907 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 908 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & (all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> (D = k1_funct_1(A,C) <-> k1_funct_1(B,D) = C))) & k1_relat_1(B) = k2_relat_1(A) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 909 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 910 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) & (all B -((all C all D B != k4_tarski(C,D)) & r2_hidden(B,A))) -> v1_relat_1(A) & v1_funct_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 911 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 912 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k10_relat_1(B,A) = k9_relat_1(k2_funct_1(B),A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 913 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 914 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 915 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k9_relat_1(B,k10_relat_1(B,A)) = A))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 916 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(k8_relat_1(A,C),B) = k1_funct_1(C,B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 917 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 918 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C)))))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 919 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 920 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 921 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_tarski(A) = k1_relat_1(B) -> k2_relat_1(B) = k1_tarski(k1_funct_1(B,A))))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 922 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A) & k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,A),B)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 923 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 924 (all A all B -(-(k1_xboole_0 != B & k1_xboole_0 = A) & (all C (v1_funct_1(C) & v1_relat_1(C) -> -(k1_relat_1(C) = B & r1_tarski(k2_relat_1(C),A)))))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 925 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 926 (exists A (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 927 (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]. 59.46/56.98 928 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) <-> v1_funct_1(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 929 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 930 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 931 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 932 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & k1_relat_1(B) = k1_relat_1(A) -> A = B))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 933 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 934 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k9_relat_1(k6_relat_1(A),B))) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 935 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(A) & v2_funct_1(B)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 936 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 937 (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]. 59.46/56.98 938 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 939 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) = A & A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A)))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 940 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 941 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,A),k2_relat_1(B))))) # label(t12_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 942 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C)) & k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 943 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 944 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 945 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & k6_relat_1(k2_relat_1(A)) = k5_relat_1(B,A) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 946 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (v1_funct_1(B) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 947 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 948 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 949 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k5_relat_1(k6_relat_1(A),C),B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 950 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k10_relat_1(k2_funct_1(B),A) = k9_relat_1(B,A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 951 (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]. 59.46/56.98 952 (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]. 59.46/56.98 953 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 954 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k9_relat_1(B,k1_tarski(A)) = k1_tarski(k1_funct_1(B,A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 955 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 956 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (A = k1_relat_1(D) & k5_relat_1(B,D) = k5_relat_1(B,C) & k1_relat_1(C) = A & k2_relat_1(B) = A -> D = C))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 957 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 958 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((-r2_hidden(B,k1_relat_1(A)) -> (C = k1_xboole_0 <-> C = k1_funct_1(A,B))) & (r2_hidden(B,k1_relat_1(A)) -> (k1_funct_1(A,B) = C <-> r2_hidden(k4_tarski(B,C),A))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 959 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B)))) <-> v3_relat_1(A)))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 960 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k9_relat_1(k8_relat_1(A,C),B),k9_relat_1(C,B)))) # label(t120_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 961 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & k1_relat_1(B) = k1_relat_1(C) & k5_relat_1(B,A) = k5_relat_1(C,A) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> C = B))))) <-> v2_funct_1(A)))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 962 (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]. 59.46/56.98 963 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k6_relat_1(A) = B <-> k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C)))))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 964 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 965 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) & v2_funct_1(B) -> A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) & k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) = A))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 966 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 967 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 968 (all A all B (v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & k10_relat_1(B,k1_tarski(C)) = k1_xboole_0)) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 969 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k2_funct_1(A) <-> (all C all D ((C = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A)) -> r2_hidden(C,k2_relat_1(A)) & D = k1_funct_1(B,C)) & (r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D -> r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C))) & k1_relat_1(B) = k2_relat_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 970 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 971 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B -((all C k1_tarski(C) != k10_relat_1(A,k1_tarski(B))) & r2_hidden(B,k2_relat_1(A))))))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 972 (exists A (v1_relat_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> f2_s3_funct_1(B) = k1_funct_1(A,B))) & f1_s3_funct_1 = k1_relat_1(A) & v1_funct_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 973 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A))) # label(t145_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 974 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A))))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 975 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 976 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 977 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),B) = k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))))) # label(t150_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 978 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 979 (all A -(r2_hidden(A,f1_s2_funct_1) & (all B -p1_s2_funct_1(A,B)))) & (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> C = B)) -> (exists A (v1_relat_1(A) & k1_relat_1(A) = f1_s2_funct_1 & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 980 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 981 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & k1_relat_1(B) = k2_relat_1(A) -> k2_funct_1(A) = B))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 982 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 983 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B all C (r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) & r2_hidden(C,k1_relat_1(A)) -> C = B))))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 984 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(B,k2_relat_1(C)) & r1_tarski(A,k2_relat_1(C)) & k10_relat_1(C,B) = k10_relat_1(C,A) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 985 (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]. 59.46/56.98 986 (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]. 59.46/56.98 987 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 988 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 989 (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]. 59.46/56.98 990 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 991 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 992 (all A (v2_funct_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)) & v1_funct_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 993 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(k5_relat_1(B,A)) = k1_relat_1(B) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 994 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 995 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> A = k2_funct_1(k2_funct_1(A))))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 996 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 997 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 998 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (C = k10_relat_1(A,B) <-> (all D (r2_hidden(k1_funct_1(A,D),B) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,C))))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 999 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1000 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,k1_funct_1(B,A)) = k1_funct_1(k5_relat_1(B,C),A)))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1001 (all A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) -> v2_funct_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1002 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1003 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(C) = A & k5_relat_1(B,D) = k5_relat_1(B,C) & A = k1_relat_1(D) -> C = D))))) -> k2_relat_1(B) = A))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1004 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1005 (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]. 59.46/56.98 1006 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((all D ((exists E (r2_hidden(E,B) & D = k1_funct_1(A,E) & r2_hidden(E,k1_relat_1(A)))) <-> r2_hidden(D,C))) <-> C = k9_relat_1(A,B))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1007 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k2_relat_1(A) = k2_relat_1(k5_relat_1(B,A)) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1008 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1009 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_relat_1(A) <-> (all B -(r2_hidden(B,k1_relat_1(A)) & v1_xboole_0(k1_funct_1(A,B))))))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1010 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> k2_funct_1(k5_relat_1(A,B)) = k5_relat_1(k2_funct_1(B),k2_funct_1(A))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1011 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(k1_funct_1(B,D) = C & r2_hidden(D,k1_relat_1(B)))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1012 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1013 (all A (v1_funct_1(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1014 (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]. 59.46/56.98 1015 (all A ((all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(C) & A = k1_relat_1(B) -> B = C))))) -> A = k1_xboole_0)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1016 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1017 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1018 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1019 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1020 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1021 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1022 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) <-> r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1023 (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]. 59.46/56.98 1024 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(A,k1_relat_1(C)) -> k9_relat_1(C,k2_tarski(A,B)) = k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1025 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1026 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1027 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1028 (all A (k1_xboole_0 != A -> (all B exists C (k1_tarski(B) = k2_relat_1(C) & A = k1_relat_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1029 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1030 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1031 (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]. 59.46/56.98 1032 (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]. 59.46/56.98 1033 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1034 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1035 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1036 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_relat_1(B) = k1_tarski(A) & k1_tarski(A) = k2_relat_1(C) & k1_relat_1(C) = k1_relat_1(B) -> C = B))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1037 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k2_funct_1(A)) & v1_relat_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1038 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1039 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1040 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1041 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k7_relat_1(C,A) = B <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A)))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1042 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1043 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k2_funct_1(A)) = k1_relat_1(A) & k1_relat_1(k2_funct_1(A)) = k2_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1044 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1045 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(B) & k5_relat_1(C,B) = B & r1_tarski(k2_relat_1(C),A) & A = k1_relat_1(C) & A = k1_relat_1(B) -> k6_relat_1(A) = C))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1046 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1047 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1048 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.46/56.98 1049 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(B,k1_funct_1(A,D)) = k1_funct_1(C,D))) -> C = k5_relat_1(A,B)))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1050 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1051 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1052 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1053 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k3_xboole_0(A,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1054 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1055 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1056 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) & r2_hidden(B,k1_relat_1(C)) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1057 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k9_relat_1(k8_relat_1(A,C),B) = k3_xboole_0(A,k9_relat_1(C,B)))) # label(t126_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1058 (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]. 59.48/56.98 1059 (all A all B all C (p1_s1_funct_1(A,B) & p1_s1_funct_1(A,C) -> C = B)) -> (exists A (v1_relat_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> p1_s1_funct_1(B,C) & r2_hidden(B,f1_s1_funct_1))) & v1_funct_1(A))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1060 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1061 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k8_relat_1(A,C) = B <-> (all D (r2_hidden(D,k1_relat_1(B)) <-> r2_hidden(k1_funct_1(C,D),A) & r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,D)))))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1062 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1063 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1064 (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]. 59.48/56.98 1065 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1066 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (k1_funct_1(A,D) = C & r2_hidden(D,k1_relat_1(A)))))) <-> k2_relat_1(A) = B)))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1067 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) & r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t76_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1068 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1069 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1070 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1071 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (B = k1_funct_1(C,A) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.98 1072 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k9_relat_1(B,k10_relat_1(B,A)) = k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1073 (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]. 59.48/56.99 1074 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1075 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1076 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & r1_tarski(A,k1_relat_1(C)) & v2_funct_1(C) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1077 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1078 (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]. 59.48/56.99 1079 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1080 (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]. 59.48/56.99 1081 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1082 (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]. 59.48/56.99 1083 (exists A (v1_relat_1(A) & k1_relat_1(A) = f1_s4_funct_1 & (all B (m1_subset_1(B,f1_s4_funct_1) -> f2_s4_funct_1(B) = k1_funct_1(A,B))) & v1_funct_1(A))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1084 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1085 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k5_relat_1(A,k2_funct_1(A)) = k6_relat_1(k1_relat_1(A)) & k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1086 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_funct_1(A) = k4_relat_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1087 (all A (v1_relat_1(A) & v1_funct_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A & A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1088 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1089 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1090 (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]. 59.48/56.99 1091 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(A) = k1_relat_1(B) & k5_relat_1(A,B) = A -> k6_relat_1(k1_relat_1(B)) = B))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1092 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1093 (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]. 59.48/56.99 1094 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k4_xboole_0(A,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1095 (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]. 59.48/56.99 1096 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_funct_1(k8_relat_1(A,B)) & v1_relat_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1097 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1098 (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]. 59.48/56.99 1099 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1100 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1101 $T # label(t24_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1102 $T # label(t53_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1103 $T # label(t22_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1104 $T # label(t39_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1105 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 59.48/56.99 1106 $T # label(t63_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1107 $T # label(t86_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1108 $T # label(t66_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1109 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 59.48/56.99 1110 $T # label(t62_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1111 $T # label(t2_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1112 (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)) & k2_xboole_0(B,D) = C -> k1_funct_1(C,A) = k1_funct_1(B,A)))))))) # label(t34_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1113 (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) -> (v2_funct_1(A) & v2_funct_1(B) & C = k2_xboole_0(A,B) & r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) -> v2_funct_1(C)))))))) # label(t37_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1114 $T # label(t82_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1115 $T # label(t73_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1116 (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]. 59.48/56.99 1117 $T # label(t40_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1118 $T # label(t42_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1119 (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)) & B = k2_xboole_0(C,D) & k1_funct_1(B,A) != k1_funct_1(D,A) & k1_funct_1(B,A) != k1_funct_1(C,A)))))))) # label(t36_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1120 (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)) -> v1_relat_1(k2_xboole_0(A,B)) & v1_funct_1(k2_xboole_0(A,B))))))) # label(t31_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1121 $T # label(t55_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1122 (all A all B (v1_relat_1(k1_tarski(k4_tarski(A,B))) & v1_funct_1(k1_tarski(k4_tarski(A,B))))) # label(t15_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1123 (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) -> (r1_tarski(C,B) & r1_tarski(A,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]. 59.48/56.99 1124 (all A (v1_relat_1(A) & v1_funct_1(A) -> (A = k1_xboole_0 -> k1_xboole_0 = k2_funct_1(A)))) # label(t49_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1125 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,k1_funct_1(C,A)),k7_relat_1(C,B)) <-> r2_hidden(A,B) & r2_hidden(A,k1_relat_1(C))))) # label(t52_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 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) -> C = B)) <-> v2_funct_1(A)))) # label(t25_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1127 $T # label(t51_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1128 $T # label(t65_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1129 $T # label(t61_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1130 $T # label(t14_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1131 $T # label(t11_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1132 $T # label(t44_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1133 (all A all B (v1_funct_1(B) & v1_relat_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]. 59.48/56.99 1134 $T # label(t57_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1135 (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) & r1_tarski(A,B) -> A = B))))) # label(t9_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1136 $T # label(t17_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1137 $T # label(t4_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1138 $T # label(t48_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1139 $T # label(t72_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1140 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> 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]. 59.48/56.99 1141 $T # label(t56_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1142 $T # label(t20_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1143 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> B = k1_funct_1(C,A)))) # label(t16_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1144 $T # label(t1_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1145 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r1_tarski(A,B) -> v2_funct_1(A)))))) # label(t26_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1146 $T # label(t74_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1147 $T # label(t10_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1148 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_xboole_0(B,C) = A -> k2_xboole_0(k1_relat_1(B),k1_relat_1(C)) = k1_relat_1(A) & k2_relat_1(A) = k2_xboole_0(k2_relat_1(B),k2_relat_1(C))))))))) # label(t33_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1149 $T # label(t7_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1150 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(B)) & B = k3_xboole_0(C,D) -> k1_funct_1(C,A) = k1_funct_1(B,A) & k1_funct_1(D,A) = k1_funct_1(B,A)))))))) # label(t29_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1151 $T # label(t85_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1152 (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]. 59.48/56.99 1153 $T # label(t60_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1154 $T # label(t5_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1155 $T # label(t81_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1156 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r1_tarski(B,A) -> v1_relat_1(B) & v1_funct_1(B))))) # label(t6_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1157 $T # label(t71_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1158 $T # label(t77_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1159 $T # label(t3_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1160 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k3_xboole_0(B,A)) & v1_funct_1(k3_xboole_0(B,A)))) # label(t27_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1161 $T # label(t84_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1162 $T # label(t68_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1163 (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) -> (k2_xboole_0(D,B) = C & 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]. 59.48/56.99 1164 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) <-> r1_tarski(k1_relat_1(A),k1_relat_1(B)) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(t8_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1165 $T # label(t43_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1166 $T # label(t21_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1167 $T # label(t41_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1168 (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) -> (k3_xboole_0(A,B) = C -> v2_funct_1(C) | -v2_funct_1(B) & -v2_funct_1(A)))))))) # label(t30_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1169 $T # label(t83_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1170 (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) -> (k3_xboole_0(B,C) = A -> 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]. 59.48/56.99 1171 (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 -> D = B))) # label(t19_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1172 $T # label(t59_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1173 (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]. 59.48/56.99 1174 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(B,C) & r1_tarski(A,k1_relat_1(B)) -> k7_relat_1(C,A) = k7_relat_1(B,A)))))) # label(t88_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1175 $T # label(t80_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1176 $T # label(t58_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1177 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> 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]. 59.48/56.99 1178 $T # label(t23_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1179 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) & v2_funct_1(B) -> k8_relat_1(k2_relat_1(A),B) = A))))) # label(t79_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1180 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(k4_tarski(C,B),k2_funct_1(A))))))) # label(t47_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1181 (all A all B (v1_relat_1(B) & v1_funct_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]. 59.48/56.99 1182 $T # label(t75_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1183 $T # label(t45_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1184 $T # label(t78_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1185 $T # label(t76_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1186 (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(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]. 59.48/56.99 1187 $T # label(t70_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1188 $T # label(t50_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1189 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,k1_funct_1(C,A)),k8_relat_1(B,C)) <-> r2_hidden(k1_funct_1(C,A),B) & r2_hidden(A,k1_relat_1(C))))) # label(t67_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1190 (all A (v1_relat_1(A) -> (all B (r6_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(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1191 (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]. 59.48/56.99 1192 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1193 (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]. 59.48/56.99 1194 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1195 (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]. 59.48/56.99 1196 (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]. 59.48/56.99 1197 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1198 (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]. 59.48/56.99 1199 (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]. 59.48/56.99 1200 (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]. 59.48/56.99 1201 (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]. 59.48/56.99 1202 (all A (v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)))) # label(t23_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1203 (all A (v1_relat_1(A) -> (v3_relat_2(A) & v8_relat_2(A) -> v1_relat_2(A)))) # label(t22_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1204 (all A (v1_relat_1(A) -> (v4_relat_2(A) <-> r1_tarski(k3_xboole_0(A,k4_relat_1(A)),k6_relat_1(k1_relat_1(A)))))) # label(t39_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1205 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1206 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1207 (all A (v1_relat_1(A) -> (v3_relat_2(A) <-> r3_relat_2(A,k3_relat_1(A))))) # label(d11_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1208 (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]. 59.48/56.99 1209 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k1_relat_1(A) = k1_relat_1(k4_relat_1(A)) & k2_relat_1(A) = k2_relat_1(k4_relat_1(A))))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1210 (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]. 59.48/56.99 1211 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v1_relat_2(A) & v1_relat_2(B) -> v1_relat_2(k2_xboole_0(A,B)) & v1_relat_2(k3_xboole_0(A,B))))))) # label(t31_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1212 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) <-> (all C all D (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) & r2_hidden(C,B) -> C = D)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1213 (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]. 59.48/56.99 1214 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1215 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v4_relat_2(A) & v2_relat_2(A)))) # label(t26_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1216 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) <-> (all C all D all E (r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),A) & r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1217 (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]. 59.48/56.99 1218 (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]. 59.48/56.99 1219 (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]. 59.48/56.99 1220 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1221 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1222 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1223 (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]. 59.48/56.99 1224 (all A (v1_relat_1(A) -> (v7_relat_2(A) -> v1_relat_2(A) & v6_relat_2(A)))) # label(t46_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1225 (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]. 59.48/56.99 1226 (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]. 59.48/56.99 1227 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(k4_tarski(C,C),A) & r2_hidden(C,B))) <-> r2_relat_2(A,B))))) # label(d2_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1228 (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]. 59.48/56.99 1229 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1230 (all A (v1_relat_1(A) -> (v2_relat_2(A) & v8_relat_2(A) -> v5_relat_2(A)))) # label(t25_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1231 (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]. 59.48/56.99 1232 (all A (v1_relat_1(A) -> (v6_relat_2(A) <-> r6_relat_2(A,k3_relat_1(A))))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1233 (all A (v1_relat_1(A) -> (v8_relat_2(A) <-> r1_tarski(k5_relat_1(A,A),A)))) # label(t44_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1234 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1235 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1236 (all A (v1_relat_1(A) -> (A = k4_relat_1(A) <-> v3_relat_2(A)))) # label(t30_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1237 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1238 (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]. 59.48/56.99 1239 (all A (v1_relat_1(A) -> (all B (r5_relat_2(A,B) <-> (all C all D -(r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) & r2_hidden(D,B) & r2_hidden(C,B))))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1240 (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]. 59.48/56.99 1241 (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]. 59.48/56.99 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(D,C),A) & -r2_hidden(k4_tarski(C,D),A))) <-> r7_relat_2(A,B))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1243 (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]. 59.48/56.99 1244 (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]. 59.48/56.99 1245 (all A (v1_relat_1(A) -> (v1_relat_2(A) <-> r1_relat_2(A,k3_relat_1(A))))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1246 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1247 (all A (v1_relat_1(A) -> (r8_relat_2(A,k3_relat_1(A)) <-> v8_relat_2(A)))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1248 (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]. 59.48/56.99 1249 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1250 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1251 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1252 (all A (v1_relat_1(A) -> (r7_relat_2(A,k3_relat_1(A)) <-> v7_relat_2(A)))) # label(d15_relat_2) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1253 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1254 (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]. 59.48/56.99 1255 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1256 (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]. 59.48/56.99 1257 (all A (v3_ordinal1(A) <-> v1_ordinal1(A) & v2_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1258 (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]. 59.48/56.99 1259 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1260 (all A (v3_ordinal1(A) -> v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1261 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1262 (all A (v3_ordinal1(A) -> -(v4_ordinal1(A) & (exists B (A = k1_ordinal1(B) & v3_ordinal1(B)))) & -((all B (v3_ordinal1(B) -> k1_ordinal1(B) != A)) & -v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1263 (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]. 59.48/56.99 1264 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1265 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1266 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1267 (all A -(all B (v3_ordinal1(B) <-> r2_hidden(B,A)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1268 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1269 (all A all B (v3_ordinal1(B) -> -(A != k1_xboole_0 & (all C (v3_ordinal1(C) -> -((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D)))) & r2_hidden(C,A)))) & r1_tarski(A,B)))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1270 (all A all B all C all D -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(D,A) & r2_hidden(C,D))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1271 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1272 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal1(C) -> (r2_hidden(A,B) & r2_hidden(C,A) -> r2_hidden(C,B)))))))) # label(t19_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1273 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r2_hidden(A,k1_ordinal1(B))))))) # label(t34_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1274 (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]. 59.48/56.99 1275 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1276 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1277 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1278 (exists A (v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1279 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1280 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1281 (all A all B (r2_hidden(A,k1_ordinal1(B)) <-> r2_hidden(A,B) | A = B)) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1282 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1283 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1284 (all A ((all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r3_xboole_0(B,C))) <-> v6_ordinal1(A))) # label(d9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1285 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1286 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) & r1_tarski(A,B) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1287 (all A ((all B all C -(r2_hidden(C,A) & -r2_hidden(C,B) & B != C & -r2_hidden(B,C) & r2_hidden(B,A))) <-> v2_ordinal1(A))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1288 (all A all B -(r1_tarski(B,A) & r2_hidden(A,B))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1289 (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]. 59.48/56.99 1290 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1291 (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]. 59.48/56.99 1292 (all A all B all C all D all E all F -(r2_hidden(A,B) & r2_hidden(E,F) & r2_hidden(F,A) & r2_hidden(D,E) & r2_hidden(C,D) & r2_hidden(B,C))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1293 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v1_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v2_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1294 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal1(B) -> k7_relat_1(A,B) = k2_ordinal1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1295 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r2_hidden(B,A) | r1_ordinal1(A,B))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1296 (all A all B (k1_ordinal1(B) = k1_ordinal1(A) -> B = A)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1297 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> (r1_tarski(A,B) <-> r1_ordinal1(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1298 (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]. 59.48/56.99 1299 (exists A (v1_relat_1(A) & f1_s4_ordinal1 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) -> (C = k2_ordinal1(A,B) & r2_hidden(B,f1_s4_ordinal1) -> k1_funct_1(A,B) = f2_s4_ordinal1(C)))))) & v5_ordinal1(A) & v1_funct_1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1300 (all A all B (m1_ordinal1(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(dt_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1301 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1302 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1303 (all A exists B (v3_ordinal1(B) & -r2_hidden(B,A) & (all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1304 (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]. 59.48/56.99 1305 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> r2_hidden(k1_ordinal1(B),A)))) <-> v4_ordinal1(A)))) # label(t41_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1306 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1307 (all A all B all C -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,A))) # label(t3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1308 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(B,A) & A != B & -r2_xboole_0(A,B)))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1309 k1_relat_1(f3_s3_ordinal1) = f1_s3_ordinal1 & k1_relat_1(f4_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f4_s3_ordinal1,A) = B -> k1_funct_1(f4_s3_ordinal1,A) = f2_s3_ordinal1(B)))))) & (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f3_s3_ordinal1,A) = B -> f2_s3_ordinal1(B) = k1_funct_1(f3_s3_ordinal1,A)))))) -> f3_s3_ordinal1 = f4_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1310 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1311 (all A k1_ordinal1(A) = k2_xboole_0(A,k1_tarski(A))) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1312 (all A (v4_ordinal1(A) <-> k3_tarski(A) = A)) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1313 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v3_ordinal1(B) & v5_ordinal1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1314 (all A (v3_ordinal1(A) -> v2_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & v1_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1315 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1316 (all A all B all C all D all E -(r2_hidden(C,D) & r2_hidden(E,A) & r2_hidden(D,E) & r2_hidden(B,C) & r2_hidden(A,B))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1317 (all A (v1_xboole_0(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1318 (exists A (p1_s1_ordinal1(A) & v3_ordinal1(A))) -> (exists A ((all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & p1_s1_ordinal1(A) & v3_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1319 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> r1_ordinal1(A,B) | r1_ordinal1(B,A))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1320 (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]. 59.48/56.99 1321 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1322 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1323 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1324 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A))) <-> v1_ordinal1(A))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1325 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1326 (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]. 59.48/56.99 1327 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1328 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> f3_s5_ordinal1(k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & f3_s5_ordinal1(C) = B & v1_relat_1(C))) <-> f2_s5_ordinal1(A) = B)))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f2_s5_ordinal1(A)))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A)) = k1_funct_1(f1_s5_ordinal1,A)))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1329 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1330 (all A (v6_ordinal1(A) & (all B (r2_hidden(B,A) -> v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B))) -> v1_funct_1(k3_tarski(A)) & v5_ordinal1(k3_tarski(A)) & v1_relat_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1331 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1332 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v5_ordinal1(A) <-> v3_ordinal1(k1_relat_1(A))))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/56.99 1333 (all A (v3_ordinal1(A) -> v1_ordinal1(k3_tarski(A)) & v2_ordinal1(k3_tarski(A)) & v3_ordinal1(k3_tarski(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1334 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1335 (all A (v1_relat_1(A) -> -((all B -(r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A))))) & k3_relat_1(A) != k1_xboole_0 & v2_wellord1(A)))) # label(t11_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1336 (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]. 59.48/57.00 1337 (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]. 59.48/57.00 1338 (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]. 59.48/57.00 1339 $T # label(t34_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1340 (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)) -> (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]. 59.48/57.00 1341 (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]. 59.48/57.00 1342 (all A all B all C (v1_relat_1(C) -> k2_wellord1(k2_wellord1(C,B),A) = k2_wellord1(k2_wellord1(C,A),B))) # label(t27_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1343 (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]. 59.48/57.00 1344 (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]. 59.48/57.00 1345 (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]. 59.48/57.00 1346 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) & r1_wellord1(A,B) & r6_relat_2(A,B) & r4_relat_2(A,B) & r8_relat_2(A,B) <-> r2_wellord1(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1347 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r2_hidden(B,k3_relat_1(A)) & r4_wellord1(A,k2_wellord1(A,k1_wellord1(A,B)))))))) # label(t57_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1348 $T # label(t4_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1349 (all A all B (v1_relat_1(B) -> k2_wellord1(B,A) = k8_relat_1(A,k7_relat_1(B,A)))) # label(t18_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1350 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) <-> (exists C (v1_relat_1(C) & r3_wellord1(A,B,C) & v1_funct_1(C)))))))) # label(d8_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1351 (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]. 59.48/57.00 1352 (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]. 59.48/57.00 1353 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> k1_xboole_0 = k3_relat_1(A) | (all B -((exists C (-r2_hidden(k4_tarski(C,B),A) & r2_hidden(C,k3_relat_1(A)))) & (all C -(r2_hidden(k4_tarski(B,C),A) & (all D -(r2_hidden(k4_tarski(B,D),A) & D != B & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,k3_relat_1(A)))) & r2_hidden(C,k3_relat_1(A)))) & r2_hidden(B,k3_relat_1(A))))))) # label(t12_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1354 $T # label(t1_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 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) -> (v1_relat_2(A) -> v1_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)) & (v8_relat_2(A) -> v8_relat_2(B))))))))) # label(t53_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1356 (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]. 59.48/57.00 1357 $T # label(t56_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1358 (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]. 59.48/57.00 1359 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k3_relat_1(k2_wellord1(C,B))) -> r2_hidden(A,B) & r2_hidden(A,k3_relat_1(C))))) # label(t19_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1360 (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) & 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]. 59.48/57.00 1361 (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))) & B != A & r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C))))) # label(t58_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1362 (all A all B (v1_relat_1(B) -> k1_xboole_0 = k1_wellord1(B,A) | r2_hidden(A,k3_relat_1(B)))) # label(t2_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1363 (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]. 59.48/57.00 1364 (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]. 59.48/57.00 1365 (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]. 59.48/57.00 1366 (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]. 59.48/57.00 1367 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_wellord1(C,B)) <-> r2_hidden(A,k2_zfmisc_1(B,B)) & r2_hidden(A,C)))) # label(t16_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1368 (all A all B (v1_relat_1(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)))) & v2_wellord1(B) & r1_tarski(A,k3_relat_1(B))))) # label(t64_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1369 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) & (all D all E (r2_hidden(E,k3_relat_1(A)) & r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & r2_hidden(D,k3_relat_1(A)) <-> r2_hidden(k4_tarski(D,E),A))) & k3_relat_1(B) = k2_relat_1(C) & k1_relat_1(C) = k3_relat_1(A) <-> r3_wellord1(A,B,C)))))))) # label(d7_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1370 (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) & v2_wellord1(A) -> (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]. 59.48/57.00 1371 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> -((all C -(r2_hidden(C,k3_relat_1(B)) & r4_wellord1(A,k2_wellord1(B,k1_wellord1(B,C))))) & (all C -(r2_hidden(C,k3_relat_1(A)) & r4_wellord1(k2_wellord1(A,k1_wellord1(A,C)),B))) & -r4_wellord1(A,B) & v2_wellord1(B) & v2_wellord1(A)))))) # label(t63_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1372 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> k1_wellord1(B,A) = k3_relat_1(k2_wellord1(B,k1_wellord1(B,A)))))) # label(t40_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1373 (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]. 59.48/57.00 1374 $T # label(t7_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1375 (all A all B (v1_relat_1(B) -> k2_wellord1(B,A) = k2_wellord1(k2_wellord1(B,A),A))) # label(t28_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1376 (all A all B all C all D (v1_relat_1(D) -> (all E (v1_relat_1(E) -> (v2_wellord1(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)) & r2_hidden(A,k3_relat_1(D)) & v2_wellord1(E) -> r1_tarski(k1_wellord1(E,C),k1_wellord1(E,B)) & r2_hidden(k4_tarski(C,B),E)))))) # label(t62_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1377 (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]. 59.48/57.00 1378 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r1_tarski(B,k3_relat_1(A)) & (all C -((all D (r2_hidden(D,B) -> r2_hidden(k4_tarski(C,D),A))) & r2_hidden(C,B))) & B != k1_xboole_0))))) # label(t10_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1379 (all A (v1_relat_1(A) -> k2_wellord1(A,k3_relat_1(A)) = A)) # label(t30_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1380 $T # label(t3_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1381 (all A (v1_relat_1(A) -> (v2_wellord1(A) <-> v1_relat_2(A) & v8_relat_2(A) & v1_wellord1(A) & v6_relat_2(A) & v4_relat_2(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1382 (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) -> r3_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A)),k7_relat_1(D,A)) & r4_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A)))))))))) # label(t59_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1383 (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]. 59.48/57.00 1384 (all A (v1_relat_1(A) -> (v1_wellord1(A) <-> (all B -(B != k1_xboole_0 & (all C -(r1_xboole_0(k1_wellord1(A,C),B) & r2_hidden(C,B))) & r1_tarski(B,k3_relat_1(A))))))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1385 (all A (v1_relat_1(A) -> (all B ((all C -(r1_tarski(C,B) & k1_xboole_0 != C & (all D -(r1_xboole_0(k1_wellord1(A,D),C) & r2_hidden(D,C))))) <-> r1_wellord1(A,B))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1386 (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]. 59.48/57.00 1387 $T # label(t46_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1388 (all A (v1_relat_1(A) -> (all B k2_wellord1(A,B) = k3_xboole_0(A,k2_zfmisc_1(B,B))))) # label(d6_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1389 (all A (v1_relat_1(A) -> (all B all C ((all D (B != D & r2_hidden(k4_tarski(D,B),A) <-> r2_hidden(D,C))) <-> k1_wellord1(A,B) = C)))) # label(d1_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1390 (all A all B all C (v1_relat_1(C) -> (r2_hidden(B,k3_relat_1(C)) & (all D (r2_hidden(D,k1_wellord1(C,A)) -> B != D & r2_hidden(k4_tarski(D,B),C))) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C) -> r2_hidden(k4_tarski(A,B),C)))) # label(t42_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1391 $T # label(t6_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1392 $T # label(t14_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1393 (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) -> r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & k1_funct_1(C,D) != k1_funct_1(C,E) | D = E))))))))) # label(t45_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1394 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1395 (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]. 59.48/57.00 1396 (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]. 59.48/57.00 1397 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r4_wellord1(B,C) & r4_wellord1(A,B) -> r4_wellord1(A,C)))))))) # label(t52_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1398 (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]. 59.48/57.00 1399 (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]. 59.48/57.00 1400 (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]. 59.48/57.00 1401 (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]. 59.48/57.00 1402 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) -> A = k3_relat_1(k2_wellord1(B,A))))) # label(t39_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1403 (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]. 59.48/57.00 1404 (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) -> v2_wellord1(B)))))))) # label(t54_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1405 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_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) -> C = D | r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,D)),A) & k1_funct_1(B,D) != k1_funct_1(B,C))) & 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]. 59.48/57.00 1406 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_wellord1(A) & r4_wellord1(A,B) -> (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]. 59.48/57.00 1407 $T # label(t44_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1408 (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) -> r3_wellord1(B,A,k2_funct_1(C))))))))) # label(t49_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1409 (all A (v1_relat_1(A) -> r4_wellord1(A,A))) # label(t48_wellord1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1410 (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]. 59.48/57.00 1411 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_relset_1(A,B,D,C) = k2_relset_1(A,B,C,D))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1412 (all A all B all C (m2_relset_1(C,A,B) -> ((all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(E,D),C)))) <-> k5_relset_1(A,B,C) = B))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1413 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> ((exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(D,E),C))) <-> r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1414 (all A all B all C all D (m2_relset_1(D,A,B) -> -((all E all F -(r2_hidden(E,A) & r2_hidden(F,B) & k4_tarski(E,F) = C)) & r2_hidden(C,D)))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1415 (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]. 59.48/57.00 1416 (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]. 59.48/57.00 1417 (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]. 59.48/57.00 1418 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1419 (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]. 59.48/57.00 1420 (all A all B (m2_relset_1(B,A,A) -> B = k5_relat_1(k6_relat_1(A),B) & k5_relat_1(B,k6_relat_1(A)) = B)) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1421 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1422 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1423 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,C) = k4_relat_1(C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1424 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k3_relset_1(A,B,C,D),A,B))) # label(dt_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1425 (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]. 59.48/57.00 1426 (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]. 59.48/57.00 1427 (all A all B all C (m2_relset_1(C,B,A) -> k5_relset_1(B,A,C) = k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)) & k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) = k4_relset_1(B,A,C))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1428 (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]. 59.48/57.00 1429 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1430 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1431 (all A all B all C all D (m2_relset_1(D,B,A) -> (r1_tarski(B,C) -> D = k8_relset_1(B,A,D,C)))) # label(t34_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1432 (all A all B all C (m2_relset_1(C,B,A) -> ((all D -((all E -r2_hidden(k4_tarski(D,E),C)) & r2_hidden(D,B))) <-> B = k4_relset_1(B,A,C)))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1433 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1434 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1435 (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]. 59.48/57.00 1436 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,k5_relset_1(B,A,C)) & (all E (m1_subset_1(E,B) -> -r2_hidden(E,k4_relset_1(B,A,C))))))))))))) # label(t50_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1437 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> C = k2_relset_1(A,B,C,C))) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1438 (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]. 59.48/57.00 1439 (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]. 59.48/57.00 1440 (all A all B all C all D all E (m2_relset_1(E,A,C) -> (r1_tarski(C,D) & r1_tarski(A,B) -> m2_relset_1(E,B,D)))) # label(t17_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1441 (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]. 59.48/57.00 1442 (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]. 59.48/57.00 1443 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1444 (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]. 59.48/57.00 1445 (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]. 59.48/57.00 1446 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1447 (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]. 59.48/57.00 1448 (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]. 59.48/57.00 1449 (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]. 59.48/57.00 1450 (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]. 59.48/57.00 1451 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1452 (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]. 59.48/57.00 1453 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(E,k10_relset_1(C,A,D,B)) <-> (exists F (r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D) & m1_subset_1(F,C)))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1454 (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]. 59.48/57.00 1455 (all A all B all C all D (m1_relset_1(D,A,B) -> k9_relset_1(A,B,C,D) = k8_relat_1(C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1456 (exists A ((all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(C,f2_s1_relset_1) & p1_s1_relset_1(B,C) & r2_hidden(B,f1_s1_relset_1))) & m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1457 (all A all B all C (m2_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k5_relset_1(B,A,k6_relset_1(A,B,C)) & k5_relset_1(A,B,C) = k4_relset_1(B,A,k6_relset_1(A,B,C)))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1458 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> B = k5_relset_1(A,B,C) & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1459 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,D) = k2_xboole_0(C,D))) # label(redefinition_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1460 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1461 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1462 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1463 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,C) -> (r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E)) <-> (exists H (r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E) & m1_subset_1(H,B)))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1464 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1465 (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]. 59.48/57.00 1466 (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]. 59.48/57.00 1467 (all A all B all C (m1_relset_1(C,A,B) -> k1_relat_1(C) = k4_relset_1(A,B,C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1468 (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]. 59.48/57.00 1469 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1470 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1471 (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]. 59.48/57.00 1472 (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]. 59.48/57.00 1473 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1474 (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]. 59.48/57.00 1475 (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]. 59.48/57.00 1476 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1477 (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]. 59.48/57.00 1478 (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]. 59.48/57.00 1479 (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]. 59.48/57.00 1480 (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]. 59.48/57.00 1481 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1482 (exists A ((all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (r2_hidden(k4_tarski(B,C),A) <-> p1_s2_relset_1(B,C)))))) & m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1483 (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]. 59.48/57.00 1484 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1485 (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]. 59.48/57.00 1486 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) -> (all E (m1_subset_1(E,A) -> ((exists F (r2_hidden(k4_tarski(E,F),D) & r2_hidden(F,B) & m1_subset_1(F,C))) <-> r2_hidden(E,k11_relset_1(A,C,D,B))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1487 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1488 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1489 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1490 (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]. 59.48/57.00 1491 (all A all B all C all D (m1_relset_1(C,A,B) -> k9_relat_1(C,D) = k10_relset_1(A,B,C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1492 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1493 (all A all B all C all D (r2_hidden(D,B) & r2_hidden(C,A) -> m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B))) # label(t8_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1494 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> C = k1_relset_1(A,B,C,C))) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1495 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k3_xboole_0(C,D) = k2_relset_1(A,B,C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1496 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k10_relset_1(A,B,C,A) & k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1497 (all A all B all C all D (m1_relset_1(C,A,B) -> k8_relset_1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1498 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> k9_relset_1(A,B,C,D) = D))) # label(t36_relset_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1499 (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]. 59.48/57.00 1500 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1501 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (k4_relset_1(A,k1_tarski(B),C) = k4_relset_1(A,k1_tarski(B),D) -> C = D))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1502 (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]. 59.48/57.00 1503 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1504 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1505 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,D) -> v1_funct_1(C) & m2_relset_1(C,A,B)))))) # label(t33_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1506 (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]. 59.48/57.00 1507 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) -> r1_tarski(k2_relat_1(C),k1_tarski(k1_funct_1(C,A))))) # label(t69_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1508 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> r1_partfun1(C,D))))) # label(t143_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1509 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1510 (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)) -> ((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]. 59.48/57.00 1511 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k5_partfun1(A,B,C) = k1_tarski(C) <-> v1_partfun1(C,A,B)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1512 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1513 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1514 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k1_xboole_0 -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1515 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1516 (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,C) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1517 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k3_partfun1(C,A,B),C))) # label(t76_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1518 (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(k3_partfun1(C,A,B),k3_partfun1(D,A,B))))))) # label(t81_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1519 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) & 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]. 59.48/57.00 1520 (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(A,C) = k1_funct_1(B,C))) & (all C (v1_funct_1(C) & v1_relat_1(C) -> k2_xboole_0(A,B) != C))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1521 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_partfun1(k1_xboole_0,A))) # label(t141_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1522 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1523 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> 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]. 59.48/57.00 1524 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> (all D (m2_relset_1(D,B,k1_xboole_0) & v1_funct_1(D) -> C = D)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1525 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (k4_relset_1(k2_zfmisc_1(A,B),C,E) = k4_relset_1(k2_zfmisc_1(A,B),C,D) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1526 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1527 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1528 (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_partfun1(C,D) & v1_partfun1(D,A,B) & v1_partfun1(C,A,B) -> C = D))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1529 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1530 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1531 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1532 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1533 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1534 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1535 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1536 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 59.48/57.00 1537 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1538 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1539 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (A != k1_xboole_0 -> k5_partfun1(A,k1_xboole_0,B) = k1_xboole_0))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1540 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1541 (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]. 59.48/57.00 1542 (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]. 59.48/57.00 1543 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1544 (all A all B all C all D all E all F (v1_funct_1(F) & m1_relset_1(F,C,D) & m1_relset_1(E,A,B) & v1_funct_1(E) -> 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]. 59.48/57.00 1545 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1546 (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) & r1_partfun1(A,B) -> A = B))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.00 1547 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A ((all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) <-> r2_hidden(B,f1_s5_partfun1) & p1_s5_partfun1(B,C) & r2_hidden(C,f2_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)) -> f4_s5_partfun1(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1) & v1_funct_1(A))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1548 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1549 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1550 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) <-> r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C)))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1551 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1552 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1553 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1554 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_partfun1(k7_relat_1(B,A),B))) # label(t144_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1555 (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]. 59.48/57.01 1556 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1557 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1558 (all A all B (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) -> r2_hidden(B,f2_s2_partfun1))) & (all A all B all C (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,C) & p1_s2_partfun1(A,B) -> C = B)) -> (exists A (m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) <-> (exists C p1_s2_partfun1(B,C)) & r2_hidden(B,f1_s2_partfun1))) & v1_funct_1(A))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1559 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1560 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1561 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1562 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k2_relat_1(C) = k9_relat_1(C,A))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1563 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1564 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1565 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> B = k1_xboole_0)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1566 (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]. 59.48/57.01 1567 (all A k4_partfun1(A,k1_xboole_0) = k1_tarski(k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1568 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1569 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1570 (all A k1_tarski(k1_xboole_0) = k4_partfun1(k1_xboole_0,A)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1571 (all A all B all C ((all D ((exists E (v1_relat_1(E) & E = D & r1_tarski(k1_relat_1(E),A) & r1_tarski(k2_relat_1(E),B) & v1_funct_1(E))) <-> r2_hidden(D,C))) <-> C = k4_partfun1(A,B))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1572 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_xboole_0,B) -> D = C)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1573 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1574 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (r1_tarski(A,C) & r1_tarski(B,D) -> v1_funct_1(E) & m2_relset_1(E,C,D)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1575 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1576 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1577 (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) -> (k2_xboole_0(A,B) = C -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,D) = k1_funct_1(B,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1578 (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]. 59.48/57.01 1579 (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]. 59.48/57.01 1580 (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]. 59.48/57.01 1581 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1582 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1583 (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]. 59.48/57.01 1584 (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) -> C = k3_partfun1(C,A,B)))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1585 (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]. 59.48/57.01 1586 (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]. 59.48/57.01 1587 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> v2_funct_1(k3_partfun1(C,A,B))))) # label(t94_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1588 (all A (v1_relat_1(A) & v8_relat_2(A) & v3_relat_2(A) -> v1_relat_1(A) & v1_relat_2(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1589 (all A all B all C (r2_hidden(A,f1_s4_partfun1) & r2_hidden(B,f2_s4_partfun1) & p1_s4_partfun1(A,B,C) -> r2_hidden(C,f3_s4_partfun1))) & (all A all B all C all D (p1_s4_partfun1(A,B,C) & p1_s4_partfun1(A,B,D) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> D = C)) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) <-> (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(C,f2_s4_partfun1) & r2_hidden(B,f1_s4_partfun1))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1590 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1591 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1592 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1593 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1594 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1595 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1596 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1597 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1598 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1599 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & r1_tarski(A,C) & r1_tarski(B,C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1600 (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]. 59.48/57.01 1601 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> ((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]. 59.48/57.01 1602 (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(B,C) & r1_tarski(A,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1603 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_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]. 59.48/57.01 1604 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1605 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> v1_funct_1(D) & m2_relset_1(D,A,C)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1606 (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 (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(D,E) = k1_funct_1(C,E)))) & k4_relset_1(A,B,D) = k4_relset_1(A,B,C) -> D = C))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1607 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1608 (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]. 59.48/57.01 1609 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1610 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) & k1_xboole_0 = B -> k1_xboole_0 = A))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1611 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1612 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1613 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1614 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1615 (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]. 59.48/57.01 1616 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1617 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> k2_partfun1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1618 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1619 (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]. 59.48/57.01 1620 (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]. 59.48/57.01 1621 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1622 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1623 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((all E (m1_subset_1(E,A) -> -(C = k1_funct_1(D,E) & r2_hidden(E,k4_relset_1(A,B,D))))) & r2_hidden(C,k2_relat_1(D))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1624 (all A exists B (v1_relat_1(B) & v1_relat_2(B) & v3_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1625 (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]. 59.48/57.01 1626 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1627 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> C = k3_partfun1(C,A,B))) # label(t87_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1628 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k2_funct_1(k3_partfun1(C,A,B)) = k3_partfun1(k2_funct_1(C),B,A)))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1629 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1630 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (D = k5_partfun1(A,B,C) <-> (all E (r2_hidden(E,D) <-> (exists F (m2_relset_1(F,A,B) & v1_partfun1(F,A,B) & r1_partfun1(C,F) & F = E & v1_funct_1(F))))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1631 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1632 (all A (v1_funct_1(A) & v1_relat_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]. 59.48/57.01 1633 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1634 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1635 (all A all B all C (r2_hidden(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t120_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1636 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),A,B))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1637 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r2_hidden(C,k9_relat_1(D,A)) & (all E (m1_subset_1(E,A) -> -(k1_funct_1(D,E) = C & r2_hidden(E,k4_relset_1(A,B,D)))))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1638 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1639 (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) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1640 (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]. 59.48/57.01 1641 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1642 (all A (v1_relat_1(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1643 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1644 (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]. 59.48/57.01 1645 (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) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1646 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> m2_relset_1(k2_partfun1(A,B,C,D),A,B) & v1_funct_1(k2_partfun1(A,B,C,D)))) # label(dt_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1647 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(D)) & r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1648 (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]. 59.48/57.01 1649 (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) & r1_partfun1(D,E) & v1_partfun1(E,A,B) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1650 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1651 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_relat_1(C) = k1_xboole_0 -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1652 (all A k6_relat_1(A) = k6_partfun1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1653 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1654 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> (exists C (v1_relat_1(C) & C = k2_xboole_0(A,B) & v1_funct_1(C)))))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1655 (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) -> 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(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1656 (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]. 59.48/57.01 1657 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> B = k1_funct_1(D,C)))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1658 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1659 (all A (v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1660 (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]. 59.48/57.01 1661 (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]. 59.48/57.01 1662 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1663 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k2_relat_1(C),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1664 (all A all B all C all D all E all F (r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))))) # label(t1_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1665 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1666 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) & k1_relat_1(D) = k1_tarski(A) -> v1_funct_1(D) & m2_relset_1(D,B,C)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1667 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1668 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1669 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(k1_xboole_0))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1670 (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) & r1_partfun1(C,D) & (all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> -(v1_partfun1(E,A,B) & r1_partfun1(C,E) & r1_partfun1(D,E))))))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1671 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1672 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1673 (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]. 59.48/57.01 1674 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1675 (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]. 59.48/57.01 1676 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1677 (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))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1678 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1679 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1680 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1681 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1682 (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),C,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1683 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A ((all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> f3_s3_partfun1(B) = k1_funct_1(A,B))) & (all B (r2_hidden(B,f1_s3_partfun1) & p1_s3_partfun1(B) <-> r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)))) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & v1_funct_1(A))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1684 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1685 (exists A (v1_relat_1(A) & f1_s1_partfun1 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s1_partfun1) -> (-p1_s1_partfun1(B) -> k1_funct_1(A,B) = f3_s1_partfun1(B)) & (p1_s1_partfun1(B) -> f2_s1_partfun1(B) = k1_funct_1(A,B)))) & v1_funct_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1686 (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]. 59.48/57.01 1687 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1688 (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]. 59.48/57.01 1689 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1690 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1691 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1692 (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]. 59.48/57.01 1693 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1694 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> v1_funct_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),B,A)))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1695 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_tarski(D,C) & r1_partfun1(C,E) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1696 (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) & (k1_xboole_0 = B -> k1_xboole_0 = A)))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1697 (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]. 59.48/57.01 1698 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1699 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1700 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(k3_partfun1(A,B,C),B,C) & v1_funct_1(k3_partfun1(A,B,C)))) # label(dt_k3_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1701 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1702 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1703 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1704 (all A all B all C all D (v1_relat_1(D) & v1_funct_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]. 59.48/57.01 1705 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k9_relset_1(A,B,C,D)) & m2_relset_1(k9_relset_1(A,B,C,D),A,B))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1706 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1707 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k3_partfun1(D,k3_xboole_0(A,C),B) = k2_partfun1(A,B,k3_partfun1(D,A,B),C))) # label(t96_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1708 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)) & m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1709 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> v2_funct_1(C))) # label(t70_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1710 (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]. 59.48/57.01 1711 (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]. 59.48/57.01 1712 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_partfun1(k8_relat_1(A,B),B))) # label(t145_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1713 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1714 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k4_mcart_1(k8_mcart_1(A,B,C,D,E),k9_mcart_1(A,B,C,D,E),k10_mcart_1(A,B,C,D,E),k11_mcart_1(A,B,C,D,E)) = E)) & k1_xboole_0 != D & k1_xboole_0 != C & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1715 (all A all B all C all D all E all F (m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(A)) -> m1_subset_1(k13_mcart_1(A,B,C,D,E,F),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))) # label(dt_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1716 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> (all I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) -> (r2_hidden(I,k4_zfmisc_1(E,F,G,H)) -> r2_hidden(k9_mcart_1(A,B,C,D,I),F) & r2_hidden(k10_mcart_1(A,B,C,D,I),G) & r2_hidden(k11_mcart_1(A,B,C,D,I),H) & r2_hidden(k8_mcart_1(A,B,C,D,I),E)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1717 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,k1_tarski(C))) -> r2_hidden(k1_mcart_1(A),B) & k2_mcart_1(A) = C)) # label(t13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1718 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(B,C,E),k3_mcart_1(A,D,E),k3_mcart_1(B,D,E)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k1_tarski(E))) # label(t43_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1719 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1720 (all A all B all C all D all E all F (k3_mcart_1(A,B,C) = k3_mcart_1(D,E,F) -> D = A & E = B & F = C)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1721 (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(A,E) & -r1_xboole_0(D,H) & -r1_xboole_0(C,G) & -r1_xboole_0(B,F))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1722 (all A all B all C -(k1_xboole_0 != A & k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k6_mcart_1(A,B,C,D) != D & k7_mcart_1(A,B,C,D) != D & D != k5_mcart_1(A,B,C,D))) & C != k1_xboole_0)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1723 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1724 (all A -((all B -(r2_hidden(B,A) & (all C all D all E all F -((r2_hidden(D,A) | r2_hidden(C,A)) & k4_mcart_1(C,D,E,F) = B)))) & k1_xboole_0 != A)) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1725 (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]. 59.48/57.01 1726 (all A -((all B -((all C all D -((r2_hidden(C,A) | r2_hidden(D,A)) & k4_tarski(C,D) = B)) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1727 (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]. 59.48/57.01 1728 (all A all B all C all D -(B != k1_xboole_0 & C != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k1_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k8_mcart_1(A,B,C,D,E) & k2_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k9_mcart_1(A,B,C,D,E) & k2_mcart_1(E) = k11_mcart_1(A,B,C,D,E) & k2_mcart_1(k1_mcart_1(E)) = k10_mcart_1(A,B,C,D,E))) & D != k1_xboole_0 & A != k1_xboole_0)) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1729 (all A all B all C -(A != k1_xboole_0 & B != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)) = D)) & k1_xboole_0 != C)) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1730 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.48/57.01 1731 (all A all B all C all D all E k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k2_tarski(D,E)) = k2_enumset1(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D),k3_mcart_1(A,C,E),k3_mcart_1(B,C,E))) # label(t44_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1732 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> F = D))))))) -> C = k1_xboole_0 | k5_mcart_1(A,B,C,E) = D | B = k1_xboole_0 | A = k1_xboole_0))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1733 (all A all B all C all D k4_tarski(k3_mcart_1(A,B,C),D) = k4_mcart_1(A,B,C,D)) # label(d4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1734 (all A all B all C all D all E all F (r2_hidden(C,F) & r2_hidden(B,E) & r2_hidden(A,D) <-> r2_hidden(k3_mcart_1(A,B,C),k3_zfmisc_1(D,E,F)))) # label(t73_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1735 (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]. 59.51/57.01 1736 (all A all B all C all D all E all F all G all H -(k1_xboole_0 != C & D != k1_xboole_0 & (exists I ((exists J (-(k8_mcart_1(E,F,G,H,J) = k8_mcart_1(A,B,C,D,I) & k11_mcart_1(A,B,C,D,I) = k11_mcart_1(E,F,G,H,J) & k10_mcart_1(A,B,C,D,I) = k10_mcart_1(E,F,G,H,J) & k9_mcart_1(E,F,G,H,J) = k9_mcart_1(A,B,C,D,I)) & I = J & m1_subset_1(J,k4_zfmisc_1(E,F,G,H)))) & m1_subset_1(I,k4_zfmisc_1(A,B,C,D)))) & k1_xboole_0 != H & k1_xboole_0 != G & k1_xboole_0 != F & E != k1_xboole_0 & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1737 (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]. 59.51/57.01 1738 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1739 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),C)) -> r2_hidden(k2_mcart_1(A),C) & k1_mcart_1(A) = B)) # label(t12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1740 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(E,F,G,H) = k4_zfmisc_1(A,B,C,D) -> k4_zfmisc_1(A,B,C,D) = k1_xboole_0 | A = E & F = B & G = C & D = H)) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1741 (all A all B all C all D k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k1_tarski(D)) = k2_tarski(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D))) # label(t40_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1742 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -(A != k1_xboole_0 & k1_xboole_0 != D & (exists F exists G exists H exists I (-(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 & k9_mcart_1(A,B,C,D,E) = G) & E = k4_mcart_1(F,G,H,I))) & k1_xboole_0 != C & k1_xboole_0 != B))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1743 (all A k17_mcart_1(A) = k1_mcart_1(k1_mcart_1(A))) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1744 (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]. 59.51/57.01 1745 (all A all B (k1_xboole_0 != k2_zfmisc_1(A,B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C != k1_mcart_1(C) & k2_mcart_1(C) != C)))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1746 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C all D all E (r2_hidden(C,D) & r2_hidden(D,E) & r2_hidden(E,B) -> r1_xboole_0(C,A))))))) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1747 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1748 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(B,k2_tarski(C,D))) -> (k2_mcart_1(A) = D | k2_mcart_1(A) = C) & r2_hidden(k1_mcart_1(A),B))) # label(t16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1749 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1750 (all A all B -(k1_xboole_0 != B & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k4_tarski(k1_mcart_1(C),k2_mcart_1(C)) = C)) & k1_xboole_0 != A)) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1751 (all A all B all C all D all E all F (k3_zfmisc_1(A,B,C) = k3_zfmisc_1(D,E,F) -> k3_zfmisc_1(A,B,C) = k1_xboole_0 | C = F & E = B & A = D)) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1752 (all A all B (k3_zfmisc_1(B,B,B) = k3_zfmisc_1(A,A,A) -> A = B)) # label(t38_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1753 (all A all B all C all D all E ((all F ((exists G exists H exists I exists J (r2_hidden(G,B) & r2_hidden(H,C) & r2_hidden(I,D) & r2_hidden(J,E) & F = k4_mcart_1(G,H,I,J))) <-> r2_hidden(F,A))) -> k4_zfmisc_1(B,C,D,E) = A)) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.01 1754 (all A all B all C all D (A != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != B <-> k1_xboole_0 != k4_zfmisc_1(A,B,C,D))) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1755 (all A all B all C (-(-r1_tarski(A,k3_zfmisc_1(A,B,C)) & -r1_tarski(A,k3_zfmisc_1(B,C,A)) & -r1_tarski(A,k3_zfmisc_1(C,A,B))) -> A = k1_xboole_0)) # label(t49_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1756 (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(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & 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]. 59.51/57.02 1757 (all A all B all C all D all E all F (m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(D,k1_zfmisc_1(A)) -> 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]. 59.51/57.02 1758 (all A all B all C (k3_zfmisc_1(A,B,C) != k1_xboole_0 <-> k1_xboole_0 != C & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1759 (all A all B all C all D all E all F all G all H (r2_hidden(D,H) & r2_hidden(C,G) & r2_hidden(B,F) & r2_hidden(A,E) <-> 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]. 59.51/57.02 1760 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1761 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> k1_mcart_1(A) = B & C = k2_mcart_1(A))) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1762 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1763 (all A all B all C (r2_hidden(k2_mcart_1(A),C) & r2_hidden(k1_mcart_1(A),B) -> r2_hidden(A,k2_zfmisc_1(B,C)) | (all D all E A != k4_tarski(D,E)))) # label(t11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1764 (all A all B all C all D -(k1_xboole_0 != C & D != k1_xboole_0 & -(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) & k11_mcart_1(A,B,C,D,E) != E & E != k9_mcart_1(A,B,C,D,E))) & k1_xboole_0 != B & A != k1_xboole_0)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1765 (all A all B all C all D k2_enumset1(k4_tarski(A,C),k4_tarski(A,D),k4_tarski(B,C),k4_tarski(B,D)) = k2_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D))) # label(t25_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1766 (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 | k8_mcart_1(A,B,C,D,F) = E | D = k1_xboole_0 | C = k1_xboole_0 | k1_xboole_0 = B))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1767 (all A all B all C -(-(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k5_mcart_1(A,B,C,D) = k1_mcart_1(k1_mcart_1(D)) & k2_mcart_1(D) = k7_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) = k2_mcart_1(k1_mcart_1(D)))) & C != k1_xboole_0 & B != k1_xboole_0 & k1_xboole_0 != A)) # label(t50_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1768 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k16_mcart_1(A) <-> k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k2_mcart_1(k1_funct_1(A,C))))))))) # label(d13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1769 (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]. 59.51/57.02 1770 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B ((all C all D (A = k4_tarski(C,D) -> B = D)) <-> B = k2_mcart_1(A))))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1771 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(B) = k1_relat_1(A) <-> k15_mcart_1(A) = B))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1772 (all A all B all C -(B != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,A) -> (k5_mcart_1(A,B,C,D) = E <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> F = E))))))) & k1_xboole_0 != C & A != k1_xboole_0)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1773 (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]. 59.51/57.02 1774 (all A all B all C all D -(A != k1_xboole_0 & k1_xboole_0 != D & (exists E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) & (exists F exists G exists H exists I (-(F = k8_mcart_1(A,B,C,D,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) & E = k4_mcart_1(F,G,H,I))))) & C != k1_xboole_0 & B != k1_xboole_0)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1775 (all A ((exists B exists C k4_tarski(B,C) = A) -> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)))) # label(t8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1776 (all A ((exists B exists C k4_tarski(B,C) = A) -> (all B ((all C all D (A = k4_tarski(C,D) -> C = B)) <-> B = k1_mcart_1(A))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 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 = I))))))))) -> B = k1_xboole_0 | k1_xboole_0 = C | k1_xboole_0 = D | k10_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = A))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1778 (all A all B all C all D all E all F (k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) = A & B = k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) & k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) = D & E = k20_mcart_1(k4_tarski(F,k4_tarski(D,E))))) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1779 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1780 (all A all B all C all D all E all F all G all H (r1_tarski(C,D) & r1_tarski(E,F) & r1_tarski(G,H) & r1_tarski(A,B) -> r1_tarski(k4_zfmisc_1(A,C,E,G),k4_zfmisc_1(B,D,F,H)))) # label(t88_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1781 (all A k2_mcart_1(k2_mcart_1(A)) = k20_mcart_1(A)) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1782 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k16_mcart_1(A)) & v1_relat_1(k16_mcart_1(A)))) # label(dt_k16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1783 (all A all B all C all D all E -((all F all G all H all I -(r2_hidden(F,B) & r2_hidden(H,D) & k4_mcart_1(F,G,H,I) = A & r2_hidden(I,E) & r2_hidden(G,C))) & r2_hidden(A,k4_zfmisc_1(B,C,D,E)))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1784 (all A all B -(k1_xboole_0 != A & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k2_mcart_1(C) != C & k1_mcart_1(C) != C)) & k1_xboole_0 != B)) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1785 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1786 (all A all B all C -(k1_xboole_0 != B & 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 (k3_mcart_1(F,G,H) = D -> G = E)) <-> E = k6_mcart_1(A,B,C,D)))))) & k1_xboole_0 != A)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1787 (all A all B all C all D k2_tarski(k3_mcart_1(A,B,C),k3_mcart_1(A,B,D)) = k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k2_tarski(C,D))) # label(t42_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1788 (all A all B all C all D k4_tarski(k4_tarski(k4_tarski(A,B),C),D) = k4_mcart_1(A,B,C,D)) # label(t31_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1789 (all A all B (k1_mcart_1(k4_tarski(A,B)) = A & B = k2_mcart_1(k4_tarski(A,B)))) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1790 (all A ((exists B exists C k4_tarski(B,C) = A) -> k2_mcart_1(A) != A & A != k1_mcart_1(A))) # label(t20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1791 (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]. 59.51/57.02 1792 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D)) # label(t53_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1793 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> H = D))))))) -> k1_xboole_0 = B | k1_xboole_0 = C | k7_mcart_1(A,B,C,E) = D | A = k1_xboole_0))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1794 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D all E all F all G (r2_hidden(C,D) & r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(G,B) & r2_hidden(F,G) -> r1_xboole_0(C,A))))))) # label(t6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1795 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D all E all F (r2_hidden(C,D) & r2_hidden(E,F) & r2_hidden(F,B) & r2_hidden(D,E) -> r1_xboole_0(C,A))))))) # label(t5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1796 (all A all B all C all D -((all E all F all G -(r2_hidden(G,D) & A = k3_mcart_1(E,F,G) & r2_hidden(F,C) & r2_hidden(E,B))) & r2_hidden(A,k3_zfmisc_1(B,C,D)))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1797 (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) & (k1_mcart_1(A) = C | k1_mcart_1(A) = B))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1798 (all A all B all C -((exists D ((exists E exists F exists G (-(G = k7_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) = F & k5_mcart_1(A,B,C,D) = E) & D = k3_mcart_1(E,F,G))) & m1_subset_1(D,k3_zfmisc_1(A,B,C)))) & k1_xboole_0 != C & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1799 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k3_zfmisc_1(k2_zfmisc_1(A,B),C,D)) # label(t54_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1800 (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]. 59.51/57.02 1801 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k15_mcart_1(A)) & v1_relat_1(k15_mcart_1(A)))) # label(dt_k15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1802 (all A all B all C all D all E all F (k3_zfmisc_1(A,B,C) = k3_zfmisc_1(D,E,F) -> k1_xboole_0 = A | E = B & C = F & A = D | k1_xboole_0 = C | B = k1_xboole_0)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1803 (all A k19_mcart_1(A) = k1_mcart_1(k2_mcart_1(A))) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1804 (all A all B all C all D k4_mcart_1(A,B,C,D) = k3_mcart_1(k4_tarski(A,B),C,D)) # label(t32_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1805 (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,C) -> ((all F all G all H (D = k3_mcart_1(F,G,H) -> E = H)) <-> k7_mcart_1(A,B,C,D) = E))))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1806 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C (r2_hidden(C,B) -> r1_xboole_0(C,A))))))) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1807 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k2_tarski(C,D))) -> B = k1_mcart_1(A) & (k2_mcart_1(A) = C | D = k2_mcart_1(A)))) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1808 (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) -> F = B & C = G & H = D & E = A)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1809 (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]. 59.51/57.02 1810 (all A all B all C all D all E all F (-r1_xboole_0(k3_zfmisc_1(A,B,C),k3_zfmisc_1(D,E,F)) -> -r1_xboole_0(A,D) & -r1_xboole_0(B,E) & -r1_xboole_0(C,F))) # label(t52_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1811 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(A,B,C,D) = k4_zfmisc_1(E,F,G,H) -> k1_xboole_0 = A | k1_xboole_0 = D | B = F & C = G & H = D & E = A | C = k1_xboole_0 | k1_xboole_0 = B)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1812 (all A all B all C all D ((all E (r2_hidden(E,A) <-> (exists F exists G exists H (r2_hidden(G,C) & r2_hidden(H,D) & E = k3_mcart_1(F,G,H) & r2_hidden(F,B))))) -> k3_zfmisc_1(B,C,D) = A)) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1813 (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]. 59.51/57.02 1814 (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]. 59.51/57.02 1815 (all A all B all C all D all E all F (r1_tarski(A,B) & r1_tarski(E,F) & r1_tarski(C,D) -> r1_tarski(k3_zfmisc_1(A,C,E),k3_zfmisc_1(B,D,F)))) # label(t77_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1816 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k1_tarski(D))) -> k2_mcart_1(A) = D & (B = k1_mcart_1(A) | k1_mcart_1(A) = C))) # label(t17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1817 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1818 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(k1_xboole_0 != A & k1_xboole_0 != C & (exists E exists F exists G (-(k7_mcart_1(A,B,C,D) = G & F = k6_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = E) & k3_mcart_1(E,F,G) = D)) & B != k1_xboole_0))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1819 (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]. 59.51/57.02 1820 (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]. 59.51/57.02 1821 (all A all B all C all D all E all F -(B != k1_xboole_0 & k1_xboole_0 != E & (exists G ((exists H (m1_subset_1(H,k3_zfmisc_1(D,E,F)) & H = G & -(k7_mcart_1(D,E,F,H) = k7_mcart_1(A,B,C,G) & k6_mcart_1(A,B,C,G) = k6_mcart_1(D,E,F,H) & k5_mcart_1(A,B,C,G) = k5_mcart_1(D,E,F,H)))) & m1_subset_1(G,k3_zfmisc_1(A,B,C)))) & F != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != C & k1_xboole_0 != A)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1822 (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) | k1_mcart_1(A) = B) & (k2_mcart_1(A) = D | E = k2_mcart_1(A)))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1823 (all A all B all C all D -(k1_xboole_0 != A & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,C) -> (F = k10_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = I))))))) & k1_xboole_0 != D & C != k1_xboole_0 & B != k1_xboole_0)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1824 (all A all B all C all D all E all F k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k2_tarski(E,F)) = k6_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(A,D,E),k3_mcart_1(A,C,F),k3_mcart_1(A,D,F),k3_mcart_1(B,C,E),k3_mcart_1(B,D,E),k3_mcart_1(B,C,F),k3_mcart_1(B,D,F))) # label(t46_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1825 (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]. 59.51/57.02 1826 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,B) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = H)) <-> F = k9_mcart_1(A,B,C,D,E)))))) & k1_xboole_0 != D & k1_xboole_0 != C & k1_xboole_0 != B & A != k1_xboole_0)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1827 (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]. 59.51/57.02 1828 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> k1_mcart_1(A) != A & k2_mcart_1(A) != A)) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1829 (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]. 59.51/57.02 1830 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> H = E))))))))) -> k1_xboole_0 = B | D = k1_xboole_0 | E = k9_mcart_1(A,B,C,D,F) | C = k1_xboole_0 | k1_xboole_0 = A))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1831 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1832 (all A -(k1_xboole_0 != A & (all B -((all C all D all E -((r2_hidden(C,A) | r2_hidden(D,A)) & B = k3_mcart_1(C,D,E))) & r2_hidden(B,A))))) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1833 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1834 (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)) -> (all F (m1_subset_1(F,A) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = G)) <-> F = k8_mcart_1(A,B,C,D,E)))))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1835 (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]. 59.51/57.02 1836 (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))))))) -> A = k1_xboole_0 | D = k6_mcart_1(A,B,C,E) | C = k1_xboole_0 | B = k1_xboole_0))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1837 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C))) # label(t10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1838 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D (r2_hidden(D,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))))))) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1839 (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))))))))) -> C = k1_xboole_0 | k11_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = D | B = k1_xboole_0 | A = k1_xboole_0))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1840 (all A all B all C all D -(k1_xboole_0 != A & B != k1_xboole_0 & k1_xboole_0 != D & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,D) -> (F = k11_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> J = F))))))) & k1_xboole_0 != C)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1841 (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]. 59.51/57.02 1842 (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(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(F,k1_zfmisc_1(B)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = k4_zfmisc_1(E,F,G,H))) # label(redefinition_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1843 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1844 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1845 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1846 (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]. 59.51/57.02 1847 (all A (v1_relat_1(A) -> -(v2_wellord1(A) & (all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & (all B -(r2_hidden(B,k3_relat_1(A)) & (all C (v3_ordinal1(C) -> -r4_wellord1(k2_wellord1(A,k1_wellord1(A,B)),k1_wellord2(C))))))))) # label(t13_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1848 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) -> (r1_wellord2(A,B) <-> A = k2_wellord2(B)))))) # label(d3_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1849 (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]. 59.51/57.02 1850 (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]. 59.51/57.02 1851 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1852 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1853 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1854 (all A (-v1_xboole_0(A) -> -((all B -(r2_hidden(B,A) & B = k1_xboole_0)) & (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))))) # label(t27_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1855 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> v2_wellord1(k2_wellord1(B,A)) & k3_relat_1(k2_wellord1(B,A)) = A))) # label(t25_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1856 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1857 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1858 (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]. 59.51/57.02 1859 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> A = k1_wellord1(k1_wellord2(B),A)))))) # label(t10_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1860 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1861 (all A -((all B -(r2_hidden(B,f2_s1_wellord2) & p1_s1_wellord2(A,B))) & r2_hidden(A,f1_s1_wellord2))) -> (exists A (v1_relat_1(A) & k1_relat_1(A) = f1_s1_wellord2 & (all B (r2_hidden(B,f1_s1_wellord2) -> p1_s1_wellord2(B,k1_funct_1(A,B)))) & r1_tarski(k2_relat_1(A),f2_s1_wellord2) & v1_funct_1(A))) # label(s1_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1862 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1863 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1864 (all A -((all B all C -(r2_hidden(C,f3_s2_wellord2) & p1_s2_wellord2(A,B,C) & r2_hidden(B,f2_s2_wellord2))) & r2_hidden(A,f1_s2_wellord2))) -> (exists A (v1_relat_1(A) & (exists B (v1_relat_1(B) & k1_relat_1(A) = f1_s2_wellord2 & 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_funct_1(A))) # label(s2_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1865 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1866 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1867 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1868 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1869 (all A (-v1_xboole_0(A) -> -((all B -(r2_hidden(B,A) & k1_xboole_0 = B)) & (all B (v1_funct_1(B) & v1_relat_1(B) -> -((all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))) & A = k1_relat_1(B))))))) # label(t28_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1870 (all A all B (v1_relat_1(B) -> (k1_wellord2(A) = B <-> (all C all D (r2_hidden(C,A) & r2_hidden(D,A) -> (r2_hidden(k4_tarski(C,D),B) <-> r1_tarski(C,D)))) & A = k3_relat_1(B)))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1871 (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]. 59.51/57.02 1872 (all A exists B (v1_relat_1(B) & r2_wellord1(B,A))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1873 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1874 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1875 (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]. 59.51/57.02 1876 (all A all B all C (r2_wellord2(A,B) & r2_wellord2(B,C) -> r2_wellord2(A,C))) # label(t22_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1877 (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]. 59.51/57.02 1878 (all A all B ((exists C (k1_relat_1(C) = A & k2_relat_1(C) = B & v2_funct_1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> r2_wellord2(A,B))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1879 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1880 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1881 (all A all B (r2_tarski(A,B) <-> r2_wellord2(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1882 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_tarski(B,C) -> v1_funct_2(D,A,C) & m2_relset_1(D,A,C) & v1_funct_1(D) | k1_xboole_0 = B & A != k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1883 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) -> D = k9_funct_2(A,B,C))) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1884 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_partfun1(C,D) -> A != k1_xboole_0 & k1_xboole_0 = B | C = D))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1885 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (k2_relat_1(C) = B <-> v2_funct_2(C,A,B)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1886 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1887 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (k2_relat_1(C) = B <-> (all D -(r2_hidden(D,B) & k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D))))))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1888 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) & v2_funct_1(D) -> k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) = C | k1_xboole_0 = B))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1889 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_2(C,A,B) & m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_1(C) -> k8_funct_2(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1890 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (B = k2_relat_1(D) & v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> v2_funct_1(D) & v2_funct_1(E) | k1_xboole_0 = C & k1_xboole_0 != B))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1891 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(A) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1892 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & B = k2_relat_1(C) -> v1_funct_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A)))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1893 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1894 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1895 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (p1_s14_funct_2(A,B) & m1_subset_1(B,f2_s14_funct_2))))) -> (exists A (m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & (all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1896 f4_s11_funct_2 != f3_s11_funct_2 -> (exists A ((all B (m1_subset_1(B,f1_s11_funct_2) -> -(f3_s11_funct_2 != B & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & B != f4_s11_funct_2))) & f6_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) = f5_s11_funct_2 & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & v1_funct_1(A))) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1897 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1898 (all A all B (v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) -> (k6_partfun1(A) = k5_funct_2(A,B,C) -> C = k6_funct_2(A,B)))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1899 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) -> (all C all D (k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(D,A) & r2_hidden(C,A) -> C = D))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1900 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1901 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1902 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_partfun1(C,D) -> k1_xboole_0 = B & A != k1_xboole_0 | r2_hidden(D,k5_partfun1(A,B,C))))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1903 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1904 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k2_funct_2(A,A,B,A) = k2_relat_1(B))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1905 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k2_relat_1(C) = B & v2_funct_1(C) & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) -> B = k1_xboole_0 | k2_funct_1(C) = D | k1_xboole_0 = A))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1906 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1907 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1908 (all A all B all C (v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (r1_tarski(B,A) -> k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) = B & k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1909 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> v1_funct_1(D) & m2_relset_1(D,A,C) & v1_funct_2(D,A,C) | A != k1_xboole_0 & k1_xboole_0 = B))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1910 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (m1_subset_1(C,f3_s7_funct_2) & p1_s7_funct_2(A,B,C))))))) -> (exists A ((all B (m1_subset_1(B,f1_s7_funct_2) -> (all C (m1_subset_1(C,f2_s7_funct_2) -> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))))) & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & v1_funct_1(A))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1911 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1912 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1913 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1914 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> -(k1_xboole_0 != A & -(v2_funct_1(C) <-> (all D all E (m2_relset_1(E,D,A) & v1_funct_2(E,D,A) & v1_funct_1(E) -> (all F (v1_funct_2(F,D,A) & m2_relset_1(F,D,A) & v1_funct_1(F) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> F = E)))))) & k1_xboole_0 != B))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1915 (all A all B (v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (C = k5_funct_2(A,B,C) -> k6_partfun1(A) = B))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1916 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (-(C != k1_xboole_0 & A != k1_xboole_0 & k1_xboole_0 = B) -> v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C)))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1917 (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]. 59.51/57.02 1918 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1919 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) & v1_funct_1(C) & -v1_xboole_0(A) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1920 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (v2_funct_1(B) & k4_funct_2(A,C,B) = B -> k6_partfun1(A) = C))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1921 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_relat_1(B,C) = k4_funct_2(A,B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1922 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1923 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (v2_funct_1(B) & k2_relat_1(B) = A -> v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1924 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)) = A)) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1925 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1926 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))))) -> E = D))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1927 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1928 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E k1_tarski(E) != B) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1929 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) & v1_funct_2(D,k1_tarski(A),B) -> (B != k1_xboole_0 -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1930 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1931 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k3_funct_2(A,B,C,B) = A))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1932 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.51/57.02 1933 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1934 (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]. 59.54/57.03 1935 (all A all B (v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> k6_partfun1(A) = k5_funct_2(A,k6_funct_2(A,B),B) & k5_funct_2(A,B,k6_funct_2(A,B)) = k6_partfun1(A))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1936 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1937 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v2_funct_2(C,A,B) & v1_funct_2(C,A,B) & v2_funct_1(C) -> v1_funct_2(C,A,B) & v3_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1938 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (k1_xboole_0 != B -> (all E (r2_hidden(E,k10_relat_1(D,C)) <-> r2_hidden(k1_funct_1(D,E),C) & r2_hidden(E,A)))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1939 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1940 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1941 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1942 (all A (r2_hidden(A,f1_s9_funct_2) -> (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)) & (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & (all B (r2_hidden(B,f1_s9_funct_2) -> (p1_s9_funct_2(B) -> f3_s9_funct_2(B) = k1_funct_1(A,B)) & (-p1_s9_funct_2(B) -> f4_s9_funct_2(B) = k1_funct_1(A,B)))) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1943 (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]. 59.54/57.03 1944 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1945 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2) & m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2) & (all B (r2_hidden(B,f1_s2_funct_2) -> k1_funct_1(A,B) = f3_s2_funct_2(B))))) # label(s2_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1946 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1947 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(k1_xboole_0 != B & -v2_funct_1(C) & (exists D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A)))))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1948 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> ((all C all D (r2_hidden(C,A) & r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) -> D = C)) <-> v2_funct_1(B)))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1949 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (B = k2_relat_1(C) & (all E all F ((r2_hidden(E,B) & k1_funct_1(D,E) = F -> r2_hidden(F,A) & k1_funct_1(C,F) = E) & (r2_hidden(F,A) & k1_funct_1(C,F) = E -> k1_funct_1(D,E) = F & r2_hidden(E,B)))) & v2_funct_1(C) -> k1_xboole_0 = A | B = k1_xboole_0 | D = k2_funct_1(C)))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1950 (all A all B all C all D all E (v1_funct_1(D) & m1_relset_1(D,A,B) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & v1_funct_2(D,A,B) & -v1_xboole_0(B) -> v1_funct_1(k7_funct_2(A,B,C,D,E)) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1951 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1952 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1953 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1954 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1955 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (exists E (k1_funct_1(C,E) != k1_funct_1(D,E) & r2_hidden(E,k4_relset_1(A,B,C)))))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1956 (all A all B all C all D all E all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) -> (r2_hidden(E,B) & r2_hidden(D,A) -> r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) | C = k1_xboole_0))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1957 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1958 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1959 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) -> B = k1_xboole_0 | v2_funct_1(C) & A = k2_relat_1(D)))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1960 (all A all B all C (m2_relset_1(C,A,B) -> k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C & C = k7_relset_1(A,B,B,B,C,k6_partfun1(B)))) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1961 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t166_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1962 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k2_relat_1(C) = k2_funct_2(A,B,C,A)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1963 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> k1_xboole_0 = B | r2_hidden(k1_funct_1(D,C),B)))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1964 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 = k1_relat_1(B) -> v1_funct_2(B,k1_xboole_0,A) & m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1965 (all A (k1_xboole_0 != A -> k1_funct_2(A,k1_xboole_0) = k1_xboole_0)) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1966 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1967 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1968 (all A all B all C (m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(k9_funct_2(A,B,C)))) # label(dt_k9_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1969 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1970 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C)))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1971 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1972 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = B -> B = k1_xboole_0 | k5_relat_1(k2_funct_1(C),C) = k6_partfun1(B) & k6_partfun1(A) = k5_relat_1(C,k2_funct_1(C))))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1973 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1974 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1975 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> D = E))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1976 (all A all B all C (k1_funct_2(A,B) = C <-> (all D ((exists E (v1_funct_1(E) & r1_tarski(k2_relat_1(E),B) & k1_relat_1(E) = A & D = E & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1977 (all A exists B (v2_funct_1(B) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) & v1_relat_1(B) & m1_relset_1(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1978 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1979 (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]. 59.54/57.03 1980 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1981 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((all D -((all E -(r2_hidden(E,A) & D = k1_funct_1(C,E))) & r2_hidden(D,B))) -> B = k1_xboole_0 | B = k2_relat_1(C)))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1982 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_2(F,B,C) & m2_relset_1(F,B,C) & v1_funct_1(F) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & -r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D))) & (C = k1_xboole_0 -> B = k1_xboole_0)))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1983 (all A all B k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B)) = k1_funct_2(A,B)) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1984 (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]. 59.54/57.03 1985 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1986 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> (r1_partfun1(C,D) <-> (all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(D,E) = k1_funct_1(C,E))))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1987 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1988 (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]. 59.54/57.03 1989 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1990 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1991 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1992 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1993 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> -r1_partfun1(C,D))) & (k1_xboole_0 = B -> k1_xboole_0 = A)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1994 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v3_funct_2(C,A,B) <-> v2_funct_1(C) & v2_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1995 (all A all B all C (m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> (v1_funct_2(C,A,B) <-> A = k4_relset_1(A,B,C))) & (k1_xboole_0 = B -> A = k1_xboole_0 | (v1_funct_2(C,A,B) <-> C = k1_xboole_0)))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1996 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1997 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1998 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> B != k1_xboole_0 & C = k1_xboole_0 | B = k1_xboole_0 & A != k1_xboole_0 | v2_funct_1(D)))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 1999 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2000 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) -> (k1_xboole_0 != B -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2001 (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]. 59.54/57.03 2002 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2003 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2004 (all A all B all C (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v1_funct_1(B) -> v1_funct_2(k5_funct_2(A,B,C),A,A) & m2_relset_1(k5_funct_2(A,B,C),A,A) & v3_funct_2(k5_funct_2(A,B,C),A,A) & v1_funct_1(k5_funct_2(A,B,C)))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2005 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> k5_partfun1(A,k1_tarski(B),C) = k1_tarski(D))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2006 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> r1_tarski(k2_relat_1(B),A) & A = k4_relset_1(A,A,B))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2007 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2008 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B) -> B = k2_relat_1(C)))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2009 (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]. 59.54/57.03 2010 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2011 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> A != k1_xboole_0 & B = k1_xboole_0 | r1_partfun1(C,D)))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2012 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2013 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(C,A) -> k1_funct_1(E,k1_funct_1(D,C)) = k1_funct_1(k5_relat_1(D,E),C) | B = k1_xboole_0))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2014 (exists A (v1_funct_1(A) & k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) = f4_s10_funct_2 & (all B (m1_subset_1(B,f1_s10_funct_2) -> (B != f3_s10_funct_2 -> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B)))) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2015 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2016 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2017 (exists A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & (all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2018 (all A all B all C all D all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (r2_hidden(k1_funct_1(E,C),D) & r2_hidden(C,A) -> k1_funct_1(E,C) = k1_funct_1(k9_relset_1(A,B,D,E),C) | k1_xboole_0 = B))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2019 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2020 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (B = k4_funct_2(A,B,C) & A = k2_relat_1(B) -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2021 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((B = k1_xboole_0 -> k1_xboole_0 = A) & r1_partfun1(C,D) & (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(D,E) & r1_partfun1(C,E))))))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2022 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(A,C) -> k2_partfun1(A,B,D,C) = D))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2023 (all A all B (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(B) -> v1_funct_2(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A) & v1_funct_1(k6_funct_2(A,B)))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2024 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) -> (B != k1_xboole_0 -> k2_relat_1(C) = k1_tarski(k1_funct_1(C,A))))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2025 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2026 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> k1_xboole_0 != A & B = k1_xboole_0 | v1_funct_1(k2_partfun1(A,B,D,C)) & m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_2(k2_partfun1(A,B,D,C),C,B)))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2027 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k10_relat_1(C,D) = k3_funct_2(A,B,C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2028 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (A = k2_relat_1(B) & A = k2_relat_1(C) -> A = k2_relat_1(k4_funct_2(A,B,C))))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2029 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A (v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2) & (all B (m1_subset_1(B,f1_s13_funct_2) -> k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B) = f3_s13_funct_2(B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2) & v1_funct_1(A))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2030 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2031 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2032 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(E) & C = k2_relat_1(k1_partfun1(A,B,B,C,D,E)) -> k2_relat_1(D) = B | k1_xboole_0 = C))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2033 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2034 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2035 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k3_funct_2(A,B,C,k2_funct_2(A,B,C,A)) = A))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2036 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) | k1_xboole_0 = B))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2037 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2038 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2039 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2) & (all B (m1_subset_1(B,f1_s12_funct_2) -> k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B))))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2040 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_1(B) & m2_relset_1(B,k1_relat_1(B),A) & v1_funct_2(B,k1_relat_1(B),A)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2041 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2042 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2043 (all A all B all C (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v1_funct_1(B) -> k5_relat_1(B,C) = k5_funct_2(A,B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2044 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (k2_relat_1(E) = C & k2_relat_1(D) = B -> B = k1_xboole_0 | C = k1_xboole_0 | C = k2_relat_1(k1_partfun1(A,B,B,C,D,E))))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2045 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> C = B))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2046 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2047 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2048 (all A -(r2_hidden(A,f1_s1_funct_2) & (all B -(p1_s1_funct_2(A,B) & r2_hidden(B,f2_s1_funct_2))))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2) & (all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2049 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_partfun1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2050 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2051 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2052 (all A all B (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(B) -> k6_funct_2(A,B) = k2_funct_1(B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2053 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E B != k1_tarski(E)) & k5_partfun1(A,B,C) = k5_partfun1(A,B,D) -> C = D))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2054 (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]. 59.54/57.03 2055 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2056 (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]. 59.54/57.03 2057 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2058 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2059 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(C,A) -> r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C))) | B = k1_xboole_0 & A != k1_xboole_0))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2060 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(C,D) = k1_funct_1(B,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2061 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((all E (r2_hidden(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> C = D))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2062 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(k1_funct_1(D,F) = E & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2063 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2064 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & m1_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(D) -> k5_relat_1(D,E) = k7_funct_2(A,B,C,D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2065 (all A all B (r2_hidden(B,f2_s6_funct_2) & r2_hidden(A,f1_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & (all B all C (r2_hidden(C,f2_s6_funct_2) & r2_hidden(B,f1_s6_funct_2) -> f4_s6_funct_2(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_1(A))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2066 (all A all B all C (v1_funct_2(C,A,k1_tarski(B)) & m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) -> D = C)))) # label(t66_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2067 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_funct_1(C) & -v1_xboole_0(C) & v1_funct_2(C,A,B) & v1_partfun1(C,A,B)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2068 (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]. 59.54/57.03 2069 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v3_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2070 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> k1_xboole_0 = B & A != k1_xboole_0 | v1_partfun1(C,A,B)))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2071 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,A) -> B = k1_funct_1(D,C)))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2072 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (k1_xboole_0 != B -> (all E ((exists F (k1_funct_1(D,F) = E & r2_hidden(F,C) & r2_hidden(F,A))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2073 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(C) & (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2074 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,A) & v1_funct_2(D,A,A) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2075 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> -(k2_relat_1(D) = B & (all E -(k1_funct_1(D,E) = C & r2_hidden(E,A))) & r2_hidden(C,B)))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2076 (all A all B all C (r2_hidden(C,k1_funct_2(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B))) # label(t121_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2077 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_2(B,A,A) & v1_relat_2(B) & v1_partfun1(B,A,A) & v1_funct_1(B) -> v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A) & v2_funct_1(B) & v1_funct_1(B)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2078 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> (v2_funct_1(C) <-> (all D all E (r2_hidden(E,A) & k1_funct_1(C,D) = k1_funct_1(C,E) & r2_hidden(D,A) -> D = E)))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2079 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> k2_funct_2(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2080 (all A all B (m2_relset_1(B,A,A) -> k7_relset_1(A,A,A,A,B,k6_partfun1(A)) = B & B = k7_relset_1(A,A,A,A,k6_partfun1(A),B))) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2081 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),B)))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2082 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2083 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2084 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2085 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2086 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2087 (all A all B exists C (m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_2(C,A,B) & v1_funct_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2088 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (B != k1_xboole_0 -> (B = k2_relat_1(C) <-> (all D (D != k1_xboole_0 -> (all E (m2_relset_1(E,B,D) & v1_funct_2(E,B,D) & v1_funct_1(E) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,E) = k1_partfun1(A,B,B,D,C,F) -> E = F))))))))))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2089 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k1_tarski(B) = k5_partfun1(A,A,k3_partfun1(B,A,A)))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2090 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E -((all F -(r2_hidden(F,A) & k1_funct_1(D,F) = E & r2_hidden(F,C))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2091 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2092 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) -> v1_funct_1(k4_funct_2(A,B,C)) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_2(k4_funct_2(A,B,C),A,A))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2093 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2094 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2095 (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]. 59.54/57.03 2096 (all A all B (v1_funct_1(k7_funct_3(A,B)) & v1_relat_1(k7_funct_3(A,B)))) # label(dt_k7_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2097 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(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,B,D) & v1_funct_2(F,B,D) -> k13_funct_3(k5_relat_1(k9_funct_3(A,B),E),k5_relat_1(k10_funct_3(A,B),F)) = k16_funct_3(A,B,C,D,E,F))))))))) # label(t98_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2098 (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,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,C) & v1_funct_2(F,A,C) -> (all G (m2_relset_1(G,A,C) & v1_funct_2(G,A,C) & v1_funct_1(G) -> (k13_funct_3(E,G) = k13_funct_3(D,F) -> k1_xboole_0 = B & k1_xboole_0 != A | E = D & G = F | k1_xboole_0 = C & k1_xboole_0 != A))))))))) # label(t83_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2099 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2100 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> 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]. 59.54/57.03 2101 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & (k1_xboole_0 = C -> k1_xboole_0 = A) & -(v1_funct_1(k13_funct_3(D,E)) & m2_relset_1(k13_funct_3(D,E),A,k2_zfmisc_1(B,C)) & v1_funct_2(k13_funct_3(D,E),A,k2_zfmisc_1(B,C)))))))) # label(t78_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2102 (all A all B all C all D all E (-v1_xboole_0(C) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & v1_funct_2(D,A,B) & v1_funct_1(D) & -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]. 59.54/57.03 2103 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2104 (all A all B (v1_relat_1(B) & v1_funct_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]. 59.54/57.03 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(k9_relat_1(B,A),k1_relat_1(C)) & r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k1_relat_1(k5_relat_1(B,C)))))))) # label(t3_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2106 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k3_funct_3(A) <-> k1_zfmisc_1(k2_relat_1(A)) = k1_relat_1(B) & (all C (r1_tarski(C,k2_relat_1(A)) -> k1_funct_1(B,C) = k10_relat_1(A,C)))))))) # label(d2_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2107 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2108 (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]. 59.54/57.03 2109 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (B = k1_relat_1(C) & B = k1_relat_1(D) & r2_hidden(A,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]. 59.54/57.03 2110 (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) -> 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]. 59.54/57.03 2111 (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]. 59.54/57.03 2112 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k9_relat_1(B,k3_tarski(A)) = k3_tarski(k10_relat_1(k3_funct_3(B),A))))) # label(t32_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2113 (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 (v1_funct_1(F) & m2_relset_1(F,C,D) & v1_funct_2(F,C,D) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,C) -> k1_funct_1(k16_funct_3(A,C,B,D,E,F),k4_tarski(G,H)) = k4_tarski(k8_funct_2(A,B,E,G),k8_funct_2(C,D,F,H)))))))))))))))))) # label(t96_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2114 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2115 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2116 (all A all B k4_funct_3(A,B) = k5_funct_3(A,B)) # label(redefinition_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2117 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t12_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2118 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2119 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2120 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2121 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k1_funct_3(B))) -> k9_relat_1(B,A) = k1_funct_1(k1_funct_3(B),A)))) # label(t8_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2122 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) & k4_funct_3(C,B) = k4_funct_3(A,B) -> C = A)) # label(t47_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.03 2123 (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]. 59.54/57.04 2124 (all A (v1_relat_1(A) & v1_funct_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]. 59.54/57.04 2125 (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,k3_xboole_0(k1_relat_1(B),k1_relat_1(C))) -> k4_tarski(k1_funct_1(B,A),k1_funct_1(C,A)) = k1_funct_1(k13_funct_3(B,C),A)))))) # label(t68_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 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]. 59.54/57.04 2127 (all A (v1_relat_1(A) & v1_funct_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) = k1_relat_1(A))) # label(t100_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2128 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(D) & -v1_xboole_0(C) -> v1_funct_1(k14_funct_3(A,B,C,D,E)) & 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)))) # label(dt_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2129 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2130 (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]. 59.54/57.04 2131 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 59.54/57.04 2132 (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]. 59.54/57.04 2133 (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]. 59.54/57.04 2134 (all A all B all C all D all E all F (v1_funct_1(F) & v1_funct_2(F,B,D) & m1_relset_1(F,B,D) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> k16_funct_3(A,B,C,D,E,F) = k15_funct_3(E,F))) # label(redefinition_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2135 (all A all B (v1_funct_1(k10_funct_3(A,B)) & m2_relset_1(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & v1_funct_2(k10_funct_3(A,B),k2_zfmisc_1(A,B),B))) # label(dt_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2136 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_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]. 59.54/57.04 2137 (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]. 59.54/57.04 2138 (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) -> k5_relat_1(k12_funct_3(A),k16_funct_3(A,A,B,C,D,E)) = k13_funct_3(D,E))))) # label(t99_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2139 (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 all F (r2_hidden(F,B) & r2_hidden(E,A) -> k1_funct_1(C,k4_tarski(E,F)) = k1_funct_1(D,k4_tarski(E,F)))) & k2_zfmisc_1(A,B) = k1_relat_1(D) & k1_relat_1(C) = k2_zfmisc_1(A,B) -> D = C))))) # label(t6_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2140 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2141 (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]. 59.54/57.04 2142 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k10_relat_1(B,k3_tarski(A)) = k3_tarski(k10_relat_1(k1_funct_3(B),A))))) # label(t19_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2143 (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)) -> k4_funct_3(k3_funct_2(A,k2_tarski(np__0,np__1),B,k1_tarski(np__1)),A) = B)) # label(t49_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2144 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(k5_relat_1(B,C))) -> r1_tarski(k9_relat_1(B,A),k1_relat_1(C))))))) # label(t2_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2145 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,C,D) & m2_relset_1(F,C,D) -> -(k16_funct_3(A,C,B,D,E,F) != k13_funct_3(k5_relat_1(k9_funct_3(A,C),E),k5_relat_1(k10_funct_3(A,C),F)) & (k1_xboole_0 = D -> C = k1_xboole_0) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t97_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2146 (all A all B (v1_relat_1(k4_funct_3(A,B)) & v1_funct_1(k4_funct_3(A,B)))) # label(dt_k4_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2147 (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s2_funct_3) & r2_hidden(C,f2_s2_funct_3) -> f3_s2_funct_3(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & k2_zfmisc_1(f1_s2_funct_3,f2_s2_funct_3) = k1_relat_1(A) & v1_relat_1(A))) # label(s2_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2148 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k11_funct_3(A) = B <-> k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> k1_funct_1(B,C) = k4_tarski(C,C)))))) # label(d7_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2149 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k3_funct_3(A)) & m2_relset_1(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_2(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))))) # label(t39_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2150 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2151 (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]. 59.54/57.04 2152 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2153 (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]. 59.54/57.04 2154 (all A all B (v1_funct_1(k5_funct_3(A,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)))) # label(dt_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2155 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k3_tarski(k9_relat_1(k3_funct_3(B),A)) = k10_relat_1(B,k3_tarski(A))))) # label(t30_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2156 (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]. 59.54/57.04 2157 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k13_funct_3(A,B)) & v1_funct_1(k13_funct_3(A,B)))) # label(dt_k13_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2158 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> v1_funct_2(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & m2_relset_1(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & v1_funct_1(k1_funct_3(C))))) # label(t22_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2159 (all A (v1_funct_1(A) & v1_relat_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]. 59.54/57.04 2160 (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]. 59.54/57.04 2161 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2162 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funct_3(A)) & m2_relset_1(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & v1_funct_2(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t21_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2163 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2164 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_zfmisc_1(k1_relat_1(A)) & (all C (r1_tarski(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k9_relat_1(A,C))) <-> B = k1_funct_3(A)))))) # label(d1_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2165 (all A all B (m2_relset_1(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) & v1_funct_2(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) & v1_funct_1(k9_funct_3(A,B)))) # label(dt_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2166 (all A all B (r1_tarski(A,B) -> k7_relat_1(k6_relat_1(B),A) = k6_relat_1(A))) # label(t1_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2167 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2168 (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) -> (k13_funct_3(A,B) = C <-> (all D (r2_hidden(D,k1_relat_1(C)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D))) & k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C)))))))) # label(d8_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2169 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D all E (r2_hidden(E,k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,E)) = k1_funct_1(C,k4_tarski(D,E)))) & k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) <-> C = k15_funct_3(A,B)))))))) # label(d9_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2170 (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]. 59.54/57.04 2171 (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]. 59.54/57.04 2172 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2173 (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 (m2_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> k4_tarski(k8_funct_2(A,B,D,F),k8_funct_2(A,C,E,F)) = k8_funct_2(A,k2_zfmisc_1(B,C),k14_funct_3(A,B,C,D,E),F))))))))))))) # label(t79_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2174 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2175 (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 (v1_relat_1(D) & v1_funct_1(D) -> k15_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)) = k5_relat_1(k15_funct_3(B,D),k15_funct_3(A,C)))))))))) # label(t92_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2176 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k7_funct_3(A,B) <-> k2_zfmisc_1(A,B) = k1_relat_1(C) & (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> k1_funct_1(C,k4_tarski(D,E)) = D))))) # label(d5_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2177 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 59.54/57.04 2178 (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]. 59.54/57.04 2179 (all A all B k9_funct_3(A,B) = k7_funct_3(A,B)) # label(redefinition_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2180 (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]. 59.54/57.04 2181 (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),k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(k15_funct_3(A,B),k4_tarski(C,D)) = k4_tarski(k1_funct_1(A,C),k1_funct_1(B,D)))))))) # label(t86_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2182 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k9_relat_1(B,k3_tarski(A)) = k3_tarski(k9_relat_1(k1_funct_3(B),A))))) # label(t16_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2183 (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]. 59.54/57.04 2184 (all A (v1_funct_1(k12_funct_3(A)) & m2_relset_1(k12_funct_3(A),A,k2_zfmisc_1(A,A)) & v1_funct_2(k12_funct_3(A),A,k2_zfmisc_1(A,A)))) # label(dt_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2185 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(B) = A & A = k1_relat_1(C) -> k5_relat_1(k12_funct_3(A),k15_funct_3(B,C)) = k13_funct_3(B,C)))))) # label(t89_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2186 (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]. 59.54/57.04 2187 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r1_tarski(B,k1_zfmisc_1(k1_relat_1(A))) & v2_funct_1(A) -> 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]. 59.54/57.04 2188 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(D) = k1_relat_1(C) & r1_tarski(k2_relat_1(D),B) & r1_tarski(k2_relat_1(C),A) -> k5_relat_1(k13_funct_3(C,D),k9_funct_3(A,B)) = C & D = k5_relat_1(k13_funct_3(C,D),k10_funct_3(A,B))))))) # label(t72_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2189 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_funct_1(k6_funct_3(A,B)) & m2_relset_1(k6_funct_3(A,B),B,A) & v1_funct_2(k6_funct_3(A,B),B,A))) # label(dt_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2190 (all A (v1_relat_1(A) & v1_funct_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]. 59.54/57.04 2191 (all A all B -(r2_hidden(A,f1_s1_funct_3) & (all C -p1_s1_funct_3(A,B,C)) & r2_hidden(B,f2_s1_funct_3))) & (all A all B all C all D (r2_hidden(A,f1_s1_funct_3) & p1_s1_funct_3(A,B,D) & p1_s1_funct_3(A,B,C) & r2_hidden(B,f2_s1_funct_3) -> C = D)) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(C,f2_s1_funct_3) & r2_hidden(B,f1_s1_funct_3) -> p1_s1_funct_3(B,C,k1_funct_1(A,k4_tarski(B,C))))) & k2_zfmisc_1(f1_s1_funct_3,f2_s1_funct_3) = k1_relat_1(A) & v1_relat_1(A))) # label(s1_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2192 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k15_funct_3(A,B)) & v1_funct_1(k15_funct_3(A,B)))) # label(dt_k15_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2193 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k2_zfmisc_1(k10_relat_1(C,A),k10_relat_1(D,B)) = k10_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)))))) # label(t94_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2194 (all A all B all C (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & -v1_xboole_0(B) -> k1_funct_3(C) = k2_funct_3(A,B,C))) # label(redefinition_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2195 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(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)) = k15_funct_3(A,B))))) # label(t87_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2196 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D all E (r2_hidden(E,B) & r2_hidden(D,A) -> k1_funct_1(C,k4_tarski(D,E)) = E)) & k1_relat_1(C) = k2_zfmisc_1(A,B) <-> C = k8_funct_3(A,B)))) # label(d6_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2197 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2198 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_3(B))) -> k10_relat_1(B,A) = k1_funct_1(k3_funct_3(B),A)))) # label(t24_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2199 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2200 (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 (m2_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> E = k7_funct_2(A,k2_zfmisc_1(B,C),C,k14_funct_3(A,B,C,D,E),k10_funct_3(B,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)))))))))) # label(t82_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2201 (all A k11_funct_3(A) = k12_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2202 (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]. 59.54/57.04 2203 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2204 (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]. 59.54/57.04 2205 (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]. 59.54/57.04 2206 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2207 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> -(-(E = k5_relat_1(k13_funct_3(D,E),k10_funct_3(B,C)) & D = k5_relat_1(k13_funct_3(D,E),k9_funct_3(B,C))) & (C = k1_xboole_0 -> A = k1_xboole_0) & (k1_xboole_0 = B -> A = k1_xboole_0)))))) # label(t81_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2208 (all A all B (A != k1_xboole_0 -> k2_relat_1(k8_funct_3(A,B)) = B)) # label(t62_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2209 (all A all B (v1_funct_1(k8_funct_3(A,B)) & v1_relat_1(k8_funct_3(A,B)))) # label(dt_k8_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2210 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k10_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t28_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2211 (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_1(k2_funct_3(A,B,C)) & m2_relset_1(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & v1_funct_2(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(dt_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2212 (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]. 59.54/57.04 2213 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(B) = k1_relat_1(A) & k13_funct_3(D,C) = k13_funct_3(A,B) & k1_relat_1(C) = k1_relat_1(D) -> B = C & A = D))))))))) # label(t74_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2214 (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]. 59.54/57.04 2215 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(k1_funct_3(A),k1_funct_3(B)) = k1_funct_3(k5_relat_1(A,B)))))) # label(t20_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2216 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,C) & v1_funct_1(F) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_2(E,A,C) -> v1_funct_1(k16_funct_3(A,B,C,D,E,F)) & m2_relset_1(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)))) # label(dt_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 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) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m2_relset_1(F,A,C) & v1_funct_2(F,A,C) & v1_funct_1(F) -> (all G (m2_relset_1(G,A,C) & v1_funct_2(G,A,C) & v1_funct_1(G) -> (k14_funct_3(A,B,C,D,F) = k14_funct_3(A,B,C,E,G) -> E = D & F = G))))))))))))) # label(t84_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2218 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k9_relat_1(k13_funct_3(B,C),A),k2_zfmisc_1(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t76_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2219 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = A & k1_relat_1(C) = A -> k1_relat_1(k13_funct_3(B,C)) = A))))) # label(t70_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2220 (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]. 59.54/57.04 2221 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2222 (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]. 59.54/57.04 2223 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> 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]. 59.54/57.04 2224 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> 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]. 59.54/57.04 2225 (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]. 59.54/57.04 2226 (all A all B (v1_relat_1(B) & v1_funct_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]. 59.54/57.04 2227 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k10_relat_1(k13_funct_3(C,D),k2_zfmisc_1(A,B)) = k3_xboole_0(k10_relat_1(C,A),k10_relat_1(D,B)))))))) # label(t77_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2228 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_1(k1_funct_3(A),k1_xboole_0) = k1_xboole_0)) # label(t9_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2229 (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))) & B = k1_relat_1(C) <-> C = k4_funct_3(A,B)))) # label(d3_funct_3) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2230 (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]. 59.54/57.04 2231 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(C) -> ((exists E exists F exists G (m1_subset_1(E,B) & m1_subset_1(F,C) & p1_s3_domain_1(E,F,G) & A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(G,D))) <-> r2_hidden(A,a_3_8_domain_1(B,C,D))))) # label(fraenkel_a_3_8_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2232 (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)) -> k13_mcart_1(A,B,C,D,E,F) = a_6_0_domain_1(A,B,C,D,E,F))))))))))))) # label(t54_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2233 (all A all B all C all D all E all F all G all H (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(H,A) & m1_subset_1(G,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k5_enumset1(B,C,D,E,F,G,H) = k12_domain_1(A,B,C,D,E,F,G,H))) # label(redefinition_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2234 (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) -> ((exists F exists G exists H exists I (m1_subset_1(G,C) & A = k5_domain_1(B,C,D,E,F,G,H,I) & p1_s4_domain_1(F,G,H,I) & m1_subset_1(I,E) & m1_subset_1(H,D) & m1_subset_1(F,B))) <-> r2_hidden(A,a_4_2_domain_1(B,C,D,E))))) # label(fraenkel_a_4_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2235 (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))))))) <-> k7_mcart_1(B,C,D,E) = A))))))))) # label(t26_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2236 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> (k6_mcart_1(B,C,D,E) = A <-> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> A = G)))))))))))))))) # label(t25_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2237 (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_7_domain_1(B,C,D))))) # label(fraenkel_a_3_7_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2238 $T # label(t8_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2239 $T # label(t19_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2240 (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_5_domain_1(A,B,C))))))) # label(t62_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2241 (all A (r2_hidden(A,a_0_3_domain_1) <-> (exists B (p2_s10_domain_1(B) & p1_s10_domain_1(B) & A = B & m1_subset_1(B,f1_s10_domain_1))))) # label(fraenkel_a_0_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2242 $T # label(t46_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2243 (all A (-v1_xboole_0(A) -> a_1_1_domain_1(A) = k1_subset_1(A))) # label(t56_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2244 $T # label(t38_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2245 (all A all B all C all D all E all F all G (m1_subset_1(C,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) & -v1_xboole_0(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]. 59.54/57.04 2246 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(E) & -v1_xboole_0(C) -> ((exists F exists G exists H exists I (m1_subset_1(G,C) & 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(F,B))) <-> r2_hidden(A,a_4_0_domain_1(B,C,D,E))))) # label(fraenkel_a_4_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2247 (all A all B all C all D all E all F all G all H (m1_subset_1(E,A) & m1_subset_1(G,C) & m1_subset_1(H,D) & m1_subset_1(F,B) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> 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]. 59.54/57.04 2248 (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]. 59.54/57.04 2249 $T # label(t3_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2250 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,B) & m1_subset_1(C,A) -> 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]. 59.54/57.04 2251 (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(B,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(I,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,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]. 59.54/57.04 2252 $T # label(t44_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2253 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> A = F))))))) <-> k5_mcart_1(B,C,D,E) = A))))))))) # label(t24_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2254 (all A all B all C (m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k3_domain_1(A,B,C) = k2_mcart_1(C))) # label(redefinition_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2255 (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]. 59.54/57.04 2256 (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(H,k1_zfmisc_1(D)) & m1_subset_1(I,k1_zfmisc_1(E)) & -v1_xboole_0(D) & -v1_xboole_0(B) -> ((exists J exists K exists L exists M (m1_subset_1(J,B) & m1_subset_1(K,C) & m1_subset_1(M,E) & A = k5_domain_1(B,C,D,E,J,K,L,M) & r2_hidden(J,F) & r2_hidden(L,H) & r2_hidden(M,I) & r2_hidden(K,G) & m1_subset_1(L,D))) <-> r2_hidden(A,a_8_0_domain_1(B,C,D,E,F,G,H,I))))) # label(fraenkel_a_8_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2257 $T # label(t29_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2258 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_2_domain_1(B,C,D)) <-> (exists E (E = A & (r2_hidden(E,C) | r2_hidden(E,D)) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2259 $T # label(t34_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2260 (all A (r2_hidden(A,a_0_0_domain_1) <-> (exists B (m1_subset_1(B,f1_s7_domain_1) & B = A & p1_s7_domain_1(B))))) # label(fraenkel_a_0_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2261 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k6_domain_1(A,B) = k1_tarski(B))) # label(redefinition_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2262 (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]. 59.54/57.04 2263 (all A all B all C all D all E all F all G all H (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) & -v1_xboole_0(A) -> m1_subset_1(k12_domain_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(A)))) # label(dt_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2264 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> m1_subset_1(k3_domain_1(A,B,C),B))) # label(dt_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2265 (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(D) = k2_mcart_1(C) & k1_mcart_1(C) = k1_mcart_1(D) -> C = D))))))))) # label(t12_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2266 $T # label(t7_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2267 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_1_domain_1(B)) <-> (exists C (A = C & -$T & m1_subset_1(C,B)))))) # label(fraenkel_a_1_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2268 (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]. 59.54/57.04 2269 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k7_domain_1(A,B,C) = k7_domain_1(A,C,B))) # label(commutativity_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2270 (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]. 59.54/57.04 2271 $T # label(t30_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 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)) -> a_3_7_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t64_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2273 (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(D,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(H,A) & m1_subset_1(I,A) & m1_subset_1(G,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k13_domain_1(A,B,C,D,E,F,G,H,I) = k6_enumset1(B,C,D,E,F,G,H,I))) # label(redefinition_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2274 (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]. 59.54/57.04 2275 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> ((exists E exists F exists G (m1_subset_1(E,B) & m1_subset_1(F,C) & A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(G,D))) <-> r2_hidden(A,a_3_0_domain_1(B,C,D))))) # label(fraenkel_a_3_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2276 $T # label(t18_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2277 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_6_domain_1(B)) <-> (exists C (A = C & p2_s6_domain_1(C) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2278 (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)) -> (k9_mcart_1(A,B,C,D,E) = k9_mcart_1(A,B,C,D,F) & k11_mcart_1(A,B,C,D,E) = k11_mcart_1(A,B,C,D,F) & k10_mcart_1(A,B,C,D,F) = k10_mcart_1(A,B,C,D,E) & k8_mcart_1(A,B,C,D,F) = k8_mcart_1(A,B,C,D,E) -> F = E))))))))))))) # label(t45_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2279 $T # label(t22_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2280 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,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]. 59.54/57.04 2281 (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]. 59.54/57.04 2282 (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) | r2_hidden(E,C) & -r2_hidden(E,D)) & E = A & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_4_domain_1(B,C,D))))) # label(fraenkel_a_3_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2283 (all A (r2_hidden(A,a_0_4_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p1_s10_domain_1(B) & B = A)))) # label(fraenkel_a_0_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2284 (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 (A = k1_domain_1(B,C,F,G) & r2_hidden(G,E) & r2_hidden(F,D) & m1_subset_1(G,C) & m1_subset_1(F,B)))))) # label(fraenkel_a_4_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2285 (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]. 59.54/57.04 2286 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F (r2_hidden(F,A) <-> (exists G ((exists H (m1_subset_1(H,C) & (exists I ((exists J (F = k4_mcart_1(G,H,I,J) & m1_subset_1(J,E))) & m1_subset_1(I,D))))) & m1_subset_1(G,B))))) -> A = k4_zfmisc_1(B,C,D,E)))))))))))) # label(t32_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2287 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = a_2_2_domain_1(A,B))))) # label(t57_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2288 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k16_domain_1(A,B,C,D) = k19_mcart_1(D))) # label(redefinition_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2289 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E ((exists F ((exists G ((exists H (E = k3_mcart_1(F,G,H) & m1_subset_1(H,D))) & m1_subset_1(G,C))) & m1_subset_1(F,B))) <-> r2_hidden(E,A))) -> k3_zfmisc_1(B,C,D) = A))))))))) # label(t16_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2290 $T # label(t11_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2291 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) -> m1_subset_1(k14_domain_1(A,B,C,D),A))) # label(dt_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2292 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_5_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & p1_s6_domain_1(C) & A = C))))) # label(fraenkel_a_1_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.04 2293 (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]. 59.54/57.04 2294 (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) & k6_mcart_1(A,B,C,E) = k6_mcart_1(A,B,C,D) & k7_mcart_1(A,B,C,D) = k7_mcart_1(A,B,C,E) -> E = D))))))))))) # label(t28_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2295 (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(D,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(C,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]. 59.54/57.05 2296 $T # label(t39_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2297 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & m1_subset_1(B,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]. 59.54/57.05 2298 (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]. 59.54/57.05 2299 (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]. 59.54/57.05 2300 $T # label(t5_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2301 (all A ((exists B exists C (f4_s9_domain_1(B,C) = A & p1_s9_domain_1(B,C) & m1_subset_1(C,f2_s9_domain_1) & m1_subset_1(B,f1_s9_domain_1))) <-> r2_hidden(A,a_0_2_domain_1))) # label(fraenkel_a_0_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2302 $T # label(t20_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2303 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists D (m1_subset_1(D,B) & D = A & r2_hidden(D,C))) <-> r2_hidden(A,a_2_1_domain_1(B,C))))) # label(fraenkel_a_2_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2304 (all A ((exists B (f3_s8_domain_1(B) = A & p1_s8_domain_1(B) & m1_subset_1(B,f1_s8_domain_1))) <-> r2_hidden(A,a_0_1_domain_1))) # label(fraenkel_a_0_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2305 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_1_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_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2306 (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_4_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t61_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2307 $T # label(t37_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2308 $T # label(t2_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2309 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k9_domain_1(A,B,C,D,E),k1_zfmisc_1(A)))) # label(dt_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2310 (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]. 59.54/57.05 2311 (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) = k8_domain_1(A,B,C,D))) # label(redefinition_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2312 $T # label(t6_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2313 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) -> k1_domain_1(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2314 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_3_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & p1_s5_domain_1(C) & C = A))))) # label(fraenkel_a_1_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2315 (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(E,C) & p1_s2_domain_1(D,E) & A = k1_domain_1(B,C,D,E) & m1_subset_1(D,B)))))) # label(fraenkel_a_2_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2316 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_1_domain_1(A,B,C) = k5_subset_1(A,B,C))))))) # label(t58_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2317 $T # label(t21_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2318 (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]. 59.54/57.05 2319 $T # label(t23_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2320 (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) -> ((exists E (m1_subset_1(E,B) & E = A & (r2_hidden(E,C) <-> -r2_hidden(E,D)))) <-> r2_hidden(A,a_3_6_domain_1(B,C,D))))) # label(fraenkel_a_3_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2321 (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) & A = D)) <-> r2_hidden(A,a_2_2_domain_1(B,C))))) # label(fraenkel_a_2_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2322 (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]. 59.54/57.05 2323 (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) -> k17_mcart_1(D) = k14_domain_1(A,B,C,D))) # label(redefinition_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2324 (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]. 59.54/57.05 2325 (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]. 59.54/57.05 2326 (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) = k2_tarski(B,C))) # label(redefinition_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2327 $T # label(t35_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2328 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> a_2_0_domain_1(A,B) = k2_zfmisc_1(A,B))))) # label(t49_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2329 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) = k2_domain_1(A,B,C))) # label(redefinition_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2330 (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) -> (k4_zfmisc_1(B,C,D,E) = A <-> (all F (r2_hidden(F,A) <-> (exists G (m1_subset_1(G,B) & (exists H ((exists I ((exists J (k4_mcart_1(G,H,I,J) = F & m1_subset_1(J,E))) & m1_subset_1(I,D))) & m1_subset_1(H,C)))))))))))))))))) # label(t33_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2331 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> (r2_hidden(A,a_2_0_domain_1(B,C)) <-> (exists D exists E (m1_subset_1(E,C) & A = k1_domain_1(B,C,D,E) & m1_subset_1(D,B)))))) # label(fraenkel_a_2_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2332 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> k18_mcart_1(D) = k15_domain_1(A,B,C,D))) # label(redefinition_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2333 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k11_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> J = A)))))))))))))))))))) # label(t43_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2334 (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 -> A = G))))))))) <-> k8_mcart_1(B,C,D,E,F) = A))))))))))) # label(t40_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2335 (all A all B all C all D (m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k8_domain_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2336 $T # label(t10_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2337 (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,D) <-> -r2_hidden(E,C)) & E = A & 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]. 59.54/57.05 2338 $T # label(t4_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2339 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> m1_subset_1(k15_domain_1(A,B,C,D),B))) # label(dt_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2340 $T # label(t14_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2341 (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]. 59.54/57.05 2342 (all A all B all C all D all E all F (-v1_xboole_0(C) & m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(D,A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k3_mcart_1(D,E,F) = k4_domain_1(A,B,C,D,E,F))) # label(redefinition_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2343 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (r2_hidden(A,k4_zfmisc_1(B,C,D,E)) <-> (exists F (m1_subset_1(F,B) & (exists G (m1_subset_1(G,C) & (exists H ((exists I (A = k4_mcart_1(F,G,H,I) & m1_subset_1(I,E))) & m1_subset_1(H,D)))))))))))))))) # label(t31_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2344 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(D) & m1_subset_1(F,B) & m1_subset_1(H,D) & m1_subset_1(G,C) & m1_subset_1(E,A) & -v1_xboole_0(C) -> 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]. 59.54/57.05 2345 $T # label(t1_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2346 $T # label(t27_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2347 $T # label(t36_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2348 (all A all B all C all D all E all F all G (-v1_xboole_0(C) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(G,k1_zfmisc_1(D)) & m1_subset_1(E,k1_zfmisc_1(B)) & -v1_xboole_0(D) & -v1_xboole_0(B) -> ((exists H exists I exists J (m1_subset_1(I,C) & m1_subset_1(J,D) & k4_domain_1(B,C,D,H,I,J) = A & r2_hidden(J,G) & r2_hidden(I,F) & 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]. 59.54/57.05 2349 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = a_2_1_domain_1(A,B))))) # label(t52_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2350 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> I = A))))))))) <-> A = k10_mcart_1(B,C,D,E,F)))))))))))) # label(t42_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2351 (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]. 59.54/57.05 2352 (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)) -> (k9_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 = H)))))))))))))))))))) # label(t41_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2353 (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,C) & -r2_hidden(E,D))) <-> r2_hidden(A,a_3_3_domain_1(B,C,D))))) # label(fraenkel_a_3_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2354 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(C,A) -> k3_enumset1(B,C,D,E,F) = k10_domain_1(A,B,C,D,E,F))) # label(redefinition_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2355 (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) -> k17_domain_1(A,B,C,D) = k20_mcart_1(D))) # label(redefinition_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2356 $T # label(t13_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2357 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p1_s6_domain_1(B) <-> p2_s6_domain_1(B)))) -> a_1_6_domain_1(A) = a_1_5_domain_1(A)))) # label(s6_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2358 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(C) & m1_subset_1(F,C) & m1_subset_1(E,B) & m1_subset_1(D,A) & -v1_xboole_0(B) -> 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]. 59.54/57.05 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 ((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))))) <-> r2_hidden(E,A))) <-> k3_zfmisc_1(B,C,D) = A))))))))) # label(t17_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2360 (all A (-v1_xboole_0(A) -> a_1_0_domain_1(A) = A)) # label(t48_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2361 (all A (r2_hidden(A,a_0_5_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p2_s10_domain_1(B) & A = B)))) # label(fraenkel_a_0_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2362 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,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]. 59.54/57.05 2363 $T # label(t47_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2364 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((exists E ((exists F ((exists G (A = k3_mcart_1(E,F,G) & m1_subset_1(G,D))) & m1_subset_1(F,C))) & m1_subset_1(E,B))) <-> r2_hidden(A,k3_zfmisc_1(B,C,D))))))))) # label(t15_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2365 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_6_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t63_domain_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2366 (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]. 59.54/57.05 2367 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2368 (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 (m1_subset_1(D,A) -> k2_binop_1(A,A,A,C,B,D) = D)) <-> r1_binop_1(A,B,C)))))))) # label(d16_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2369 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k1_funct_1(A,k4_tarski(B,C)) = k1_binop_1(A,B,C)))) # label(d1_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2370 (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) -> (r1_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(C,B,D)))))))) # label(d5_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2371 (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) & 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) -> (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,E),k2_binop_1(A,A,A,C,D,F)) = k2_binop_1(A,A,A,C,D,k2_binop_1(A,A,A,B,E,F)))))))))))))))) # label(t24_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2372 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(D) & m1_subset_1(E,A) & m1_subset_1(F,B) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> 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]. 59.54/57.05 2373 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2374 (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) -> (all E (m1_subset_1(E,A) -> k1_binop_1(B,k1_binop_1(B,C,D),E) = k1_binop_1(B,C,k1_binop_1(B,D,E)))))))) <-> v2_binop_1(B,A)))) # label(d3_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2375 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2376 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2377 (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) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,B,C,k2_binop_1(A,A,A,B,D,E)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E))))))) <-> v2_binop_1(B,A)))))) # label(d14_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2378 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2379 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2380 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2381 (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_binop_1(B,A) <-> (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)))))))))) # label(d13_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2382 (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) -> (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]. 59.54/57.05 2383 (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]. 59.54/57.05 2384 (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 (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) -> 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)))))))) <-> r6_binop_1(A,B,C)))))) # label(t23_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2385 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2386 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2387 (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 (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) -> (r6_binop_1(A,C,B) <-> r4_binop_1(A,C,B))))))))) # label(t26_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2388 (all A (-v1_xboole_0(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,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r7_binop_1(A,B,C) <-> (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))))))))))))) # label(d20_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2389 (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) -> k1_binop_1(B,D,C) = k1_binop_1(B,C,D))))) <-> v1_binop_1(B,A)))) # label(d2_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2390 (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) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = C))))))) # label(d15_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2391 (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) <-> r3_binop_1(A,C,B))))))) # label(t15_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2392 (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]. 59.54/57.05 2393 (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 (m1_subset_1(C,A) -> ((all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D) & D = k1_binop_1(B,D,C))) <-> r3_binop_1(A,C,B)))))) # label(t11_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2394 (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 (r3_binop_1(A,C,B) & m1_subset_1(C,A))) -> (all C (m1_subset_1(C,A) -> (k3_binop_1(A,B) = C <-> r3_binop_1(A,C,B))))))) # label(d8_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2395 (all 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 = k1_binop_1(C,D,B)))))))) # label(d6_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2396 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((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]. 59.54/57.05 2397 (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) -> (r4_binop_1(A,B,C) & r5_binop_1(A,B,C) <-> r6_binop_1(A,B,C)))))) # label(d11_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2398 (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 (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,D,C))))))))) # label(t13_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2399 (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_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) -> k2_binop_1(A,B,C,D,F,G) = k2_binop_1(A,B,C,E,F,G))))) -> D = E))))))))))) # label(t2_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2400 (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]. 59.54/57.05 2401 (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_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (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]. 59.54/57.05 2402 (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 (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) <-> (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]. 59.54/57.05 2403 (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) -> k1_binop_1(B,C,C) = C)) <-> v3_binop_1(B,A)))) # label(d4_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2404 (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 (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(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(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(d10_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2405 (all A (m1_relset_1(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) -> (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) -> v1_xboole_0(A) & v1_binop_1(A,k1_xboole_0) & v2_binop_1(A,k1_xboole_0) & v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_funct_1(A)))) # label(cc1_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2406 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2407 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2408 (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) -> (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,C,k2_binop_1(A,A,A,B,D,E),k2_binop_1(A,A,A,B,D,F)) = k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,E,F))))))))))))))) # label(d18_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2409 (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) & 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) -> (r4_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t28_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2410 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2411 (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 (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> r1_binop_1(A,C,B))))))) # label(t14_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2412 (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) -> (r2_binop_1(A,B,C) & r1_binop_1(A,B,C) <-> r3_binop_1(A,B,C)))))) # label(d7_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2413 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2414 (all A (m1_subset_1(A,f1_s1_binop_1) -> (all B (m1_subset_1(B,f1_s1_binop_1) -> (exists C (m1_subset_1(C,f1_s1_binop_1) & p1_s1_binop_1(A,B,C))))))) -> (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]. 59.54/57.05 2415 (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 (m1_subset_1(D,A) -> D = k2_binop_1(A,A,A,C,D,B))) <-> r2_binop_1(A,B,C)))))))) # label(d17_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2416 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2417 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & -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]. 59.54/57.05 2418 (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 (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) -> (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,E),F) = 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)))))))) <-> r5_binop_1(A,B,C)))))))) # label(d19_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2419 (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 (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D))))))))) # label(t12_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2420 (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) -> (r3_binop_1(A,C,B) & r3_binop_1(A,D,B) -> C = D))))))) # label(t18_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2421 (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,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) -> (r5_binop_1(A,C,B) <-> r6_binop_1(A,C,B))))))))) # label(t27_binop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2422 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)) = k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2423 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k5_relat_1(k2_funcop_1(B,C),A) = k2_funcop_1(B,k1_funct_1(A,C)))))) # label(t23_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2424 (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 (m2_relset_1(D,A,A) & v1_funct_2(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]. 59.54/57.05 2425 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k13_funct_3(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]. 59.54/57.05 2426 (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(A,C) = k7_relat_1(B,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]. 59.54/57.05 2427 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2428 (all A (v1_relat_1(A) -> (all B all C (A = k2_zfmisc_1(B,C) -> k1_xboole_0 = B | C = k1_xboole_0 | B = k1_relat_1(A) & k2_relat_1(A) = C)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2429 (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) -> 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]. 59.54/57.05 2430 (all A (k1_xboole_0 = k2_relat_1(k2_funcop_1(k1_xboole_0,A)) & k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2431 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)))) <-> v1_funcop_1(A)))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 2432 (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) -> (all E (m1_subset_1(E,B) -> m2_relset_1(k4_funcop_1(C,D,E),A,B) & v1_funct_2(k4_funcop_1(C,D,E),A,B) & v1_funct_1(k4_funcop_1(C,D,E)))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.05 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 (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> 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]. 59.54/57.05 2434 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (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) -> k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) = k8_funct_2(B,A,D,G))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2435 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> (all D all E (k4_tarski(D,E) = k1_funct_1(A,C) -> k4_tarski(E,D) = k1_funct_1(B,C))) & -(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) <-> B = k1_funcop_1(A)))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2436 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k4_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A)))))) # label(d4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2437 (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(B,D) = k7_relat_1(A,D) -> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D)))))))))) # label(t29_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2438 (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 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]. 59.54/57.06 2439 (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) -> k6_funcop_1(B,A,C,D,D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2440 (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) -> (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]. 59.54/57.06 2441 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t15_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2442 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2443 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2444 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,B,A) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & v1_funct_1(D) & v1_funct_1(C) & -v1_xboole_0(A) -> k6_funcop_1(A,B,C,D,E) = k3_funcop_1(C,D,E))) # label(redefinition_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2445 (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]. 59.54/57.06 2446 (all A all B all C all D (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(B) & -v1_xboole_0(A) -> k2_relat_1(D) = k9_funcop_1(A,B,C,D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2447 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(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,D,k8_funcop_1(B,A,C,F,E)) = k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E)))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2448 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D all E (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]. 59.54/57.06 2449 (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) -> (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]. 59.54/57.06 2450 (all A all B all C (v1_relat_1(A) & v1_funct_1(C) & v1_relat_1(C) & v1_funct_1(A) -> v1_relat_1(k5_funcop_1(A,B,C)) & v1_funct_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2451 (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]. 59.54/57.06 2452 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2453 (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 (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> v1_funct_1(k3_funcop_1(C,D,E)) & m2_relset_1(k3_funcop_1(C,D,E),A,B) & v1_funct_2(k3_funcop_1(C,D,E),A,B))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2454 (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) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (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,k8_funct_2(B,A,E,G),F))) -> D = k7_funcop_1(A,B,C,E,F)))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2455 (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_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,B) & m2_relset_1(F,A,B) -> ((all G (m1_subset_1(G,A) -> k8_funct_2(A,B,F,G) = k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)))) -> k6_funcop_1(B,A,C,D,E) = F))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2456 (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 (v1_relat_1(D) & v1_funct_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]. 59.54/57.06 2457 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(A,k7_relat_1(B,C))))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2458 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A))) -> k1_funct_1(k5_funcop_1(B,D,A),C) = k1_binop_1(B,D,k1_funct_1(A,C)))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2459 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) -> m2_relset_1(k2_relat_1(D),B,C))))))))) # label(t72_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2460 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)) = k7_funcop_1(B,A,C,D,E))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2461 (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 (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E) = k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F))))))))))))) # label(t60_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2462 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k5_funcop_1(B,C,A) = k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2463 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k3_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,C),A))))))) # label(d3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2464 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2465 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> k5_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2466 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) -> m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k8_funcop_1(A,B,C,D,E)))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2467 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (v3_binop_1(C,B) -> D = k6_funcop_1(B,A,C,D,D)))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2468 (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) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2469 (exists A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2470 (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 (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> 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]. 59.54/57.06 2471 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2472 (all A all B k2_zfmisc_1(A,k1_tarski(B)) = k2_funcop_1(A,B)) # label(d2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2473 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & m1_subset_1(E,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) -> m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k7_funcop_1(A,B,C,D,E)))) # label(dt_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2474 (all A all B (v1_xboole_0(B) -> v2_funct_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_xboole_0(k2_funcop_1(B,A)))) # label(fc3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2475 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k4_funcop_1(C,k5_relat_1(B,A),D) = k5_relat_1(B,k4_funcop_1(C,A,D))))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2476 (all A k12_funct_3(A) = k13_funct_3(k6_partfun1(A),k6_partfun1(A))) # label(t2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2477 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2478 (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) -> k10_funcop_1(A,B,C,D) = k1_funcop_1(D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2479 (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) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,A) & m2_relset_1(D,A,A) -> k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)) = k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2480 (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) -> (all F (v1_funct_1(F) & v1_funct_2(F,A,B) & m2_relset_1(F,A,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F)) = k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F)))))))))))))) # label(t76_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2481 (all A all B all C all D (-v1_xboole_0(C) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)) = D)) # label(involutiveness_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2482 (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_funct_1(k5_funcop_1(C,E,D)) & v1_funct_2(k5_funcop_1(C,E,D),A,B) & m2_relset_1(k5_funcop_1(C,E,D),A,B))))))))))) # label(t65_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2483 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funcop_1(A)) & v1_relat_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2484 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C))))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2485 (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]. 59.54/57.06 2486 (all A all B all C (-r2_hidden(B,C) -> k1_xboole_0 = k10_relat_1(k2_funcop_1(A,B),C))) # label(t22_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2487 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D 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]. 59.54/57.06 2488 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> B = k1_funct_1(A,C))) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2489 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 59.54/57.06 2490 (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) -> (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]. 59.54/57.06 2491 (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) -> k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t70_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2492 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2493 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E) = k8_funct_2(B,A,D,E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2494 (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]. 59.54/57.06 2495 (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) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t56_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2496 (all A all B all C all D all E (v1_funct_1(C) & 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_xboole_0(B) & -v1_xboole_0(A) -> 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]. 59.54/57.06 2497 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2498 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_2(k2_funcop_1(A,C),A,B) & v1_funct_1(k2_funcop_1(A,C)))))) # label(t58_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2499 (all A all B all C k2_funcop_1(A,k4_tarski(C,B)) = k1_funcop_1(k2_funcop_1(A,k4_tarski(B,C)))) # label(t26_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2500 (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]. 59.54/57.06 2501 (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]. 59.54/57.06 2502 (all A all B (-v1_xboole_0(B) -> v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2503 (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) -> ((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)))) & k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) -> D = k3_funcop_1(C,A,B)))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2504 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & v1_funct_2(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(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]. 59.54/57.06 2505 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2506 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2507 (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_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)) = k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F))))))))))))) # label(t48_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2508 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) -> v1_funct_1(k3_funcop_1(A,B,C)) & v1_relat_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2509 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funcop_1(k1_funcop_1(A)) = A)) # label(involutiveness_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2510 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(A) = k1_relat_1(B) -> 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]. 59.54/57.06 2511 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(A) & k1_relat_1(B) = k1_xboole_0 -> A = B))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2512 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2513 (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 (v1_relat_1(D) & v1_funct_1(D) -> k5_relat_1(k3_funcop_1(D,B,C),A) = k3_funcop_1(k5_relat_1(D,A),B,C))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2514 (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_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,k7_funcop_1(B,A,C,D,F)) = k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F)))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2515 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2516 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2517 (all A all B (v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2518 (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_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(k3_funcop_1(C,A,B),D))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2519 (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)) -> 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]. 59.54/57.06 2520 (all A all B (k1_xboole_0 != A -> k2_relat_1(k2_funcop_1(A,B)) = k1_tarski(B))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2521 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(B != k1_xboole_0 & r2_hidden(C,k1_relat_1(A)) & k1_xboole_0 = k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)))))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2522 (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) -> (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]. 59.54/57.06 2523 (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 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]. 59.54/57.06 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_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) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,D,E) = k6_funcop_1(B,A,C,E,D)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2525 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2526 (all A all B all C (r2_hidden(B,C) -> k10_relat_1(k2_funcop_1(A,B),C) = A)) # label(t20_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2527 (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_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(A,C) = k7_relat_1(B,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]. 59.54/57.06 2528 (all A all B A = k10_relat_1(k2_funcop_1(A,B),k1_tarski(B))) # label(t21_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2529 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> 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]. 59.54/57.06 2530 (all A all B all C (r2_hidden(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(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2531 (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) -> (all E (m1_subset_1(E,A) -> 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))) = k1_funct_1(k1_funcop_1(D),E))))))))))) # label(t71_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2532 (all A all B (k1_relat_1(k2_funcop_1(A,B)) = A & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2533 (all A all B (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(A) -> v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)))) # label(fc7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2534 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & 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_1(C) -> 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]. 59.54/57.06 2535 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B))))))) # label(t46_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2536 (all A (v1_funct_1(A) & v1_relat_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]. 59.54/57.06 2537 (all A all B all C k7_relat_1(k2_funcop_1(A,B),C) = k2_funcop_1(k3_xboole_0(A,C),B)) # label(t18_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2538 (all A all B all C (r2_hidden(B,A) -> k1_funct_1(k2_funcop_1(A,C),B) = C)) # label(t13_funcop_1) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2539 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = k2_funct_4(k2_funct_4(C))))) # label(t53_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2540 (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]. 59.54/57.06 2541 (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]. 59.54/57.06 2542 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k3_funct_4(A,B) <-> (all D (r2_hidden(D,k1_relat_1(C)) <-> (exists E exists F exists G exists H (r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & r2_hidden(k4_tarski(E,F),k1_relat_1(A)) & D = k4_tarski(k4_tarski(E,G),k4_tarski(F,H)))))) & (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)))))))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2543 (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]. 59.54/57.06 2544 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> k1_funct_4(A,B) = B & k1_funct_4(B,A) = B))))) # label(t79_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2545 (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_1(k2_funct_4(D)) & 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))))) # label(t51_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2546 (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(A,B)) <-> r1_partfun1(A,B)))))) # label(t29_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2547 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (r2_hidden(k4_tarski(D,E),k1_relat_1(A)) & k4_tarski(E,D) = C)))) & (all C all D (r2_hidden(k4_tarski(C,D),k1_relat_1(A)) -> k1_funct_1(A,k4_tarski(C,D)) = k1_funct_1(B,k4_tarski(D,C)))) <-> k2_funct_4(A) = B))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2548 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_partfun1(B,C) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2549 (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 -> D = k2_funct_4(k2_funct_4(D))))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2550 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_xboole_0(k1_relat_1(B),k1_relat_1(C)) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k1_funct_1(k1_funct_4(B,C),A)))))) # label(t17_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2551 (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]. 59.54/57.06 2552 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k1_funct_4(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]. 59.54/57.06 2553 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (k1_relat_1(F) = k2_zfmisc_1(C,D) & k1_relat_1(E) = k2_zfmisc_1(A,B) -> k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) = k1_relat_1(k3_funct_4(E,F))))))) # label(t61_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2554 (all A (v1_funct_1(A) & v1_relat_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]. 59.54/57.06 2555 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2556 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(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]. 59.54/57.06 2557 (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)) -> k1_funct_4(A,B) = B))))) # label(t20_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2558 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_funct_1(k1_funct_4(A,B)) & v1_relat_1(k1_funct_4(A,B)))) # label(dt_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2559 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t36_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2560 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (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]. 59.54/57.06 2561 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2562 (all A (v1_relat_1(A) & v1_funct_1(A) -> A = k1_funct_4(k1_xboole_0,A))) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2563 (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]. 59.54/57.06 2564 (all A all B (r1_tarski(A,B) <-> r1_tarski(k6_partfun1(A),k6_partfun1(B)))) # label(t4_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2565 (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]. 59.54/57.06 2566 (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_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]. 59.54/57.06 2567 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (C != k1_xboole_0 -> 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]. 59.54/57.06 2568 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> k2_funct_4(k2_funct_4(D)) = D)) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2569 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> k1_funct_4(B,C) = C)))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2570 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> D = k1_funct_4(C,D)))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2571 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (-r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2572 (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) -> D = k2_funct_4(k2_funct_4(D)))))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2573 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_funct_4(k2_funct_4(A)),A))) # label(t52_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2574 (all A (v1_relat_1(A) & v1_funct_1(A) -> A = k1_funct_4(A,k1_xboole_0))) # label(t22_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2575 (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]. 59.54/57.06 2576 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)))))) # label(t30_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2577 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k1_relat_1(E) = k2_tarski(A,B) & D = k1_funct_1(E,B) & C = k1_funct_1(E,A) -> E = k4_funct_4(A,B,C,D)))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2578 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_tarski(A,k1_funct_4(A,B))))))) # label(t33_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2579 (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]. 59.54/57.06 2580 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (v1_partfun1(D,A,B) -> k1_funct_4(C,D) = D))))) # label(t37_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2581 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k3_funct_4(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t59_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.06 2582 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (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]. 59.54/57.06 2583 (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))) -> k1_funct_1(k3_funct_4(E,F),k4_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k4_tarski(k1_funct_1(E,k4_tarski(A,C)),k1_funct_1(F,k4_tarski(B,D)))))))) # label(t58_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2584 (all A all B all C all D (B != A -> D = k1_funct_1(k4_funct_4(A,B,C,D),B) & C = k1_funct_1(k4_funct_4(A,B,C,D),A))) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2585 (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 (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> k1_funct_4(C,D) = D)))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2586 (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]. 59.54/57.07 2587 (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(B),C) & r1_tarski(k1_relat_1(A),C) -> A = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t82_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2588 (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]. 59.54/57.07 2589 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k1_relat_1(k2_funct_4(C)) = k2_zfmisc_1(B,A)))) # label(t47_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2590 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B A = k1_funct_4(A,k7_relat_1(A,B))))) # label(t80_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2591 (all A all B all C all D all E all F 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) -> (all H (v1_funct_2(H,k2_zfmisc_1(D,E),F) & m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_1(H) -> -(C != k1_xboole_0 & -(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]. 59.54/57.07 2592 (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) -> F = D & E = C | A = B)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2593 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 59.54/57.07 2594 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k7_relat_1(k1_funct_4(A,B),k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),A))))) # label(t25_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2595 (all A all B all C k4_funct_4(A,B,C,C) = k2_funcop_1(k2_tarski(A,B),C)) # label(t68_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2596 (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]. 59.54/57.07 2597 (all A (v1_relat_1(A) & v1_funct_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]. 59.54/57.07 2598 (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]. 59.54/57.07 2599 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) <-> k2_xboole_0(A,B) = k1_funct_4(A,B)))))) # label(t31_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2600 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r1_tarski(k1_relat_1(A),C) & r1_tarski(k1_relat_1(B),D) & r1_xboole_0(C,D) -> A = k7_relat_1(k1_funct_4(A,B),C) & B = k7_relat_1(k1_funct_4(A,B),D))))))) # label(t81_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2601 (all A all B all C all D all E (-v1_xboole_0(E) -> (all F (-v1_xboole_0(F) -> (all G (v1_funct_2(G,k2_zfmisc_1(A,B),E) & m2_relset_1(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]. 59.54/57.07 2602 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r1_tarski(k2_funcop_1(k1_tarski(A),k1_funct_1(B,A)),B)))) # label(t8_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2603 (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(k1_funct_4(A,B))) & r1_tarski(k1_relat_1(B),k1_relat_1(k1_funct_4(A,B))))))) # label(t11_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2604 (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]. 59.54/57.07 2605 (all A (v1_relat_1(A) & v1_funct_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(A,C) = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t76_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2606 (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]. 59.54/57.07 2607 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(A)) = A))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2608 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k1_relat_1(B) -> k1_funct_4(A,C) = k1_funct_4(k1_funct_4(A,B),C)))))))) # label(t78_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2609 (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]. 59.54/57.07 2610 (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]. 59.54/57.07 2611 (all A all B all C all D (k1_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(A,B) & r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)))) # label(t65_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2612 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r1_tarski(k1_relat_1(A),k2_xboole_0(B,C)) -> A = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)))))) # label(t74_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2613 (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) -> (C = k1_funct_4(A,B) <-> (all D (r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D)) & (-r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(A,D)))) & k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2614 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_partfun1(A,B) & r1_tarski(k2_relat_1(D),k1_relat_1(B)) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B)) = k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B))))))))))) # label(t73_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2615 (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(B,A) = k1_funct_4(A,B)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2616 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> 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]. 59.54/57.07 2617 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> D = B | k1_xboole_0 = A)) # label(t7_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2618 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_relat_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]. 59.54/57.07 2619 (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) -> 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]. 59.54/57.07 2620 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2621 (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(B,A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2622 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,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]. 59.54/57.07 2623 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t9_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2624 (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]. 59.54/57.07 2625 (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]. 59.54/57.07 2626 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2627 (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(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]. 59.54/57.07 2628 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(k1_relat_1(A),C) -> k7_relat_1(B,C) = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t77_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2629 (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]. 59.54/57.07 2630 (all A -((all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))) & (all B all C -r1_tarski(A,k2_zfmisc_1(B,C))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.54/57.07 2631 (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]. 59.54/57.07 2632 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(B,k7_relat_1(A,k2_relat_1(B))) = k5_relat_1(B,A))))) # label(t2_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2633 (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) = k2_xboole_0(A,B)))))) # label(t32_funct_4) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2634 (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]. 59.70/57.19 2635 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> f3_s11_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s11_ordinal2) -> B = k1_xboole_0 | f4_s11_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B)))) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> f2_s11_ordinal2 = k1_funct_1(A,k1_xboole_0)) & f1_s11_ordinal2 = k1_relat_1(A) & v1_ordinal2(A) & v1_funct_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2636 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2637 (exists A (v1_funct_1(A) & f1_s5_ordinal2 = k1_relat_1(A) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s5_ordinal2) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s5_ordinal2) -> k1_xboole_0 = B | f4_s5_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B)))) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s5_ordinal2(B,k1_funct_1(A,B))))) & v5_ordinal1(A) & v1_relat_1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2638 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2639 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2640 (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]. 59.70/57.19 2641 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2642 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2643 (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]. 59.70/57.19 2644 (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]. 59.70/57.19 2645 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2646 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2647 (all A (v3_ordinal1(A) -> A = k3_tarski(k1_ordinal1(A)))) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2648 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k11_ordinal2(A)))) # label(dt_k11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.19 2649 (all A (v3_ordinal1(A) -> (all B (f2_s6_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & B = k1_ordinal2(C) & f4_s6_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s6_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> D = k1_xboole_0 | f6_s6_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_relat_1(C) = k1_ordinal1(A) & v1_relat_1(C))))))) & (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_xboole_0) = f4_s6_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A)) = f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s6_ordinal2) -> A = k1_xboole_0 | f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,A)))) & f3_s6_ordinal2 = k1_relat_1(f1_s6_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> f2_s6_ordinal2(A) = k1_funct_1(f1_s6_ordinal2,A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2650 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> k12_ordinal2(k2_ordinal1(B,A)) = k13_ordinal2(A,B))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2651 (all A all B (v3_ordinal1(B) -> v1_ordinal2(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2652 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2653 (exists A (v1_ordinal1(A) & v3_ordinal1(A) & v4_ordinal1(A) & v2_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2654 (all A all B (v3_ordinal1(B) -> (k7_ordinal2(A) = B <-> r1_tarski(k2_ordinal2(A),B) & (all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C))))))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2655 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2656 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2657 (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]. 59.70/57.20 2658 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2659 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_ordinal1(A) -> k1_ordinal2(B) = k1_funct_1(B,A)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2660 (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]. 59.70/57.20 2661 (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]. 59.70/57.20 2662 (all A all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) & v3_ordinal1(A) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2663 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k9_ordinal2(A)))) # label(dt_k9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2664 (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]. 59.70/57.20 2665 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> k1_xboole_0 = A | (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k14_ordinal2(B,D)))) -> k14_ordinal2(B,A) = k8_ordinal2(C))))))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2666 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2667 (all A (v3_ordinal1(A) -> (r2_hidden(k1_xboole_0,A) & v4_ordinal1(A) -> r1_ordinal1(k5_ordinal2,A)))) # label(t19_ordinal2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 59.70/57.20 2668 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2669 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(A,k16_ordinal2(A,B)) = k16_ordinal2(A,k1_ordinal1(B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 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]. 59.70/57.21 2671 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2672 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(A,k1_xboole_0))) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2673 (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]. 59.70/57.21 2674 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2675 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f4_s15_ordinal2(A) = B <-> (exists C (v1_relat_1(C) & k1_ordinal2(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s15_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f3_s15_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f1_s15_ordinal2 & k1_ordinal1(A) = k1_relat_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C)))))))) -> (all A (v3_ordinal1(A) -> f2_s15_ordinal2(A,f4_s15_ordinal2(A)) = f4_s15_ordinal2(k1_ordinal1(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2676 (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]. 59.70/57.21 2677 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k15_ordinal2(A,B)))) # label(dt_k15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2678 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2679 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> (v2_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,C) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C)))))))))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2680 (all A (v3_ordinal1(A) -> (all B -(r2_hidden(A,k7_ordinal2(B)) & (all C (v3_ordinal1(C) -> -(r1_ordinal1(A,C) & r2_hidden(C,B)))))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2681 (exists A ((exists B (v1_funct_1(B) & v1_ordinal2(B) & k1_relat_1(B) = k1_ordinal1(f1_s13_ordinal2) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s13_ordinal2(C,k1_funct_1(B,C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(C) -> f4_s13_ordinal2(C,k2_ordinal1(B,C)) = k1_funct_1(B,C) | k1_xboole_0 = C))) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & k1_ordinal2(B) = A & v5_ordinal1(B) & v1_relat_1(B))) & v3_ordinal1(A))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2682 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(A != B & (exists C (v5_ordinal1(C) & k1_ordinal2(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s13_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C))) & (exists C (v5_ordinal1(C) & v1_ordinal2(C) & k1_ordinal2(C) = A & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s13_ordinal2(D,k1_funct_1(C,D))))) & v1_funct_1(C) & v1_relat_1(C)))))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2683 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2684 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2685 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2686 (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]. 59.70/57.21 2687 (all A (v3_ordinal1(A) -> A = k15_ordinal2(k4_ordinal2,A) & k15_ordinal2(A,k4_ordinal2) = A)) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2688 (all A all B (v1_funct_1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_relat_1(A) -> v1_ordinal2(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2689 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2690 (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]. 59.70/57.21 2691 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2692 (exists A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2693 (all A (v3_ordinal1(A) -> (p1_s1_ordinal2(A) -> p1_s1_ordinal2(k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s1_ordinal2(B)))) & v4_ordinal1(A) -> p1_s1_ordinal2(A) | A = k1_xboole_0))) & p1_s1_ordinal2(k1_xboole_0) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2694 (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]. 59.70/57.21 2695 (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]. 59.70/57.21 2696 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2697 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v5_ordinal1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k1_funct_1(D,k1_ordinal1(E)) = k14_ordinal2(k1_funct_1(D,E),B)))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(A)) & v4_ordinal1(E) -> k1_xboole_0 = E | k1_funct_1(D,E) = k3_tarski(k8_ordinal2(k2_ordinal1(D,E)))))) & k1_xboole_0 = k1_funct_1(D,k1_xboole_0) & k1_relat_1(D) = k1_ordinal1(A) & C = k1_ordinal2(D) & v1_ordinal2(D) & v1_funct_1(D) & v1_relat_1(D))) <-> k15_ordinal2(A,B) = C))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.70/57.21 2698 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v5_ordinal1(C) & B = k1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s14_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f2_s14_ordinal2 & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C))) <-> B = f1_s14_ordinal2(A)))))) -> f2_s14_ordinal2 = f1_s14_ordinal2(k1_xboole_0) # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2699 (all A (v3_ordinal1(A) -> (exists B (v3_ordinal1(B) & (exists C (v3_ordinal1(C) & v4_ordinal1(B) & v4_ordinal2(C) & A = k14_ordinal2(B,C))))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2700 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k14_ordinal2(A,k4_ordinal2))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2701 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> ((exists B (r1_ordinal2(B,A) & v3_ordinal1(B))) -> (all B (v3_ordinal1(B) -> (r1_ordinal2(B,A) <-> k12_ordinal2(A) = B)))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2702 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2703 (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]. 59.79/57.28 2704 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2705 (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]. 59.79/57.28 2706 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2707 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2708 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k16_ordinal2(A,B) <-> (exists D (v1_relat_1(D) & v1_funct_1(D) & v1_ordinal2(D) & k1_ordinal1(B) = k1_relat_1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k15_ordinal2(A,k1_funct_1(D,E))))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_funct_1(D,E) = k12_ordinal2(k2_ordinal1(D,E)) | E = k1_xboole_0))) & k4_ordinal2 = k1_funct_1(D,k1_xboole_0) & C = k1_ordinal2(D) & v5_ordinal1(D)))))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2709 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2710 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2711 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2712 (all A all B (B = k2_ordinal2(A) <-> (all C (r2_hidden(C,A) & v3_ordinal1(C) <-> r2_hidden(C,B))))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2713 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)) & k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2714 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2715 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.79/57.28 2716 k1_relat_1(f1_s12_ordinal2) = f3_s12_ordinal2 & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_xboole_0) = f4_s12_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f3_s12_ordinal2) & v4_ordinal1(A) -> k1_xboole_0 = A | k1_funct_1(f1_s12_ordinal2,A) = f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & v1_ordinal2(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & f4_s12_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f6_s12_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & v5_ordinal1(C) & v1_relat_1(C))) <-> B = f2_s12_ordinal2(A)))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> k1_funct_1(f1_s12_ordinal2,A) = f2_s12_ordinal2(A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2717 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2718 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2719 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2720 (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]. 59.80/57.30 2721 (all A all B ((all C ((exists D (v4_ordinal1(D) & D = C & v3_ordinal1(D))) & r2_hidden(C,A) <-> r2_hidden(C,B))) <-> B = k3_ordinal2(A))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2722 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k16_ordinal2(B,D)))) & A = k1_relat_1(C) -> k12_ordinal2(C) = k16_ordinal2(B,A)))) | A = k1_xboole_0))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2723 (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]. 59.80/57.30 2724 (all A (v3_ordinal1(A) -> k7_ordinal2(k1_tarski(A)) = k1_ordinal1(A))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2725 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2726 (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]. 59.80/57.30 2727 (all A (v3_ordinal1(A) -> k16_ordinal2(k4_ordinal2,A) = k4_ordinal2 & k16_ordinal2(A,k4_ordinal2) = A)) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2728 k1_relat_1(f5_s4_ordinal2) = f1_s4_ordinal2 & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f1_s4_ordinal2) & v4_ordinal1(A) -> A = k1_xboole_0 | f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,A)))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A)) = f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,A) | k1_xboole_0 = A))) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) -> f5_s4_ordinal2 = f6_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2729 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2730 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k1_relat_1(A) = k1_relat_1(C) & B = k9_ordinal2(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C))) <-> k10_ordinal2(A) = B))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2731 (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]. 59.80/57.30 2732 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) -> (A != k1_xboole_0 -> ((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -((all E (v3_ordinal1(E) -> -(r2_hidden(E,k1_relat_1(B)) & (all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,F),D) & r2_hidden(C,k1_funct_1(B,F)))))))) & r2_hidden(A,D) & r2_hidden(C,A)))))) <-> r1_ordinal2(A,B))) & (k1_xboole_0 = A -> ((exists C ((all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) & r1_ordinal1(C,D) -> k1_xboole_0 = k1_funct_1(B,D)))) & r2_hidden(C,k1_relat_1(B)) & v3_ordinal1(C))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2733 (all A (v3_ordinal1(A) -> (all B all C (r1_tarski(B,C) & r2_hidden(A,B) -> r1_ordinal1(k6_ordinal2(C),k6_ordinal2(B)))))) # label(t24_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2734 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(k1_ordinal1(A),k1_ordinal1(B)) <-> r1_ordinal1(A,B)))))) # label(t1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2735 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k14_ordinal2(A,B) <-> (exists D (v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) & v1_ordinal2(D) & C = k1_ordinal2(D) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_funct_1(D,E) = k8_ordinal2(k2_ordinal1(D,E)) | E = k1_xboole_0))) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_ordinal1(k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & k1_funct_1(D,k1_xboole_0) = A & k1_relat_1(D) = k1_ordinal1(B)))))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2736 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f2_s9_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f3_s9_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & k1_funct_1(C,k1_xboole_0) = f1_s9_ordinal2 & k1_ordinal2(C) = B & v1_relat_1(C))) <-> f4_s9_ordinal2(A) = B)))) -> (all A (v3_ordinal1(A) -> f2_s9_ordinal2(A,f4_s9_ordinal2(A)) = f4_s9_ordinal2(k1_ordinal1(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2737 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2738 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2739 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2740 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2741 (all A (v3_ordinal1(A) -> (all B ((exists C (k1_funct_1(C,k1_xboole_0) = f2_s8_ordinal2 & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f4_s8_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s8_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_relat_1(C) = k1_ordinal1(A) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> f1_s8_ordinal2(A) = B)))) -> f1_s8_ordinal2(k1_xboole_0) = f2_s8_ordinal2 # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.30 2742 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_relat_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) & A = k1_relat_1(C) -> k15_ordinal2(A,B) = k3_tarski(k8_ordinal2(C))))) | k1_xboole_0 = A))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.31 2743 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (v4_ordinal1(B) & C = k1_funct_1(A,B) & r2_hidden(B,k1_relat_1(A)) -> r1_ordinal2(C,k2_ordinal1(A,B)) | B = k1_xboole_0))))) <-> v3_ordinal2(A)))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.31 2744 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.31 2745 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = k11_ordinal2(A) <-> (exists C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & B = k8_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k1_relat_1(A) = k1_relat_1(C) & v1_funct_1(C)))))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.31 2746 (exists A (v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> k1_funct_1(A,B) = f2_s3_ordinal2(B)))) & k1_relat_1(A) = f1_s3_ordinal2 & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.31 2747 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.31 2748 (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]. 59.80/57.31 2749 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((exists B (v3_ordinal1(B) & r1_tarski(k2_relat_1(A),B))) <-> v1_ordinal2(A)))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.31 2750 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f3_s16_ordinal2(A) <-> (exists C (v5_ordinal1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s16_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f6_s16_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | D = k1_xboole_0))) & f4_s16_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_ordinal1(A) = k1_relat_1(C) & B = k1_ordinal2(C) & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C)))))))) & f2_s16_ordinal2 != k1_xboole_0 & v4_ordinal1(f2_s16_ordinal2) & k1_relat_1(f1_s16_ordinal2) = f2_s16_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> f3_s16_ordinal2(A) = k1_funct_1(f1_s16_ordinal2,A)))) -> f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) = f3_s16_ordinal2(f2_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.80/57.31 2751 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & k1_ordinal2(B) = A & k1_relat_1(B) = k1_ordinal1(f1_s7_ordinal2) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(B,C) = f4_s7_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s7_ordinal2(C,k1_funct_1(B,C))))) & f2_s7_ordinal2 = k1_funct_1(B,k1_xboole_0) & v5_ordinal1(B))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 59.80/57.31 2752 (all A all B -(A != B & (exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_xboole_0 = D | k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_ordinal2(C) = B & v1_relat_1(C))) & (exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = A & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(D) -> D = k1_xboole_0 | k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D))))) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & v1_funct_1(C))))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 59.83/57.31 2753 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.31 2754 (all A (k5_ordinal2 = A <-> v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v4_ordinal1(A) & r2_hidden(k1_xboole_0,A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.31 2755 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.31 2756 (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> f3_s10_ordinal2(A) = k1_funct_1(f1_s10_ordinal2,A)))) & k1_relat_1(f1_s10_ordinal2) = f2_s10_ordinal2 & v4_ordinal1(f2_s10_ordinal2) & f2_s10_ordinal2 != k1_xboole_0 & (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(C) & v5_ordinal1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> f6_s10_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s10_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f4_s10_ordinal2 & k1_ordinal1(A) = k1_relat_1(C) & B = k1_ordinal2(C) & v1_relat_1(C))) <-> B = f3_s10_ordinal2(A))))) -> f3_s10_ordinal2(f2_s10_ordinal2) = f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.31 2757 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> A = k1_xboole_0 | v4_ordinal1(k14_ordinal2(B,A))))))) # label(t32_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.31 2758 (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]. 59.83/57.31 2759 $T # label(t3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.31 2760 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v3_ordinal1(A) -> v1_relat_1(k4_ordinal3(A,B)) & v1_ordinal2(k4_ordinal3(A,B)) & v5_ordinal1(k4_ordinal3(A,B)) & v1_funct_1(k4_ordinal3(A,B)))) # label(dt_k4_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.31 2761 (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]. 59.83/57.31 2762 (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)) -> k1_xboole_0 = B | r1_ordinal1(A,C)))))))) # label(t38_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.31 2763 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) -> (k1_ordinal3(A,B) = C <-> k1_relat_1(C) = k1_relat_1(B) & (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]. 59.83/57.31 2764 $T # label(t64_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.31 2765 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> (C = k4_ordinal3(A,B) <-> (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(C) = k1_relat_1(B)))))))) # label(d5_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.31 2766 (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(k14_ordinal2(A,C),k14_ordinal2(B,D)) | -r1_ordinal1(A,B) & -r2_hidden(A,B)))))))))) # label(t20_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2767 (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(k14_ordinal2(A,C),k14_ordinal2(B,D))))))))))) # label(t21_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2768 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(A,k15_ordinal2(C,B)) & r2_hidden(A,k15_ordinal2(B,C)) | C = k1_xboole_0))))))) # label(t35_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2769 (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]. 59.83/57.32 2770 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (A != k1_xboole_0 -> r1_ordinal1(B,k15_ordinal2(B,A)) & r1_ordinal1(B,k15_ordinal2(A,B))))))) # label(t39_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2771 $T # label(t14_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2772 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> -(-r2_hidden(A,B) & (all D (v3_ordinal1(D) -> -(k14_ordinal2(B,D) = A & r2_hidden(D,C)))) & r2_hidden(A,k14_ordinal2(B,C))))))))) # label(t42_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2773 (all A all B (v3_ordinal1(A) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> v1_relat_1(k1_ordinal3(A,B)) & v1_funct_1(k1_ordinal3(A,B)) & v1_ordinal2(k1_ordinal3(A,B)) & v5_ordinal1(k1_ordinal3(A,B)))) # label(dt_k1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2774 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (A != k1_xboole_0 -> k3_tarski(k14_ordinal2(B,A)) = k14_ordinal2(B,k3_tarski(A))))))) # label(t53_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2775 (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]. 59.83/57.32 2776 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k15_ordinal2(A,B) = k15_ordinal2(C,B) -> A = C | k1_xboole_0 = B))))))) # label(t36_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2777 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k5_ordinal3(k14_ordinal2(A,B),A) = B)))) # label(t65_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2778 (all A all B (v3_ordinal1(A) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) & v1_relat_1(B) -> v1_ordinal2(k2_ordinal3(A,B)) & v5_ordinal1(k2_ordinal3(A,B)) & v1_funct_1(k2_ordinal3(A,B)) & v1_relat_1(k2_ordinal3(A,B)))) # label(dt_k2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2779 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k1_xboole_0 != A -> B = k6_ordinal3(k15_ordinal2(B,A),A)))))) # label(t81_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2780 $T # label(t61_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2781 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k14_ordinal2(A,k14_ordinal2(B,C)) = k14_ordinal2(k14_ordinal2(A,B),C))))))) # label(t33_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2782 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(k5_ordinal3(A,C),k5_ordinal3(B,C)) | -r2_hidden(C,A) & -r1_ordinal1(C,A)))))))) # label(t66_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 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) -> -r2_hidden(C,D) & -(k1_xboole_0 != D & r1_ordinal1(C,D)) | r2_hidden(k15_ordinal2(A,C),k15_ordinal2(B,D))))))))))) # label(t22_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2784 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(A),k1_ordinal1(B)) <-> r2_hidden(A,B)))))) # label(t5_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2785 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k7_ordinal3(A,B) = k5_ordinal3(A,k15_ordinal2(k6_ordinal3(A,B),B)))))) # label(d8_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2786 $T # label(d1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 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 -> k7_ordinal3(A,C) = D & k6_ordinal3(A,C) = B))))))))) # label(t79_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2788 (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]. 59.83/57.32 2789 (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(k15_ordinal2(A,C),k15_ordinal2(B,D))))))))))) # label(t23_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2790 $T # label(t44_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2791 (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]. 59.83/57.32 2792 (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]. 59.83/57.32 2793 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v1_ordinal1(k3_xboole_0(A,B)) & v3_ordinal1(k3_xboole_0(A,B)) & v2_ordinal1(k3_xboole_0(A,B)))) # label(fc2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2794 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k14_ordinal2(k1_funct_1(B,D),A) = k1_funct_1(C,D)))) & k1_relat_1(B) = k1_relat_1(C) <-> C = k2_ordinal3(A,B)))))))) # label(d3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2795 (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]. 59.83/57.32 2796 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(k1_xboole_0 != A & (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -(r2_hidden(D,A) & B = k14_ordinal2(k15_ordinal2(C,A),D))))))))))) # label(t55_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2797 (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]. 59.83/57.32 2798 (all A (v3_ordinal1(A) -> (r2_hidden(A,k4_ordinal2) -> A = k1_xboole_0))) # label(t17_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2799 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(A,k14_ordinal2(B,C)) & r2_hidden(A,k14_ordinal2(C,B))))))))) # label(t28_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2800 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> r2_hidden(k1_xboole_0,k5_ordinal3(B,A)) & k1_xboole_0 != k5_ordinal3(B,A)))))) # label(t68_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2801 $T # label(t45_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2802 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> B = k2_xboole_0(A,B) | A = k2_xboole_0(A,B))))) # label(t15_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2803 (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]. 59.83/57.32 2804 (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]. 59.83/57.32 2805 (all A (v3_ordinal1(A) -> k5_ordinal3(A,k1_xboole_0) = A & k5_ordinal3(k1_xboole_0,A) = k1_xboole_0)) # label(t69_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2806 (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]. 59.83/57.32 2807 (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]. 59.83/57.32 2808 (all A all B (r1_tarski(k1_ordinal1(A),B) -> r1_tarski(A,B))) # label(t2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2809 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> -(C != k1_xboole_0 & k14_ordinal2(A,C) = B))) & r2_hidden(A,B)))))) # label(t31_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2810 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k14_ordinal2(A,B) = k1_xboole_0 -> k1_xboole_0 = A & k1_xboole_0 = B))))) # label(t29_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2811 (all A (v3_ordinal1(A) -> k7_ordinal3(A,k1_xboole_0) = A & k1_xboole_0 = k7_ordinal3(k1_xboole_0,A) & k6_ordinal3(k1_xboole_0,A) = k1_xboole_0)) # label(t83_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2812 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(k1_xboole_0 = k15_ordinal2(A,B) & A != k1_xboole_0 & B != k1_xboole_0))))) # label(t34_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2813 (all A all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) & v3_ordinal1(A) -> v1_funct_1(k3_ordinal3(A,B)) & v5_ordinal1(k3_ordinal3(A,B)) & v1_ordinal2(k3_ordinal3(A,B)) & v1_relat_1(k3_ordinal3(A,B)))) # label(dt_k3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2814 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(k8_ordinal2(A)) -> B = k1_xboole_0 | k15_ordinal2(k8_ordinal2(A),B) = k8_ordinal2(k4_ordinal3(B,A)) | k1_relat_1(A) = k1_xboole_0))))) # label(t52_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2815 (all A (v3_ordinal1(A) -> A = k6_ordinal2(k1_tarski(A)))) # label(t12_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2816 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k3_xboole_0(A,B) = A | k3_xboole_0(A,B) = B)))) # label(t16_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2817 (all A (v3_ordinal1(A) -> k2_ordinal2(k1_tarski(A)) = k1_tarski(A))) # label(t9_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2818 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k15_ordinal2(A,k1_funct_1(B,D))))) & k1_relat_1(C) = k1_relat_1(B) <-> k3_ordinal3(A,B) = C))))))) # label(d4_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2819 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v1_ordinal1(k2_xboole_0(A,B)) & v2_ordinal1(k2_xboole_0(A,B)) & v3_ordinal1(k2_xboole_0(A,B)))) # label(fc1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 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]. 59.83/57.32 2821 (all A (v3_ordinal1(A) -> k5_ordinal3(A,A) = k1_xboole_0)) # label(t67_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2822 (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]. 59.83/57.32 2823 (all A (v3_ordinal1(A) -> k6_ordinal2(A) = k1_xboole_0)) # label(t11_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2824 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k4_ordinal2,A) & v4_ordinal1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) -> (k1_relat_1(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(D,B) -> k1_funct_1(C,D) = k15_ordinal2(D,A)))) -> k15_ordinal2(B,A) = k8_ordinal2(C)))) | B = k1_xboole_0))))) # label(t57_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2825 (all A v3_ordinal1(k3_tarski(k2_ordinal2(A)))) # label(t7_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2826 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k7_ordinal3(A,B)))) # label(dt_k7_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2827 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v3_ordinal1(C) -> (k1_relat_1(B) = k1_relat_1(A) & (all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (k1_funct_1(A,D) = E & r2_hidden(D,k1_relat_1(A)) -> k15_ordinal2(E,C) = k1_funct_1(B,D)))))) & v4_ordinal1(k8_ordinal2(A)) -> C = k1_xboole_0 | k8_ordinal2(B) = k15_ordinal2(k8_ordinal2(A),C) | k1_xboole_0 = k1_relat_1(A)))))))) # label(t50_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2828 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (B = k1_xboole_0 -> (C = k6_ordinal3(A,B) <-> k1_xboole_0 = C)) & (B != k1_xboole_0 -> ((exists D (v3_ordinal1(D) & A = k14_ordinal2(k15_ordinal2(C,B),D) & r2_hidden(D,B))) <-> k6_ordinal3(A,B) = C)))))))) # label(d7_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2829 $T # label(t43_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2830 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,k14_ordinal2(C,A)) -> k1_xboole_0 = A | r2_hidden(k5_ordinal3(B,C),A)))))))) # label(t73_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2831 $T # label(t4_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2832 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k5_ordinal3(A,B)))) # label(dt_k5_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2833 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (-r1_ordinal1(B,A) -> (k5_ordinal3(A,B) = C <-> C = k1_xboole_0)) & (r1_ordinal1(B,A) -> (C = k5_ordinal3(A,B) <-> A = k14_ordinal2(B,C))))))))) # label(d6_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2834 (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]. 59.83/57.32 2835 $T # label(t59_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2836 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> B = k2_ordinal2(B))))) # label(t8_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2837 (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]. 59.83/57.32 2838 (all A r1_tarski(A,k1_ordinal1(A))) # label(t1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2839 (all A (v3_ordinal1(A) -> -(r1_ordinal1(A,k4_ordinal2) & A != k1_xboole_0 & k4_ordinal2 != A))) # label(t19_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2840 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k15_ordinal2(A,k15_ordinal2(B,C)) = k15_ordinal2(k15_ordinal2(A,B),C))))))) # label(t58_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2841 $T # label(t40_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2842 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v3_ordinal1(C) -> (k1_relat_1(A) = k1_relat_1(B) & (all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = E -> k14_ordinal2(C,E) = k1_funct_1(B,D)))))) -> k8_ordinal2(B) = k14_ordinal2(C,k8_ordinal2(A)) | k1_relat_1(A) = k1_xboole_0))))))) # label(t47_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2843 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k15_ordinal2(A,B) = k4_ordinal2 -> k4_ordinal2 = A & B = k4_ordinal2))))) # label(t41_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2844 (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]. 59.83/57.32 2845 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> (k1_xboole_0 != k1_relat_1(A) -> k8_ordinal2(k1_ordinal3(B,A)) = k14_ordinal2(B,k8_ordinal2(A))))))) # label(t51_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2846 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(k15_ordinal2(k6_ordinal3(A,B),B),k7_ordinal3(A,B)) = A)))) # label(t78_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2847 (all A (v3_ordinal1(A) -> (k1_xboole_0 != A -> r2_hidden(k1_xboole_0,A)))) # label(t10_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2848 $T # label(t63_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2849 (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) -> (k14_ordinal2(k15_ordinal2(D,A),E) = k14_ordinal2(k15_ordinal2(B,A),C) & r2_hidden(E,A) & r2_hidden(C,A) -> B = D & E = C))))))))))) # label(t56_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2850 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> -(v4_ordinal1(B) & (all D (v3_ordinal1(D) -> -(r2_hidden(A,k15_ordinal2(D,C)) & r2_hidden(D,B)))) & r2_hidden(A,k15_ordinal2(B,C))))))))) # label(t49_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2851 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k5_ordinal3(k5_ordinal3(A,B),C) = k5_ordinal3(A,k14_ordinal2(B,C)))))))) # label(t70_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2852 $T # label(t46_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2853 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k14_ordinal2(A,B) = k14_ordinal2(A,C) -> C = B))))))) # label(t24_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2854 $T # label(t62_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2855 (all A (v3_ordinal1(A) -> k1_xboole_0 = k7_ordinal3(A,k4_ordinal2) & k6_ordinal3(A,k4_ordinal2) = A)) # label(t84_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2856 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> k14_ordinal2(A,k5_ordinal3(B,A)) = B))))) # label(t60_ordinal3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2857 (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(k10_arytm_3(A,B),C) = k10_arytm_3(A,k10_arytm_3(B,C)))))))) # label(t57_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2858 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> k15_ordinal2(A,B) = k15_ordinal2(B,A))))) # label(t4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2859 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (r2_hidden(k1_xboole_0,B) & r2_arytm_3(A,B) -> r1_ordinal1(A,B)))))) # label(t15_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2860 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> A = k4_arytm_3(A,A) & A = k3_arytm_3(A,A))) # label(t21_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2861 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (k2_arytm_3(B,k6_ordinal3(A,B)) = A <-> r2_arytm_3(B,A)))))) # label(t11_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2862 (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]. 59.83/57.32 2863 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> m1_subset_1(k9_arytm_3(A,B),k6_arytm_3))) # label(dt_k9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2864 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (r2_arytm_3(A,B) <-> (exists C (v3_ordinal1(C) & k2_arytm_3(A,C) = B & v4_ordinal2(C)))))))) # label(t9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2865 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]. 59.83/57.32 2866 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> -(A != k1_xboole_0 & k1_xboole_0 = k5_arytm_3(A,B)))))) # label(t30_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2867 (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]. 59.83/57.32 2868 (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) -> -(k4_ordinal2 != C & C != k1_xboole_0 & r1_arytm_3(B,C) & A = k4_tarski(B,C)))))) & -r2_hidden(A,k5_ordinal2)))) # label(t35_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2869 (all A all B (m1_subset_1(B,k6_arytm_3) -> ((exists C (m1_subset_1(C,k6_arytm_3) & C = A & -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]. 59.83/57.32 2870 (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]. 59.83/57.32 2871 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (v3_ordinal1(B) & m1_subset_1(B,k6_arytm_3) -> -(-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]. 59.83/57.32 2872 (exists A (v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A) & m1_subset_1(A,k6_arytm_3))) # label(rc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2873 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (A != k1_xboole_0 -> 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]. 59.83/57.32 2874 (all A all B -r2_hidden(k4_tarski(A,B),k5_ordinal2)) # label(t38_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2875 (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]. 59.83/57.32 2876 (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) & k10_arytm_3(A,B) = k10_arytm_3(C,D)))))))))) # label(t89_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2877 (all A -r2_hidden(k4_tarski(k12_arytm_3,A),k6_arytm_3)) # label(t68_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2878 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (k4_arytm_3(A,B) = k4_ordinal2 <-> r1_arytm_3(A,B)))))) # label(t25_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2879 (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) & C != B & C = A & r3_arytm_3(B,C)))))))) # label(t97_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2880 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> k3_arytm_3(B,A) = k3_arytm_3(A,B))) # label(commutativity_k3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2881 (all A (v1_xboole_0(A) & v3_ordinal1(A) -> v4_ordinal2(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2882 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> v1_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & v4_ordinal2(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)))) # label(fc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2883 (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]. 59.83/57.32 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) -> -(r3_arytm_3(A,k10_arytm_3(B,C)) & (all D (m1_subset_1(D,k6_arytm_3) -> (all E (m1_subset_1(E,k6_arytm_3) -> -(r3_arytm_3(D,B) & r3_arytm_3(E,C) & A = k10_arytm_3(D,E))))))))))))) # label(t95_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2885 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (A != k1_xboole_0 -> k4_ordinal2 = k5_arytm_3(A,k1_xboole_0)) & k5_arytm_3(k1_xboole_0,A) = k1_xboole_0)) # label(t31_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2886 (all A all B (v3_ordinal1(A) & v4_ordinal2(B) & v3_ordinal1(B) & v4_ordinal2(A) -> v2_ordinal1(k5_ordinal3(A,B)) & v3_ordinal1(k5_ordinal3(A,B)) & v4_ordinal2(k5_ordinal3(A,B)) & v1_ordinal1(k5_ordinal3(A,B)))) # label(fc4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2887 (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]. 59.83/57.32 2888 (all A (m1_subset_1(A,k6_arytm_3) -> A = k10_arytm_3(A,k12_arytm_3))) # label(t56_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2889 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> k10_arytm_3(A,B) = 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))))))) # label(d10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2890 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> k5_arytm_3(A,k4_ordinal2) = A & k5_arytm_3(k4_ordinal2,A) = k4_ordinal2)) # label(t29_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2891 (all A all B (v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) & v3_ordinal1(A) -> k1_arytm_3(A,B) = k1_arytm_3(B,A))) # label(commutativity_k1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2892 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (-(B = k1_xboole_0 & k1_xboole_0 = A) -> 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]. 59.83/57.32 2893 (all A (v3_ordinal1(A) & m1_subset_1(A,k6_arytm_3) -> (all B (v3_ordinal1(B) & m1_subset_1(B,k6_arytm_3) -> k2_arytm_3(A,B) = k11_arytm_3(A,B))))) # label(t65_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2894 (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]. 59.83/57.32 2895 (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(C,B) = k10_arytm_3(A,B) -> A = C))))))) # label(t69_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2896 (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]. 59.83/57.32 2897 (all A (m1_subset_1(A,k6_arytm_3) -> -(k7_arytm_3(A) != k1_xboole_0 & A = k1_xboole_0) & -(A != k1_xboole_0 & k7_arytm_3(A) = k1_xboole_0))) # label(t43_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2898 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> k6_ordinal3(A,k4_arytm_3(A,B)) = k5_arytm_3(A,B))))) # label(d5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2899 (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]. 59.83/57.32 2900 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k5_ordinal2) -> (-r2_hidden(A,k5_ordinal2) -> (B = k8_arytm_3(A) <-> (exists C (v3_ordinal1(C) & v4_ordinal2(C) & k4_tarski(C,B) = A)))) & (r2_hidden(A,k5_ordinal2) -> (B = k8_arytm_3(A) <-> k4_ordinal2 = B)))))) # label(d8_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2901 (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]. 59.83/57.32 2902 (all A all B (v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) & v3_ordinal1(A) -> v4_ordinal2(k7_ordinal3(A,B)) & v3_ordinal1(k7_ordinal3(A,B)) & v2_ordinal1(k7_ordinal3(A,B)) & v1_ordinal1(k7_ordinal3(A,B)))) # label(fc7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2903 (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) -> -((all C (m1_subset_1(C,k6_arytm_3) -> (r2_hidden(C,A) -> r3_arytm_3(C,B)))) & r2_hidden(B,A)))) & r2_hidden(A,k6_arytm_3)))) # label(t99_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2904 (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]. 59.83/57.32 2905 $T # label(t12_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2906 (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)) -> k12_arytm_3 = A | r3_arytm_3(B,C)))))))) # label(t88_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2907 (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]. 59.83/57.32 2908 (all A (v3_ordinal1(A) -> (all B (m1_subset_1(B,A) -> v2_ordinal1(B) & v3_ordinal1(B) & v1_ordinal1(B))))) # label(cc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2909 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> k2_arytm_3(A,B) = k2_arytm_3(B,A))) # label(commutativity_k2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2910 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (r2_arytm_3(A,B) & r2_arytm_3(A,k1_arytm_3(B,C)) -> r2_arytm_3(A,C)))))))) # label(t16_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2911 (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) -> (k15_ordinal2(C,D) = A & B = k15_ordinal2(C,E) -> C = k4_ordinal2))))))) <-> r1_arytm_3(A,B)))))) # label(d1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2912 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> k4_arytm_3(A,k1_xboole_0) = A & k3_arytm_3(A,k1_xboole_0) = k1_xboole_0)) # label(t19_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2913 (all A all B (v3_ordinal1(B) & v4_ordinal2(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]. 59.83/57.32 2914 (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]. 59.83/57.32 2915 (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) -> -(r3_arytm_3(D,B) & C != E & r3_arytm_3(E,C) & A = k10_arytm_3(D,E)))))) & C != k12_arytm_3 & -r3_arytm_3(k10_arytm_3(B,C),A)))))))) # label(t98_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2916 (all A (m1_subset_1(A,k6_arytm_3) -> (r3_arytm_3(A,k12_arytm_3) -> A = k12_arytm_3))) # label(t72_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2917 f2_s2_arytm_3 = k13_arytm_3 & k12_arytm_3 = f1_s2_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) -> (exists A (m1_subset_1(A,k6_arytm_3) & r2_hidden(A,k5_ordinal2) & -p1_s2_arytm_3(k10_arytm_3(A,f2_s2_arytm_3)) & p1_s2_arytm_3(A))) # label(s2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2918 (all A all B (v3_ordinal1(B) & v4_ordinal2(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]. 59.83/57.32 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(k11_arytm_3(A,B),C) = k11_arytm_3(A,k11_arytm_3(B,C)))))))) # label(t58_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2920 (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(C,D) = k10_arytm_3(A,B) & r3_arytm_3(A,C) -> r3_arytm_3(D,B)))))))))) # label(t93_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2921 (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]. 59.83/57.32 2922 (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]. 59.83/57.32 2923 (all A all B (v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) & v3_ordinal1(A) -> k4_arytm_3(A,B) = k4_arytm_3(B,A))) # label(commutativity_k4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2924 (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) & -r3_arytm_3(B,D) & k11_arytm_3(C,D) = k11_arytm_3(A,B)))))))))) # label(t91_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2925 (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) -> B != k11_arytm_3(A,C))) & k12_arytm_3 != A))))) # label(t61_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2926 (all A (r2_hidden(A,a_0_0_arytm_3) <-> (exists B exists C (r1_arytm_3(B,C) & C != k1_xboole_0 & k4_tarski(B,C) = A & m1_subset_1(C,k5_ordinal2) & m1_subset_1(B,k5_ordinal2))))) # label(fraenkel_a_0_0_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2927 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (-(A = k1_xboole_0 & k1_xboole_0 = B) -> r1_arytm_3(k5_arytm_3(A,B),k5_arytm_3(B,A))))))) # label(t27_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2928 (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]. 59.83/57.32 2929 $T # label(t84_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2930 (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,C) <-> r3_arytm_3(k10_arytm_3(A,B),k10_arytm_3(C,B))))))))) # label(t83_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2931 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (k12_arytm_3 = k10_arytm_3(A,B) -> k12_arytm_3 = A))))) # label(t70_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 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) -> -(r3_arytm_3(A,k11_arytm_3(B,C)) & (all D (m1_subset_1(D,k6_arytm_3) -> -(A = k11_arytm_3(B,D) & r3_arytm_3(D,C))))))))))) # label(t87_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2933 (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(C,A)))) & -r3_arytm_3(B,A)))))) # label(t101_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2934 (all A (v3_ordinal1(A) -> (r1_arytm_3(k1_xboole_0,A) -> k4_ordinal2 = A))) # label(t7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2935 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> k11_arytm_3(A,B) = 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))))))) # label(d11_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2936 (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]. 59.83/57.32 2937 (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(C,B) & -r3_arytm_3(B,A)))))))) # label(t77_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2938 (all A all B -v3_ordinal1(k4_tarski(A,B))) # label(t36_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2939 $T # label(dt_k6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2940 (all A all B (v3_ordinal1(B) & v4_ordinal2(B) & v4_ordinal2(A) & v3_ordinal1(A) -> m1_subset_1(k4_arytm_3(A,B),k5_ordinal2))) # label(dt_k4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2941 (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(B,A) | -r3_arytm_3(C,B) & r3_arytm_3(A,B)) & r3_arytm_3(C,A)))))))) # label(t76_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2942 (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]. 59.83/57.32 2943 (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]. 59.83/57.32 2944 (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]. 59.83/57.32 2945 (all A (m1_subset_1(A,k5_ordinal2) -> (all B (m1_subset_1(B,k5_ordinal2) -> (r1_arytm_3(A,B) & B != k4_ordinal2 & B != k1_xboole_0 <-> r2_hidden(k4_tarski(A,B),k6_arytm_3)))))) # label(t39_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2946 (exists A (m1_subset_1(A,k6_arytm_3) & v3_ordinal1(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A) & v1_xboole_0(A))) # label(rc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2947 (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,k11_arytm_3(C,A)) & r2_hidden(C,k5_ordinal2)))) & A != k12_arytm_3))))) # label(t103_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2948 (all A all B (v3_ordinal1(A) & v4_ordinal2(B) & v3_ordinal1(B) & v4_ordinal2(A) -> v2_ordinal1(k14_ordinal2(A,B)) & v3_ordinal1(k14_ordinal2(A,B)) & v4_ordinal2(k14_ordinal2(A,B)) & v1_ordinal1(k14_ordinal2(A,B)))) # label(fc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2949 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (B = k15_ordinal2(A,C) & v3_ordinal1(C))) <-> r2_arytm_3(A,B)))))) # label(d2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.32 2950 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (B = k10_arytm_3(A,B) <-> A = k12_arytm_3))))) # label(t92_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2951 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) -> m1_subset_1(k3_arytm_3(A,B),k5_ordinal2))) # label(dt_k3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2952 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> k1_xboole_0 = k9_arytm_3(k1_xboole_0,A) & B = k9_arytm_3(B,k4_ordinal2))))) # label(t46_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2953 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -(k11_arytm_3(A,B) = k12_arytm_3 & A != k12_arytm_3 & B != k12_arytm_3))))) # label(t86_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2954 (all A (v3_ordinal1(A) -> r1_arytm_3(k4_ordinal2,A))) # label(t6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2955 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (m1_subset_1(C,k5_ordinal2) -> (C = k3_arytm_3(A,B) <-> (all D (v3_ordinal1(D) & v4_ordinal2(D) -> (r2_arytm_3(A,D) & r2_arytm_3(B,D) -> r2_arytm_3(C,D)))) & r2_arytm_3(B,C) & r2_arytm_3(A,C)))))))) # label(d3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2956 (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) & k10_arytm_3(A,C) = B)) <-> r3_arytm_3(A,B)))))) # label(d12_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2957 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (A != k1_xboole_0 -> k5_arytm_3(B,C) = k5_arytm_3(k2_arytm_3(B,A),k2_arytm_3(C,A))))))))) # label(t33_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2958 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) -> k2_arytm_3(A,B) = k15_ordinal2(A,B))) # label(redefinition_k2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2959 (all A (m1_subset_1(A,k5_ordinal2) -> (all B (m1_subset_1(B,k5_ordinal2) -> (r1_arytm_3(A,B) -> k1_xboole_0 = B | k8_arytm_3(k9_arytm_3(A,B)) = B & A = k7_arytm_3(k9_arytm_3(A,B))))))) # label(t49_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2960 (all A (m1_subset_1(A,k6_arytm_3) -> (v3_ordinal1(A) -> v3_ordinal1(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A)))) # label(cc4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2961 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (m1_subset_1(C,k5_ordinal2) -> ((all D (v4_ordinal2(D) & v3_ordinal1(D) -> (r2_arytm_3(D,B) & r2_arytm_3(D,A) -> r2_arytm_3(D,C)))) & r2_arytm_3(C,B) & r2_arytm_3(C,A) <-> C = k4_arytm_3(A,B)))))))) # label(d4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2962 (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) & k10_arytm_3(A,D) = B))) & r3_arytm_3(B,k10_arytm_3(A,C)) & r3_arytm_3(A,B)))))))) # label(t94_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2963 (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) -> A = B))))) # label(t73_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2964 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) & v4_ordinal2(B) & v4_ordinal2(A) -> v1_ordinal1(k15_ordinal2(A,B)) & v2_ordinal1(k15_ordinal2(A,B)) & v4_ordinal2(k15_ordinal2(A,B)) & v3_ordinal1(k15_ordinal2(A,B)))) # label(fc5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2965 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (A != B & r3_arytm_3(A,B) <-> -r3_arytm_3(B,A)))))) # label(t75_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2966 (all A (m1_subset_1(A,k6_arytm_3) -> k11_arytm_3(A,k13_arytm_3) = A)) # label(t59_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2967 (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) & (all D (m1_subset_1(D,k6_arytm_3) -> -(r3_arytm_3(D,B) & -r3_arytm_3(D,A) & r3_arytm_3(D,C)))) & -r3_arytm_3(B,A)))))))) # label(t96_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2968 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (k1_xboole_0 = k4_arytm_3(A,B) -> k1_xboole_0 = A))))) # label(t20_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2969 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v3_ordinal1(C) & v4_ordinal2(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]. 59.83/57.33 2970 (all A (v3_ordinal1(A) & v4_ordinal2(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) -> 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]. 59.83/57.33 2971 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (k1_xboole_0 != A -> k9_arytm_3(A,A) = k4_ordinal2))) # label(t47_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2972 (exists A (-v1_xboole_0(A) & v3_ordinal1(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2973 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (k1_xboole_0 != A -> k5_arytm_3(A,B) = k8_arytm_3(k9_arytm_3(B,A)) & k7_arytm_3(k9_arytm_3(B,A)) = k5_arytm_3(B,A)))))) # label(t48_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2974 (all A all B (v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) & v3_ordinal1(A) -> k14_ordinal2(A,B) = k1_arytm_3(A,B))) # label(redefinition_k1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2975 (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]. 59.83/57.33 2976 (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) -> r3_arytm_3(A,C)))))))) # label(t74_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2977 (all A (m1_subset_1(A,k6_arytm_3) -> (r2_hidden(A,k5_ordinal2) <-> k8_arytm_3(A) = k4_ordinal2))) # label(t44_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2978 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (A != k1_xboole_0 -> 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]. 59.83/57.33 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]. 59.83/57.33 2980 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) -> m1_subset_1(k5_arytm_3(A,B),k5_ordinal2))) # label(dt_k5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2981 (all A all B (m1_subset_1(B,k6_arytm_3) & m1_subset_1(A,k6_arytm_3) -> r3_arytm_3(B,A) | r3_arytm_3(A,B))) # label(connectedness_r3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2982 (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]. 59.83/57.33 2983 (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]. 59.83/57.33 2984 (all A all B (m1_subset_1(B,k6_arytm_3) & m1_subset_1(A,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]. 59.83/57.33 2985 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(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]. 59.83/57.33 2986 (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]. 59.83/57.33 2987 $T # label(t67_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2988 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) & v4_ordinal2(B) & v4_ordinal2(A) -> v2_ordinal1(k6_ordinal3(A,B)) & v4_ordinal2(k6_ordinal3(A,B)) & v3_ordinal1(k6_ordinal3(A,B)) & v1_ordinal1(k6_ordinal3(A,B)))) # label(fc6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2989 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (all D (v3_ordinal1(D) & v4_ordinal2(D) -> -(A != k1_xboole_0 & 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)) & k1_xboole_0 != B))))))))) # label(t52_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2990 (all A (v4_ordinal2(A) & v3_ordinal1(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]. 59.83/57.33 2991 (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(B,C) != A & B != k10_arytm_3(A,C))))))) # label(t100_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2992 (all A (m1_subset_1(A,k6_arytm_3) -> (-r2_hidden(A,k5_ordinal2) -> k8_arytm_3(A) != k4_ordinal2 & k4_tarski(k7_arytm_3(A),k8_arytm_3(A)) = A))) # label(t42_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2993 (all A (v3_ordinal1(A) & m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) & v3_ordinal1(B) -> k1_arytm_3(A,B) = k10_arytm_3(A,B))))) # label(t64_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2994 (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]. 59.83/57.33 2995 (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]. 59.83/57.33 2996 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (r2_arytm_3(B,A) & r2_arytm_3(A,B) -> B = A))))) # label(t13_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2997 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (k4_ordinal2 = k5_arytm_3(B,A) -> k9_arytm_3(A,B) = k5_arytm_3(A,B)) & -(B != k1_xboole_0 & k4_tarski(k5_arytm_3(A,B),k5_arytm_3(B,A)) != k9_arytm_3(A,B) & k4_ordinal2 != k5_arytm_3(B,A)) & (B = k1_xboole_0 -> k1_xboole_0 = k9_arytm_3(A,B)))))) # label(d9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2998 (all A (v4_ordinal2(A) & v3_ordinal1(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) -> -(B != k1_xboole_0 & k1_xboole_0 != A & -(k9_arytm_3(D,A) = k9_arytm_3(C,B) <-> k2_arytm_3(B,D) = k2_arytm_3(C,A))))))))))) # label(t51_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 2999 (all A (v4_ordinal2(A) & v3_ordinal1(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]. 59.83/57.33 3000 (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) = k11_arytm_3(A,B) -> A = k12_arytm_3 | B = C))))))) # label(t62_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3001 (all A all B (m1_subset_1(A,k6_arytm_3) & m1_subset_1(B,k6_arytm_3) -> k11_arytm_3(A,B) = k11_arytm_3(B,A))) # label(commutativity_k11_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3002 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k5_ordinal2) -> (-r2_hidden(A,k5_ordinal2) -> ((exists C (A = k4_tarski(B,C) & v4_ordinal2(C) & v3_ordinal1(C))) <-> B = k7_arytm_3(A))) & (r2_hidden(A,k5_ordinal2) -> (k7_arytm_3(A) = B <-> A = B)))))) # label(d7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3003 (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]. 59.83/57.33 3004 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (k1_xboole_0 != A -> k4_ordinal2 = k5_arytm_3(A,A)))) # label(t32_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3005 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> -(-(k1_xboole_0 = A & k1_xboole_0 = B) & (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (all D (v3_ordinal1(D) & v4_ordinal2(D) -> (all E (v3_ordinal1(E) & v4_ordinal2(E) -> -(r1_arytm_3(D,E) & B = k2_arytm_3(C,E) & A = k2_arytm_3(C,D))))))))))))) # label(t8_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3006 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (k1_xboole_0 != A -> k1_xboole_0 != k4_arytm_3(B,A) & k1_xboole_0 != k6_ordinal3(A,k4_arytm_3(B,A))))))) # label(t23_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3007 (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]. 59.83/57.33 3008 (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) -> (r3_arytm_3(C,B) & r2_hidden(B,A) -> r2_hidden(C,A)))))) & (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(D,A) & D != C & D != B & C != B & r2_hidden(C,A) & r2_hidden(B,A))))))))))) # label(t82_arytm_3) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3009 (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]. 59.83/57.33 3010 $T # label(t5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3011 (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]. 59.83/57.33 3012 $T # label(dt_k2_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3013 (all A all B (m1_subset_1(A,k1_arytm_2) & m1_subset_1(B,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]. 59.83/57.33 3014 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (A = k13_arytm_3 -> B = k8_arytm_2(A,B)))))) # label(t16_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3015 (all A all B all C (m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) & m2_subset_1(C,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (r2_hidden(A,a_2_1_arytm_2(B,C)) <-> (exists D exists E (r2_hidden(E,C) & r2_hidden(D,B) & k11_arytm_3(D,E) = A & m1_subset_1(E,k6_arytm_3) & m1_subset_1(D,k6_arytm_3)))))) # label(fraenkel_a_2_1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3016 (all A (m1_subset_1(A,k2_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) -> -(k11_arytm_3(C,D) = k8_arytm_2(A,B) & D = B & C = A))))) & r2_hidden(B,k6_arytm_3) & r2_hidden(A,k6_arytm_3)))))) # label(t22_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3017 (all A all B (m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) -> k8_arytm_2(B,A) = k8_arytm_2(A,B))) # label(commutativity_k8_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3018 (all A all B (m1_subset_1(B,k2_arytm_2) & m1_subset_1(A,k2_arytm_2) -> k7_arytm_2(B,A) = k7_arytm_2(A,B))) # label(commutativity_k7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3019 (all A all B (m1_subset_1(B,k2_arytm_2) & m1_subset_1(A,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]. 59.83/57.33 3020 (all A all B (m1_subset_1(B,k1_arytm_2) & m1_subset_1(A,k1_arytm_2) -> k5_arytm_2(B,A) = k5_arytm_2(A,B))) # label(commutativity_k5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3021 (all A -r2_hidden(k4_tarski(k12_arytm_3,A),k2_arytm_2)) # label(t3_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3022 (all A all B (m1_subset_1(B,k2_arytm_2) & m1_subset_1(A,k2_arytm_2) -> r1_arytm_2(A,B) | r1_arytm_2(B,A))) # label(connectedness_r1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3023 (all A (m1_subset_1(A,k1_zfmisc_1(k2_arytm_2)) -> (all B (m1_subset_1(B,k1_zfmisc_1(k2_arytm_2)) -> -((exists C (r2_hidden(C,A) & m1_subset_1(C,k2_arytm_2))) & (exists C (m1_subset_1(C,k2_arytm_2) & r2_hidden(C,B))) & (all C (m1_subset_1(C,k2_arytm_2) -> (exists D ((exists E (m1_subset_1(E,k2_arytm_2) & -(r1_arytm_2(D,C) & r1_arytm_2(C,E)) & r2_hidden(E,B) & r2_hidden(D,A))) & m1_subset_1(D,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))))))))))) # label(t9_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3024 (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(k8_arytm_2(A,B),k8_arytm_2(A,C)) = k8_arytm_2(A,k7_arytm_2(B,C)))))))) # label(t14_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3025 (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]. 59.83/57.33 3026 (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(k7_arytm_2(A,B),C) = k7_arytm_2(A,k7_arytm_2(B,C)))))))) # label(t7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3027 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k12_arytm_3 = A -> k12_arytm_3 = k8_arytm_2(A,B)))))) # label(t4_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3028 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k12_arytm_3 = B -> k7_arytm_2(A,B) = A) & (A = k12_arytm_3 -> k7_arytm_2(A,B) = B) & -(k12_arytm_3 != B & k4_arytm_2(k5_arytm_2(k3_arytm_2(A),k3_arytm_2(B))) != k7_arytm_2(A,B) & k12_arytm_3 != A))))) # label(d8_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3029 (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) -> a_2_1_arytm_2(A,B) = k6_arytm_2(A,B))))) # label(d7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3030 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> k8_arytm_2(A,B) = k4_arytm_2(k6_arytm_2(k3_arytm_2(A),k3_arytm_2(B))))))) # label(d9_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3031 (all A (m1_subset_1(A,k2_arytm_2) -> (r2_hidden(A,k5_ordinal2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r2_hidden(B,k5_ordinal2) & r1_arytm_2(B,A) & A != B <-> r2_hidden(B,A))))))) # label(t19_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3032 (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) & k7_arytm_2(A,C) != B)))))) # label(t11_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3033 (all A (m1_subset_1(A,k2_arytm_2) -> -(k12_arytm_3 != A & (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]. 59.83/57.33 3034 (all A all B (m1_subset_1(B,k6_arytm_3) -> ((exists C (m1_subset_1(C,k6_arytm_3) & -r3_arytm_3(B,C) & C = A)) <-> r2_hidden(A,a_1_0_arytm_2(B))))) # label(fraenkel_a_1_0_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3035 (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]. 59.83/57.33 3036 (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) -> B != k7_arytm_2(A,C)))))))) # label(t10_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3037 (all A (r2_hidden(A,a_0_1_arytm_2) <-> (exists B (B != k12_arytm_3 & A = a_1_0_arytm_2(B) & m1_subset_1(B,k6_arytm_3))))) # label(fraenkel_a_0_1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3038 (all A all B (m1_subset_1(B,k1_arytm_2) & m1_subset_1(A,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]. 59.83/57.33 3039 (all A (m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> ((exists C ((all D (m1_subset_1(D,k6_arytm_3) -> (-r3_arytm_3(C,D) <-> r2_hidden(D,A)))) & m1_subset_1(C,k6_arytm_3))) -> ((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)) <-> k4_arytm_2(A) = B)) & ((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)))))) -> (A = B <-> k4_arytm_2(A) = B)))))) # label(d4_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3040 (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]. 59.83/57.33 3041 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r2_hidden(B,k5_ordinal2) & r2_hidden(A,k5_ordinal2) -> r2_hidden(k7_arytm_2(B,A),k5_ordinal2)))))) # label(t17_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3042 (all A (r2_hidden(A,a_0_0_arytm_2) <-> (exists B (A = 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 (r2_hidden(D,B) & -r3_arytm_3(D,C) & m1_subset_1(D,k6_arytm_3)))))) & m1_subset_1(B,k1_zfmisc_1(k6_arytm_3)))))) # label(fraenkel_a_0_0_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3043 (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) & r2_hidden(E,C) & r2_hidden(D,B) & A = k10_arytm_3(D,E) & m1_subset_1(E,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]. 59.83/57.33 3044 (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) -> C = B))))))) # label(t12_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3045 (all A all B (m1_subset_1(B,k1_arytm_2) & m1_subset_1(A,k1_arytm_2) -> k6_arytm_2(B,A) = k6_arytm_2(A,B))) # label(commutativity_k6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3046 (all A all B (m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,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]. 59.83/57.33 3047 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r2_hidden(B,k6_arytm_3) -> r2_hidden(A,k6_arytm_3) | (r1_arytm_2(A,B) <-> -r2_hidden(B,A))) & -(-(r2_hidden(A,k6_arytm_3) & -r2_hidden(B,k6_arytm_3)) & -(r2_hidden(B,k6_arytm_3) & -r2_hidden(A,k6_arytm_3)) & -(r1_arytm_2(A,B) <-> r1_tarski(A,B)) & -(r2_hidden(B,k6_arytm_3) & r2_hidden(A,k6_arytm_3))) & (r2_hidden(A,k6_arytm_3) -> (r1_arytm_2(A,B) <-> r2_hidden(A,B)) | r2_hidden(B,k6_arytm_3)) & (r2_hidden(A,k6_arytm_3) & r2_hidden(B,k6_arytm_3) -> ((exists C ((exists D (D = B & r3_arytm_3(C,D) & A = C & m1_subset_1(D,k6_arytm_3))) & m1_subset_1(C,k6_arytm_3))) <-> r1_arytm_2(A,B))))))) # label(d5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3048 (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]. 59.83/57.33 3049 (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) -> (B = k3_arytm_2(A) <-> B = A)) & (r2_hidden(A,k6_arytm_3) -> ((exists C (B = a_1_0_arytm_2(C) & C = A & m1_subset_1(C,k6_arytm_3))) <-> B = k3_arytm_2(A))))))) # label(d3_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3050 (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 -> r1_arytm_2(C,A)))))))) # label(t20_arytm_2) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3051 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(k1_xboole_0 = k8_arytm_2(A,B) & k1_xboole_0 != B & k1_xboole_0 != A))))) # label(t2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3052 (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]. 59.83/57.33 3053 (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]. 59.83/57.33 3054 (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]. 59.83/57.33 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(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]. 59.83/57.33 3056 (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]. 59.83/57.33 3057 (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) -> k1_arytm_1(k7_arytm_2(C,B),A) = k7_arytm_2(C,k1_arytm_1(B,A))))))))) # label(t13_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 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) -> 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]. 59.83/57.33 3059 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k1_xboole_0 = k1_arytm_1(B,A) & r1_arytm_2(A,B) -> A = B))))) # label(t10_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 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(A,B) & r1_arytm_2(A,C) -> 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]. 59.83/57.33 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) -> -(k2_arytm_1(C,k1_arytm_1(A,B)) != k2_arytm_1(B,k1_arytm_1(A,C)) & -r1_arytm_2(A,C) & -r1_arytm_2(A,B)))))))) # label(t23_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3062 (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(k8_arytm_2(C,B),k8_arytm_2(C,A)) = k8_arytm_2(C,k1_arytm_1(B,A))))))))) # label(t26_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 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,B) -> r1_arytm_2(k1_arytm_1(C,B),k1_arytm_1(C,A))))))))) # label(t16_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3064 $T # label(dt_k2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3065 (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,A) & r1_arytm_2(A,B) -> 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]. 59.83/57.33 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(B,C) & r1_arytm_2(A,B) -> r1_arytm_2(A,C)))))))) # label(t3_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 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) -> (r1_arytm_2(B,A) -> (C = k1_arytm_1(A,B) <-> A = k7_arytm_2(C,B))) & (-r1_arytm_2(B,A) -> (C = k1_xboole_0 <-> C = k1_arytm_1(A,B))))))))) # label(d1_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3068 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (-r1_arytm_2(B,A) -> k4_tarski(k1_xboole_0,k1_arytm_1(B,A)) = k2_arytm_1(A,B)) & (r1_arytm_2(B,A) -> k2_arytm_1(A,B) = k1_arytm_1(A,B)))))) # label(d2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3069 (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]. 59.83/57.33 3070 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k1_xboole_0 = B & r1_arytm_2(A,B) -> A = k1_xboole_0))))) # label(t5_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3071 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k1_xboole_0 = A -> B = k1_xboole_0 | k4_tarski(k1_xboole_0,B) = k2_arytm_1(A,B)))))) # label(t19_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3072 (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(k7_arytm_2(A,C),k7_arytm_2(B,C))))))))) # label(t7_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3073 (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(C,A),B) = k7_arytm_2(k1_arytm_1(B,A),C)))))))) # label(t15_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3074 (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(C,k1_arytm_1(A,B)) = k2_arytm_1(k7_arytm_2(C,B),A)))))))) # label(t21_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 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) -> r1_arytm_2(A,C) | k7_arytm_2(k1_arytm_1(B,A),C) = k2_arytm_1(B,k1_arytm_1(A,C))))))))) # label(t22_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 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) -> k2_arytm_1(k1_arytm_1(B,A),C) = k2_arytm_1(B,k7_arytm_2(A,C))))))))) # label(t24_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3077 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r1_arytm_2(A,B) & r1_arytm_2(B,A) -> A = B))))) # label(t4_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 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) -> r1_arytm_2(k1_arytm_1(A,C),k1_arytm_1(B,C))))))))) # label(t17_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 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,B) & k2_arytm_1(k8_arytm_2(C,B),k8_arytm_2(C,A)) != k4_tarski(k1_xboole_0,k8_arytm_2(C,k1_arytm_1(A,B))) & k1_xboole_0 != C))))))) # label(t27_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 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 = k1_arytm_1(A,B) | k2_arytm_1(k8_arytm_2(C,B),k8_arytm_2(C,A)) = k4_tarski(k1_xboole_0,k8_arytm_2(C,k1_arytm_1(A,B))) | k1_xboole_0 = C))))))) # label(t28_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3081 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(k1_xboole_0 = k1_arytm_1(A,B) & -r1_arytm_2(A,B)))))) # label(t9_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3082 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (A = k1_xboole_0 -> r1_arytm_2(A,B)))))) # label(t6_arytm_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3083 (all A -((all B -((all C (r2_hidden(C,A) -> r1_tarski(C,B))) & r2_hidden(B,A))) & v6_ordinal1(A) & A != k1_xboole_0 & v1_finset_1(A))) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3084 (all A all B all C (v1_finset_1(A) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3085 (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]. 59.83/57.33 3086 (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]. 59.83/57.33 3087 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3088 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3089 (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]. 59.83/57.33 3090 (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]. 59.83/57.33 3091 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3092 (all A all B (v1_finset_1(k2_zfmisc_1(B,A)) -> A = k1_xboole_0 | v1_finset_1(B))) # label(t22_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3093 (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]. 59.83/57.33 3094 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3095 (all A -(v1_finset_1(A) & k1_xboole_0 != A & v6_ordinal1(A) & (all B -(r2_hidden(B,A) & (all C (r2_hidden(C,A) -> r1_tarski(B,C))))))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3096 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3097 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (-p1_s1_finset_1(B) -> f3_s1_finset_1(B) = k1_funct_1(A,B)) & (p1_s1_finset_1(B) -> k1_funct_1(A,B) = f2_s1_finset_1(B))))) & f1_s1_finset_1 = k1_relat_1(A))) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3098 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3099 (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]. 59.83/57.33 3100 (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]. 59.83/57.33 3101 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_finset_1(A) <-> v1_finset_1(k1_relat_1(A))))) # label(t29_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3102 p1_s2_finset_1(k1_xboole_0) & (all A all B (r1_tarski(B,f1_s2_finset_1) & p1_s2_finset_1(B) & r2_hidden(A,f1_s2_finset_1) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) & v1_finset_1(f1_s2_finset_1) -> p1_s2_finset_1(f1_s2_finset_1) # label(s2_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3103 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3104 (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]. 59.83/57.33 3105 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3106 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3107 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3108 (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]. 59.83/57.33 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]. 59.83/57.33 3110 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3111 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3112 (all A (v1_finset_1(A) <-> (exists B (r2_hidden(k1_relat_1(B),k5_ordinal2) & A = k2_relat_1(B) & v1_funct_1(B) & v1_relat_1(B))))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3113 (all A (v1_finset_1(A) <-> v1_finset_1(k1_zfmisc_1(A)))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3114 (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]. 59.83/57.33 3115 (all A all B all C all D (v1_finset_1(C) & v1_finset_1(D) & v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(t21_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3116 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_xboole_0(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3117 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3118 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v1_finset_1(A) -> v1_finset_1(k9_relat_1(B,A))))) # label(t17_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3119 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3120 (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]. 59.83/57.33 3121 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3122 (exists A (-v1_xboole_0(A) & v1_finset_1(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3123 (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]. 59.83/57.33 3124 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3125 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(D) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3126 (all A all B (v1_finset_1(B) & r1_tarski(A,B) -> v1_finset_1(A))) # label(t13_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3127 (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]. 59.83/57.33 3128 (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]. 59.83/57.33 3129 (all A exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_ordinal1(B) & v3_ordinal1(B) & v1_finset_1(B) & v4_ordinal2(B) & v2_ordinal1(B) & v2_funct_1(B) & v1_funct_1(B))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3130 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.33 3131 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3132 (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]. 59.83/57.34 3133 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k2_relat_1(A))))) # label(t26_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3134 (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]. 59.83/57.34 3135 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -((all C -((all D (r2_hidden(D,B) & r1_tarski(C,D) -> D = C)) & r2_hidden(C,B))) & B != k1_xboole_0))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3136 (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]. 59.83/57.34 3137 (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]. 59.83/57.34 3138 (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]. 59.83/57.34 3139 (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]. 59.83/57.34 3140 $T # label(t8_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3141 (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]. 59.83/57.34 3142 (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]. 59.83/57.34 3143 (all A (v3_finsub_1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_xboole_0(B,C),A))))) # label(d3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3144 (all A (-v1_xboole_0(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v1_finsub_1(k1_zfmisc_1(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3145 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k2_finsub_1(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3146 $T # label(t22_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3147 (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]. 59.83/57.34 3148 (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]. 59.83/57.34 3149 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k2_finsub_1(A,B,C),A))) # label(dt_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3150 (all A (-v1_xboole_0(A) & v4_finsub_1(A) -> (all B (v4_finsub_1(B) & -v1_xboole_0(B) -> v4_finsub_1(k3_xboole_0(A,B)) & -v1_xboole_0(k3_xboole_0(A,B)))))) # label(t21_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3151 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k3_xboole_0(B,C),A) & r2_hidden(k5_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t16_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3152 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> k3_xboole_0(B,C) = k3_finsub_1(A,B,C))) # label(redefinition_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3153 (all A all B all C (-v1_xboole_0(C) & v4_finsub_1(C) -> (m1_subset_1(B,C) & m1_subset_1(A,C) -> m1_subset_1(k3_xboole_0(A,B),C)))) # label(t13_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3154 (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,B) = B)) # label(idempotence_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3155 $T # label(t6_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3156 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,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]. 59.83/57.34 3157 $T # label(t11_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3158 (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]. 59.83/57.34 3159 (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]. 59.83/57.34 3160 (all A (v4_finsub_1(A) -> v3_finsub_1(A) & v1_finsub_1(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3161 $T # label(t5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3162 (all A (v3_finsub_1(A) & v1_finsub_1(A) -> v4_finsub_1(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3163 $T # label(t12_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3164 (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]. 59.83/57.34 3165 (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]. 59.83/57.34 3166 $T # label(t7_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3167 (exists A (-v1_xboole_0(A) & v4_finsub_1(A) & v3_finsub_1(A) & v2_finsub_1(A) & v1_finsub_1(A))) # label(rc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3168 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k1_finsub_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3169 (all A (v1_finset_1(A) -> k5_finsub_1(A) = k1_zfmisc_1(A))) # label(t27_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3170 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> k3_finsub_1(A,B,B) = B)) # label(idempotence_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3171 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k4_finsub_1(A,C,B) = k4_finsub_1(A,B,C))) # label(commutativity_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 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]. 59.83/57.34 3173 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> m1_subset_1(k4_finsub_1(A,B,C),A))) # label(dt_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3174 $T # label(t2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3175 (all A ((all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_xboole_0(B,C),A) & r2_hidden(k2_xboole_0(B,C),A))) <-> v4_finsub_1(A))) # label(t10_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3176 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k4_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t15_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3177 (all A v4_finsub_1(k5_finsub_1(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3178 $T # label(t33_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3179 (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]. 59.83/57.34 3180 $T # label(t4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3181 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k1_finsub_1(A,C,B) = k1_finsub_1(A,B,C))) # label(commutativity_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3182 (all A r1_tarski(k5_finsub_1(A),k1_zfmisc_1(A))) # label(t26_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3183 (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(k1_finsub_1(A,B,C),A))) # label(dt_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3184 (all A all B (v4_finsub_1(B) -> (k5_finsub_1(A) = B <-> (all C (v1_finset_1(C) & r1_tarski(C,A) <-> r2_hidden(C,B)))))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3185 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) -> k3_finsub_1(A,C,B) = k3_finsub_1(A,B,C))) # label(commutativity_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3186 (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]. 59.83/57.34 3187 (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]. 59.83/57.34 3188 $T # label(t19_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3189 $T # label(t31_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3190 (all A v4_finsub_1(k1_zfmisc_1(A))) # label(t20_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3191 $T # label(t1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3192 (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]. 59.83/57.34 3193 $T # label(t9_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3194 (all A (v4_finsub_1(A) <-> v3_finsub_1(A) & v1_finsub_1(A))) # label(d4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3195 $T # label(t29_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3196 $T # label(t3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3197 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k5_xboole_0(B,C) = k4_finsub_1(A,B,C))) # label(redefinition_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3198 (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]. 59.83/57.34 3199 (all A v3_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t49_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3200 (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) -> k4_setwiseo(A,B,C,D) = k1_enumset1(B,C,D))) # label(redefinition_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3201 (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]. 59.83/57.34 3202 (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) -> p1_s2_setwiseo(k5_setwiseo(f1_s2_setwiseo,A,k2_setwiseo(f1_s2_setwiseo,B))) | r2_hidden(B,A)))))) & p1_s2_setwiseo(k1_setwiseo(f1_s2_setwiseo)) -> (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]. 59.83/57.34 3203 (all A all B all C (r2_hidden(A,B) | C = A <-> r2_hidden(A,k2_xboole_0(B,k1_tarski(C))))) # label(t6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.83/57.34 3204 (all A all B (m2_relset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_1(B) -> (B = k9_setwiseo(A) <-> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k5_setwiseo(A,C,D) = k2_binop_1(k5_finsub_1(A),k5_finsub_1(A),k5_finsub_1(A),B,C,D)))))))) # label(d4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3205 (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]. 59.86/57.35 3206 $T # label(t7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3207 (all A k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)) = k1_xboole_0) # label(t55_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3208 (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]. 59.86/57.35 3209 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> B = k10_setwiseo(A,A,B,k11_setwiseo(A)))))) # label(t71_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3210 (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]. 59.86/57.35 3211 (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]. 59.86/57.35 3212 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k3_setwiseo(A,C,B) = k3_setwiseo(A,B,C))) # label(commutativity_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3213 (all A all B all C -(r1_tarski(A,k2_xboole_0(B,k1_tarski(C))) & -r1_tarski(A,B) & -r2_hidden(C,A))) # label(t5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3214 (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 (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F)) = k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E)))))))))))))) # label(t29_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3215 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> (B = C <-> r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),C))))))) # label(t68_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3216 (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) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_setwiseo(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)) -> 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,k5_setwiseo(B,E,F),D)))))))))))))) # label(t42_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3217 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k2_xboole_0(B,C) = k5_setwiseo(A,B,C))) # label(redefinition_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3218 (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 (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) -> D = k1_xboole_0 & -v1_setwiseo(C,B) | (all F (m1_subset_1(F,B) -> ((exists G (v1_funct_1(G) & v1_funct_2(G,k5_finsub_1(A),B) & m2_relset_1(G,k5_finsub_1(A),B) & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> (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))))) | k1_xboole_0 = H))) & (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) -> H = k1_funct_1(G,k1_xboole_0)))) & k8_funct_2(k5_finsub_1(A),B,G,D) = F)) <-> k7_setwiseo(A,B,C,D,E) = F)))))))))))))) # label(d3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3219 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all 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(D,A) & v3_binop_1(D,A) & v1_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (k1_xboole_0 != E -> (all F (v1_funct_2(F,B,k5_finsub_1(C)) & m2_relset_1(F,B,k5_finsub_1(C)) & v1_funct_1(F) -> (all G (v1_funct_2(G,k5_finsub_1(C),A) & m2_relset_1(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)) -> k8_funct_2(k5_finsub_1(C),A,G,k5_setwiseo(C,H,I)) = 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)))))) -> 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]. 59.86/57.35 3220 $T # label(t2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3221 $T # label(t24_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3222 (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,B) = B)) # label(idempotence_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3223 (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) -> (v1_binop_1(D,A) & v2_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) & m2_relset_1(F,B,C) & v1_funct_2(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]. 59.86/57.35 3224 (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) -> (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)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> -(k1_xboole_0 != F & 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)) & k1_xboole_0 != E)))))))))))))) # label(t30_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3225 (all A (v1_funct_1(k9_setwiseo(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)))) # label(dt_k9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3226 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,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]. 59.86/57.35 3227 $T # label(t20_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.35 3228 (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]. 59.86/57.36 3229 (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,A) -> (all F (m1_subset_1(F,A) -> k10_setwiseo(A,B,k4_setwiseo(A,D,E,F),C) = 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)))))))))))) # label(t58_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3230 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k5_setwiseo(B,k10_setwiseo(A,B,D,C),k10_setwiseo(A,B,E,C)) = k10_setwiseo(A,B,k5_setwiseo(A,D,E),C))))))))) # label(t62_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3231 (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 (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (v1_binop_1(C,A) & v1_setwiseo(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F)) = k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E)))))))))))))) # label(t41_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3232 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k5_finsub_1(A)))))) # label(rc2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3233 (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]. 59.86/57.36 3234 (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]. 59.86/57.36 3235 (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)) -> k5_setwiseo(B,k10_setwiseo(A,B,E,C),k8_funct_2(A,k5_finsub_1(B),C,D)) = k10_setwiseo(A,B,k5_setwiseo(A,E,k2_setwiseo(A,D)),C))))))))) # label(t60_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3236 (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 (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> (r2_hidden(F,D) -> k7_setwiseo(B,A,C,D,E) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,F),k7_setwiseo(B,A,C,D,E)))))))))))))))) # label(t31_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3237 (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) -> (v1_binop_1(C,B) & v2_binop_1(C,B) & v3_binop_1(C,B) -> -v1_setwiseo(C,B) & k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> (k7_setwiseo(A,B,C,D,E) = F <-> (exists G (v1_funct_1(G) & m2_relset_1(G,k5_finsub_1(A),B) & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> k1_funct_1(G,k1_xboole_0) = H))) & (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,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))))))))) & (all H (m1_subset_1(H,A) -> k8_funct_2(A,B,E,H) = k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)))) & F = k8_funct_2(k5_finsub_1(A),B,G,D) & v1_funct_2(G,k5_finsub_1(A),B))))))))))))))))) # label(t25_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3238 (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) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (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 (v1_funct_2(F,B,A) & m2_relset_1(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]. 59.86/57.36 3239 (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 (m1_subset_1(D,k5_finsub_1(B)) -> (k2_funct_2(B,A,C,D) = k1_xboole_0 -> D = k1_xboole_0))))))))) # label(t19_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3240 (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]. 59.86/57.36 3241 (all A (v1_xboole_0(k1_setwiseo(A)) & m1_subset_1(k1_setwiseo(A),k5_finsub_1(A)))) # label(dt_k1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3242 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & m1_subset_1(D,k5_finsub_1(A)) & v1_funct_2(C,A,B) -> k8_setwiseo(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3243 (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_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> D = k1_xboole_0 | (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> (r2_hidden(G,D) -> F = k8_funct_2(B,A,E,G)))) -> k7_setwiseo(B,A,C,D,E) = F)))))))))))))) # label(t33_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3244 (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) = k2_tarski(B,C))) # label(redefinition_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3245 $T # label(t46_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3246 (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]. 59.86/57.36 3247 (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) -> (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]. 59.86/57.36 3248 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s1_setwiseo) -> (all C (m1_subset_1(C,f1_s1_setwiseo) -> (r2_hidden(C,f2_s1_setwiseo) & p1_s1_setwiseo(C,B) <-> 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_2(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo)))) # label(s1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3249 (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]. 59.86/57.36 3250 (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) <-> (exists C (r3_binop_1(A,C,B) & m1_subset_1(C,A)))))))) # label(d2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3251 (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) -> (v3_binop_1(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(D,D),D) & v1_funct_2(E,k2_zfmisc_1(D,D),D) -> (v3_binop_1(E,D) & v2_binop_1(E,D) & v1_binop_1(E,D) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(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) -> 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)))))) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> (H != k1_xboole_0 -> 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]. 59.86/57.36 3252 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m2_relset_1(D,A,k5_finsub_1(B)) & v1_funct_2(D,A,k5_finsub_1(B)) & v1_funct_1(D) -> k7_setwiseo(A,k5_finsub_1(B),k9_setwiseo(B),C,D) = k10_setwiseo(A,B,C,D))))))) # label(d5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3253 (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) <-> r3_binop_1(A,k3_binop_1(A,B),B)))))) # label(t22_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3254 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k3_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3255 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,A,k5_finsub_1(A)) & v1_funct_2(B,A,k5_finsub_1(A)) -> ((all C (m1_subset_1(C,A) -> k8_funct_2(A,k5_finsub_1(A),B,C) = k2_setwiseo(A,C))) <-> B = k11_setwiseo(A)))))) # label(t67_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3256 (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 (m2_relset_1(E,A,B) & v1_funct_2(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]. 59.86/57.36 3257 (all A (-v1_xboole_0(A) -> (all B all C all D (v1_funct_2(D,A,k5_finsub_1(B)) & m2_relset_1(D,A,k5_finsub_1(B)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k5_finsub_1(B),k5_finsub_1(C)) & v1_funct_2(E,k5_finsub_1(B),k5_finsub_1(C)) -> (k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k1_setwiseo(B)) = k1_setwiseo(C) & (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)) -> k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k10_setwiseo(A,B,F,D)) = k10_setwiseo(A,C,F,k7_funct_2(A,k5_finsub_1(B),k5_finsub_1(C),D,E))))))))))) # label(t72_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3258 (all A k1_xboole_0 = k1_setwiseo(A)) # label(d1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3259 (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]. 59.86/57.36 3260 (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_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (v3_binop_1(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> (all F (m1_subset_1(F,B) -> (k2_setwiseo(B,F) = k2_funct_2(A,B,E,D) -> F = k7_setwiseo(A,B,C,D,E))))))))))))))) # label(t34_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3261 $T # label(t21_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3262 (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,B) -> k2_funct_2(B,A,C,k1_tarski(D)) = k1_tarski(k8_funct_2(B,A,C,D)))))))))) # label(t13_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3263 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v3_binop_1(D,A) & v1_binop_1(D,A) & v2_binop_1(D,A) & v1_setwiseo(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> (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]. 59.86/57.36 3264 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(D) & v1_funct_2(D,A,k5_finsub_1(B)) & m1_relset_1(D,A,k5_finsub_1(B)) & m1_subset_1(C,k5_finsub_1(A)) -> m1_subset_1(k10_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3265 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k1_tarski(B) = k2_setwiseo(A,B))) # label(redefinition_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3266 $T # label(t48_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3267 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (r2_hidden(E,k10_setwiseo(A,B,D,C)) <-> (exists F (r2_hidden(F,D) & r2_hidden(E,k8_funct_2(A,k5_finsub_1(B),C,F)) & m1_subset_1(F,A))))))))))) # label(t70_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3268 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,k5_finsub_1(A)) & 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]. 59.86/57.36 3269 $T # label(t66_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 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]. 59.86/57.36 3271 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (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]. 59.86/57.36 3272 (all A v2_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t51_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3273 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> -((all C (m1_subset_1(C,A) -> -r2_hidden(C,B))) & k1_xboole_0 != B))))) # label(t18_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3274 $T # label(t17_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3275 (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) -> (v3_binop_1(C,B) & v1_setwiseo(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> (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,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,G,E) = k7_setwiseo(A,B,C,F,D))))))))))))))))) # label(t43_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3276 (all A r3_binop_1(k5_finsub_1(A),k1_setwiseo(A),k9_setwiseo(A))) # label(t52_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3277 $T # label(t1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3278 (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) -> k10_setwiseo(A,B,k2_setwiseo(A,D),C) = k8_funct_2(A,k5_finsub_1(B),C,D))))))) # label(t56_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3279 $T # label(t47_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3280 (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) -> (v3_binop_1(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) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (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,E,G) = k2_funct_2(A,B,D,F) -> k1_xboole_0 = F | k7_setwiseo(A,B,C,G,E) = k7_setwiseo(A,B,C,F,D))))))))))))))))) # label(t35_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3281 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (v2_binop_1(D,B) & v1_setwiseo(D,B) & v3_binop_1(D,B) & v1_binop_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,k5_finsub_1(C)) & m2_relset_1(E,A,k5_finsub_1(C)) -> (all F (v1_funct_1(F) & v1_funct_2(F,k5_finsub_1(C),B) & m2_relset_1(F,k5_finsub_1(C),B) -> (k3_binop_1(B,D) = k8_funct_2(k5_finsub_1(C),B,F,k1_setwiseo(C)) & (all G (m1_subset_1(G,k5_finsub_1(C)) -> (all H (m1_subset_1(H,k5_finsub_1(C)) -> 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)) = k8_funct_2(k5_finsub_1(C),B,F,k5_setwiseo(C,G,H)))))) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> k7_setwiseo(A,B,D,G,k7_funct_2(A,k5_finsub_1(C),B,E,F)) = k8_funct_2(k5_finsub_1(C),B,F,k10_setwiseo(A,C,G,E)))))))))))))))) # label(t65_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3282 (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 (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> k3_binop_1(A,C) = k7_setwiseo(B,A,C,k1_setwiseo(B),D)))))))))) # label(t40_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3283 (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) = k5_setwiseo(A,C,B))) # label(commutativity_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3284 (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]. 59.86/57.36 3285 (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]. 59.86/57.36 3286 (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) & 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)) -> (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) | E = k1_xboole_0)))))))))))))) # label(t32_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3287 (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) -> (v1_binop_1(C,B) & v3_binop_1(C,B) & v1_setwiseo(C,B) & v2_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(D,D),D) & v1_funct_2(E,k2_zfmisc_1(D,D),D) -> (v1_binop_1(E,D) & v3_binop_1(E,D) & v1_setwiseo(E,D) & v2_binop_1(E,D) -> (all F (m2_relset_1(F,A,B) & v1_funct_2(F,A,B) & v1_funct_1(F) -> (all G (m2_relset_1(G,B,D) & v1_funct_2(G,B,D) & v1_funct_1(G) -> (k8_funct_2(B,D,G,k3_binop_1(B,C)) = k3_binop_1(D,E) & (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)))))) -> (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]. 59.86/57.36 3288 (all A v1_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t50_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3289 (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)) -> k10_setwiseo(A,B,k1_setwiseo(A),C) = k1_xboole_0)))) # label(t59_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3290 (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]. 59.86/57.36 3291 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,k5_finsub_1(A)) & m1_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) & -v1_xboole_0(A) -> m1_subset_1(k7_setwiseo(A,B,C,D,E),B))) # label(dt_k7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3292 (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,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v3_binop_1(C,A) & r6_binop_1(A,D,C) & v2_binop_1(C,A) & v1_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) -> 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]. 59.86/57.36 3293 (all A (v1_funct_1(k11_setwiseo(A)) & m2_relset_1(k11_setwiseo(A),A,k5_finsub_1(A)) & v1_funct_2(k11_setwiseo(A),A,k5_finsub_1(A)))) # label(dt_k11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3294 (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) -> (v2_binop_1(C,A) & v1_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]. 59.86/57.36 3295 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (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]. 59.86/57.36 3296 $T # label(t9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3297 $T # label(t10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3298 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k5_finsub_1(A)) & v1_funct_2(B,A,k5_finsub_1(A)) -> ((all C (r2_hidden(C,A) -> k1_tarski(C) = k1_funct_1(B,C))) <-> k11_setwiseo(A) = B))) # label(d6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3299 (all A v1_setwiseo(k9_setwiseo(A),k5_finsub_1(A))) # label(t53_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3300 (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) & v1_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k3_setwiseo(B,E,F),D) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F))))))))))))))) # label(t27_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3301 (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 | k1_xboole_0 = B | p1_s3_setwiseo(k5_setwiseo(f1_s3_setwiseo,A,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)) -> (k1_xboole_0 != A -> p1_s3_setwiseo(A)))) # label(s3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3302 (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]. 59.86/57.36 3303 (all A (r2_hidden(A,a_0_30_fraenkel) <-> (exists B exists C (p1_s16_fraenkel(B,C) & A = f3_s16_fraenkel(B,C) & m1_subset_1(C,f2_s16_fraenkel) & m1_subset_1(B,f1_s16_fraenkel))))) # label(fraenkel_a_0_30_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3304 (all A (m1_subset_1(A,f1_s19_fraenkel) -> (all B (m1_subset_1(B,f2_s19_fraenkel) -> (p1_s19_fraenkel(A,B) & B = f4_s19_fraenkel <-> p2_s19_fraenkel(A,B)))))) -> a_0_34_fraenkel = a_0_35_fraenkel # label(s19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3305 (all A ((exists B exists C (p1_s13_fraenkel(B,C) & A = f4_s13_fraenkel(B,C) & m1_subset_1(C,f2_s13_fraenkel) & m1_subset_1(B,f1_s13_fraenkel))) <-> r2_hidden(A,a_0_22_fraenkel))) # label(fraenkel_a_0_22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3306 v1_finset_1(f4_s25_fraenkel) & (all A (m2_fraenkel(A,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (all B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (k7_relat_1(B,f3_s25_fraenkel) = k7_relat_1(A,f3_s25_fraenkel) -> f5_s25_fraenkel(A) = f5_s25_fraenkel(B)))))) & v1_finset_1(f3_s25_fraenkel) -> v1_finset_1(a_0_40_fraenkel) # label(s25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3307 (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]. 59.86/57.36 3308 (all A ((exists B exists C (m1_subset_1(C,f2_s12_fraenkel) & f3_s12_fraenkel(B,C) = A & p1_s12_fraenkel(B,C) & m1_subset_1(B,f1_s12_fraenkel))) <-> r2_hidden(A,a_0_20_fraenkel))) # label(fraenkel_a_0_20_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3309 (all A ((exists B (m1_subset_1(B,f3_s13_fraenkel) & p2_s13_fraenkel(B) & r2_hidden(B,a_0_22_fraenkel) & B = A)) <-> r2_hidden(A,a_0_21_fraenkel))) # label(fraenkel_a_0_21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3310 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (k7_relat_1(C,E) = k7_relat_1(D,E) -> (all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k8_funct_2(A,B,C,F) = k8_funct_2(A,B,D,F)))))))))))))) # label(t3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3311 (all A ((exists B exists C (A = f3_s20_fraenkel(B,C) & C = f4_s20_fraenkel & p1_s20_fraenkel(B,C) & m1_subset_1(C,f2_s20_fraenkel) & m1_subset_1(B,f1_s20_fraenkel))) <-> r2_hidden(A,a_0_36_fraenkel))) # label(fraenkel_a_0_36_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3312 (all A (-v1_xboole_0(A) -> (all B all C all D (m2_fraenkel(D,B,A,k1_fraenkel(B,A)) -> k7_relat_1(D,C) = k7_relat_1(D,k3_xboole_0(B,C)))))) # label(t15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3313 (all A (r2_hidden(A,a_0_14_fraenkel) <-> (exists B exists C (p1_s8_fraenkel(B,C) & f3_s8_fraenkel(B,C) = A & m1_subset_1(C,f2_s8_fraenkel) & m1_subset_1(B,f1_s8_fraenkel))))) # label(fraenkel_a_0_14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3314 k7_relat_1(f4_s9_fraenkel,f3_s9_fraenkel) = k7_relat_1(f5_s9_fraenkel,f3_s9_fraenkel) & (all A (m1_subset_1(A,f1_s9_fraenkel) -> (r2_hidden(A,f3_s9_fraenkel) -> (p2_s9_fraenkel(A) <-> p1_s9_fraenkel(A))))) -> a_0_16_fraenkel = a_0_17_fraenkel # label(s9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3315 (all A all B all C (-v1_xboole_0(C) & v1_fraenkel(C) -> ((all D (m1_subset_1(D,C) -> m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D))) <-> m1_fraenkel(C,A,B)))) # label(d2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3316 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3317 (all A ((exists B (p1_s20_fraenkel(B,f4_s20_fraenkel) & f3_s20_fraenkel(B,f4_s20_fraenkel) = A & m1_subset_1(B,f1_s20_fraenkel))) <-> r2_hidden(A,a_0_37_fraenkel))) # label(fraenkel_a_0_37_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3318 (all A ((exists B (A = f5_s25_fraenkel(B) & r1_tarski(k2_funct_2(f1_s25_fraenkel,f2_s25_fraenkel,B,f3_s25_fraenkel),f4_s25_fraenkel) & m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)))) <-> r2_hidden(A,a_0_40_fraenkel))) # label(fraenkel_a_0_40_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3319 (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]. 59.86/57.36 3320 (all A ((exists B (m1_subset_1(B,f1_s17_fraenkel) & f3_s17_fraenkel(B) = A & p1_s17_fraenkel(B) & r2_hidden(f3_s17_fraenkel(B),f2_s17_fraenkel))) <-> r2_hidden(A,a_0_32_fraenkel))) # label(fraenkel_a_0_32_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3321 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(C,B) & r1_tarski(D,A) -> k1_xboole_0 = k1_funct_2(C,D) | (all E (m1_subset_1(E,k1_funct_2(C,D)) -> v1_funct_1(E) & m2_relset_1(E,B,A))))))) # label(t6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3322 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3323 (all A (r2_hidden(A,a_0_29_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s15_fraenkel) & p2_s15_fraenkel(B) & p1_s15_fraenkel(B,C) & A = f3_s15_fraenkel(B,C) & m1_subset_1(B,f1_s15_fraenkel))))) # label(fraenkel_a_0_29_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3324 (all A ((exists B (m1_subset_1(B,f1_s9_fraenkel) & k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f4_s9_fraenkel,B) = A & r2_hidden(B,f3_s9_fraenkel) & p1_s9_fraenkel(B))) <-> r2_hidden(A,a_0_16_fraenkel))) # label(fraenkel_a_0_16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3325 (all A (m1_subset_1(A,f1_s6_fraenkel) -> (p1_s6_fraenkel(A) -> f2_s6_fraenkel(A) = f3_s6_fraenkel(A)))) -> a_0_11_fraenkel = a_0_10_fraenkel # label(s6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3326 (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]. 59.86/57.36 3327 (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]. 59.86/57.36 3328 (all A all B (-v1_xboole_0(B) -> k1_funct_2(A,B) = k1_fraenkel(A,B))) # label(redefinition_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.36 3329 (all A (m1_subset_1(A,f1_s4_fraenkel) -> (all B (m1_subset_1(B,f2_s4_fraenkel) -> (p2_s4_fraenkel(A,B) <-> p1_s4_fraenkel(A,B)))))) -> a_0_6_fraenkel = a_0_7_fraenkel # label(s4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3330 (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]. 59.86/57.37 3331 (exists A (m1_subset_1(A,k5_finsub_1(f1_s24_fraenkel)) & (all B (m1_subset_1(B,f1_s24_fraenkel) -> ((exists C (p1_s24_fraenkel(B,C) & B = f4_s24_fraenkel(C) & r2_hidden(C,f3_s24_fraenkel) & m1_subset_1(C,f2_s24_fraenkel))) <-> r2_hidden(B,A)))))) # label(s24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3332 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3333 (all A (r2_hidden(A,a_0_19_fraenkel) <-> (exists B exists C (p1_s11_fraenkel(B,C) & f3_s11_fraenkel(B,C) = A & m1_subset_1(C,f2_s11_fraenkel) & m1_subset_1(B,f1_s11_fraenkel))))) # label(fraenkel_a_0_19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3334 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3335 (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]. 59.86/57.37 3336 (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]. 59.86/57.37 3337 (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]. 59.86/57.37 3338 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]. 59.86/57.37 3339 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k1_funct_2(A,B)))) # label(t16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3340 (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]. 59.86/57.37 3341 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3342 (all A (r2_hidden(A,a_0_26_fraenkel) <-> (exists B (A = f2_s14_fraenkel(B) & p2_s14_fraenkel(B) & p1_s14_fraenkel(B) & m1_subset_1(B,f1_s14_fraenkel))))) # label(fraenkel_a_0_26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3343 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (all D (m1_subset_1(D,C) <-> m2_fraenkel(D,A,B,C))))) # label(redefinition_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3344 (all A (r2_hidden(A,a_0_23_fraenkel) <-> (exists B exists C (A = f4_s13_fraenkel(B,C) & p1_s13_fraenkel(B,C) & p2_s13_fraenkel(f4_s13_fraenkel(B,C)) & m1_subset_1(C,f2_s13_fraenkel) & m1_subset_1(B,f1_s13_fraenkel))))) # label(fraenkel_a_0_23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3345 (all A ((exists B exists C (f3_s16_fraenkel(B,C) = A & p2_s16_fraenkel(B,C) & m1_subset_1(C,f2_s16_fraenkel) & m1_subset_1(B,f1_s16_fraenkel))) <-> r2_hidden(A,a_0_31_fraenkel))) # label(fraenkel_a_0_31_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3346 (all A (m1_subset_1(A,f1_s5_fraenkel) -> f3_s5_fraenkel(A) = f2_s5_fraenkel(A))) -> a_0_8_fraenkel = a_0_9_fraenkel # label(s5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3347 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3348 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (exists D m2_fraenkel(D,A,B,C)))) # label(existence_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3349 (all A (r2_hidden(A,a_0_15_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & m1_subset_1(C,f2_s8_fraenkel) & A = f3_s8_fraenkel(C,B) & p2_s8_fraenkel(B,C))))) # label(fraenkel_a_0_15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3350 (all A ((exists B exists C (m1_subset_1(B,f1_s4_fraenkel) & p1_s4_fraenkel(B,C) & A = f3_s4_fraenkel(B,C) & m1_subset_1(C,f2_s4_fraenkel))) <-> r2_hidden(A,a_0_6_fraenkel))) # label(fraenkel_a_0_6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3351 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(C,B) & r1_tarski(D,A) -> (all E (m1_subset_1(E,k1_funct_2(C,D)) -> (exists F (m2_fraenkel(F,B,A,k1_fraenkel(B,A)) & k7_relat_1(F,C) = E)))) | k1_xboole_0 = k1_funct_2(C,D))))) # label(t14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3352 (all A (r2_hidden(A,a_0_13_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & p1_s7_fraenkel(B,C) & A = f4_s7_fraenkel(B,C) & m1_subset_1(C,f2_s7_fraenkel))))) # label(fraenkel_a_0_13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3353 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3354 (exists A (v1_fraenkel(A) & -v1_xboole_0(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3355 (all A (r2_hidden(A,a_0_27_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s15_fraenkel) & m1_subset_1(C,f2_s15_fraenkel) & f3_s15_fraenkel(B,C) = A & r2_hidden(B,a_0_28_fraenkel) & p1_s15_fraenkel(B,C))))) # label(fraenkel_a_0_27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3356 (all A (r2_hidden(A,a_0_4_fraenkel) <-> (exists B (m1_subset_1(B,f1_s3_fraenkel) & A = f2_s3_fraenkel(B) & p1_s3_fraenkel(B))))) # label(fraenkel_a_0_4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3357 (all A (r2_hidden(A,a_0_28_fraenkel) <-> (exists B (m1_subset_1(B,f1_s15_fraenkel) & p2_s15_fraenkel(B) & A = B)))) # label(fraenkel_a_0_28_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3358 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3359 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> m1_fraenkel(k2_setwiseo(k1_zfmisc_1(k2_zfmisc_1(A,B)),C),A,B))) # label(t10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3360 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k1_funct_2(A,B)) & v1_fraenkel(k1_funct_2(A,B)))) # label(fc2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3361 (all A (r2_hidden(A,a_0_39_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s22_fraenkel) & m1_subset_1(C,f2_s22_fraenkel) & f5_s22_fraenkel(B,C) = A & r2_hidden(B,f3_s22_fraenkel) & r2_hidden(C,f4_s22_fraenkel))))) # label(fraenkel_a_0_39_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3362 (all A (m1_subset_1(A,f1_s26_fraenkel) -> -(r2_hidden(A,f3_s26_fraenkel) & (all B (m1_subset_1(B,f2_s26_fraenkel) -> -p1_s26_fraenkel(A,B)))))) -> (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s26_fraenkel) -> (r2_hidden(B,f3_s26_fraenkel) -> p1_s26_fraenkel(B,k8_funct_2(f1_s26_fraenkel,f2_s26_fraenkel,A,B))))) & m2_relset_1(A,f1_s26_fraenkel,f2_s26_fraenkel) & v1_funct_2(A,f1_s26_fraenkel,f2_s26_fraenkel))) # label(s26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3363 (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]. 59.86/57.37 3364 (all A (r2_hidden(A,a_0_34_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s19_fraenkel) & m1_subset_1(C,f2_s19_fraenkel) & p2_s19_fraenkel(B,C) & A = f3_s19_fraenkel(B,C))))) # label(fraenkel_a_0_34_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3365 (all A (r2_hidden(A,a_0_9_fraenkel) <-> (exists B (p1_s5_fraenkel(B) & A = f3_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))))) # label(fraenkel_a_0_9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3366 (all A (r2_hidden(A,a_0_2_fraenkel) <-> (exists B exists C (p1_s2_fraenkel(B,C) & f3_s2_fraenkel(B,C) = A & m1_subset_1(C,f2_s2_fraenkel) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3367 (all A (m1_subset_1(A,f1_s23_fraenkel) -> (all B (m1_subset_1(B,f1_s23_fraenkel) -> (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(B,C) & p1_s23_fraenkel(A,B) -> p1_s23_fraenkel(A,C)))))))) & (all A (m1_subset_1(A,f1_s23_fraenkel) -> p1_s23_fraenkel(A,A))) -> (all A (m1_subset_1(A,f1_s23_fraenkel) -> -((all B (m1_subset_1(B,f1_s23_fraenkel) -> -(r2_hidden(B,f2_s23_fraenkel) & p1_s23_fraenkel(B,A) & (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(C,B) & r2_hidden(C,f2_s23_fraenkel) -> p1_s23_fraenkel(B,C))))))) & r2_hidden(A,f2_s23_fraenkel)))) # label(s23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3368 (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]. 59.86/57.37 3369 (all A ((exists B (p1_s6_fraenkel(B) & A = f2_s6_fraenkel(B) & m1_subset_1(B,f1_s6_fraenkel))) <-> r2_hidden(A,a_0_10_fraenkel))) # label(fraenkel_a_0_10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3370 (all A (r2_hidden(A,a_0_12_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s7_fraenkel) & p1_s7_fraenkel(B,C) & f3_s7_fraenkel(B,C) = A & m1_subset_1(B,f1_s7_fraenkel))))) # label(fraenkel_a_0_12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3371 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3372 (all A (m1_subset_1(A,f1_s16_fraenkel) -> (all B (m1_subset_1(B,f2_s16_fraenkel) -> -(p1_s16_fraenkel(A,B) & (all C (m1_subset_1(C,f1_s16_fraenkel) -> -(p2_s16_fraenkel(C,B) & f3_s16_fraenkel(A,B) = f3_s16_fraenkel(C,B))))))))) -> r1_tarski(a_0_30_fraenkel,a_0_31_fraenkel) # label(s16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3373 (all A ((exists B (f3_s18_fraenkel(B) = A & -r2_hidden(f3_s18_fraenkel(B),f2_s18_fraenkel) & p1_s18_fraenkel(B) & m1_subset_1(B,f1_s18_fraenkel))) <-> r2_hidden(A,a_0_33_fraenkel))) # label(fraenkel_a_0_33_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3374 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3375 (all A (r2_hidden(A,a_0_18_fraenkel) <-> (exists B (m1_subset_1(B,f1_s10_fraenkel) & p1_s10_fraenkel(B) & A = B)))) # label(fraenkel_a_0_18_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3376 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3377 (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]. 59.86/57.37 3378 (all A (r2_hidden(A,a_0_25_fraenkel) <-> (exists B (p2_s14_fraenkel(B) & B = A & m1_subset_1(B,f1_s14_fraenkel))))) # label(fraenkel_a_0_25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3379 (all A ((exists B (m1_subset_1(B,f1_s9_fraenkel) & p2_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel) & A = k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f5_s9_fraenkel,B))) <-> r2_hidden(A,a_0_17_fraenkel))) # label(fraenkel_a_0_17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3380 (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]. 59.86/57.37 3381 (all A (v1_fraenkel(A) -> (all B (m1_subset_1(B,A) -> v1_relat_1(B) & v1_funct_1(B))))) # label(cc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3382 (all A ((exists B (m1_subset_1(B,f1_s6_fraenkel) & p1_s6_fraenkel(B) & A = f3_s6_fraenkel(B))) <-> r2_hidden(A,a_0_11_fraenkel))) # label(fraenkel_a_0_11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3383 (all A ((exists B (m1_subset_1(B,f1_s5_fraenkel) & A = f2_s5_fraenkel(B) & p1_s5_fraenkel(B))) <-> r2_hidden(A,a_0_8_fraenkel))) # label(fraenkel_a_0_8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3384 (all A ((exists B (f2_s1_fraenkel(B) = A & p2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel))) <-> r2_hidden(A,a_0_1_fraenkel))) # label(fraenkel_a_0_1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3385 (all A (r2_hidden(A,a_0_0_fraenkel) <-> (exists B (m1_subset_1(B,f1_s1_fraenkel) & p1_s1_fraenkel(B) & f2_s1_fraenkel(B) = A)))) # label(fraenkel_a_0_0_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3386 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3387 (all A (r2_hidden(A,a_0_5_fraenkel) <-> (exists B (p2_s3_fraenkel(B) & f2_s3_fraenkel(B) = A & m1_subset_1(B,f1_s3_fraenkel))))) # label(fraenkel_a_0_5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3388 (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]. 59.86/57.37 3389 (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]. 59.86/57.37 3390 (all A ((exists B (m1_subset_1(B,f1_s19_fraenkel) & A = f3_s19_fraenkel(B,f4_s19_fraenkel) & p1_s19_fraenkel(B,f4_s19_fraenkel))) <-> r2_hidden(A,a_0_35_fraenkel))) # label(fraenkel_a_0_35_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3391 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (all D (m2_fraenkel(D,A,B,C) -> m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D))))) # label(dt_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3392 (all A (m1_subset_1(A,f1_s7_fraenkel) -> (all B (m1_subset_1(B,f2_s7_fraenkel) -> f4_s7_fraenkel(A,B) = f3_s7_fraenkel(A,B))))) -> a_0_13_fraenkel = a_0_12_fraenkel # label(s7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3393 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3394 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3395 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3396 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 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]. 59.86/57.37 3398 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (np__0 = A -> (k4_arytm_0(A) = B <-> np__0 = B)) & (A != np__0 -> (B = k4_arytm_0(A) <-> k2_arytm_0(A,B) = k13_arytm_3)))))) # label(d5_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3399 (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]. 59.86/57.37 3400 (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 -> np__0 = A))))) # label(t19_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3401 (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]. 59.86/57.37 3402 (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]. 59.86/57.37 3403 (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]. 59.86/57.37 3404 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> -(np__0 != A & B != np__0 & k2_arytm_0(A,B) = np__0))))) # label(t23_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 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) -> (r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_arytm_2) -> ((exists D ((exists E (k2_arytm_1(D,E) = C & B = k4_tarski(np__0,E) & D = A & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,k2_arytm_2))) <-> k1_arytm_0(A,B) = C)) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,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) & E = B & C = k2_arytm_1(E,D) & m1_subset_1(E,k2_arytm_2))))))) & -(-(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2)) & -(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) & B = k4_tarski(np__0,E) & k4_tarski(np__0,k7_arytm_2(D,E)) = C & k4_tarski(np__0,D) = A)))) <-> C = k1_arytm_0(A,B)) & -(r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)))) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2) -> ((exists D (m1_subset_1(D,k2_arytm_2) & (exists E (k7_arytm_2(D,E) = C & B = E & A = D & m1_subset_1(E,k2_arytm_2))))) <-> C = k1_arytm_0(A,B))))))))) # label(d2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3406 (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]. 59.86/57.37 3407 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k1_arytm_0(B,A) = k1_arytm_0(A,B))) # label(commutativity_k1_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3408 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k3_arytm_0(k1_arytm_0(A,B)) = k1_arytm_0(k3_arytm_0(A),k3_arytm_0(B)))))) # label(t27_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3409 (all A all B k13_arytm_3 != k4_tarski(A,B)) # label(t7_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3410 (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]. 59.86/57.37 3411 (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,k2_arytm_0(B,C)) = k2_arytm_0(k2_arytm_0(A,B),C))))))) # label(t15_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3412 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k2_arytm_0(A,B),k1_numbers))) # label(dt_k2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3413 (all A (m1_subset_1(A,k2_arytm_2) -> (A != k12_arytm_3 -> r2_hidden(k4_tarski(k12_arytm_3,A),k1_numbers)))) # label(t2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3414 (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) -> B = C | k12_arytm_3 = A))))))) # label(t8_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3415 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (np__0 = B -> k2_arytm_0(A,B) = np__0))))) # label(t14_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3416 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k2_arytm_0(k4_arytm_0(A),k4_arytm_0(B)) = k4_arytm_0(k2_arytm_0(A,B)))))) # label(t24_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3417 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (k13_arytm_3 = B -> A = k2_arytm_0(A,B)))))) # label(t21_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3418 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (B = np__0 -> k1_arytm_0(A,B) = A))))) # label(t13_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3419 $T # label(t9_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3420 (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]. 59.86/57.37 3421 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (np__0 != B -> k5_funct_4(k1_numbers,np__0,k13_arytm_3,A,B) = k5_arytm_0(A,B)) & (np__0 = B -> k5_arytm_0(A,B) = A))))) # label(d7_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3422 (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) -> D = B & A = C))))))))) # label(t12_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3423 (all A (m1_subset_1(A,k1_numbers) -> k3_arytm_0(k3_arytm_0(A)) = A)) # label(involutiveness_k3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3424 $T # label(d6_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3425 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k12_arytm_3 = k2_arytm_1(A,B) -> A = B))))) # label(t6_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3426 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k2_arytm_0(B,A) = k2_arytm_0(A,B))) # label(commutativity_k2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3427 (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_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> np__0 = A | ((exists D (m1_subset_1(D,k2_arytm_2) & (exists E (m1_subset_1(E,k2_arytm_2) & k4_tarski(np__0,E) = B & C = k4_tarski(np__0,k8_arytm_2(D,E)) & D = A)))) <-> C = k2_arytm_0(A,B))) & (r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (k2_arytm_0(A,B) = C <-> (exists D (m1_subset_1(D,k2_arytm_2) & (exists E (k8_arytm_2(E,D) = C & B = k4_tarski(np__0,E) & A = k4_tarski(np__0,D) & m1_subset_1(E,k2_arytm_2))))))) & -(-(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2)) & -(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & np__0 != B & r2_hidden(B,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))) & -(k2_arytm_0(A,B) = C <-> C = np__0) & -(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & A != np__0 & r2_hidden(A,k2_arytm_2))) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (k2_arytm_0(A,B) = C <-> (exists D ((exists E (k4_tarski(np__0,D) = A & C = k4_tarski(np__0,k8_arytm_2(E,D)) & E = B & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,k2_arytm_2)))) | B = np__0) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2) -> (k2_arytm_0(A,B) = C <-> (exists D (m1_subset_1(D,k2_arytm_2) & (exists E (B = E & C = k8_arytm_2(D,E) & A = D & m1_subset_1(E,k2_arytm_2))))))))))))) # label(d3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3428 (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]. 59.86/57.37 3429 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (k1_arytm_0(A,B) = np__0 <-> k3_arytm_0(A) = B))))) # label(d4_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3430 (all A (m1_subset_1(A,k2_numbers) -> (exists B (m1_subset_1(B,k1_numbers) & (exists C (m1_subset_1(C,k1_numbers) & k5_arytm_0(B,C) = A)))))) # label(t11_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3431 (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]. 59.86/57.37 3432 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (np__0 != B -> k2_arytm_0(k2_arytm_0(A,B),k4_arytm_0(B)) = A))))) # label(t22_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3433 (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(A,k1_arytm_0(B,C)) = k1_arytm_0(k1_arytm_0(A,B),C))))))) # label(t25_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3434 (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]. 59.86/57.37 3435 (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]. 59.86/57.37 3436 $T # label(d1_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3437 (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 & k13_arytm_3 = k2_arytm_0(A,C) -> C = B | A = np__0))))))) # label(t20_arytm_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3438 (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]. 59.86/57.37 3439 (exists A v1_xcmplx_0(A)) # label(rc1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3440 $T # label(dt_k3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3441 (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]. 59.86/57.37 3442 (all A (m1_subset_1(A,k1_numbers) -> v1_xcmplx_0(A))) # label(cc1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3443 (exists A (-v1_xboole_0(A) & v1_xcmplx_0(A))) # label(rc2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3444 (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]. 59.86/57.37 3445 (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) & 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(F,k1_numbers))) & m1_subset_1(E,k1_numbers))))) <-> k2_xcmplx_0(A,B) = C)))))) # label(d4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 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]. 59.86/57.37 3447 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)))) # label(dt_k5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3448 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> k2_xcmplx_0(B,A) = k2_xcmplx_0(A,B))) # label(commutativity_k2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3449 (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]. 59.86/57.37 3450 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3451 (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]. 59.86/57.37 3452 (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]. 59.86/57.37 3453 $T # label(dt_k7_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3454 (all A (v1_xcmplx_0(A) -> k4_xcmplx_0(k4_xcmplx_0(A)) = A)) # label(involutiveness_k4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3455 (all A (v1_xcmplx_0(A) <-> r2_hidden(A,k2_numbers))) # label(d2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3456 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3457 (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 ((exists G (m1_subset_1(G,k1_numbers) & k5_arytm_0(F,G) = B & C = 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))) & k5_arytm_0(D,E) = A)) & m1_subset_1(F,k1_numbers))))) & m1_subset_1(D,k1_numbers))) <-> k3_xcmplx_0(A,B) = C)))))) # label(d5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3458 (all A (v1_xcmplx_0(A) -> (v1_xboole_0(A) <-> A = np__0))) # label(d3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3459 (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]. 59.86/57.37 3460 $T # label(dt_k2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3461 $T # label(dt_k6_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3462 (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]. 59.86/57.37 3463 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 = A -> (B = np__0 <-> B = k5_xcmplx_0(A))) & (np__0 != A -> (k3_xcmplx_0(A,B) = np__1 <-> k5_xcmplx_0(A) = B)))))) # label(d7_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3464 (all A (v4_ordinal2(A) -> v1_xcmplx_0(A))) # label(cc2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3465 (all A all B (-v1_xboole_0(B) & v1_xcmplx_0(B) & v1_xcmplx_0(A) & -v1_xboole_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v1_xboole_0(k7_xcmplx_0(A,B)))) # label(fc9_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3466 (all A (v1_xcmplx_0(A) & -v1_xboole_0(A) -> -v1_xboole_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc6_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3467 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)))) # label(dt_k4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3468 $T # label(dt_k1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3469 (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]. 59.86/57.37 3470 (all A (v1_xcmplx_0(A) -> np__0 = k7_xcmplx_0(np__0,A))) # label(t5_arithm) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3471 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(A,np__0) = A)) # label(t4_arithm) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3472 (all A (v1_xcmplx_0(A) -> A = k2_xcmplx_0(A,np__0))) # label(t1_arithm) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3473 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(np__1,A) = A)) # label(t3_arithm) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3474 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(A,np__0) = np__0)) # label(t2_arithm) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3475 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(A,np__1) = A)) # label(t6_arithm) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3476 (exists A (-v1_xboole_0(A) & v3_xreal_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3477 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc15_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3478 (all A all B (v2_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v1_xreal_0(A) -> -v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3479 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3480 (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]. 59.86/57.37 3481 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3482 (all A (v1_xreal_0(A) -> v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3483 (all A (v1_xboole_0(A) & v1_xreal_0(A) -> v1_xreal_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3484 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & v2_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3485 (all A all B (v2_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3486 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3487 (all A all B (-v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)))) # label(fc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3488 (all A (v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & -v3_xreal_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3489 (all A (-v1_xboole_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(A) & v2_xreal_0(A) & v1_xcmplx_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3490 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3491 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3492 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(B,A)) & -v2_xreal_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3493 (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]. 59.86/57.37 3494 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3495 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)))) # label(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3496 (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]. 59.86/57.37 3497 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> -v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & -v3_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)))) # label(fc20_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3498 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3499 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(B,A)) & -v2_xreal_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3500 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3501 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3502 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3503 (all A all B (-v2_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3504 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3505 (all A (v1_xreal_0(A) & v3_xreal_0(A) -> v1_xcmplx_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) & -v1_xboole_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3506 (exists A (v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3507 (all A (-v1_xboole_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(A) & v3_xreal_0(A) & v1_xreal_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3508 (exists A (-v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v1_xboole_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3509 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3510 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> -v2_xreal_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc25_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3511 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) -> ((exists C (m1_subset_1(C,k2_arytm_2) & (exists D (B = D & r1_arytm_2(C,D) & A = C & m1_subset_1(D,k2_arytm_2))))) <-> r1_xreal_0(A,B))) & -(-(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_arytm_2) <-> r1_xreal_0(A,B)) & -(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2))) & (r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (m1_subset_1(D,k2_arytm_2) & k4_tarski(np__0,D) = B & r1_arytm_2(D,C) & A = k4_tarski(np__0,C))))))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3512 (all A all B (v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) -> -v2_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3513 (all A (v1_xreal_0(A) -> (v3_xreal_0(A) <-> -r1_xreal_0(np__0,A)))) # label(d4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3514 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.37 3515 (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]. 59.86/57.37 3516 (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]. 59.86/57.38 3517 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3518 (all A (-v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v1_xboole_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3519 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc18_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3520 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & -v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)))) # label(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3521 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> -v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & -v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3522 (all A (v1_xreal_0(A) & v2_xreal_0(A) -> -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(cc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3523 (all A all B (-v2_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v1_xreal_0(A) -> -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc23_xreal_0) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3524 (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(t7_real) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3525 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (v2_xreal_0(A) & r1_xreal_0(A,B) -> v2_xreal_0(B)))))) # label(t1_real) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3526 (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]. 59.86/57.38 3527 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> v1_xboole_0(A) | v3_xreal_0(A) | v2_xreal_0(B)))))) # label(t6_real) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3528 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,B) & -v2_xreal_0(B) & v2_xreal_0(A)))))) # label(t4_real) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3529 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-v3_xreal_0(A) & v3_xreal_0(B) & r1_xreal_0(A,B)))))) # label(t3_real) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3530 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-v3_xreal_0(B) & -v2_xreal_0(A) & -r1_xreal_0(A,B)))))) # label(t8_real) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3531 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B)))))) # label(t5_real) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3532 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> B = k7_xcmplx_0(B,k3_xcmplx_0(A,k7_xcmplx_0(np__1,A)))))))) # label(t111_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3533 (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)) -> A = C))))))) # label(t153_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3534 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C)) = k6_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t171_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3535 (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]. 59.86/57.38 3536 (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]. 59.86/57.38 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)) = k3_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(C,B)))))))))) # label(t86_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3538 (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) = k7_xcmplx_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A))))))))) # label(t92_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3539 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 = k7_xcmplx_0(np__1,k3_xcmplx_0(A,B)) & np__0 != B & A != np__0))))) # label(t112_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3540 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> k3_xcmplx_0(k3_xcmplx_0(B,k7_xcmplx_0(np__1,A)),A) = B))))) # label(t110_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3541 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),np__3) = A)) # label(t68_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3542 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = k3_xcmplx_0(B,A) -> A = np__0 | np__1 = B))))) # label(t7_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3543 (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]. 59.86/57.38 3544 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k5_xcmplx_0(B) = k5_xcmplx_0(A) -> A = B))))) # label(t202_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3545 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k2_xcmplx_0(A,B),B) = A)))) # label(t26_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3546 (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)) = k6_xcmplx_0(C,B))))))) # label(t23_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3547 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != B & (all C (v1_xcmplx_0(C) -> A != k7_xcmplx_0(B,C)))))))) # label(t234_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3548 (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]. 59.86/57.38 3549 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(A,k6_xcmplx_0(B,B)) = A)))) # label(t17_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3550 (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]. 59.86/57.38 3551 (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]. 59.86/57.38 3552 (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(A,k3_xcmplx_0(B,C)))))))) # label(t79_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3553 (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]. 59.86/57.38 3554 (all A (v1_xcmplx_0(A) -> (np__0 != A -> np__1 = k7_xcmplx_0(A,A)))) # label(t60_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3555 (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]. 59.86/57.38 3556 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> -(A != np__0 & k2_xcmplx_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) != k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)),k3_xcmplx_0(A,B)) & np__0 != B))))))))) # label(t117_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3557 (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]. 59.86/57.38 3558 (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]. 59.86/57.38 3559 (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]. 59.86/57.38 3560 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A),np__4) = A)) # label(t70_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3561 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k2_xcmplx_0(k2_xcmplx_0(A,B),k4_xcmplx_0(B)))))) # label(t137_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3562 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> 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]. 59.86/57.38 3563 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(A),B)) = k7_xcmplx_0(A,B))))) # label(t191_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3564 (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,k3_xcmplx_0(C,A)),A)))))))) # label(t93_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3565 (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]. 59.86/57.38 3566 (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(C),B),A))))))) # label(t160_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3567 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(A,k3_xcmplx_0(np__2,A)) = k4_xcmplx_0(A))) # label(t187_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 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(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]. 59.86/57.38 3569 (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]. 59.86/57.38 3570 (all A (v1_xcmplx_0(A) -> (A != np__0 -> k7_xcmplx_0(k4_xcmplx_0(A),A) = k4_xcmplx_0(np__1)))) # label(t198_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3571 (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]. 59.86/57.38 3572 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k6_xcmplx_0(A,A),B) = k4_xcmplx_0(B))))) # label(t230_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3573 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(A,B) = A -> np__1 = B | A = np__0))))) # label(t61_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3574 (all A (v1_xcmplx_0(A) -> -(np__1 != A & k4_xcmplx_0(np__1) != A & A = k7_xcmplx_0(np__1,A) & A != np__0))) # label(t200_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3575 (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]. 59.86/57.38 3576 (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]. 59.86/57.38 3577 (all A (v1_xcmplx_0(A) -> -(k4_xcmplx_0(np__1) != A & np__1 != A & np__1 = k3_xcmplx_0(A,A)))) # label(t183_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3578 (all A (v1_xcmplx_0(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)) = A)) # label(t69_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3579 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(A,B) = k6_xcmplx_0(A,k4_xcmplx_0(B)))))) # label(t151_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3580 (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) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),A),B))))))) # label(t166_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3581 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> 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]. 59.86/57.38 3582 (all A (v1_xcmplx_0(A) -> np__0 = k7_xcmplx_0(A,np__0))) # label(t49_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3583 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,B) = k3_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)))))) # label(t177_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3584 (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,B) = k7_xcmplx_0(D,A) -> k3_xcmplx_0(C,A) = k3_xcmplx_0(D,B) | np__0 = B | A = np__0))))))))) # label(t96_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3585 (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]. 59.86/57.38 3586 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,k7_xcmplx_0(np__1,B)) = k3_xcmplx_0(A,B))))) # label(t101_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3587 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(A,k4_xcmplx_0(B)) = k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B)))))) # label(t141_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3588 (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]. 59.86/57.38 3589 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(A,k7_xcmplx_0(A,np__2)) = k7_xcmplx_0(A,np__2))) # label(t122_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3590 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k2_xcmplx_0(A,k4_xcmplx_0(B)) = np__0 -> B = A))))) # label(t136_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3591 (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]. 59.86/57.38 3592 (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(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,C)))))))))) # label(t85_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3593 (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]. 59.86/57.38 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]. 59.86/57.38 3595 (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]. 59.86/57.38 3596 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k4_xcmplx_0(A),B))))) # label(t175_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3597 (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(B,C)) = k2_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t37_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3598 (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]. 59.86/57.38 3599 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> B = k3_xcmplx_0(B,k7_xcmplx_0(A,A))))))) # label(t89_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3600 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,k4_xcmplx_0(B)) = k3_xcmplx_0(k4_xcmplx_0(A),B))))) # label(t176_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3601 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != A & B != np__0 & np__1 != k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(B,A))))))) # label(t113_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3602 (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]. 59.86/57.38 3603 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C))))))) # label(t1_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3604 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k7_xcmplx_0(B,A) = k7_xcmplx_0(C,A) -> np__0 = A | C = B))))))) # label(t53_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3605 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k6_xcmplx_0(A,B),C) = k4_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(B,A),C)))))))) # label(t186_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3606 (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]. 59.86/57.38 3607 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(A,np__2) = k2_xcmplx_0(k7_xcmplx_0(A,np__4),k7_xcmplx_0(A,np__4)))) # label(t72_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3608 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k3_xcmplx_0(A,k2_xcmplx_0(B,k7_xcmplx_0(C,A))) = k2_xcmplx_0(k3_xcmplx_0(A,B),C)))))))) # label(t237_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3609 (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]. 59.86/57.38 3610 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> B = k7_xcmplx_0(B,k7_xcmplx_0(A,A))))))) # label(t51_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3611 (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]. 59.86/57.38 3612 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_xcmplx_0(k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B))) = k3_xcmplx_0(A,B))))) # label(t207_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3613 (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(k6_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)))))))))) # label(t123_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3614 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = k2_xcmplx_0(A,B) -> np__0 = B))))) # label(t3_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3615 (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]. 59.86/57.38 3616 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C)) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t167_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3617 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(A,C) = k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),B))))))) # label(t226_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3618 (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]. 59.86/57.38 3619 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = k7_xcmplx_0(k2_xcmplx_0(A,B),np__2) -> B = A))))) # label(t67_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3620 (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]. 59.86/57.38 3621 (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)) = k7_xcmplx_0(k3_xcmplx_0(A,C),B))))))) # label(t78_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3622 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 = k3_xcmplx_0(A,B) & A != np__0 & B != np__0))))) # label(t6_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3623 (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]. 59.86/57.38 3624 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != A & np__0 != B & np__0 = k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B))))))) # label(t209_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3625 (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(B),C),A) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t147_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3626 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(B,A) = k4_xcmplx_0(k6_xcmplx_0(A,B)))))) # label(t143_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3627 (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]. 59.86/57.38 3628 (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(k2_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)))))))))) # label(t64_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3629 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(np__1,B)) = k7_xcmplx_0(np__1,k3_xcmplx_0(A,B)))))) # label(t103_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3630 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(B) = k6_xcmplx_0(k6_xcmplx_0(A,B),A))))) # label(t232_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3631 (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]. 59.86/57.38 3632 (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,C),k3_xcmplx_0(B,D)) = k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)))))))))) # label(t77_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3633 (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]. 59.86/57.38 3634 (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]. 59.86/57.38 3635 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k2_xcmplx_0(A,k4_xcmplx_0(C)) = k6_xcmplx_0(A,B) -> C = B))))))) # label(t154_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3636 (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]. 59.86/57.38 3637 (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]. 59.86/57.38 3638 (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),k6_xcmplx_0(C,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)))))))))) # label(t45_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3639 (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]. 59.86/57.38 3640 (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,B),k7_xcmplx_0(A,C)))))))) # label(t105_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3641 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(B != np__0 & k7_xcmplx_0(A,B) = np__0 & np__0 != A))))) # label(t50_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3642 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k3_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(C,A)) = k3_xcmplx_0(B,C)))))))) # label(t91_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3643 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A) = k3_xcmplx_0(np__4,A))) # label(t13_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3644 (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]. 59.86/57.38 3645 (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]. 59.86/57.38 3646 (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) = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),C),A))))))) # label(t156_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3647 (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]. 59.86/57.38 3648 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> k3_xcmplx_0(k7_xcmplx_0(B,A),A) = B))))) # label(t88_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3649 (all A (v1_xcmplx_0(A) -> (np__0 = k4_xcmplx_0(A) -> np__0 = A))) # label(t135_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3650 (all A (v1_xcmplx_0(A) -> np__0 = k7_xcmplx_0(A,np__0))) # label(t62_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3651 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))) = A)))) # label(t152_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3652 (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]. 59.86/57.38 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) -> (k6_xcmplx_0(C,D) = k6_xcmplx_0(A,B) -> k6_xcmplx_0(B,D) = k6_xcmplx_0(A,C)))))))))) # label(t24_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3654 (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]. 59.86/57.38 3655 (all A (v1_xcmplx_0(A) -> (np__0 != A -> k4_xcmplx_0(np__1) = k7_xcmplx_0(A,k4_xcmplx_0(A))))) # label(t199_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3656 (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]. 59.86/57.38 3657 (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]. 59.86/57.38 3658 (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]. 59.86/57.38 3659 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k7_xcmplx_0(A,np__2),k7_xcmplx_0(A,np__2)) = A)) # label(t66_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3660 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__1 = k7_xcmplx_0(A,B) -> A = B))))) # label(t58_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3661 (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]. 59.86/57.38 3662 (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) -> k6_xcmplx_0(C,B) = k2_xcmplx_0(A,D)))))))))) # label(t35_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3663 (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]. 59.86/57.38 3664 (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),k6_xcmplx_0(B,C)) = k6_xcmplx_0(A,B))))))) # label(t22_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3665 (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]. 59.86/57.38 3666 (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]. 59.86/57.38 3667 (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]. 59.86/57.38 3668 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(C,k7_xcmplx_0(A,B)) = k7_xcmplx_0(A,k7_xcmplx_0(B,C)))))))) # label(t82_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3669 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,k5_xcmplx_0(B)) = k3_xcmplx_0(A,B))))) # label(t221_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3670 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> 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]. 59.86/57.38 3671 (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]. 59.86/57.38 3672 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> 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]. 59.86/57.38 3673 (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]. 59.86/57.38 3674 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> 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]. 59.86/57.38 3675 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(A != np__0 & B != np__0 & k3_xcmplx_0(A,k5_xcmplx_0(B)) = np__0))))) # label(t208_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3676 (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]. 59.86/57.38 3677 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_xcmplx_0(B,A) = k4_xcmplx_0(A) -> k4_xcmplx_0(np__1) = B | A = np__0))))) # label(t182_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3678 (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) -> A = k4_xcmplx_0(B) | k7_xcmplx_0(C,A) = k7_xcmplx_0(k2_xcmplx_0(C,D),k2_xcmplx_0(A,B)) | B = np__0 | np__0 = A))))))))) # label(t201_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 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(k6_xcmplx_0(A,B),C),B) = k2_xcmplx_0(A,C))))))) # label(t227_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3680 (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]. 59.86/57.38 3681 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k6_xcmplx_0(A,B)) = k2_xcmplx_0(k4_xcmplx_0(A),B))))) # label(t162_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3682 (all A (v1_xcmplx_0(A) -> k5_xcmplx_0(k7_xcmplx_0(np__1,A)) = A)) # label(t219_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3683 (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]. 59.86/57.38 3684 (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]. 59.86/57.38 3685 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,k4_xcmplx_0(B)) = k7_xcmplx_0(k4_xcmplx_0(A),B))))) # label(t193_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3686 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> B = k7_xcmplx_0(k3_xcmplx_0(B,A),A)))))) # label(t90_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3687 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k5_xcmplx_0(B) = k7_xcmplx_0(np__1,A) -> A = B))))) # label(t220_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 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) -> -(B != np__0 & k6_xcmplx_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) != k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)),k3_xcmplx_0(A,B)) & np__0 != A))))))))) # label(t131_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3689 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_xcmplx_0(k3_xcmplx_0(A,k5_xcmplx_0(B))) = k3_xcmplx_0(k5_xcmplx_0(A),B))))) # label(t206_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3690 (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(C,B) -> A = C))))))) # label(t19_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3691 (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]. 59.86/57.38 3692 (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]. 59.86/57.38 3693 (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]. 59.86/57.38 3694 (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]. 59.86/57.38 3695 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__1 = k3_xcmplx_0(A,B) -> k5_xcmplx_0(B) = A))))) # label(t211_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3696 (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]. 59.86/57.38 3697 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(B,A) = k7_xcmplx_0(np__1,k7_xcmplx_0(A,B)))))) # label(t57_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3698 (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(A,B),C))))))) # label(t83_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3699 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__1 = k3_xcmplx_0(A,B) -> A = k7_xcmplx_0(np__1,B)))))) # label(t74_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3700 (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]. 59.86/57.38 3701 (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]. 59.86/57.38 3702 (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]. 59.86/57.38 3703 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)))))) # label(t192_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3704 (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) -> C = A))))))) # label(t2_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3705 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(A,A) = np__0)) # label(t14_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3706 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(A,k4_xcmplx_0(np__1)) = k4_xcmplx_0(A))) # label(t194_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3707 (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) -> k7_xcmplx_0(C,B) = k7_xcmplx_0(D,A) | B = np__0 | np__0 = A))))))))) # label(t95_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3708 (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(k2_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),k2_xcmplx_0(C,D)))))))))) # label(t46_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3709 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> k7_xcmplx_0(A,k7_xcmplx_0(A,B)) = B))))) # label(t52_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3710 (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(A,k7_xcmplx_0(C,B)))))))) # label(t80_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3711 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(A,B) = k4_xcmplx_0(np__1) -> A = k4_xcmplx_0(B) & B = k4_xcmplx_0(A)))))) # label(t196_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3712 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k4_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C)) = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t170_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3713 (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]. 59.86/57.38 3714 (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]. 59.86/57.38 3715 (all A (v1_xcmplx_0(A) -> (A != np__0 -> k3_xcmplx_0(A,k7_xcmplx_0(np__1,A)) = np__1))) # label(t107_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3716 (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]. 59.86/57.38 3717 (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(A,B),C)) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t168_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3718 (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]. 59.86/57.38 3719 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__1 = k3_xcmplx_0(A,k5_xcmplx_0(B)) -> A = B))))) # label(t210_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3720 (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]. 59.86/57.38 3721 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(A,A) = k3_xcmplx_0(np__2,A))) # label(t11_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3722 (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]. 59.86/57.38 3723 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(B,A),C),A) = k6_xcmplx_0(B,k7_xcmplx_0(C,A))))))))) # label(t128_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3724 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_xcmplx_0(A) = k7_xcmplx_0(A,B) -> np__0 = A | k4_xcmplx_0(np__1) = B))))) # label(t197_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3725 (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]. 59.86/57.38 3726 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(np__1,A) = k7_xcmplx_0(np__1,B) -> A = B))))) # label(t59_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3727 (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]. 59.86/57.38 3728 (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]. 59.86/57.38 3729 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(k5_xcmplx_0(A),B) = k5_xcmplx_0(k3_xcmplx_0(A,B)))))) # label(t223_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3730 (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]. 59.86/57.38 3731 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),A),B))))) # label(t139_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3732 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k7_xcmplx_0(C,B),A) = k3_xcmplx_0(k7_xcmplx_0(A,B),C))))))) # label(t76_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3733 $T # label(t212_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3734 (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) = k7_xcmplx_0(D,B) -> A = np__0 | np__0 = B | k3_xcmplx_0(C,B) = k7_xcmplx_0(D,A)))))))))) # label(t97_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3735 (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(B,C)) = k2_xcmplx_0(A,k6_xcmplx_0(C,B)))))))) # label(t38_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3736 (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]. 59.86/57.38 3737 (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]. 59.86/57.38 3738 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k3_xcmplx_0(A,k2_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))) = k2_xcmplx_0(B,C)))))))) # label(t115_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3739 (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]. 59.86/57.38 3740 (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]. 59.86/57.38 3741 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(np__1)))) # label(t195_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3742 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(B,A))))) # label(t215_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3743 (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) = k2_xcmplx_0(k6_xcmplx_0(C,B),A))))))) # label(t30_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3744 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(A,np__2) = k7_xcmplx_0(k2_xcmplx_0(A,A),np__4))) # label(t73_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 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) -> 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]. 59.86/57.38 3746 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k4_xcmplx_0(A),B) = k6_xcmplx_0(k4_xcmplx_0(B),A))))) # label(t144_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 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) -> k6_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,D)),k7_xcmplx_0(C,D)) = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),D))))))))) # label(t125_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3748 (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]. 59.86/57.38 3749 (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) -> B = C))))))) # label(t20_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3750 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = k6_xcmplx_0(A,B) -> np__0 = B))))) # label(t16_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3751 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(A != np__0 & B != np__0 & k2_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) != k3_xcmplx_0(k2_xcmplx_0(A,B),k5_xcmplx_0(k3_xcmplx_0(A,B)))))))) # label(t213_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3752 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,k2_xcmplx_0(B,C)) = k6_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t36_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3753 (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) -> A = np__0 | B = C))))))) # label(t5_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3754 (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),B) = k6_xcmplx_0(k2_xcmplx_0(A,B),C))))))) # label(t29_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3755 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != B & k3_xcmplx_0(k6_xcmplx_0(B,A),k5_xcmplx_0(k3_xcmplx_0(A,B))) != k6_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) & np__0 != A))))) # label(t214_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3756 (all A (v1_xcmplx_0(A) -> -(np__0 != A & A = k5_xcmplx_0(A) & A != np__1 & k4_xcmplx_0(np__1) != A))) # label(t225_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3757 (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]. 59.86/57.38 3758 (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(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)),A) = k2_xcmplx_0(B,C)))))))) # label(t116_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3759 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_xcmplx_0(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)))))) # label(t205_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3760 (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]. 59.86/57.38 3761 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(B,A) = k7_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)))))) # label(t216_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3762 (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) -> A = np__0 | A = B | k7_xcmplx_0(C,A) = k7_xcmplx_0(k6_xcmplx_0(C,D),k6_xcmplx_0(A,B)) | np__0 = B))))))))) # label(t124_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3763 (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]. 59.86/57.38 3764 (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]. 59.86/57.38 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) -> k3_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)))))))))) # label(t42_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3766 (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),k6_xcmplx_0(C,D)) = k3_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C)))))))))) # label(t41_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3767 (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),k6_xcmplx_0(C,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)))))))))) # label(t47_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3768 (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]. 59.86/57.38 3769 (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(k5_xcmplx_0(B),k5_xcmplx_0(A))))))) # label(t87_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3770 (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(k7_xcmplx_0(C,A),B) | r1_xreal_0(np__0,A)))))))) # label(t80_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3771 (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(np__0,B) | r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B))))))))) # label(t123_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3772 (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]. 59.86/57.38 3773 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(B,k4_xcmplx_0(A)) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t197_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3774 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,A) & (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,A) & -r1_xreal_0(B,C))))))))) # label(t7_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3775 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,np__0) & r1_xreal_0(k3_xcmplx_0(A,B),np__0)))))) # label(t131_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.38 3776 (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]. 59.86/57.39 3777 (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]. 59.86/57.39 3778 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) & -r1_xreal_0(B,k4_xcmplx_0(A)) & -r1_xreal_0(np__0,A)))))) # label(t209_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3779 (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,A) & r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) & r1_xreal_0(C,D)))))))))) # label(t16_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3780 (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]. 59.86/57.39 3781 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k5_xcmplx_0(A),np__0) & -r1_xreal_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]. 59.86/57.39 3782 (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]. 59.86/57.39 3783 (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),np__1) & -r1_xreal_0(A,B)))))) # label(t190_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3784 (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]. 59.86/57.39 3785 (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(np__0,B) & -r1_xreal_0(A,np__0)) & -r1_xreal_0(np__0,k3_xcmplx_0(A,B))))))) # label(t135_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3786 (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]. 59.86/57.39 3787 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (np__0 = k2_xcmplx_0(A,B) & r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) -> np__0 = A))))) # label(t29_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 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]. 59.86/57.39 3789 (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]. 59.86/57.39 3790 (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(k3_xcmplx_0(C,A),B) & r1_xreal_0(C,k7_xcmplx_0(B,A))))))))) # label(t85_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3791 (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(C,A) & -r1_xreal_0(D,B) & r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & r1_xreal_0(np__0,A)))))))))) # label(t98_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3792 (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]. 59.86/57.39 3793 (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]. 59.86/57.39 3794 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(k7_xcmplx_0(A,B),np__0) & -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,np__0)) & -(-r1_xreal_0(np__0,A) & -r1_xreal_0(np__0,B))))))) # label(t146_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3795 (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,k3_xcmplx_0(B,A)) & r1_xreal_0(B,k7_xcmplx_0(C,A))))))))) # label(t84_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3796 (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]. 59.86/57.39 3797 (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(k5_xcmplx_0(A),k5_xcmplx_0(B))))))) # label(t88_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3798 (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]. 59.86/57.39 3799 (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,B) & 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(D,C) & -r1_xreal_0(np__1,A)))))))))) # label(t180_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3800 (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,k3_xcmplx_0(A,B))))))) # label(t134_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3801 (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]. 59.86/57.39 3802 (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(k5_xcmplx_0(A),np__0)))))) # label(t93_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3803 (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(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A)) & -r1_xreal_0(A,np__0)))))))) # label(t76_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3804 (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]. 59.86/57.39 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(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(C,B) & r1_xreal_0(A,np__1) & r1_xreal_0(np__0,A)))))))))) # label(t177_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3806 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k7_xcmplx_0(A,np__2),np__0) & -r1_xreal_0(A,np__0)))) # label(t217_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3807 (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]. 59.86/57.39 3808 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(B),A) -> r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) | r1_xreal_0(np__0,A)))))) # label(t206_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3809 (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(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B))))))))))) # label(t109_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3810 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,k4_xcmplx_0(A)) -> r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) | r1_xreal_0(A,np__0)))))) # label(t203_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3811 (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]. 59.86/57.39 3812 (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,np__0) & -r1_xreal_0(C,B) & r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B))))))))) # label(t102_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3813 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,k4_xcmplx_0(A)) & r1_xreal_0(k2_xcmplx_0(B,A),np__0)))))) # label(t64_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3814 (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]. 59.86/57.39 3815 (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(C,D),k3_xcmplx_0(A,B)) & r1_xreal_0(B,D) & -r1_xreal_0(C,A) & -r1_xreal_0(B,np__0)))))))))) # label(t99_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3816 (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]. 59.86/57.39 3817 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k4_xcmplx_0(np__1),A) & r1_xreal_0(k5_xcmplx_0(A),k4_xcmplx_0(np__1))))) # label(t216_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3818 (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]. 59.86/57.39 3819 (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__1) & r1_xreal_0(np__0,A) -> 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]. 59.86/57.39 3820 (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]. 59.86/57.39 3821 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) & -r1_xreal_0(A,B)))))) # label(t89_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3822 (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]. 59.86/57.39 3823 (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]. 59.86/57.39 3824 (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,np__0) & -r1_xreal_0(C,B) & r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C))))))))) # label(t78_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3825 (all A (v1_xreal_0(A) -> (all B (v1_xreal_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(t141_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3826 (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]. 59.86/57.39 3827 (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,k7_xcmplx_0(A,B))))))) # label(t138_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3828 (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(k5_xcmplx_0(A),np__0)))))) # label(t91_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3829 (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]. 59.86/57.39 3830 (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]. 59.86/57.39 3831 (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(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) & -r1_xreal_0(np__0,B) & -r1_xreal_0(A,np__0)))))))) # label(t101_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3832 (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(B,np__0) & -r1_xreal_0(np__0,A)))))) # label(t143_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 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]. 59.86/57.39 3834 (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]. 59.86/57.39 3835 (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]. 59.86/57.39 3836 (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]. 59.86/57.39 3837 (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]. 59.86/57.39 3838 (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]. 59.86/57.39 3839 (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]. 59.86/57.39 3840 (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]. 59.86/57.39 3841 (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(np__0,A) -> r1_xreal_0(np__0,B) | r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C))))))))) # label(t121_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3842 (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),k2_xcmplx_0(C,D)) <-> r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(D,B))))))))))) # label(t23_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3843 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (exists C (v1_xreal_0(C) & -r1_xreal_0(C,A) & -r1_xreal_0(C,B))))))) # label(t5_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3844 (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(k7_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & -r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A))))))))))) # label(t112_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3845 (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]. 59.86/57.39 3846 (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))))))))))) # label(t15_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3847 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(A,np__0) -> np__0 = k3_xcmplx_0(A,B)))))) # label(t128_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3848 (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]. 59.86/57.39 3849 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,A) & r1_xreal_0(np__0,k6_xcmplx_0(A,B))))))) # label(t51_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3850 (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]. 59.86/57.39 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(A,np__0) & -r1_xreal_0(B,np__0) & 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))))))))))) # label(t108_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3852 (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(B,np__0) & -r1_xreal_0(np__0,A)))))))))) # label(t116_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3853 (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]. 59.86/57.39 3854 (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]. 59.86/57.39 3855 (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(np__1,k7_xcmplx_0(A,B))))))) # label(t191_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3856 (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]. 59.86/57.39 3857 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(B,np__1) -> r1_xreal_0(k3_xcmplx_0(A,B),A)))))) # label(t155_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3858 (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,A) & r1_xreal_0(C,np__0) & r1_xreal_0(D,C) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D))))))))))) # label(t69_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3859 (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(B,k4_xcmplx_0(A)) & -r1_xreal_0(A,B)))))) # label(t96_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3860 (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,k7_xcmplx_0(B,C)) & -r1_xreal_0(np__1,C)))) -> r1_xreal_0(A,B)))))) # label(t211_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3861 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (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(A,np__0) -> r1_xreal_0(k3_xcmplx_0(A,B),np__1)))))) # label(t167_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3862 (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]. 59.86/57.39 3863 (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]. 59.86/57.39 3864 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k2_xcmplx_0(B,np__1),A) & r1_xreal_0(A,B)))))) # label(t147_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3865 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,k3_xcmplx_0(A,B)) & -r1_xreal_0(np__1,B) & -r1_xreal_0(A,np__0)))))) # label(t159_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3866 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(B),k4_xcmplx_0(A)) <-> r1_xreal_0(A,B)))))) # label(t26_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3867 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__1,A) & r1_xreal_0(np__1,B) -> r1_xreal_0(np__1,k3_xcmplx_0(A,B))))))) # label(t161_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3868 (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]. 59.86/57.39 3869 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k6_xcmplx_0(np__1,A),np__0) & -r1_xreal_0(np__1,A)))) # label(t151_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3870 (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]. 59.86/57.39 3871 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(B,np__1) & r1_xreal_0(A,k3_xcmplx_0(A,B))))))) # label(t160_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3872 (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]. 59.86/57.39 3873 (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]. 59.86/57.39 3874 (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(A,np__1) & r1_xreal_0(B,C) & r1_xreal_0(D,C) -> 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]. 59.86/57.39 3875 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) & -r1_xreal_0(A,k4_xcmplx_0(B)) & -r1_xreal_0(A,np__0)))))) # label(t200_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3876 (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(B,C) & 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(A,np__0)))))))))) # label(t179_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3877 (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(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))))))))) # label(t74_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3878 (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]. 59.86/57.39 3879 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> A != k7_xcmplx_0(B,C))) & np__0 != B))))) # label(t227_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3880 (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(A,C) & r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & -r1_xreal_0(D,B) & -r1_xreal_0(B,np__0)))))))))) # label(t100_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3881 (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(k3_xcmplx_0(C,A),B) & r1_xreal_0(k7_xcmplx_0(B,A),C)))))))) # label(t86_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3882 (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]. 59.86/57.39 3883 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,k3_xcmplx_0(C,B)) & -r1_xreal_0(np__1,C) & -r1_xreal_0(C,np__0)))) -> r1_xreal_0(A,np__0)))))) # label(t171_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 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(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(A,np__0) | r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) | r1_xreal_0(np__0,B)))))))))) # label(t106_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 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(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) | r1_xreal_0(np__0,B) | r1_xreal_0(np__0,A)))))))))) # label(t105_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3886 (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(B,k7_xcmplx_0(C,A)) | r1_xreal_0(A,np__0)))))))) # label(t79_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3887 (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(k3_xcmplx_0(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(np__0,B)))))))))) # label(t114_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3888 (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]. 59.86/57.39 3889 (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]. 59.86/57.39 3890 (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]. 59.86/57.39 3891 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(A,k7_xcmplx_0(A,np__3))))) # label(t223_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3892 (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(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)))))))))) # label(t117_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3893 (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]. 59.86/57.39 3894 (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]. 59.86/57.39 3895 (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(C,np__0) -> r1_xreal_0(k3_xcmplx_0(B,C),k3_xcmplx_0(A,C))))))))) # label(t67_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3896 (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]. 59.86/57.39 3897 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,A) & r1_xreal_0(k6_xcmplx_0(B,A),np__0)))))) # label(t52_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3898 (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(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) | r1_xreal_0(B,np__0)))))))) # label(t122_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3899 (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]. 59.86/57.39 3900 (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]. 59.86/57.39 3901 (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(k7_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & -r1_xreal_0(B,np__0) & -r1_xreal_0(A,np__0)))))))))) # label(t113_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3902 (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(np__1,k7_xcmplx_0(B,A))))))) # label(t194_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3903 (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(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)))))))))) # label(t115_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3904 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(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)) & r1_xreal_0(np__0,A)))))) # label(t97_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3905 (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(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),B) -> A = np__0 | 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]. 59.86/57.39 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(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]. 59.86/57.39 3907 (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(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A))))))))) # label(t75_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3908 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(B,A) & r1_xreal_0(k7_xcmplx_0(B,A),np__1)))))) # label(t189_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3909 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & k2_xcmplx_0(A,B) = np__0 & r1_xreal_0(B,np__0) -> np__0 = A))))) # label(t30_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3910 (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(k3_xcmplx_0(A,B),np__0)))))) # label(t133_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3911 (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]. 59.86/57.39 3912 (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(B,A)) & -r1_xreal_0(A,np__0)))))) # label(t193_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3913 (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(k3_xcmplx_0(B,D),k3_xcmplx_0(A,C)) & -r1_xreal_0(np__0,C) & r1_xreal_0(B,A) & -r1_xreal_0(np__0,A)))))))))) # label(t72_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3914 (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(k4_xcmplx_0(A),B) & r1_xreal_0(B,A)))))) # label(t95_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3915 (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(k7_xcmplx_0(B,C),k7_xcmplx_0(B,A)) | r1_xreal_0(A,np__0)))))))) # label(t120_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3916 (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]. 59.86/57.39 3917 (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]. 59.86/57.39 3918 (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]. 59.86/57.39 3919 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(np__1,B) -> r1_xreal_0(k3_xcmplx_0(A,B),A)))))) # label(t156_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3920 (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]. 59.86/57.39 3921 (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(B,k2_xcmplx_0(A,C))))))))) # label(t40_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3922 (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(A),k5_xcmplx_0(B)) & r1_xreal_0(B,A)))))) # label(t94_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3923 (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]. 59.86/57.39 3924 (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(B,D) & r1_xreal_0(B,C) & 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]. 59.86/57.39 3925 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(B,np__0) -> r1_xreal_0(np__0,k3_xcmplx_0(A,B))))))) # label(t130_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3926 (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]. 59.86/57.39 3927 (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]. 59.86/57.39 3928 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (exists C (-r1_xreal_0(B,C) & -r1_xreal_0(A,C) & v1_xreal_0(C))))))) # label(t6_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3929 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(B,k6_xcmplx_0(A,np__1)) & r1_xreal_0(A,B)))))) # label(t149_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3930 (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(B,k6_xcmplx_0(C,A))))))))) # label(t54_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3931 (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]. 59.86/57.39 3932 (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]. 59.86/57.39 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(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]. 59.86/57.39 3934 (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]. 59.86/57.39 3935 (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(B,np__0) & -r1_xreal_0(np__0,A)) & -r1_xreal_0(np__0,k7_xcmplx_0(A,B))))))) # label(t145_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3936 (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]. 59.86/57.39 3937 (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]. 59.86/57.39 3938 (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]. 59.86/57.39 3939 (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(A,np__1) -> 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]. 59.86/57.39 3940 (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]. 59.86/57.39 3941 (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]. 59.86/57.39 3942 (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,B),k7_xcmplx_0(A,C)) & -r1_xreal_0(B,C) & -r1_xreal_0(np__0,B)))))))) # label(t103_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3943 (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]. 59.86/57.39 3944 (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]. 59.86/57.39 3945 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(np__1,B) & r1_xreal_0(k3_xcmplx_0(A,B),A)))))) # label(t158_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3946 (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]. 59.86/57.39 3947 (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]. 59.86/57.39 3948 (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,k2_xcmplx_0(A,B))))))) # label(t63_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3949 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k3_xcmplx_0(A,B),np__0) & -r1_xreal_0(np__0,B) & -r1_xreal_0(np__0,A)))))) # label(t132_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3950 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(k4_xcmplx_0(A),B) & r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) & -r1_xreal_0(np__0,A)))))) # label(t201_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3951 (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(t48_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3952 (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]. 59.86/57.39 3953 (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,C) & r1_xreal_0(np__0,D) & k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) = np__0 & np__0 != C & np__0 != A & r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A)))))))))) # label(t73_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3954 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(A),B) -> r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) | r1_xreal_0(np__0,A)))))) # label(t205_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3955 (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,B) & 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(A,np__1)))))))))) # label(t178_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3956 (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]. 59.86/57.39 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(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & -r1_xreal_0(np__0,B) & -r1_xreal_0(A,np__0)))))))))) # label(t110_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3958 (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,k6_xcmplx_0(B,A)) & -r1_xreal_0(C,B)))))))) # label(t53_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3959 (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(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A))))))))) # label(t71_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3960 (all A (v1_xreal_0(A) -> -(r1_xreal_0(A,k7_xcmplx_0(A,np__2)) & -r1_xreal_0(A,np__0)))) # label(t218_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3961 (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(D,C) & r1_xreal_0(A,B)))))))))) # label(t17_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3962 (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(np__0,k5_xcmplx_0(A)) | r1_xreal_0(A,B)))))) # label(t92_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3963 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(B != A & r1_xreal_0(k6_xcmplx_0(B,A),np__0) & r1_xreal_0(k6_xcmplx_0(A,B),np__0)))))) # label(t57_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3964 (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(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t196_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3965 (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(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))))))) # label(t202_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3966 (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]. 59.86/57.39 3967 (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(C,A),k7_xcmplx_0(D,B)) | r1_xreal_0(B,np__0) | r1_xreal_0(A,np__0)))))))))) # label(t104_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3968 (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]. 59.86/57.39 3969 (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]. 59.86/57.39 3970 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,k4_xcmplx_0(B)) & r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) & -r1_xreal_0(np__0,A)))))) # label(t210_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3971 (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(C,B) & r1_xreal_0(A,np__0)))))))) # label(t38_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 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(np__0,C) & r1_xreal_0(C,D) & r1_xreal_0(A,B) & r1_xreal_0(np__0,A) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D))))))))))) # label(t68_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3973 (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]. 59.86/57.39 3974 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k3_xcmplx_0(A,B),A) & -r1_xreal_0(B,np__1)))))) # label(t157_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3975 (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(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D))))))))))) # label(t9_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3976 (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]. 59.86/57.39 3977 (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]. 59.86/57.39 3978 (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]. 59.86/57.39 3979 (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) & -(A = np__0 & C = np__0) & -(np__0 = B & np__0 = C) & -(A = np__1 & B = np__0) & k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(k6_xcmplx_0(np__1,A),C)) = np__0 & r1_xreal_0(np__0,C) & r1_xreal_0(np__0,B)))))))) # label(t172_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3980 (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(k6_xcmplx_0(C,A),B) & -r1_xreal_0(np__0,A)))))))) # label(t56_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3981 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,k4_xcmplx_0(np__1)) & r1_xreal_0(k4_xcmplx_0(np__1),B) & r1_xreal_0(np__1,k3_xcmplx_0(A,B)) & r1_xreal_0(B,np__0) & r1_xreal_0(A,np__0)))))) # label(t168_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3982 (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(k2_xcmplx_0(B,A),C)))))))) # label(t37_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3983 (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]. 59.86/57.39 3984 (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(np__0,A) | r1_xreal_0(C,k7_xcmplx_0(B,A))))))))) # label(t82_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3985 (all A (v1_xreal_0(A) -> -(r1_xreal_0(np__0,A) & -r1_xreal_0(k4_xcmplx_0(A),np__0)) & -(r1_xreal_0(k4_xcmplx_0(A),np__0) & -r1_xreal_0(np__0,A)))) # label(t60_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3986 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(B,np__1) & np__1 = k3_xcmplx_0(A,B) & r1_xreal_0(A,np__1) & r1_xreal_0(np__0,A) -> np__1 = A))))) # label(t152_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3987 (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(np__1,k3_xcmplx_0(A,B)) & -r1_xreal_0(np__1,A)))))) # label(t164_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3988 (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(k6_xcmplx_0(C,A),B) & r1_xreal_0(A,np__0)))))))) # label(t55_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 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(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) & -r1_xreal_0(A,np__0)))))))))) # label(t119_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3990 (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,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C))) -> 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]. 59.86/57.39 3991 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(k3_xcmplx_0(A,B),np__0) & -(-r1_xreal_0(np__0,B) & -r1_xreal_0(np__0,A)) & -(-r1_xreal_0(B,np__0) & -r1_xreal_0(A,np__0))))))) # label(t136_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3992 (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,A) & r1_xreal_0(C,D) & r1_xreal_0(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C))))))))))) # label(t10_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3993 (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]. 59.86/57.39 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(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) & -r1_xreal_0(np__0,A)))))))))) # label(t118_xreal_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3995 (all A all B (v4_ordinal2(B) -> ((exists C (A = C & -r1_xreal_0(B,C) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_0_axioms(B))))) # label(fraenkel_a_1_0_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3996 $T # label(t2_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.39 3997 (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]. 59.86/57.39 3998 $T # label(t1_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 3999 $T # label(t8_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4000 (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) -> (exists D ((exists E (v1_xreal_0(E) & r2_hidden(D,A) & -(r1_xreal_0(C,E) & r1_xreal_0(D,C)) & r2_hidden(E,B))) & v1_xreal_0(D))))) & (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r2_hidden(C,A) & r2_hidden(D,B) -> r1_xreal_0(C,D))))))))))) # label(t26_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4001 $T # label(t3_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4002 (all A (v1_xreal_0(A) -> -((all B (v1_xreal_0(B) -> np__1 != k3_xcmplx_0(A,B))) & np__0 != A))) # label(t20_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4003 $T # label(t21_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4004 $T # label(t4_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4005 $T # label(t7_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4006 $T # label(t22_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4007 (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]. 59.86/57.40 4008 $T # label(t15_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4009 $T # label(t12_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4010 $T # label(t23_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4011 (all A (v4_ordinal2(A) -> a_1_0_axioms(A) = A)) # label(t30_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4012 $T # label(t6_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4013 (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]. 59.86/57.40 4014 $T # label(t24_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4015 $T # label(t27_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4016 $T # label(t14_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4017 $T # label(t13_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4018 $T # label(t11_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4019 $T # label(t9_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4020 $T # label(t18_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4021 $T # label(t10_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4022 $T # label(t25_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4023 $T # label(t17_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4024 $T # label(t5_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4025 $T # label(t16_axioms) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4026 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k5_real_1(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k5_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4027 $T # label(t6_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4028 $T # label(t76_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4029 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k3_xcmplx_0(A,B) = k4_real_1(A,B))) # label(redefinition_k4_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4030 $T # label(d1_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4031 $T # label(t12_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4032 $T # label(t85_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4033 $T # label(t72_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4034 $T # label(t57_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4035 $T # label(t36_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4036 $T # label(t45_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4037 $T # label(t11_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4038 $T # label(t84_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4039 $T # label(t56_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4040 $T # label(t69_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4041 $T # label(t68_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4042 $T # label(t30_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4043 $T # label(t19_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4044 $T # label(t3_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4045 $T # label(t47_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4046 (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]. 59.86/57.40 4047 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k4_real_1(A,B),k1_numbers))) # label(dt_k4_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4048 $T # label(t52_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4049 $T # label(t91_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4050 $T # label(t79_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4051 $T # label(t87_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4052 (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]. 59.86/57.40 4053 $T # label(t50_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4054 $T # label(t41_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4055 $T # label(t32_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4056 $T # label(t17_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4057 $T # label(t78_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4058 (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]. 59.86/57.40 4059 $T # label(t61_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4060 $T # label(t27_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4061 $T # label(t43_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4062 $T # label(t71_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4063 $T # label(t53_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4064 (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(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)))))))))) # label(t73_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4065 $T # label(d2_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4066 (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]. 59.86/57.40 4067 $T # label(t10_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4068 $T # label(t44_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4069 $T # label(t88_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4070 $T # label(t18_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4071 $T # label(t81_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4072 $T # label(t67_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4073 $T # label(t5_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4074 $T # label(t70_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4075 (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]. 59.86/57.40 4076 (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]. 59.86/57.40 4077 $T # label(t39_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4078 $T # label(t4_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4079 $T # label(t38_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4080 $T # label(t64_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4081 $T # label(t90_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4082 $T # label(t37_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4083 $T # label(d3_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4084 $T # label(t21_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4085 $T # label(t28_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4086 $T # label(t59_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4087 $T # label(t49_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4088 (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]. 59.86/57.40 4089 $T # label(t22_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4090 $T # label(t42_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4091 $T # label(t48_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4092 (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))) & -(r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) & (r1_xreal_0(A,B) & -r1_xreal_0(D,C) | -r1_xreal_0(B,A) & r1_xreal_0(C,D))))))))))) # label(t92_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4093 $T # label(t58_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4094 (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]. 59.86/57.40 4095 $T # label(t82_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4096 $T # label(t14_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4097 $T # label(t62_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4098 $T # label(t20_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4099 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k2_xcmplx_0(A,B) = k3_real_1(A,B))) # label(redefinition_k3_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4100 $T # label(t65_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4101 (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]. 59.86/57.40 4102 $T # label(t89_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4103 $T # label(t16_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4104 $T # label(t66_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4105 $T # label(t54_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4106 $T # label(d4_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4107 $T # label(t60_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4108 $T # label(t75_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4109 (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]. 59.86/57.40 4110 $T # label(t2_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4111 $T # label(t13_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4112 $T # label(t51_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4113 $T # label(t55_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4114 $T # label(t1_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4115 (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]. 59.86/57.40 4116 $T # label(t77_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4117 $T # label(t15_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4118 $T # label(t33_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4119 $T # label(t29_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4120 $T # label(t40_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4121 $T # label(t46_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4122 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k3_real_1(A,B),k1_numbers))) # label(dt_k3_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4123 $T # label(t9_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4124 $T # label(t63_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4125 $T # label(t31_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4126 $T # label(t80_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4127 (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]. 59.86/57.40 4128 $T # label(t24_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4129 $T # label(t35_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4130 $T # label(t83_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4131 $T # label(t8_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4132 $T # label(t23_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4133 (all A (m1_subset_1(A,k1_numbers) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc1_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4134 $T # label(t86_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4135 (all A (v1_xreal_0(A) -> A = k6_xcmplx_0(A,np__0))) # label(t25_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4136 $T # label(t7_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4137 (all A (m1_subset_1(A,k1_numbers) -> k5_xcmplx_0(A) = k2_real_1(A))) # label(redefinition_k2_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4138 $T # label(t34_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4139 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k4_real_1(A,B) = k4_real_1(B,A))) # label(commutativity_k4_real_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4140 (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]. 59.86/57.40 4141 (all A (v1_xcmplx_0(A) -> k5_square_1(k4_xcmplx_0(A)) = k5_square_1(A))) # label(t61_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4142 (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(A,B) <-> r1_xreal_0(A,k1_square_1(B,C))))))))) # label(t39_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4143 $T # label(t88_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4144 (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]. 59.86/57.40 4145 $T # label(t9_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4146 (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(k5_square_1(A),k5_square_1(B))))))) # label(t77_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4147 $T # label(t24_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4148 (all A (m1_subset_1(A,k1_numbers) -> k9_square_1(A) = k8_square_1(A))) # label(redefinition_k9_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4149 (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(np__1,k6_xcmplx_0(A,B)) = k7_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(k5_square_1(A),k5_square_1(B)))))))) # label(t71_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4150 (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]. 59.86/57.40 4151 $T # label(t27_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4152 $T # label(t58_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4153 $T # label(t21_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4154 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,k3_xcmplx_0(A,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))))))) # label(t25_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4155 $T # label(t13_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4156 $T # label(t28_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4157 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> k7_xcmplx_0(np__1,k6_xcmplx_0(k8_square_1(B),k8_square_1(A))) = k7_xcmplx_0(k2_xcmplx_0(k8_square_1(B),k8_square_1(A)),k6_xcmplx_0(B,A)) | r1_xreal_0(B,A)))))) # label(t108_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4158 $T # label(t100_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4159 (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(np__1,k2_xcmplx_0(A,B)) = k7_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(k5_square_1(A),k5_square_1(B)))))))) # label(t70_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4160 $T # label(t7_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4161 $T # label(t31_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4162 $T # label(t33_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4163 (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]. 59.86/57.40 4164 $T # label(t18_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4165 (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]. 59.86/57.40 4166 $T # label(t8_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4167 (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]. 59.86/57.40 4168 (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]. 59.86/57.40 4169 (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]. 59.86/57.40 4170 $T # label(t3_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4171 $T # label(t80_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4172 (all A (m1_subset_1(A,k2_numbers) -> v1_xcmplx_0(A))) # label(cc1_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4173 (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]. 59.86/57.40 4174 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,np__0) -> k8_square_1(k5_square_1(A)) = k4_xcmplx_0(A)))) # label(t90_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4175 (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]. 59.86/57.40 4176 (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) -> B = k1_square_1(A,B)))))) # label(d1_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4177 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> k7_xcmplx_0(k6_xcmplx_0(k8_square_1(B),k8_square_1(A)),k6_xcmplx_0(B,A)) = k7_xcmplx_0(np__1,k2_xcmplx_0(k8_square_1(B),k8_square_1(A))) | r1_xreal_0(B,A)))))) # label(t106_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4178 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> k8_square_1(k5_square_1(A)) = A))) # label(t89_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4179 (all A (v1_xreal_0(A) -> -(A != np__0 & r1_xreal_0(k5_square_1(A),np__0)))) # label(t74_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4180 $T # label(t98_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4181 (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]. 59.86/57.40 4182 $T # label(t47_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4183 $T # label(t42_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4184 $T # label(t4_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4185 (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]. 59.86/57.40 4186 (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]. 59.86/57.40 4187 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k5_square_1(A)) & v1_xreal_0(k5_square_1(A)))) # label(fc2_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4188 $T # label(t41_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4189 (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(k8_square_1(A),k8_square_1(B))))))) # label(t94_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4190 (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]. 59.86/57.40 4191 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> A = k3_square_1(A,A))) # label(idempotence_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4192 $T # label(t52_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4193 (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(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]. 59.86/57.40 4194 $T # label(t17_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4195 $T # label(t36_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4196 $T # label(t91_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4197 (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]. 59.86/57.40 4198 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k2_xcmplx_0(k1_square_1(A,B),k2_square_1(A,B)) = k2_xcmplx_0(A,B))))) # label(t53_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4199 $T # label(t15_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4200 (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]. 59.86/57.40 4201 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> A = k2_square_1(A,A))) # label(idempotence_k2_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4202 $T # label(t81_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4203 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k8_square_1(A),np__0)))) # label(t93_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4204 (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]. 59.86/57.40 4205 $T # label(t5_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4206 (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]. 59.86/57.40 4207 (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]. 59.86/57.40 4208 (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]. 59.86/57.40 4209 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (p2_s1_square_1(B) & p1_s1_square_1(A) -> r1_xreal_0(A,B)))))) -> (exists A (v1_xreal_0(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)))))))) # label(s1_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4210 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> k1_square_1(A,A) = A)) # label(idempotence_k1_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4211 $T # label(t29_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4212 $T # label(t1_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4213 (all A (v1_xreal_0(A) -> v1_xreal_0(k8_square_1(A)))) # label(dt_k8_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4214 $T # label(t30_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4215 (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(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]. 59.86/57.40 4216 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,A) & r1_xreal_0(k8_square_1(B),k8_square_1(A)) & r1_xreal_0(np__0,A)))))) # label(t95_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4217 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_square_1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k5_square_1(A),k5_square_1(B)))))) # label(t68_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4218 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> k2_square_1(A,B) = k2_square_1(B,A))) # label(commutativity_k2_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4219 (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]. 59.86/57.40 4220 (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]. 59.86/57.40 4221 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & A = k5_square_1(B) <-> B = k8_square_1(A))))))) # label(d4_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4222 (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(k5_square_1(B),k5_square_1(A))))))) # label(t78_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4223 (all A (v1_xreal_0(A) -> (np__0 = k8_square_1(A) & r1_xreal_0(np__0,A) -> np__0 = A))) # label(t92_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4224 (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]. 59.86/57.40 4225 $T # label(t48_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4226 (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]. 59.86/57.40 4227 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__1) & r1_xreal_0(k5_square_1(A),A)))) # label(t76_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4228 (all A (v1_xcmplx_0(A) -> k5_square_1(k6_xcmplx_0(A,np__1)) = k2_xcmplx_0(k6_xcmplx_0(k5_square_1(A),k3_xcmplx_0(np__2,A)),np__1))) # label(t66_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4229 (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]. 59.86/57.40 4230 (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]. 59.86/57.40 4231 $T # label(t44_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4232 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> A = k2_square_1(A,B) | k2_square_1(A,B) = B)))) # label(t49_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4233 $T # label(t23_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4234 $T # label(dt_k5_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4235 (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]. 59.86/57.40 4236 $T # label(t79_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4237 $T # label(t45_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4238 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k1_square_1(A,B) = B | A = k1_square_1(A,B))))) # label(t38_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4239 (all A (m1_subset_1(A,k1_numbers) -> k5_square_1(A) = k7_square_1(A))) # label(redefinition_k7_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4240 $T # label(t32_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4241 (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]. 59.86/57.40 4242 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> k1_square_1(B,A) = k1_square_1(A,B))) # label(commutativity_k1_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4243 $T # label(t12_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4244 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k3_square_1(A,B) = k1_square_1(A,B))) # label(redefinition_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4245 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k2_square_1(A,k1_square_1(A,B)) = A)))) # label(t54_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4246 (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]. 59.86/57.40 4247 $T # label(t22_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4248 $T # label(t26_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4249 $T # label(t34_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4250 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k5_square_1(A),k5_square_1(B)) = k3_xcmplx_0(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B)))))) # label(t67_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4251 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k4_square_1(B,A) = k4_square_1(A,B))) # label(commutativity_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4252 (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]. 59.86/57.40 4253 $T # label(t87_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4254 $T # label(t6_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4255 $T # label(t20_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4256 $T # label(t10_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4257 (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]. 59.86/57.40 4258 $T # label(t43_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4259 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__1) & r1_xreal_0(np__1,k7_xcmplx_0(np__1,A))))) # label(t2_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4260 $T # label(t62_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4261 $T # label(t37_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4262 $T # label(t11_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4263 $T # label(t19_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4264 (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(B) = k8_square_1(A) -> B = A))))) # label(t96_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4265 $T # label(t14_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4266 (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]. 59.86/57.40 4267 $T # label(t16_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4268 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k5_square_1(A)))) # label(fc1_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4269 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) -> 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]. 59.86/57.40 4270 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k4_square_1(A,B) = k2_square_1(A,B))) # label(redefinition_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4271 (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]. 59.86/57.40 4272 $T # label(t16_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4273 $T # label(t17_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4274 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,B) & r1_nat_1(A,k2_xcmplx_0(B,C)) -> r1_nat_1(A,C)))))))) # label(t57_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4275 $T # label(t4_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4276 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_nat_1(A,B) <-> k3_xcmplx_0(A,k3_nat_1(B,A)) = B))))) # label(t49_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4277 $T # label(t35_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4278 (all A (v4_ordinal2(A) -> r1_xreal_0(np__0,A))) # label(t18_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4279 (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]. 59.86/57.40 4280 (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) | np__0 = C))))))) # label(t66_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4281 (exists A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & -v1_xboole_0(A) & v3_ordinal1(A))) # label(rc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4282 (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]. 59.86/57.40 4283 (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]. 59.86/57.40 4284 (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]. 59.86/57.40 4285 $T # label(t33_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4286 (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(k2_xcmplx_0(A,B),C) = k4_nat_1(B,C)))))))) # label(t67_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4287 (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]. 59.86/57.40 4288 $T # label(t12_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4289 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> A = k5_nat_1(A,A))) # label(idempotence_k5_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4290 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]. 59.86/57.40 4291 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k3_xcmplx_0(A,B) = np__1 -> np__1 = B & A = np__1))))) # label(t40_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4292 (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]. 59.86/57.40 4293 $T # label(t25_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4294 (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) -> (k6_nat_1(A,B) = C <-> r1_nat_1(C,A) & r1_nat_1(C,B) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_nat_1(D,A) & r1_nat_1(D,B) -> r1_nat_1(D,C))))))))))) # label(d5_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4295 (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]. 59.86/57.40 4296 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(-r1_xreal_0(np__2,A) & np__0 != A & np__1 != A))) # label(t71_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4297 $T # label(t31_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4298 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k6_nat_1(B,A) = k6_nat_1(A,B))) # label(commutativity_k6_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4299 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k2_nat_1(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k2_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4300 $T # label(t45_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4301 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,C) & r1_nat_1(A,B) -> r1_nat_1(A,k2_xcmplx_0(B,C))))))))) # label(t55_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4302 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (np__0 != A -> B = k3_nat_1(k3_xcmplx_0(A,B),A)))))) # label(t68_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4303 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(A != np__0 & p1_s7_nat_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(p1_s7_nat_1(B) & -r1_xreal_0(A,B))))))) & (exists A (m2_subset_1(A,k1_numbers,k5_numbers) & p1_s7_nat_1(A))) -> p1_s7_nat_1(np__0) # label(s7_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4304 $T # label(t44_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4305 $T # label(t11_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4306 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k5_nat_1(A,B) = k5_nat_1(B,A))) # label(commutativity_k5_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4307 $T # label(t15_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4308 (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]. 59.86/57.40 4309 (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]. 59.86/57.40 4310 (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]. 59.86/57.40 4311 (exists A (-v1_xboole_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v2_ordinal1(A) & m1_subset_1(A,k5_numbers))) # label(rc3_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4312 (all A (v4_ordinal2(A) -> -(np__0 != A & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k1_nat_1(B,np__1) != A))))) # label(t22_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4313 (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]. 59.86/57.40 4314 (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]. 59.86/57.40 4315 $T # label(t34_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4316 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B != np__0 -> k3_nat_1(k2_nat_1(A,B),B) = A))))) # label(t72_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4317 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(r1_xreal_0(B,k2_xcmplx_0(A,np__1)) & B != A & k2_xcmplx_0(A,np__1) != B & r1_xreal_0(A,B)))))) # label(t27_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4318 $T # label(t6_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4319 (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) -> (r1_nat_1(B,C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_nat_1(A,D) & r1_nat_1(B,D) -> r1_nat_1(C,D)))) & r1_nat_1(A,C) <-> k5_nat_1(A,B) = C))))))) # label(d4_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4320 $T # label(t30_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4321 (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]. 59.86/57.40 4322 (all A (v4_ordinal2(A) -> np__0 = k4_nat_1(A,np__2) | k4_nat_1(A,np__2) = np__1)) # label(t62_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4323 (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]. 59.86/57.40 4324 (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]. 59.86/57.40 4325 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (k6_xcmplx_0(A,k3_xcmplx_0(D,C)) = B & k4_nat_1(A,C) = np__0 -> k4_nat_1(B,C) = np__0))))))))) # label(t65_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4326 (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]. 59.86/57.40 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 (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & k1_nat_1(k2_nat_1(A,C),D) = B & -r1_xreal_0(A,D)))))))))) # label(t42_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4328 $T # label(t3_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4329 (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]. 59.86/57.40 4330 (exists A (v1_xreal_0(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & -v1_xboole_0(A))) # label(rc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4331 $T # label(t36_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4332 $T # label(t9_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4333 -r1_xreal_0(f3_s8_nat_1,np__0) & -r1_xreal_0(f2_s8_nat_1,f3_s8_nat_1) & 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)))) & f3_s8_nat_1 = f1_s8_nat_1(np__1) -> (exists A (m2_subset_1(A,k1_numbers,k5_numbers) & np__0 = f1_s8_nat_1(k1_nat_1(A,np__1)) & f1_s8_nat_1(A) = k6_nat_1(f2_s8_nat_1,f3_s8_nat_1))) # label(s8_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4334 (all A (v4_ordinal2(A) -> v4_ordinal2(A) & v1_xcmplx_0(A) & -v3_xreal_0(A) & v1_xreal_0(A))) # label(cc3_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4335 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k1_nat_1(A,B) = k1_nat_1(B,A))) # label(commutativity_k1_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4336 (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]. 59.86/57.40 4337 $T # label(t14_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4338 (all A (v4_ordinal2(A) -> -(r1_xreal_0(A,np__0) & np__0 != A))) # label(t19_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4339 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,B) & r1_nat_1(B,C) -> r1_nat_1(A,C)))))))) # label(t51_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4340 (all A (v4_ordinal2(A) -> k4_nat_1(A,A) = np__0)) # label(t77_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4341 (all A (v4_ordinal2(A) -> (-r1_xreal_0(np__1,A) -> A = np__0))) # label(t39_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4342 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4343 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,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]. 59.86/57.40 4344 (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]. 59.86/57.40 4345 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xreal_0(A) & -v3_xreal_0(A) & v1_xcmplx_0(A))) # label(cc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4346 (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 (p1_s6_nat_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (p1_s6_nat_1(B) -> r1_xreal_0(B,A)))) & m2_subset_1(A,k1_numbers,k5_numbers))) # label(s6_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.40 4347 (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]. 59.86/57.40 4348 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (np__0 = k4_nat_1(A,B) -> k1_nat_1(k3_nat_1(A,B),k3_nat_1(C,B)) = k3_nat_1(k2_xcmplx_0(A,C),B)))))))) # label(t69_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4349 (all A (v4_ordinal2(A) -> r1_nat_1(A,np__0) & r1_nat_1(np__1,A))) # label(t53_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4350 $T # label(t32_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4351 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (-(-(C = np__0 & np__0 = B) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(-r1_xreal_0(B,D) & k2_xcmplx_0(k3_xcmplx_0(B,C),D) = A)))) <-> k3_nat_1(A,B) = C))))))) # label(d1_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4352 (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]. 59.86/57.41 4353 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,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]. 59.86/57.41 4354 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_nat_1(A,B) & r1_nat_1(B,A) -> A = B))))) # label(t52_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4355 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> r1_nat_1(A,A))) # label(reflexivity_r1_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4356 $T # label(t1_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4357 (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]. 59.86/57.41 4358 $T # label(t13_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4359 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_xcmplx_0(A,B) = np__0 -> B = np__0 & np__0 = A))))) # label(t23_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4360 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(A != np__0 & r1_xreal_0(k2_xcmplx_0(B,A),B)))))) # label(t41_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4361 (all A (v4_ordinal2(A) -> (p1_s2_nat_1(A) -> p1_s2_nat_1(k2_xcmplx_0(A,np__1))))) & p1_s2_nat_1(np__0) -> (all A (v4_ordinal2(A) -> p1_s2_nat_1(A))) # label(s2_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4362 (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]. 59.86/57.41 4363 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(A,k4_nat_1(B,A))))))) # label(t46_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4364 $T # label(t10_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4365 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (p1_s3_nat_1(A,B) <-> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(A = k1_nat_1(C,np__1) & p1_s3_nat_1(C,D) & B = f2_s3_nat_1(A,D)))))) & -(A = np__0 & f1_s3_nat_1 = 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]. 59.86/57.41 4366 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_nat_1(A,B) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & B = k3_xcmplx_0(A,C)))))))) # label(d3_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4367 (all A all B (-v1_xboole_0(B) & v4_ordinal2(B) & v4_ordinal2(A) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc4_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4368 $T # label(t7_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4369 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_nat_1(B,A) -> r1_xreal_0(B,A) | r1_xreal_0(A,np__0)))))) # label(t54_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4370 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> v4_ordinal2(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4371 (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]. 59.86/57.41 4372 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k2_nat_1(B,A) = k2_nat_1(A,B))) # label(commutativity_k2_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4373 (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]. 59.86/57.41 4374 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v2_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v3_ordinal1(A))) # label(cc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4375 (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]. 59.86/57.41 4376 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(B != A & r1_xreal_0(B,A) & -r1_xreal_0(k1_nat_1(B,np__1),A)))))) # label(t70_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4377 $T # label(t48_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4378 (all A (v4_ordinal2(A) -> np__0 = k4_nat_1(np__0,A))) # label(t78_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4379 (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) -> C = D & F = E | r1_xreal_0(B,F) | r1_xreal_0(B,E)))))))))))))) # label(t43_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4380 $T # label(t50_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4381 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & -v1_xboole_0(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc3_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4382 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(r1_xreal_0(A,k2_xcmplx_0(B,np__1)) & -r1_xreal_0(A,B) & k2_xcmplx_0(B,np__1) != A))))) # label(t26_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4383 $T # label(t24_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4384 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k4_nat_1(A,B) = C <-> -(-(B = np__0 & C = np__0) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(k2_xcmplx_0(k3_xcmplx_0(B,D),C) = A & -r1_xreal_0(B,C)))))))))))) # label(d2_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4385 $T # label(t8_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4386 $T # label(t5_nat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4387 (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]. 59.86/57.41 4388 (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]. 59.86/57.41 4389 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k5_int_1(A,B)))) # label(dt_k5_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4390 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r1_xreal_0(np__1,C) & C = k6_xcmplx_0(B,A)))) & -r1_xreal_0(B,A)))))) # label(t78_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4391 (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]. 59.86/57.41 4392 (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]. 59.86/57.41 4393 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4394 (all A (v1_xreal_0(A) -> k4_int_1(A) = k3_int_1(A))) # label(redefinition_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4395 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4396 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4397 (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]. 59.86/57.41 4398 (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]. 59.86/57.41 4399 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_int_1(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc8_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4400 (all A (m1_subset_1(A,k5_numbers) -> v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc5_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4401 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc1_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4402 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4403 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4404 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc4_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4405 (exists A (v1_int_1(A) & p1_s5_int_1(A))) & (all A (v1_int_1(A) -> (p1_s5_int_1(A) -> r1_xreal_0(f1_s5_int_1,A)))) -> (exists A (p1_s5_int_1(A) & (all B (v1_int_1(B) -> (p1_s5_int_1(B) -> r1_xreal_0(A,B)))) & v1_int_1(A))) # label(s5_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4406 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4407 (all A (v1_int_1(A) <-> r2_hidden(A,k4_numbers))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4408 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4409 (all A (v1_xreal_0(A) -> v1_xreal_0(k3_int_1(A)) & v1_xcmplx_0(k3_int_1(A)))) # label(fc10_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4410 (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]. 59.86/57.41 4411 (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]. 59.86/57.41 4412 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_xcmplx_0(k1_int_1(A),B) = k1_int_1(k2_xcmplx_0(A,B)))))) # label(t51_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4413 (all A (v1_int_1(A) -> v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc3_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4414 (all A (v1_int_1(A) -> r1_int_1(np__0,A,A) & r1_int_1(A,np__0,A))) # label(t33_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4415 (all A (v1_xreal_0(A) -> k1_int_1(k1_int_1(A)) = k1_int_1(A))) # label(t63_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4416 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4417 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4418 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4419 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> k1_int_1(A) = k2_int_1(A)))) # label(t59_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4420 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k4_int_1(A),np__0) & -v1_int_1(A)) & -(-r1_xreal_0(k4_int_1(A),np__0) & v1_int_1(A)))) # label(t72_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4421 (all A (v1_xreal_0(A) -> k1_int_1(A) = k2_int_1(k1_int_1(A)))) # label(t65_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4422 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4423 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k1_int_1(A)) & m2_subset_1(k1_int_1(A),k1_numbers,k5_numbers) & m2_subset_1(k2_int_1(A),k1_numbers,k5_numbers) & r1_xreal_0(np__0,k2_int_1(A))))) # label(t80_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4424 (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]. 59.86/57.41 4425 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4426 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)))) # label(fc6_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4427 (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]. 59.86/57.41 4428 (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]. 59.86/57.41 4429 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & m1_subset_1(A,k1_numbers))) # label(rc1_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4430 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4431 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(k2_xcmplx_0(A,np__1),B) & r1_xreal_0(A,B) <-> B = k2_int_1(A)))))) # label(d5_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4432 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4433 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (k1_int_1(A) = B <-> -r1_xreal_0(B,k6_xcmplx_0(A,np__1)) & r1_xreal_0(B,A)))))) # label(d4_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4434 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4435 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4436 (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]. 59.86/57.41 4437 (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]. 59.86/57.41 4438 (all A (v1_xreal_0(A) -> k2_int_1(A) = k2_int_1(k2_int_1(A)))) # label(t64_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4439 (all A (v1_int_1(A) -> np__0 = k5_int_1(A,np__0))) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4440 (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]. 59.86/57.41 4441 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4442 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4443 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> A = k1_int_1(A)))) # label(t47_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4444 (all A (v1_xreal_0(A) -> (k4_int_1(A) = np__0 <-> v1_int_1(A)))) # label(t71_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4445 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4446 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(A,k6_xcmplx_0(C,B),D) <-> r1_int_1(k2_xcmplx_0(A,B),C,D)))))))))) # label(t40_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4447 (all A (v1_int_1(A) -> (p1_s2_int_1(A) & r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(k2_xcmplx_0(A,np__1))))) & p1_s2_int_1(f1_s2_int_1) -> (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(A)))) # label(s2_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4448 (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]. 59.86/57.41 4449 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) <-> r1_int_1(k6_xcmplx_0(A,C),B,C)))))))) # label(t43_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4450 (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]. 59.86/57.41 4451 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4452 (all A (v1_xreal_0(A) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> B != A & A != k1_real_1(B))) & v1_int_1(A)))) # label(t8_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4453 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4454 (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]. 59.86/57.41 4455 (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]. 59.86/57.41 4456 (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]. 59.86/57.41 4457 (all A (v1_xreal_0(A) -> -(-v1_int_1(A) & r1_xreal_0(k2_int_1(A),A)) & -(-r1_xreal_0(k2_int_1(A),A) & v1_int_1(A)))) # label(t55_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4458 (all A (v1_xreal_0(A) -> (all B (v4_ordinal2(B) -> (A = B | k4_xcmplx_0(B) = A -> v1_int_1(A)))))) # label(t7_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4459 (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]. 59.86/57.41 4460 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (np__1 = k3_xcmplx_0(A,B) <-> A = k1_real_1(np__1) & k1_real_1(np__1) = B | B = np__1 & A = np__1))))) # label(t22_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4461 (all A (v1_int_1(A) -> (r1_xreal_0(A,f1_s3_int_1) & p1_s3_int_1(A) -> p1_s3_int_1(k6_xcmplx_0(A,np__1))))) & p1_s3_int_1(f1_s3_int_1) -> (all A (v1_int_1(A) -> (r1_xreal_0(A,f1_s3_int_1) -> p1_s3_int_1(A)))) # label(s3_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4462 (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]. 59.86/57.41 4463 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4464 (all A (v1_int_1(A) -> np__0 = k6_int_1(A,A))) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4465 (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]. 59.86/57.41 4466 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4467 (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]. 59.86/57.41 4468 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)))) # label(fc9_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4469 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4470 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> ((exists C (v1_int_1(C) & B = k3_xcmplx_0(A,C))) <-> r2_int_1(A,B)))))) # label(d9_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4471 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(A,C) & r1_xreal_0(A,B) -> B = C | r1_xreal_0(k2_xcmplx_0(A,np__1),C) | r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))))) # label(t45_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4472 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4473 (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]. 59.86/57.41 4474 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4475 (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]. 59.86/57.41 4476 (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]. 59.86/57.41 4477 (all A (v1_xreal_0(A) -> (k1_int_1(A) = k2_int_1(A) <-> k2_xcmplx_0(k1_int_1(A),np__1) != k2_int_1(A)))) # label(t66_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4478 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4479 (all A (v1_xreal_0(A) -> k6_xcmplx_0(A,k1_int_1(A)) = k3_int_1(A))) # label(d6_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4480 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,k1_int_1(A)) & v1_int_1(A)) & -(r1_xreal_0(A,k1_int_1(A)) & -v1_int_1(A)))) # label(t48_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4481 (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]. 59.86/57.41 4482 (all A (A = k4_numbers <-> (all B (-(all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k1_real_1(C) != B & B != C)) <-> r2_hidden(B,A))))) # label(d1_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4483 (exists A (p1_s6_int_1(A) & v1_int_1(A))) & (all A (v1_int_1(A) -> (p1_s6_int_1(A) -> r1_xreal_0(A,f1_s6_int_1)))) -> (exists A (v1_int_1(A) & (all B (v1_int_1(B) -> (p1_s6_int_1(B) -> r1_xreal_0(B,A)))) & p1_s6_int_1(A))) # label(s6_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4484 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4485 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4486 (all A (v1_xreal_0(A) -> k2_xcmplx_0(k1_int_1(A),k4_int_1(A)) = A)) # label(t68_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4487 (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]. 59.86/57.41 4488 (all A (m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(A) & -v3_xreal_0(A) & v1_int_1(A) & v1_xreal_0(A) & v4_ordinal2(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4489 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4490 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k3_xcmplx_0(A,D),k3_xcmplx_0(B,E),C)))))))))))) # label(t39_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4491 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4492 (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]. 59.86/57.41 4493 (all A (v1_int_1(A) -> (np__0 != A -> np__1 = k5_int_1(A,A)))) # label(t76_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4494 (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]. 59.86/57.41 4495 (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]. 59.86/57.41 4496 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4497 (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]. 59.86/57.41 4498 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B = np__0 -> np__0 = k6_int_1(A,B)) & (np__0 != B -> k6_xcmplx_0(A,k3_xcmplx_0(k5_int_1(A,B),B)) = k6_int_1(A,B)))))) # label(d8_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4499 p1_s4_int_1(f1_s4_int_1) & (all A (v1_int_1(A) -> (p1_s4_int_1(A) -> p1_s4_int_1(k2_xcmplx_0(A,np__1)) & p1_s4_int_1(k6_xcmplx_0(A,np__1))))) -> (all A (v1_int_1(A) -> p1_s4_int_1(A))) # label(s4_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4500 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4501 (all A (v1_int_1(A) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4502 (all A (v1_xreal_0(A) -> -(v1_int_1(A) & -r1_xreal_0(k2_int_1(A),k1_int_1(A))) & -(r1_xreal_0(k2_int_1(A),k1_int_1(A)) & -v1_int_1(A)))) # label(t60_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4503 (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]. 59.86/57.41 4504 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(B,A) & r1_xreal_0(C,A) -> r1_xreal_0(B,k6_xcmplx_0(A,np__1)) | B = C | r1_xreal_0(C,k6_xcmplx_0(A,np__1))))))))) # label(t44_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4505 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k1_real_1(np__1) = k3_xcmplx_0(A,B) <-> np__1 = B & k1_real_1(np__1) = A | B = k1_real_1(np__1) & A = np__1))))) # label(t23_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4506 (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]. 59.86/57.41 4507 (all A (v1_xreal_0(A) -> (np__0 != A -> np__1 = k1_int_1(k7_xcmplx_0(A,A))))) # label(t74_int_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4508 (all A all B (v1_rat_1(B) & m1_subset_1(A,k5_numbers) -> 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(fc14_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4509 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (k1_rat_1(A) = k2_rat_1(B) & k1_rat_1(B) = k2_rat_1(A) -> B = k7_xcmplx_0(np__1,A) & -r1_xreal_0(A,np__0)) & (k7_xcmplx_0(np__1,A) = B -> k1_rat_1(A) = k2_rat_1(B) & k2_rat_1(A) = k1_rat_1(B) | r1_xreal_0(A,np__0)))))) # label(t88_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4510 $T # label(t20_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4511 $T # label(t52_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4512 (all A (v1_rat_1(A) -> k1_rat_1(k4_xcmplx_0(A)) = k1_rat_1(A) & k4_xcmplx_0(k2_rat_1(A)) = k2_rat_1(k4_xcmplx_0(A)))) # label(t87_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4513 $T # label(t78_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4514 $T # label(t54_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4515 (all A all B (m1_subset_1(B,k5_numbers) & v1_rat_1(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_rat_1(k2_xcmplx_0(A,B)))) # label(fc10_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4516 $T # label(t59_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4517 $T # label(t51_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4518 $T # label(t32_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4519 (all A (k3_numbers = A <-> (all B ((exists C ((exists D (v1_int_1(D) & B = k7_xcmplx_0(C,D))) & v1_int_1(C))) <-> r2_hidden(B,A))))) # label(d1_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4520 (exists A (v1_xreal_0(A) & v1_rat_1(A) & v1_xcmplx_0(A) & m1_subset_1(A,k1_numbers))) # label(rc1_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4521 (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 (k2_nat_1(F,D) = A & k3_xcmplx_0(E,D) = B & m2_subset_1(F,k1_numbers,k5_numbers))))) & -r1_xreal_0(D,np__1)))) -> A = np__0 | A = k1_rat_1(C) & B = k2_rat_1(C)))))))) # label(t63_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4522 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_rat_1(C) -> -(np__0 != B & (all D (v1_int_1(D) -> -(k3_xcmplx_0(k2_rat_1(C),D) = A & B = k3_xcmplx_0(k1_rat_1(C),D)))) & k7_xcmplx_0(A,B) = C))))))) # label(t61_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4523 (all A (v1_rat_1(A) -> (exists B (v1_int_1(B) & (exists C (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)))))) & np__0 != C & m2_subset_1(C,k1_numbers,k5_numbers))))))) # label(t25_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4524 $T # label(t70_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4525 $T # label(t19_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4526 (all A (v1_rat_1(A) -> v1_int_1(k2_rat_1(A)))) # label(dt_k2_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4527 $T # label(t4_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4528 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (k1_rat_1(B) = k4_xcmplx_0(k2_rat_1(A)) & k2_rat_1(B) = k1_real_1(k1_rat_1(A)) -> B = k7_xcmplx_0(np__1,A) & -r1_xreal_0(np__0,A)) & (k7_xcmplx_0(np__1,A) = 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)))))) # label(t89_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4529 (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]. 59.86/57.41 4530 $T # label(t39_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4531 $T # label(t5_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4532 (all A (v1_rat_1(A) -> A = k7_xcmplx_0(k2_rat_1(A),k1_rat_1(A)) & A = k3_xcmplx_0(k2_rat_1(A),k2_real_1(k1_rat_1(A))) & k3_xcmplx_0(k2_real_1(k1_rat_1(A)),k2_rat_1(A)) = A)) # label(t37_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4533 $T # label(t35_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4534 $T # label(t11_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4535 $T # label(t12_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4536 $T # label(t85_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4537 (all A all B (v1_rat_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(fc2_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4538 $T # label(t53_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4539 (all A (v1_rat_1(A) -> (np__1 = A <-> k2_rat_1(A) = k1_rat_1(A)))) # label(t47_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4540 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (k1_rat_1(A) = k1_rat_1(B) & k2_rat_1(A) = k2_rat_1(B) -> B = A))))) # label(t84_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4541 (exists A v1_rat_1(A)) # label(rc2_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4542 (all A (v1_int_1(A) -> v1_rat_1(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc2_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4543 $T # label(t23_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4544 (all A (v1_rat_1(A) -> k2_rat_1(A) = k3_xcmplx_0(k1_rat_1(A),A))) # label(d4_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4545 (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]. 59.86/57.41 4546 (all A (v1_xreal_0(A) -> (all B (v1_rat_1(B) -> (r1_xreal_0(A,B) <-> r1_xreal_0(k3_xcmplx_0(A,k1_rat_1(B)),k2_rat_1(B))))))) # label(t81_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4547 (all A all B (v1_rat_1(B) & v1_int_1(A) -> 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]. 59.86/57.41 4548 (all A (v1_rat_1(A) -> (A = np__0 <-> k2_rat_1(A) = np__0))) # label(t36_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4549 $T # label(t43_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4550 (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]. 59.86/57.41 4551 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v1_rat_1(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc17_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4552 (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]. 59.86/57.41 4553 (all A all B (v1_rat_1(B) & v1_int_1(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_rat_1(k2_xcmplx_0(A,B)))) # label(fc7_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4554 (all A (v1_rat_1(A) -> v1_xreal_0(k4_xcmplx_0(A)) & v1_rat_1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc16_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4555 (all A (v1_rat_1(A) -> (exists B ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & np__0 != C & k7_xcmplx_0(B,C) = A)) & v1_int_1(B))))) # label(t24_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4556 $T # label(t10_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4557 $T # label(t74_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4558 (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]. 59.86/57.41 4559 (all A (v1_rat_1(A) -> (r1_xreal_0(A,np__1) <-> r1_xreal_0(k2_rat_1(A),k1_rat_1(A))))) # label(t73_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4560 $T # label(t71_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4561 (all A (v1_rat_1(A) -> (r1_xreal_0(A,k1_real_1(np__1)) <-> r1_xreal_0(k2_rat_1(A),k1_real_1(k1_rat_1(A)))))) # label(t65_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4562 $T # label(t17_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4563 (all A (v1_rat_1(A) -> (v1_int_1(A) -> A = k2_rat_1(A) & k1_rat_1(A) = np__1))) # label(t40_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4564 (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]. 59.86/57.41 4565 (all A all B (v1_rat_1(B) & m1_subset_1(A,k5_numbers) -> 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(fc13_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4566 (all A all B (v1_int_1(B) & v1_rat_1(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_rat_1(k2_xcmplx_0(A,B)))) # label(fc4_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4567 (all A (v1_rat_1(A) -> (k2_rat_1(A) = A | k1_rat_1(A) = np__1 -> v1_int_1(A)))) # label(t41_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4568 (all A all B (m1_subset_1(B,k5_numbers) & v1_rat_1(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_rat_1(k6_xcmplx_0(A,B)))) # label(fc11_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4569 $T # label(t69_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4570 (all A -(v1_rat_1(A) & (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> -(np__0 != C & k7_xcmplx_0(B,C) = A))))))) # label(t3_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4571 (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]. 59.86/57.41 4572 $T # label(t26_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4573 (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(B,A) & -r1_xreal_0(k2_rat_1(B),k3_xcmplx_0(A,k1_rat_1(B)))))))) # label(t80_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4574 (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]. 59.86/57.41 4575 (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]. 59.86/57.41 4576 (all A (v1_rat_1(A) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(np__0,k2_rat_1(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]. 59.86/57.41 4577 $T # label(t15_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4578 (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(np__1),A) & -r1_xreal_0(k1_real_1(k1_rat_1(A)),k2_rat_1(A))))) # label(t64_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4579 $T # label(t28_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4580 $T # label(t82_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4581 (all A all B (v1_int_1(B) & 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(fc6_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4582 (all A all B (v1_int_1(A) & v1_rat_1(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_rat_1(k6_xcmplx_0(A,B)))) # label(fc8_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4583 $T # label(t55_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4584 (all A (v1_rat_1(A) -> -(-r1_xreal_0(k1_rat_1(A),np__1) & v1_int_1(A)) & -(r1_xreal_0(k1_rat_1(A),np__1) & -v1_int_1(A)))) # label(t45_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4585 (all A (v1_rat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> ((all C (v1_int_1(C) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k7_xcmplx_0(C,D) = A -> r1_xreal_0(B,D) | D = np__0))))) & (exists C (k7_xcmplx_0(C,B) = A & v1_int_1(C))) & np__0 != B <-> B = k1_rat_1(A)))))) # label(d3_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4586 (all A -(r2_hidden(A,k3_numbers) & (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> -(np__0 != C & A = k7_xcmplx_0(B,C)))))))) # label(t1_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4587 $T # label(t2_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4588 $T # label(t75_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4589 (all A all B (m1_subset_1(B,k5_numbers) & v1_rat_1(A) -> 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(fc12_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4590 $T # label(t79_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4591 (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]. 59.86/57.41 4592 (all A all B (v1_rat_1(B) & v1_rat_1(A) -> 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(fc1_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4593 $T # label(t33_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4594 $T # label(t56_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4595 (all A (v1_rat_1(A) -> v1_rat_1(k5_xcmplx_0(A)))) # label(t21_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4596 $T # label(t58_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4597 (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]. 59.86/57.41 4598 (all A (v1_rat_1(A) -> (np__0 != A -> k7_xcmplx_0(k2_rat_1(A),A) = k1_rat_1(A)))) # label(t38_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4599 (all A (v1_rat_1(A) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc1_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4600 (all A all B (m1_subset_1(A,k5_numbers) & v1_rat_1(B) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_rat_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc15_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4601 $T # label(t31_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4602 (all A (v1_rat_1(A) -> (k2_rat_1(A) = A <-> np__1 = k1_rat_1(A)))) # label(t42_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4603 (all A (v1_rat_1(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_rat_1(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)))) # label(fc18_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4604 (all A all B (v1_int_1(B) & 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(fc5_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4605 $T # label(t9_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4606 $T # label(t8_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4607 $T # label(t68_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4608 (all A (v1_rat_1(A) -> (k4_xcmplx_0(k2_rat_1(A)) = k1_rat_1(A) <-> A = k1_real_1(np__1)))) # label(t49_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4609 $T # label(t83_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4610 $T # label(t14_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4611 (all A (v1_int_1(A) -> v1_rat_1(A))) # label(t7_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4612 (all A (v1_rat_1(A) -> (r1_xreal_0(np__0,A) -> m2_subset_1(A,k1_numbers,k5_numbers) | k1_rat_1(A) != np__1 & k2_rat_1(A) != A))) # label(t44_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4613 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_rat_1(C) -> -(A != np__0 & C = k7_xcmplx_0(B,A) & (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)))))))))) # label(t60_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4614 $T # label(t18_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4615 (all A (v1_rat_1(A) -> (r1_xreal_0(A,np__0) <-> r1_xreal_0(k2_rat_1(A),np__0)))) # label(t77_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4616 (all A (v1_rat_1(A) -> (k1_real_1(k1_rat_1(A)) = k2_rat_1(A) <-> A = k1_real_1(np__1)))) # label(t48_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4617 (all A (v1_rat_1(A) <-> r2_hidden(A,k3_numbers))) # label(d2_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4618 $T # label(t57_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4619 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,A) & (all C (v1_rat_1(C) -> -(-r1_xreal_0(B,C) & -r1_xreal_0(C,A))))))))) # label(t22_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4620 $T # label(t13_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4621 (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]. 59.86/57.41 4622 (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 (m2_subset_1(D,k1_numbers,k5_numbers) & k1_rat_1(A) = k2_nat_1(D,B) & k3_xcmplx_0(C,B) = k2_rat_1(A)))))))))) # label(t62_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4623 (all A ((exists B ((exists C (v1_int_1(C) & k7_xcmplx_0(B,C) = A)) & v1_int_1(B))) -> v1_rat_1(A))) # label(t6_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4624 (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(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)))))))) # label(t86_rat_1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4625 (all A (v1_funct_1(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) -> (k34_binop_2 = A <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k10_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C)))))))) # label(d10_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4626 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k11_binop_2(B,A) = k11_binop_2(A,B))) # label(commutativity_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4627 (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]. 59.86/57.41 4628 (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]. 59.86/57.41 4629 (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]. 59.86/57.41 4630 (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]. 59.86/57.41 4631 (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]. 59.86/57.41 4632 (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]. 59.86/57.41 4633 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k3_binop_2(A,B) = k3_binop_2(B,A))) # label(commutativity_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4634 (all 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) & 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) = k5_binop_2(B,C))))) <-> k29_binop_2 = A))) # label(d5_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4635 (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) -> (A = k36_binop_2 <-> (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) = k12_binop_2(B,C)))))))) # label(d12_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4636 (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) -> k4_binop_2(B,C) = k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C))))) <-> A = k28_binop_2))) # label(d4_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4637 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k15_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.41 4638 (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]. 59.86/57.41 4639 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k9_binop_2(B,A) = k9_binop_2(A,B))) # label(commutativity_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4640 (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))))) <-> k35_binop_2 = A))) # label(d11_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4641 (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]. 59.86/57.42 4642 (all A (v1_funct_2(A,k2_numbers,k2_numbers) & m2_relset_1(A,k2_numbers,k2_numbers) & v1_funct_1(A) -> (k26_binop_2 = A <-> (all B (m1_subset_1(B,k2_numbers) -> k2_binop_2(B) = k8_funct_2(k2_numbers,k2_numbers,A,B)))))) # label(d2_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4643 (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]. 59.86/57.42 4644 (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]. 59.86/57.42 4645 (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]. 59.86/57.42 4646 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> k20_binop_2(B,A) = k20_binop_2(A,B))) # label(commutativity_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4647 (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]. 59.86/57.42 4648 (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) = k3_binop_2(B,C))))) <-> A = k27_binop_2))) # label(d3_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4649 (all A (m1_subset_1(A,k1_numbers) -> A = k8_binop_2(k8_binop_2(A)))) # label(involutiveness_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4650 (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) -> (A = k47_binop_2 <-> (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)))))))) # label(d23_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4651 (all A (m1_subset_1(A,k1_numbers) -> k7_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4652 (all A (v1_funct_2(A,k1_numbers,k1_numbers) & m2_relset_1(A,k1_numbers,k1_numbers) & v1_funct_1(A) -> (k32_binop_2 = A <-> (all B (m1_subset_1(B,k1_numbers) -> k8_funct_2(k1_numbers,k1_numbers,A,B) = k8_binop_2(B)))))) # label(d8_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4653 (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]. 59.86/57.42 4654 (all A (m1_subset_1(A,k1_numbers) -> k5_xcmplx_0(A) = k8_binop_2(A))) # label(redefinition_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4655 (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) -> (A = k39_binop_2 <-> (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)))))))) # label(d15_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4656 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k17_binop_2(A,B) = k17_binop_2(B,A))) # label(commutativity_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4657 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k6_binop_2(A,B),k2_numbers))) # label(dt_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4658 (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]. 59.86/57.42 4659 (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]. 59.86/57.42 4660 (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]. 59.86/57.42 4661 (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) -> k16_binop_2(B,C) = k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C))))) <-> A = k40_binop_2))) # label(d16_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4662 (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) -> ((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) = k21_binop_2(B,C))))) <-> k45_binop_2 = A))) # label(d21_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4663 (all A (v1_funct_1(A) & v1_funct_2(A,k4_numbers,k4_numbers) & m2_relset_1(A,k4_numbers,k4_numbers) -> (k43_binop_2 = A <-> (all B (m1_subset_1(B,k4_numbers) -> k8_funct_2(k4_numbers,k4_numbers,A,B) = k19_binop_2(B)))))) # label(d19_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4664 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k23_binop_2(A,B) = k23_binop_2(B,A))) # label(commutativity_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4665 (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 (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & m2_relset_1(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) -> ((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))))) -> B = A))))) # label(s2_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4666 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k17_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4667 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k6_xcmplx_0(A,B) = k21_binop_2(A,B))) # label(redefinition_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4668 (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]. 59.86/57.42 4669 (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]. 59.86/57.42 4670 (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]. 59.86/57.42 4671 (all A (v1_funct_1(A) & m2_relset_1(A,k2_numbers,k2_numbers) & v1_funct_2(A,k2_numbers,k2_numbers) -> ((all B (m1_subset_1(B,k2_numbers) -> k1_binop_2(B) = k8_funct_2(k2_numbers,k2_numbers,A,B))) <-> A = k25_binop_2))) # label(d1_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4672 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k2_xcmplx_0(A,B) = k3_binop_2(A,B))) # label(redefinition_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4673 (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]. 59.86/57.42 4674 (all A (m1_subset_1(A,k3_numbers) -> v1_xcmplx_0(A) & v1_rat_1(A) & v1_xreal_0(A))) # label(cc1_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4675 (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]. 59.86/57.42 4676 (all A (v1_funct_1(A) & v1_funct_2(A,k3_numbers,k3_numbers) & m2_relset_1(A,k3_numbers,k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> k8_funct_2(k3_numbers,k3_numbers,A,B) = k14_binop_2(B))) <-> k38_binop_2 = A))) # label(d14_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4677 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k6_xcmplx_0(A,B) = k4_binop_2(A,B))) # label(redefinition_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4678 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k12_binop_2(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4679 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> k22_binop_2(B,A) = k22_binop_2(A,B))) # label(commutativity_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4680 (all A (v1_funct_1(A) & v1_funct_2(A,f1_s1_binop_2,f2_s1_binop_2) & m2_relset_1(A,f1_s1_binop_2,f2_s1_binop_2) -> (all B (m2_relset_1(B,f1_s1_binop_2,f2_s1_binop_2) & v1_funct_2(B,f1_s1_binop_2,f2_s1_binop_2) & v1_funct_1(B) -> ((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]. 59.86/57.42 4681 (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]. 59.86/57.42 4682 (all A (v1_funct_1(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) -> (k44_binop_2 = A <-> (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]. 59.86/57.42 4683 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k24_binop_2(B,A) = k24_binop_2(A,B))) # label(commutativity_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4684 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,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]. 59.86/57.42 4685 (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]. 59.86/57.42 4686 (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]. 59.86/57.42 4687 (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]. 59.86/57.42 4688 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k24_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4689 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k2_xcmplx_0(A,B) = k23_binop_2(A,B))) # label(redefinition_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4690 (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) -> (k41_binop_2 = A <-> (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]. 59.86/57.42 4691 (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]. 59.86/57.42 4692 (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]. 59.86/57.42 4693 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k15_binop_2(A,B),k3_numbers))) # label(dt_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4694 (all A (v1_funct_1(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) -> (k33_binop_2 = A <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k9_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C)))))))) # label(d9_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4695 (all 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) & v1_funct_1(A) -> (k30_binop_2 = A <-> (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]. 59.86/57.42 4696 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,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]. 59.86/57.42 4697 (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) -> k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C) = k24_binop_2(B,C))))) <-> A = k48_binop_2))) # label(d24_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4698 (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]. 59.86/57.42 4699 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k11_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4700 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k18_binop_2(A,B),k3_numbers))) # label(dt_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4701 (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]. 59.86/57.42 4702 (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]. 59.86/57.42 4703 (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]. 59.86/57.42 4704 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k9_binop_2(A,B),k1_numbers))) # label(dt_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4705 (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]. 59.86/57.42 4706 (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]. 59.86/57.42 4707 (all A (v1_funct_1(A) & v1_funct_2(A,k1_numbers,k1_numbers) & m2_relset_1(A,k1_numbers,k1_numbers) -> ((all B (m1_subset_1(B,k1_numbers) -> k8_funct_2(k1_numbers,k1_numbers,A,B) = k7_binop_2(B))) <-> k31_binop_2 = A))) # label(d7_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4708 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k5_binop_2(B,A) = k5_binop_2(A,B))) # label(commutativity_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4709 (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]. 59.86/57.42 4710 (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) -> (A = k46_binop_2 <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k22_binop_2(B,C) = k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C)))))))) # label(d22_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4711 (all A (v1_funct_2(A,k3_numbers,k3_numbers) & m2_relset_1(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]. 59.86/57.42 4712 (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) -> (k42_binop_2 = A <-> (all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k18_binop_2(B,C) = k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C)))))))) # label(d18_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4713 (all A (m1_subset_1(A,k2_numbers) -> k1_binop_2(k1_binop_2(A)) = A)) # label(involutiveness_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4714 (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]. 59.86/57.42 4715 (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]. 59.86/57.42 4716 (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]. 59.86/57.42 4717 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4718 (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]. 59.86/57.42 4719 (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]. 59.86/57.42 4720 (all A all B all C (v4_ordinal2(A) & v4_ordinal2(C) & v4_ordinal2(B) -> v3_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4721 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4722 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4723 (all A all B (v4_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4724 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4725 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4726 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d9_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4727 (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]. 59.86/57.42 4728 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> v1_membered(A) & v2_membered(A))) # label(cc6_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4729 (all A (-v1_xboole_0(A) & v3_membered(A) -> (exists B (r2_hidden(B,A) & v1_rat_1(B))))) # label(t8_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4730 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xcmplx_0(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d16_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4731 (all A (v1_xboole_0(A) -> v4_membered(A) & v5_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4732 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4733 (all A all B (v2_membered(A) -> v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc30_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4734 (all A all B (v5_membered(A) -> v4_membered(k4_xboole_0(A,B)) & v5_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]. 59.86/57.42 4735 (all A all B (v4_membered(A) & v4_membered(B) -> v4_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4736 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4737 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d10_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4738 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4739 (exists A (-v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v4_membered(A) & v5_membered(A) & v3_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4740 (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]. 59.86/57.42 4741 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4742 (all A all B all C (v1_rat_1(B) & v1_rat_1(C) & v1_rat_1(A) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4743 (all A (v1_membered(A) -> ((all B (v1_xcmplx_0(B) -> r2_hidden(B,A))) -> k2_numbers = A))) # label(t11_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4744 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d7_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4745 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d8_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4746 (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]. 59.86/57.42 4747 (all A ((all B (r2_hidden(B,A) -> v1_xreal_0(B))) <-> v2_membered(A))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4748 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4749 (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]. 59.86/57.42 4750 (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]. 59.86/57.42 4751 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4752 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4753 (all A ((all B (r2_hidden(B,A) -> v1_xcmplx_0(B))) <-> v1_membered(A))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4754 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4755 (exists A ((all B (v4_ordinal2(B) -> (p1_s5_membered(B) <-> r2_hidden(B,A)))) & v5_membered(A))) # label(s5_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4756 (all A (v3_membered(A) <-> (all B (r2_hidden(B,A) -> v1_rat_1(B))))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4757 (all A ((all B (r2_hidden(B,A) -> v4_ordinal2(B))) <-> v5_membered(A))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4758 (all A all B (v3_membered(A) & v3_membered(B) -> v1_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)))) # label(fc44_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4759 (all A ((all B (r2_hidden(B,A) -> v1_int_1(B))) <-> v4_membered(A))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4760 (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]. 59.86/57.42 4761 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4762 (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]. 59.86/57.42 4763 (all A (v1_int_1(A) -> v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4764 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> B = A))))) # label(d14_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4765 (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]. 59.86/57.42 4766 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A)))) <-> r1_xboole_0(A,B)))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4767 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4768 (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]. 59.86/57.42 4769 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B) & v4_membered(B) & v3_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4770 (all A all B (v4_membered(A) & v4_membered(B) -> v4_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4771 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4772 (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]. 59.86/57.42 4773 (all A (v1_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_xcmplx_0(B))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4774 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_rat_1(B) & v1_int_1(B) & v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4775 (all A (m1_subset_1(A,k1_zfmisc_1(k3_numbers)) -> v1_membered(A) & v3_membered(A) & v2_membered(A))) # label(cc7_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4776 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_rat_1(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d18_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4777 (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]. 59.86/57.42 4778 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4779 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4780 (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]. 59.86/57.42 4781 (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]. 59.86/57.42 4782 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4783 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> 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]. 59.86/57.42 4784 (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]. 59.86/57.42 4785 (all A (v1_rat_1(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4786 (all A all B (v3_membered(B) & r2_hidden(B,A) -> v3_membered(k1_setfam_1(A)))) # label(t28_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4787 (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]. 59.86/57.42 4788 (all A all B (r2_hidden(B,A) & v5_membered(B) -> v5_membered(k1_setfam_1(A)))) # label(t30_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4789 (all A (-v1_xboole_0(A) & v2_membered(A) -> (exists B (r2_hidden(B,A) & v1_xreal_0(B))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 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]. 59.86/57.42 4791 (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]. 59.86/57.42 4792 (all A all B (v2_membered(A) & v2_membered(B) -> v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4793 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_membered(k2_tarski(A,B)))) # label(fc12_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4794 (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]. 59.86/57.42 4795 (all A all B (v2_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4796 (all A (v4_ordinal2(A) -> v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc11_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4797 (all A all B (v5_membered(B) & v5_membered(A) -> v2_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4798 (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]. 59.86/57.42 4799 (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]. 59.86/57.42 4800 (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]. 59.86/57.42 4801 (all A all B (v2_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc29_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4802 (all A all B all C (v1_xcmplx_0(B) & v1_xcmplx_0(C) & v1_xcmplx_0(A) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4803 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v1_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4804 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v1_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4805 (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]. 59.86/57.42 4806 (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]. 59.86/57.42 4807 (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]. 59.86/57.42 4808 (all A all B (v1_int_1(A) & v1_int_1(B) -> 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]. 59.86/57.42 4809 (all A all B (v1_membered(B) & v1_membered(A) -> v1_membered(k2_xboole_0(A,B)))) # label(fc22_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4810 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4811 (all A all B (v3_membered(B) & v3_membered(A) -> v3_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc24_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4812 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4813 (all A all B all C (v1_xreal_0(C) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc18_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4814 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) & v1_int_1(B) & v4_ordinal2(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4815 (all A (-v1_xboole_0(A) & v5_membered(A) -> (exists B (r2_hidden(B,A) & v4_ordinal2(B))))) # label(t10_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4816 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4817 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4818 (all A all B all C (v1_int_1(A) & v1_int_1(C) & v1_int_1(B) -> v2_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4819 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> -(r2_hidden(C,B) & r2_hidden(C,A)))) <-> r1_xboole_0(A,B)))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4820 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v2_membered(A) & v3_membered(A) & v4_membered(A) & v1_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4821 (exists A ((all B (v1_int_1(B) -> (r2_hidden(B,A) <-> p1_s4_membered(B)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4822 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4823 (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]. 59.86/57.42 4824 (all A all B (r2_hidden(B,A) & v4_membered(B) -> v4_membered(k1_setfam_1(A)))) # label(t29_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4825 (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]. 59.86/57.42 4826 (exists A (v3_membered(A) & (all B (v1_rat_1(B) -> (p1_s3_membered(B) <-> r2_hidden(B,A)))))) # label(s3_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4827 (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]. 59.86/57.42 4828 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> A = B))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4829 (all A all B (v4_membered(A) -> v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4830 (all A all B (v5_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4831 (all A all B (v5_membered(A) & v5_membered(B) -> v5_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4832 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4833 $T # label(t98_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4834 $T # label(t16_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4835 (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]. 59.86/57.42 4836 (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]. 59.86/57.42 4837 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_complex1(B) = np__0 & k3_complex1(A) = np__0 -> k4_complex1(k3_xcmplx_0(A,B)) = np__0 & k3_complex1(k3_xcmplx_0(A,B)) = k1_real_1(k4_real_1(k4_complex1(A),k4_complex1(B)))))))) # label(t31_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4838 $T # label(t69_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4839 $T # label(t99_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4840 (all A (v1_xcmplx_0(A) -> (np__0 = k15_complex1(A) -> np__0 = A))) # label(t114_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4841 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k9_complex1(A,B),k2_numbers))) # label(dt_k9_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4842 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k9_complex1(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k9_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4843 (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]. 59.86/57.42 4844 $T # label(t103_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4845 (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]. 59.86/57.42 4846 $T # label(t41_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4847 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> (k4_complex1(B) = np__0 & np__0 = k4_complex1(A) -> np__0 = k3_complex1(B) | np__0 = k4_complex1(k13_complex1(A,B)) & k3_complex1(k13_complex1(A,B)) = k6_real_1(k3_complex1(A),k3_complex1(B))))))) # label(t109_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4848 $T # label(t94_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4849 $T # label(t87_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4850 (all A (v1_xcmplx_0(A) -> k1_real_1(k4_complex1(A)) = k4_complex1(k15_complex1(A)) & k3_complex1(A) = k3_complex1(k15_complex1(A)))) # label(t112_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4851 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 = k17_complex1(k6_xcmplx_0(A,B)) <-> A = B))))) # label(t147_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4852 $T # label(t111_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4853 (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]. 59.86/57.42 4854 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> 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)) & k3_complex1(k13_complex1(A,B)) = 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)))))))) # label(t82_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4855 $T # label(t46_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4856 $T # label(t59_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4857 $T # label(t66_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4858 $T # label(d4_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4859 (all A (v1_xcmplx_0(A) -> (np__0 = k17_complex1(A) -> A = np__0))) # label(t131_complex1) # label(axiom) # label(non_clause). [assumption]. 59.86/57.42 4860 (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]. 59.86/57.42 4861 $T # label(t18_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4862 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k16_complex1(A)) & v1_xreal_0(k16_complex1(A)))) # label(fc4_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4863 (all A (v1_xcmplx_0(A) -> m1_subset_1(k18_complex1(A),k1_numbers))) # label(dt_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4864 (all A (v1_xcmplx_0(A) -> m1_subset_1(k17_complex1(A),k1_numbers))) # label(dt_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4865 (all A (v1_xreal_0(A) -> k7_square_1(k17_complex1(A)) = k5_square_1(A))) # label(t161_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4866 (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]. 59.95/57.43 4867 $T # label(t21_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4868 (all A (m1_subset_1(A,k2_numbers) -> A = k10_complex1(k10_complex1(A)))) # label(involutiveness_k10_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4869 (all A (v1_xcmplx_0(A) -> k17_complex1(k15_complex1(A)) = k17_complex1(A))) # label(t139_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4870 $T # label(t67_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4871 $T # label(t70_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4872 $T # label(t102_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4873 (all A (m1_subset_1(A,k2_numbers) -> (k4_complex1(A) = np__0 -> k15_complex1(A) = A))) # label(t124_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4874 (all A (v1_xcmplx_0(A) -> (np__0 = A <-> k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))) = np__0))) # label(t13_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4875 $T # label(t6_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4876 $T # label(t75_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4877 (all A (v1_xcmplx_0(A) -> r1_xreal_0(k4_complex1(A),k17_complex1(A)))) # label(t141_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4878 $T # label(t104_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4879 $T # label(t57_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4880 $T # label(t43_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4881 (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]. 59.95/57.43 4882 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k8_complex1(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k8_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4883 $T # label(t52_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4884 (all A (v1_xcmplx_0(A) -> k17_complex1(k3_xcmplx_0(A,A)) = k17_complex1(k3_xcmplx_0(A,k15_complex1(A))))) # label(t155_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4885 (all A (m1_subset_1(A,k2_numbers) -> A = k12_complex1(k12_complex1(A)))) # label(involutiveness_k12_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4886 (all A (m1_subset_1(A,k2_numbers) -> k12_complex1(A) = k5_xcmplx_0(A))) # label(redefinition_k12_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4887 $T # label(t97_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4888 $T # label(t84_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4889 (all A (m1_subset_1(A,k2_numbers) -> (k3_complex1(A) = np__0 -> k4_complex1(k12_complex1(A)) = k1_real_1(k2_real_1(k4_complex1(A))) & k3_complex1(k12_complex1(A)) = np__0 | np__0 = k4_complex1(A)))) # label(t80_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4890 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k1_square_1(A,B) = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),k17_complex1(k6_xcmplx_0(A,B))),np__2))))) # label(t159_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4891 $T # label(t4_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4892 $T # label(t105_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4893 $T # label(t86_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4894 $T # label(t47_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4895 $T # label(t7_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4896 $T # label(d1_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4897 $T # label(t39_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4898 $T # label(t58_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4899 (all A (m1_subset_1(A,k2_numbers) -> (np__0 = k4_complex1(A) -> 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]. 59.95/57.43 4900 $T # label(t88_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4901 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k8_complex1(A,B) = 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)))))) # label(d9_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4902 (all A (m1_subset_1(A,k2_numbers) -> v1_xcmplx_0(A))) # label(cc1_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4903 (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]. 59.95/57.43 4904 $T # label(t10_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4905 $T # label(t55_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4906 (all A (v1_xcmplx_0(A) -> m1_subset_1(k15_complex1(A),k2_numbers))) # label(dt_k15_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4907 $T # label(t56_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4908 $T # label(t68_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4909 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_complex1(A) = k4_complex1(B) & k3_complex1(B) = k3_complex1(A) <-> A = B))))) # label(d5_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4910 (all A (v1_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)) & k4_complex1(k5_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)))))) # label(t64_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4911 (all A (m1_subset_1(A,k2_numbers) -> 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)) = k12_complex1(A))) # label(d13_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4912 $T # label(t108_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4913 $T # label(t62_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4914 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k9_complex1(A,B) = k9_complex1(B,A))) # label(commutativity_k9_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4915 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(A != B & r1_xreal_0(k17_complex1(k6_xcmplx_0(A,B)),np__0)) & -(B = A & -r1_xreal_0(k17_complex1(k6_xcmplx_0(A,B)),np__0)))))) # label(t148_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4916 $T # label(t53_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4917 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k5_arytm_0(A,B) = k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)))))) # label(t27_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4918 $T # label(t40_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4919 $T # label(t44_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4920 (all A (m1_subset_1(A,k2_numbers) -> k5_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))) = k3_complex1(k9_complex1(A,A)) & k4_real_1(np__2,k4_real_1(k3_complex1(A),k4_complex1(A))) = k4_complex1(k9_complex1(A,A)))) # label(t32_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4921 $T # label(t23_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4922 (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]. 59.95/57.43 4923 (all A (v1_xcmplx_0(A) -> k17_complex1(A) = k17_complex1(k4_xcmplx_0(A)))) # label(t138_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4924 $T # label(t106_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4925 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k11_complex1(A,B),k2_numbers))) # label(dt_k11_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4926 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k15_complex1(k2_xcmplx_0(A,B)) = k8_complex1(k15_complex1(A),k15_complex1(B)))))) # label(t118_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4927 $T # label(t74_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4928 (all A (v1_xcmplx_0(A) -> (np__0 = k4_complex1(A) -> k17_complex1(k3_complex1(A)) = k17_complex1(A)))) # label(t136_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4929 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),k17_complex1(k6_xcmplx_0(A,B))),np__2) = k2_square_1(A,B))))) # label(t160_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4930 (all A (v1_xcmplx_0(A) -> k16_complex1(A) = k17_complex1(A))) # label(redefinition_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4931 (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]. 59.95/57.43 4932 $T # label(t60_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4933 (all A (v1_xcmplx_0(A) -> k14_complex1(A) = k6_xcmplx_0(k3_complex1(A),k3_xcmplx_0(k4_complex1(A),k7_complex1)))) # label(d15_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4934 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k15_complex1(k11_complex1(A,B)) = k11_complex1(k15_complex1(A),k15_complex1(B)))))) # label(t120_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4935 $T # label(t83_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4936 (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]. 59.95/57.43 4937 (all A (m1_subset_1(A,k2_numbers) -> k10_complex1(A) = k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_xcmplx_0(k1_real_1(k4_complex1(A)),k7_complex1)))) # label(d11_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4938 $T # label(t92_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4939 (all A (v1_xcmplx_0(A) -> (k3_complex1(A) = np__0 -> k17_complex1(k4_complex1(A)) = k17_complex1(A)))) # label(t137_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4940 $T # label(t85_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4941 (all A (v1_xcmplx_0(A) -> v1_xreal_0(k1_complex1(A)) & v1_xcmplx_0(k1_complex1(A)))) # label(fc1_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4942 (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]. 59.95/57.43 4943 (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]. 59.95/57.43 4944 (all A (v1_xcmplx_0(A) -> r1_xreal_0(np__0,k17_complex1(A)))) # label(t132_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4945 (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]. 59.95/57.43 4946 (all A (v1_xreal_0(A) -> k17_complex1(A) = A | k17_complex1(A) = k4_xcmplx_0(A))) # label(t157_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4947 $T # label(t95_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4948 $T # label(t51_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4949 $T # label(t1_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4950 (all A (v1_xcmplx_0(A) -> m1_subset_1(k3_complex1(A),k1_numbers))) # label(dt_k3_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4951 $T # label(t50_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4952 (all A (v1_xcmplx_0(A) -> r1_xreal_0(k3_complex1(A),k17_complex1(A)))) # label(t140_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4953 $T # label(t96_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4954 (all A (m1_subset_1(A,k2_numbers) -> k4_complex1(k9_complex1(A,k15_complex1(A))) = np__0 & k3_complex1(k9_complex1(A,k15_complex1(A))) = k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))))) # label(t126_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4955 (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]. 59.95/57.43 4956 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> (np__0 = k3_complex1(B) & k3_complex1(A) = np__0 -> np__0 = k4_complex1(B) | k4_complex1(k13_complex1(A,B)) = np__0 & k3_complex1(k13_complex1(A,B)) = k6_real_1(k4_complex1(A),k4_complex1(B))))))) # label(t110_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4957 (all A (v1_funct_1(A) & v1_funct_2(A,np__2,k1_numbers) & m2_relset_1(A,np__2,k1_numbers) -> (exists B (m1_subset_1(B,k1_numbers) & (exists C (k5_funct_4(k1_numbers,np__0,np__1,B,C) = A & m1_subset_1(C,k1_numbers))))))) # label(t5_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4958 $T # label(t11_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4959 (all A (v1_xcmplx_0(A) -> k17_complex1(A) = k17_complex1(k17_complex1(A)))) # label(projectivity_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4960 (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(C,k3_xcmplx_0(D,k7_complex1)) = k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) -> C = A & B = D))))))))) # label(t163_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4961 (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]. 59.95/57.43 4962 $T # label(t107_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4963 (all A (v1_xcmplx_0(A) -> k16_complex1(k16_complex1(A)) = k16_complex1(A))) # label(projectivity_k16_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4964 $T # label(t73_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4965 $T # label(t8_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4966 (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]. 59.95/57.43 4967 $T # label(t3_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4968 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_complex1(B) = k4_complex1(A) & k3_complex1(A) = k3_complex1(B) -> A = B))))) # label(t9_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4969 (all A (v1_xcmplx_0(A) -> k18_complex1(k18_complex1(A)) = k18_complex1(A))) # label(projectivity_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4970 (all A (v1_xcmplx_0(A) -> m1_subset_1(k4_complex1(A),k1_numbers))) # label(dt_k4_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4971 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))) = k3_complex1(k3_xcmplx_0(A,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))))))) # label(t24_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4972 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k6_xcmplx_0(A,B) = k11_complex1(A,B))) # label(redefinition_k11_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4973 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k8_complex1(A,B),k2_numbers))) # label(dt_k8_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4974 $T # label(dt_k2_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4975 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (A = np__0 & B = np__0 <-> k2_xcmplx_0(k5_square_1(A),k5_square_1(B)) = np__0))))) # label(t2_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4976 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k14_complex1(A)))) # label(dt_k14_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4977 $T # label(t45_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4978 $T # label(t65_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4979 (all A (m1_subset_1(A,k1_numbers) -> np__0 = k3_complex1(k3_xcmplx_0(A,k7_complex1)))) # label(t25_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4980 $T # label(t49_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4981 $T # label(t54_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4982 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_complex1(B) = np__0 & np__0 = k4_complex1(A) -> k4_complex1(k3_xcmplx_0(A,B)) = np__0 & k4_real_1(k3_complex1(A),k3_complex1(B)) = k3_complex1(k3_xcmplx_0(A,B))))))) # label(t30_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4983 $T # label(dt_k1_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4984 (all A (m1_subset_1(A,k2_numbers) -> np__0 = k4_complex1(k8_complex1(A,k15_complex1(A))) & k4_real_1(np__2,k3_complex1(A)) = k3_complex1(k8_complex1(A,k15_complex1(A))))) # label(t127_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4985 $T # label(t101_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4986 (all A (m1_subset_1(A,k2_numbers) -> k12_complex1(k15_complex1(A)) = k15_complex1(k12_complex1(A)))) # label(t122_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4987 $T # label(t36_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4988 $T # label(t117_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4989 $T # label(t63_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4990 (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]. 59.95/57.43 4991 (all A (v1_xcmplx_0(A) -> A = k15_complex1(k15_complex1(A)))) # label(involutiveness_k15_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4992 (all A (m1_subset_1(A,k2_numbers) -> k4_complex1(k11_complex1(A,k15_complex1(A))) = k4_real_1(np__2,k4_complex1(A)) & np__0 = k3_complex1(k11_complex1(A,k15_complex1(A))))) # label(t128_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4993 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k7_xcmplx_0(A,B) = k13_complex1(A,B))) # label(redefinition_k13_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4994 (all A (v1_xcmplx_0(A) -> k3_complex1(A) = k1_complex1(A))) # label(redefinition_k3_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4995 (all A (v1_xcmplx_0(A) -> k18_complex1(A) = k16_complex1(A))) # label(redefinition_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4996 $T # label(t89_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4997 (all A (v1_xcmplx_0(A) -> k15_complex1(A) = k14_complex1(A))) # label(redefinition_k15_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4998 $T # label(t20_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 4999 $T # label(t90_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5000 $T # label(t93_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5001 (all A (v1_xcmplx_0(A) -> (all B ((r2_hidden(A,k1_numbers) -> (B = np__0 <-> k2_complex1(A) = B)) & (-r2_hidden(A,k1_numbers) -> (B = k2_complex1(A) <-> (exists C (v1_funct_1(C) & v1_funct_2(C,np__2,k1_numbers) & k1_funct_1(C,np__1) = B & C = A & m2_relset_1(C,np__2,k1_numbers))))))))) # label(d3_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5002 $T # label(t100_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5003 (all A (m1_subset_1(A,k2_numbers) -> k10_complex1(A) = k4_xcmplx_0(A))) # label(redefinition_k10_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5004 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k13_complex1(A,B),k2_numbers))) # label(dt_k13_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5005 $T # label(t22_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5006 (all A (v1_xcmplx_0(A) -> k4_complex1(A) = k2_complex1(A))) # label(redefinition_k4_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5007 (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]. 59.95/57.43 5008 $T # label(t78_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5009 (all A (v1_xcmplx_0(A) -> A = k14_complex1(k14_complex1(A)))) # label(involutiveness_k14_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5010 (all A (v1_xcmplx_0(A) -> -(np__0 = A & -r1_xreal_0(k17_complex1(A),np__0)) & -(r1_xreal_0(k17_complex1(A),np__0) & A != np__0))) # label(t133_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5011 $T # label(t71_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5012 $T # label(t14_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5013 (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)) & k4_complex1(k11_complex1(A,B)) = k5_real_1(k4_complex1(A),k4_complex1(B)))))) # label(t48_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5014 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_real_1(k4_complex1(A),k4_complex1(B)) = k4_complex1(k2_xcmplx_0(A,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]. 59.95/57.43 5015 (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]. 59.95/57.43 5016 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> B = k4_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) & A = k3_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))))))) # label(t28_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5017 $T # label(t42_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5018 (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]. 59.95/57.43 5019 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k8_complex1(A,B) = k8_complex1(B,A))) # label(commutativity_k8_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5020 $T # label(t61_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5021 $T # label(t81_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5022 (all A (v1_xreal_0(A) -> k8_square_1(k5_square_1(A)) = k17_complex1(A))) # label(t158_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5023 $T # label(t33_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5024 (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]. 59.95/57.43 5025 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k16_complex1(A)))) # label(dt_k16_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5026 (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]. 59.95/57.43 5027 $T # label(t35_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5028 (all A (v1_xcmplx_0(A) -> k17_complex1(k3_xcmplx_0(A,A)) = k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))))) # label(t154_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5029 $T # label(t91_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5030 $T # label(t77_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5031 $T # label(t76_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5032 (all A (v1_xcmplx_0(A) -> k1_real_1(k3_complex1(A)) = k3_complex1(k4_xcmplx_0(A)) & k4_complex1(k4_xcmplx_0(A)) = k1_real_1(k4_complex1(A)))) # label(t34_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5033 (all A (v1_xcmplx_0(A) -> (all B ((r2_hidden(A,k1_numbers) -> (A = B <-> B = k1_complex1(A))) & (-r2_hidden(A,k1_numbers) -> (B = k1_complex1(A) <-> (exists C (v1_funct_1(C) & m2_relset_1(C,np__2,k1_numbers) & C = A & B = k1_funct_1(C,np__0) & v1_funct_2(C,np__2,k1_numbers))))))))) # label(d2_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5034 $T # label(t38_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5035 (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]. 59.95/57.43 5036 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,np__0) -> k4_xcmplx_0(A) = k17_complex1(A)))) # label(t156_complex1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5037 $T # label(t18_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5038 (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]. 59.95/57.43 5039 (all A (v1_xreal_0(A) -> k7_xcmplx_0(np__1,k1_absvalue(A)) = k1_absvalue(k7_xcmplx_0(np__1,A)))) # label(t39_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5040 $T # label(t16_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5041 $T # label(t13_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5042 (all A (m1_subset_1(A,k1_numbers) -> k2_absvalue(A) = k1_absvalue(A))) # label(redefinition_k2_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5043 (all A (v1_xreal_0(A) -> A = k18_complex1(A) | k4_xcmplx_0(A) = k18_complex1(A))) # label(t1_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5044 $T # label(t5_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5045 (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]. 59.95/57.43 5046 (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]. 59.95/57.43 5047 (all A (v1_xreal_0(A) -> (k1_absvalue(A) = np__0 -> np__0 = A))) # label(t33_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5048 (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]. 59.95/57.43 5049 $T # label(t3_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5050 $T # label(t2_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5051 (all A (v1_xreal_0(A) -> k1_absvalue(k1_absvalue(A)) = k1_absvalue(A))) # label(t36_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5052 $T # label(t22_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5053 $T # label(t30_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5054 $T # label(t4_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5055 $T # label(t19_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5056 (all A (v1_xreal_0(A) -> (A != np__0 -> 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]. 59.95/57.43 5057 (all A (v1_xreal_0(A) -> -(k1_absvalue(A) = np__1 & r1_xreal_0(A,np__0)))) # label(t31_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5058 $T # label(t29_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5059 (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]. 59.95/57.43 5060 (all A (v1_xreal_0(A) -> -(k1_absvalue(A) = k1_real_1(np__1) & r1_xreal_0(np__0,A)))) # label(t32_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5061 $T # label(dt_k1_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5062 (all A (v1_xreal_0(A) -> -(np__0 != A & r1_xreal_0(np__0,A) & k18_complex1(A) = k4_xcmplx_0(A)))) # label(t9_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5063 (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]. 59.95/57.43 5064 (all A (v1_xreal_0(A) -> r1_xreal_0(k1_real_1(k18_complex1(A)),A) & r1_xreal_0(A,k18_complex1(A)))) # label(t11_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5065 $T # label(t10_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5066 (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]. 59.95/57.43 5067 (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]. 59.95/57.43 5068 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,k3_xcmplx_0(A,B)) -> k3_real_1(k18_complex1(A),k18_complex1(B)) = k18_complex1(k2_xcmplx_0(A,B))))))) # label(t24_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5069 (all A (v1_xreal_0(A) -> k6_real_1(np__1,k18_complex1(A)) = k18_complex1(k7_xcmplx_0(np__1,A)))) # label(t15_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5070 (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]. 59.95/57.43 5071 (all A (v1_xreal_0(A) -> (-r1_xreal_0(np__0,A) -> k1_real_1(np__1) = k1_absvalue(A)) & (r1_xreal_0(np__0,A) & r1_xreal_0(A,np__0) -> np__0 = k1_absvalue(A)) & (-r1_xreal_0(A,np__0) -> k1_absvalue(A) = np__1))) # label(d2_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5072 (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(C),D) & r1_xreal_0(k18_complex1(A),B) -> r1_xreal_0(k18_complex1(k2_xcmplx_0(A,C)),k2_xcmplx_0(B,D))))))))))) # label(t21_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5073 $T # label(t28_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5074 (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]. 59.95/57.43 5075 (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]. 59.95/57.43 5076 (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]. 59.95/57.43 5077 (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]. 59.95/57.43 5078 $T # label(t17_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5079 $T # label(t6_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5080 (all A (v1_xreal_0(A) -> (k18_complex1(A) = np__0 <-> A = np__0))) # label(t7_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5081 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(A),B) & r1_xreal_0(B,A) <-> r1_xreal_0(k18_complex1(B),A)))))) # label(t12_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5082 (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) -> A = k16_complex1(A)))) # label(d1_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5083 $T # label(t8_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5084 $T # label(t27_absvalue) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5085 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5086 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5087 (all A all B (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> (exists C (r1_tarski(A,k2_relat_1(C)) & B = k1_relat_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5088 (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]. 59.95/57.43 5089 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5090 (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]. 59.95/57.43 5091 (all A all B ((exists C k1_tarski(C) = A) <-> r2_wellord2(A,k1_tarski(B)))) # label(t48_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5092 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5093 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5094 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B = k4_card_1(A) <-> k1_card_1(B) = k1_card_1(A)))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5095 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5096 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5097 (all A all B (v1_finset_1(A) & r2_wellord2(A,B) -> v1_finset_1(B))) # label(t68_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5098 (all A all B ((exists C (k1_relat_1(C) = A & r1_tarski(k2_relat_1(C),B) & v2_funct_1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t26_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5099 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (A = B <-> r2_wellord2(A,B)))))) # label(t8_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5100 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5101 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5102 (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]. 59.95/57.43 5103 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5104 (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]. 59.95/57.43 5105 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5106 (all A (v1_card_1(A) <-> (exists B (v3_ordinal1(B) & A = B & (all C (v3_ordinal1(C) -> (r2_wellord2(C,B) -> r1_ordinal1(B,C)))))))) # label(d1_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5107 (all A (v1_card_1(A) -> (v2_card_1(A) <-> (all B (v1_card_1(B) -> k2_card_1(B) != A))))) # label(d7_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5108 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5109 (all A (v1_card_1(A) -> v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5110 p1_s1_card_1(k1_xboole_0) & (all A (v1_card_1(A) -> (p1_s1_card_1(A) -> p1_s1_card_1(k2_card_1(A))))) & (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s1_card_1(B)))) & v2_card_1(A) -> k1_xboole_0 = A | p1_s1_card_1(A)))) -> (all A (v1_card_1(A) -> p1_s1_card_1(A))) # label(s1_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5111 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5112 (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]. 59.95/57.43 5113 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5114 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_card_1(A)) & v1_card_1(k3_card_1(A)) & v2_ordinal1(k3_card_1(A)) & v1_ordinal1(k3_card_1(A)))) # label(fc1_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5115 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5116 (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]. 59.95/57.43 5117 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5118 (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]. 59.95/57.43 5119 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5120 (all A all B all C (r1_tarski(A,B) & r2_wellord2(A,C) & r1_tarski(B,C) -> r2_wellord2(B,C) & r2_wellord2(A,B))) # label(t44_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5121 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5122 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5123 (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]. 59.95/57.43 5124 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5125 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_card_1(A),k1_card_1(B)) <-> -r1_xreal_0(B,A)))))) # label(t73_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5126 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5127 (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]. 59.95/57.43 5128 (all A (m1_subset_1(A,k5_numbers) -> v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_finset_1(A) & v1_xreal_0(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5129 (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]. 59.95/57.43 5130 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k3_card_1(A) = k3_card_1(B) -> B = A))))) # label(t42_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5131 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r1_tarski(k3_card_1(A),k3_card_1(B))))))) # label(t43_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5132 (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]. 59.95/57.43 5133 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5134 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5135 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v4_ordinal2(A) & v1_xreal_0(A) & v1_card_1(A) & -v3_xreal_0(A) & v1_xcmplx_0(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5136 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5137 (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]. 59.95/57.43 5138 (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]. 59.95/57.43 5139 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5140 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5141 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5142 (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]. 59.95/57.43 5143 (all A all B ((exists C A = k1_tarski(C)) <-> k1_card_1(A) = k1_card_1(k1_tarski(B)))) # label(t49_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5144 (all A all B (r2_wellord2(A,B) -> k2_card_1(B) = k2_card_1(A))) # label(t35_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5145 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5146 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5147 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5148 (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]. 59.95/57.43 5149 (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]. 59.95/57.43 5150 (all A (v1_finset_1(A) -> v1_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5151 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5152 (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]. 59.95/57.43 5153 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.43 5154 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5155 (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]. 59.95/57.44 5156 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5157 (all A (v1_card_1(A) & v1_finset_1(A) -> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & A = k1_card_1(B))))) # label(t86_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5158 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_relat_1(B)) -> r2_wellord2(A,k9_relat_1(B,A))))) # label(t60_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5159 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5160 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5161 (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]. 59.95/57.44 5162 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> r1_xreal_0(A,B)))))) # label(t72_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5163 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k1_funct_1(B,C) = k3_card_1(C)))) & A = k1_relat_1(B) -> k1_card_1(k8_ordinal2(B)) = k3_card_1(A)))) | k1_xboole_0 = A))) # label(t40_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5164 (all A (v3_ordinal1(A) -> k2_card_1(k3_card_1(A)) = k3_card_1(k1_ordinal1(A)))) # label(t39_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5165 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_ordinal1(A,B) <-> r1_xreal_0(A,B)))))) # label(t56_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5166 (all A all B (r2_wellord2(A,B) <-> k1_card_1(B) = k1_card_1(A))) # label(t21_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5167 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5168 (all A all B (v1_card_1(B) -> (B = k2_card_1(A) <-> (all C (v1_card_1(C) -> (r2_hidden(k1_card_1(A),C) -> r1_tarski(B,C)))) & r2_hidden(k1_card_1(A),B)))) # label(d6_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5169 (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]. 59.95/57.44 5170 (all A (v3_ordinal1(A) -> (all B ((exists C (B = k1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | k1_card_1(k8_ordinal2(k2_ordinal1(C,D))) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k2_card_1(k3_tarski(k1_tarski(k1_funct_1(C,D)))) = k1_funct_1(C,k1_ordinal1(D))))) & k1_card_1(k5_numbers) = k1_funct_1(C,k1_xboole_0) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> k3_card_1(A) = B)))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5171 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5172 (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]. 59.95/57.44 5173 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) -> B = A))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5174 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5175 (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]. 59.95/57.44 5176 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5177 (exists A (v1_ordinal1(A) & v2_ordinal1(A) & v1_card_1(A) & v1_finset_1(A) & v3_ordinal1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5178 (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]. 59.95/57.44 5179 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5180 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5181 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5182 (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]. 59.95/57.44 5183 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> v1_finset_1(A) & v1_finset_1(k1_card_1(A)))) # label(t69_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5184 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5185 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5186 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5187 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5188 (all A (A = k1_xboole_0 <-> r2_wellord2(A,k1_xboole_0))) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5189 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(k1_nat_1(k3_finseq_1(C),A),k4_finseq_1(k7_finseq_1(C,B)))))))))) # label(t41_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5190 (all A (v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)))) # label(fc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5191 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k4_finseq_1(A) = k4_finseq_1(B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) -> A = B))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5192 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5193 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (r1_tarski(k1_relat_1(A),k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) <-> v2_finseq_1(A)))) # label(d12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5194 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k2_finseq_1(np__1) & A = k1_funct_1(B,np__1) <-> B = k9_finseq_1(A)))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5195 (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]. 59.95/57.44 5196 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (exists C (m2_finseq_1(C,B) & A = k3_finseq_1(C))))))) # label(t24_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5197 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5198 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5199 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5200 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (np__1 = k3_finseq_1(B) & k2_relat_1(B) = k1_tarski(A) <-> k9_finseq_1(A) = B))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5201 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k7_finseq_1(A,k1_xboole_0) = A & A = k7_finseq_1(k1_xboole_0,A))) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5202 (all A all B all C (v1_relat_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)) & v1_finset_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)))) # label(fc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5203 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))))))) # label(t39_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5204 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5205 (all A all B all C (v1_funct_1(k11_finseq_1(A,B,C)) & v1_relat_1(k11_finseq_1(A,B,C)))) # label(fc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5206 (all A all B all C (k11_finseq_1(A,B,C) = k7_finseq_1(k10_finseq_1(A,B),k9_finseq_1(C)) & k7_finseq_1(k9_finseq_1(A),k10_finseq_1(B,C)) = k11_finseq_1(A,B,C))) # label(t60_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5207 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5208 (all A (v1_xboole_0(k6_finseq_1(A)) & m2_finseq_1(k6_finseq_1(A),A))) # label(dt_k6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5209 (exists A (v1_relat_1(A) & v1_finseq_1(A) & v1_finset_1(A) & v1_funct_1(A) & -v1_xboole_0(A))) # label(rc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5210 (all A (v1_funct_1(k9_finseq_1(A)) & v1_relat_1(k9_finseq_1(A)))) # label(dt_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5211 (all A (v4_ordinal2(A) -> r2_hidden(A,k2_finseq_1(A)) | np__0 = A)) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5212 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (v2_funct_1(B) & v2_funct_1(A) & k2_relat_1(A) = k2_relat_1(B) -> k3_finseq_1(B) = k3_finseq_1(A)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5213 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5214 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5215 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5216 (all A (v1_relat_1(A) & v1_funct_1(A) -> -((all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -r1_tarski(A,B))) & (exists B (r1_tarski(k1_relat_1(A),k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers)))))) # label(t15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5217 (all A all B (m1_finseq_1(B,A) -> v1_relat_1(k16_finseq_1(A,B,np__0)) & v2_funct_1(k16_finseq_1(A,B,np__0)) & v1_finset_1(k16_finseq_1(A,B,np__0)) & v1_finseq_1(k16_finseq_1(A,B,np__0)) & v1_funct_1(k16_finseq_1(A,B,np__0)) & v1_xboole_0(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5218 (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]. 59.95/57.44 5219 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(D,k3_relat_1(A)) & (exists E (v1_relat_1(E) & D = k1_funct_1(E,k3_finseq_1(E)) & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,F) -> r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,k1_nat_1(F,np__1))),A) | r1_xreal_0(k3_finseq_1(E),F)))) & C = k1_funct_1(E,np__1) & r1_xreal_0(np__1,k3_finseq_1(E)) & v1_finseq_1(E) & v1_funct_1(E))) & r2_hidden(C,k3_relat_1(A)))) <-> k17_finseq_1(A) = B))))) # label(d16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5220 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5221 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5222 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k12_finseq_1(A,B) = k5_finseq_1(B))) # label(redefinition_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5223 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5224 (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]. 59.95/57.44 5225 (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]. 59.95/57.44 5226 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5227 (all A all B (m2_finseq_1(B,A) -> m2_relset_1(B,k5_numbers,A) & v1_finseq_1(B) & v1_funct_1(B))) # label(dt_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5228 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5229 (all A (v4_ordinal2(A) -> k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,np__1)),k1_tarski(k2_xcmplx_0(A,np__1))) = k2_finseq_1(A))) # label(t12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5230 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (B = k9_finseq_1(A) <-> A = k1_funct_1(B,np__1) & k3_finseq_1(B) = np__1))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5231 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5232 (all A all B (v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)))) # label(fc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5233 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (r1_xreal_0(A,k3_finseq_1(B)) & k7_relat_1(B,k2_finseq_1(A)) = C -> A = k3_finseq_1(C) & k2_finseq_1(A) = k4_finseq_1(C)))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5234 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k7_relat_1(B,A)) & v2_finseq_1(k7_relat_1(B,A)) & v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)) & v2_finseq_1(k8_relat_1(A,B)) & v1_funct_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5235 (all A all B (v4_ordinal2(B) -> ((exists C (C = A & r1_xreal_0(np__1,C) & r1_xreal_0(C,B) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_0_finseq_1(B))))) # label(fraenkel_a_1_0_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5236 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> k3_finseq_1(A) = k1_card_1(A))) # label(redefinition_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5237 (exists A all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & r2_hidden(C,k13_finseq_1(f1_s4_finseq_1)) & p1_s4_finseq_1(C) & C = B)) <-> r2_hidden(B,A))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5238 (exists A (v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v2_funct_1(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5239 (all A k9_finseq_1(A) = k5_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5240 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (k3_finseq_1(A) = np__0 <-> k1_xboole_0 = A))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5241 (exists A (-v1_xboole_0(A) & v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A))) # label(rc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5242 (all A k9_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5243 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> k1_relat_1(A) = k2_relat_1(k14_finseq_1(k1_relat_1(A))))) # label(t71_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5244 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(A = k4_tarski(C,k1_funct_1(B,C)) & r2_hidden(C,k4_finseq_1(B))))) & r2_hidden(A,B)))) # label(t16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5245 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5246 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & -v1_xboole_0(B) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> -v1_xboole_0(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5247 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5248 (all A all B all C (m1_finseq_1(C,A) & m1_finseq_1(B,A) -> m2_finseq_1(k8_finseq_1(A,B,C),A))) # label(dt_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 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 (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> -(k7_finseq_1(A,B) = k7_finseq_1(C,D) & r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) & (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> C != k7_finseq_1(A,E)))))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5250 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B))) -> k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) | r1_xreal_0(C,k3_finseq_1(A))))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5251 (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]. 59.95/57.44 5252 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)))))))) # label(t45_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5253 (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]. 59.95/57.44 5254 (all A ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(A,k2_finseq_1(B)))) -> (k1_xboole_0 = k14_finseq_1(A) <-> k1_xboole_0 = A))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5255 (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]. 59.95/57.44 5256 (all A all B k10_finseq_1(A,B) = k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B))) # label(d9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5257 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(r2_hidden(D,k4_finseq_1(B)) & C = k1_nat_1(k3_finseq_1(A),D)))) & -r2_hidden(C,k4_finseq_1(A))))))))) # label(t38_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5258 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (m2_finseq_1(k7_finseq_1(A,B),C) -> m2_finseq_1(B,C) & m2_finseq_1(A,C))))))) # label(t50_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5259 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5260 (all A all B (v1_funct_1(A) & v1_finseq_1(A) & -v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v1_relat_1(A) -> -v1_xboole_0(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5261 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (p1_s1_finseq_1(A,C) & p1_s1_finseq_1(A,B) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) -> C = B)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((all B -p1_s1_finseq_1(A,B)) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1))))) -> (exists A (v1_relat_1(A) & v1_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_1)) -> p1_s1_finseq_1(B,k1_funct_1(A,B))))) & k2_finseq_1(f1_s1_finseq_1) = k4_finseq_1(A) & v1_funct_1(A))) # label(s1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5262 (all A all B all C (m1_finseq_1(B,A) & m1_finseq_1(C,A) -> k8_finseq_1(A,B,C) = k7_finseq_1(B,C))) # label(redefinition_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5263 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (C = k7_finseq_1(A,B) <-> k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) = k4_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D)))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(A,D))))))))))) # label(d7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5264 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t84_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5265 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(r2_hidden(A,k2_finseq_1(f2_s5_finseq_1)) & (all B (m1_subset_1(B,f1_s5_finseq_1) -> -p1_s5_finseq_1(A,B)))))) -> (exists A (m2_finseq_1(A,f1_s5_finseq_1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f2_s5_finseq_1)) -> p1_s5_finseq_1(B,k1_funct_1(A,B))))) & k4_finseq_1(A) = k2_finseq_1(f2_s5_finseq_1))) # label(s5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5266 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5267 (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]. 59.95/57.44 5268 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> A = k4_card_1(k1_card_1(A)) & k4_card_1(A) = A)) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5269 (all A (v4_ordinal2(A) -> k4_card_1(k2_finseq_1(A)) = A)) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5270 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> v1_relat_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A))))))) # label(t20_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5271 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k7_finseq_1(A,B)))))) # label(t44_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5272 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A)) = k2_finseq_1(A)))))) # label(t9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5273 (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]. 59.95/57.44 5274 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),np__1) = A)) # label(t58_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5275 (exists A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5276 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> -(A != k1_xboole_0 & (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C k7_finseq_1(B,k9_finseq_1(C)) != A)))))) # label(t63_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5277 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5278 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(k3_finseq_1(B),C) -> k16_finseq_1(A,B,C) = B))))) # label(t79_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5279 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) <-> r1_tarski(k2_finseq_1(A),k2_finseq_1(B))))))) # label(t7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5280 (all A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k15_finseq_1(A)) & v1_relat_1(k15_finseq_1(A)))) # label(dt_k15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5281 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k7_finseq_1(A,B) = k1_xboole_0 -> k1_xboole_0 = A & B = k1_xboole_0))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5282 (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]. 59.95/57.44 5283 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(np__1,C) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5284 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (k1_xboole_0 = A <-> k1_xboole_0 = k2_relat_1(A)))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5285 (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]. 59.95/57.44 5286 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> v1_relat_1(k7_relat_1(B,k2_finseq_1(A))) & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))) & v1_funct_1(k7_relat_1(B,k2_finseq_1(A))))))) # label(t19_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5287 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (C = k10_finseq_1(A,B) <-> B = k1_funct_1(C,np__2) & A = k1_funct_1(C,np__1) & k3_finseq_1(C) = np__2))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5288 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> k4_finseq_1(A) = k1_relat_1(A))) # label(redefinition_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5289 (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]. 59.95/57.44 5290 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> A = k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),np__1)))) # label(t59_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5291 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k2_finseq_1(B) -> A = B))))) # label(t8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5292 (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]. 59.95/57.44 5293 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (A = k6_finseq_1(B) <-> np__0 = k3_finseq_1(A))))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5294 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(k2_finseq_1(A),k2_finseq_1(B)) -> B = A))))) # label(t74_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5295 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5296 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)) & v1_finseq_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5297 (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]. 59.95/57.44 5298 (all A all B (v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_finset_1(k10_relat_1(A,B)))) # label(fc18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5299 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5300 (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]. 59.95/57.44 5301 (all A (v4_ordinal2(A) -> k2_finseq_1(k2_xcmplx_0(A,np__1)) = k2_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5302 (all A (v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & -v1_xboole_0(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5303 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k9_finseq_1(A) = B <-> k2_relat_1(B) = k1_tarski(A) & k4_finseq_1(B) = k2_finseq_1(np__1)))) # label(t55_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5304 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(B)) & r1_xreal_0(np__1,C) -> k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C)) = k1_funct_1(B,C)))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5305 (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]. 59.95/57.44 5306 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5307 (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]. 59.95/57.44 5308 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(A,k2_finseq_1(B)) <-> r1_xreal_0(np__1,A) & r1_xreal_0(A,B)))))) # label(t3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5309 (all A ((exists B (r1_tarski(A,k2_finseq_1(B)) & v4_ordinal2(B))) -> (all B (m2_finseq_1(B,k5_numbers) -> (k14_finseq_1(A) = B <-> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(k1_funct_1(B,C) = E & r1_xreal_0(F,E) & k1_funct_1(B,D) = F & r1_xreal_0(D,k3_finseq_1(B)) & -r1_xreal_0(D,C) & r1_xreal_0(np__1,C)))))))))) & k2_relat_1(B) = A))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5310 (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]. 59.95/57.44 5311 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5312 (all A exists B (v1_relat_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v1_funct_1(B) & m1_relset_1(B,k5_numbers,A))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5313 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (k4_finseq_1(A) = k1_xboole_0 <-> A = k1_xboole_0))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5314 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5315 (all A all B all C all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (np__3 = k3_finseq_1(D) & B = k1_funct_1(D,np__2) & k1_funct_1(D,np__3) = C & k1_funct_1(D,np__1) = A <-> D = k11_finseq_1(A,B,C)))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5316 (all A (v1_finset_1(A) <-> (exists B (v1_relat_1(B) & v1_funct_1(B) & k2_relat_1(B) = A & v1_finseq_1(B))))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5317 (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]. 59.95/57.44 5318 (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]. 59.95/57.44 5319 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> A = k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)))))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5320 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) & r1_xreal_0(k1_nat_1(k3_finseq_1(A),np__1),C) -> k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t36_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5321 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k2_finseq_1(B) = k1_relat_1(A) <-> B = k3_finseq_1(A)))))) # label(d3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5322 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A))) # label(cc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5323 (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]. 59.95/57.44 5324 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5325 (all A (v1_relat_1(A) -> (v1_finseq_1(A) <-> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k2_finseq_1(B) = k1_relat_1(A)))))) # label(d2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5326 (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]. 59.95/57.44 5327 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> -(r2_hidden(A,k4_finseq_1(B)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(r2_hidden(k1_nat_1(k3_finseq_1(C),D),k4_finseq_1(k7_finseq_1(C,B))) & A = D)))))))) # label(t40_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5328 (all A all B (v1_finseq_1(A) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_finseq_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(dt_k7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5329 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k5_subset_1(k5_numbers,k2_finseq_1(A),k2_finseq_1(B)) = k2_finseq_1(A) -> r1_xreal_0(A,B)))))) # label(t10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5330 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k1_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5331 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5332 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5333 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.44 5334 (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]. 59.95/57.44 5335 (all A k1_tarski(k4_tarski(np__1,A)) = k5_finseq_1(A)) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5336 (all A (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) -> v1_finset_1(k1_relat_1(A)))) # label(fc17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5337 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5338 p1_s3_finseq_1(k1_xboole_0) & (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (p1_s3_finseq_1(A) -> p1_s3_finseq_1(k7_finseq_1(A,k9_finseq_1(B))))))) -> (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5339 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s2_finseq_1)) -> f2_s2_finseq_1(B) = k1_funct_1(A,B)))) & k3_finseq_1(A) = f1_s2_finseq_1 & v1_finseq_1(A))) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5340 (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]. 59.95/57.45 5341 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C))) -> r1_xreal_0(B,np__0) | r2_hidden(B,k2_finseq_1(A)) & r2_hidden(B,k2_finseq_1(k2_xcmplx_0(A,C)))))))))) # label(t82_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5342 (exists A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5343 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) = k3_finseq_1(k7_finseq_1(A,B)))))) # label(t35_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5344 (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]. 59.95/57.45 5345 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5346 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (k7_finseq_1(B,C) = k7_finseq_1(B,A) | k7_finseq_1(C,B) = k7_finseq_1(A,B) -> C = A))))))) # label(t46_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5347 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k3_finseq_1(A) = k3_finseq_1(B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(np__1,C) -> k1_funct_1(B,C) = k1_funct_1(A,C)))) -> B = A))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5348 (all A exists B (m1_finseq_1(B,A) & v1_xboole_0(B) & v1_finseq_1(B) & v1_finset_1(B) & v2_funct_1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5349 (all A k6_finseq_1(A) = k1_xboole_0) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5350 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k1_funct_1(k5_zf_lang(A,B),np__1) = np__1 & k1_funct_1(k4_zf_lang(A,B),np__1) = np__0)))) # label(t31_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5351 (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) -> -r1_zf_lang(C,k4_zf_lang(A,B)))))))) # label(t69_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5352 (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) -> -r1_zf_lang(C,k5_zf_lang(A,B)))))))) # label(t70_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.45 5353 (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 (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D (r1_xreal_0(np__1,C) & A = k1_funct_1(D,np__1) & B = k1_funct_1(D,C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> -(-r1_xreal_0(C,E) & (all F (v1_zf_lang(F) & m2_finseq_1(F,k5_numbers) -> (all G (m2_finseq_1(G,k5_numbers) & v1_zf_lang(G) -> -(G = k1_funct_1(D,k1_nat_1(E,np__1)) & r1_zf_lang(F,G) & k1_funct_1(D,E) = F))))) & r1_xreal_0(np__1,E)))) & C = k3_finseq_1(D) & v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D)))))))))) # label(d40_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.48 5354 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> 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]. 59.95/57.48 5355 (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) -> C = D & B = A))))))))) # label(t12_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.48 5356 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> 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]. 59.95/57.48 5357 (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) -> (r3_zf_lang(B,k8_zf_lang(A,C)) -> r2_zf_lang(B,C)))))))) # label(t92_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.48 5358 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> 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]. 59.95/57.48 5359 (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) -> (v6_zf_lang(A) & p1_s1_zf_lang(k24_zf_lang(A)) -> p1_s1_zf_lang(A)))) & (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v5_zf_lang(A) & p1_s1_zf_lang(k22_zf_lang(A)) & p1_s1_zf_lang(k21_zf_lang(A)) -> p1_s1_zf_lang(A)))) & (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) -> p1_s1_zf_lang(A))) # label(s1_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.48 5360 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (v6_zf_lang(A) -> (B = k24_zf_lang(A) <-> r1_zf_lang(B,A))))))) # label(t77_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.48 5361 (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]. 59.95/57.48 5362 (all A all B all C (m1_subset_1(B,k1_zf_lang) & m1_finseq_1(C,k5_numbers) & v1_zf_lang(C) & m1_subset_1(A,k1_zf_lang) -> v1_zf_lang(k15_zf_lang(A,B,C)) & m2_finseq_1(k15_zf_lang(A,B,C),k5_numbers))) # label(dt_k15_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.48 5363 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> v1_zf_lang(k25_zf_lang(A)) & m2_finseq_1(k25_zf_lang(A),k5_numbers))) # label(dt_k25_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.48 5364 $T # label(t3_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.48 5365 $T # label(t17_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.48 5366 (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) -> k13_zf_lang(A,k15_zf_lang(B,C,D)) = k17_zf_lang(A,B,C,D))))))))) # label(d27_zf_lang) # label(axiom) # label(non_clause). [assumption]. 59.95/57.48 5367 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v7_zf_lang(A) -> k19_zf_lang(A) = k1_funct_1(A,np__3)))) # label(d29_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5368 (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) -> -r1_zf_lang(C,B))) & r3_zf_lang(A,B)))))) # label(t84_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5369 (all A all B (m1_finseq_1(A,k5_numbers) & v1_zf_lang(B) & m1_finseq_1(B,k5_numbers) & v1_zf_lang(A) -> 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]. 62.17/59.64 5370 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> ((exists B (m2_finseq_1(B,k5_numbers) & k6_zf_lang(B) = A & v1_zf_lang(B))) <-> v4_zf_lang(A)))) # label(d12_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5371 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_nat_1(np__5,A) = k2_zf_lang(A))) # label(d2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5372 (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]. 62.17/59.64 5373 $T # label(t5_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5374 $T # label(t13_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5375 (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]. 62.17/59.64 5376 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k6_zf_lang(k8_zf_lang(A,k6_zf_lang(B))) = k13_zf_lang(A,B))))) # label(d19_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5377 (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) -> (r3_zf_lang(B,C) & r3_zf_lang(A,B) -> r3_zf_lang(A,C)))))))) # label(t85_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5378 (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) -> r2_hidden(k4_zf_lang(B,C),A) & r2_hidden(k5_zf_lang(B,C),A))))) & (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 (-v1_xboole_0(B) -> ((all C (r2_hidden(C,B) -> m2_finseq_1(C,k5_numbers))) & (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_zf_lang(C,D),B) & r2_hidden(k5_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 (m2_finseq_1(C,k5_numbers) -> (all D (m2_finseq_1(D,k5_numbers) -> (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k7_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)))))) -> r1_tarski(A,B)))) & (all B (m2_finseq_1(B,k5_numbers) -> (all C (m2_finseq_1(C,k5_numbers) -> (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k7_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 (r2_hidden(B,A) -> m2_finseq_1(B,k5_numbers))) <-> A = k9_zf_lang))) # label(d8_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5379 $T # label(t18_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5380 (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]. 62.17/59.64 5381 (exists A (m1_finseq_1(A,k5_numbers) & v1_relat_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_zf_lang(A) & v1_funct_1(A))) # label(rc1_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5382 $T # label(t8_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5383 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (m2_finseq_1(D,k5_numbers) & r2_zf_lang(D,A) & D = C & v1_zf_lang(D))))) <-> k29_zf_lang(A) = B)))) # label(d42_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5384 $T # label(t68_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5385 (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]. 62.17/59.64 5386 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v5_zf_lang(A) -> r3_zf_lang(k22_zf_lang(A),A) & r3_zf_lang(k21_zf_lang(A),A)))) # label(t95_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5387 (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) & r2_zf_lang(B,A) -> A = B))))) # label(t87_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5388 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 62.17/59.64 5389 (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(k5_zf_lang(A,B)) = k1_tarski(k5_zf_lang(A,B)))))) # label(t103_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5390 (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,k6_zf_lang(B)) -> r2_zf_lang(A,B)))))) # label(t90_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5391 (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) -> r3_zf_lang(A,B)))))) # label(t82_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5392 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (k29_zf_lang(A) = k1_tarski(A) <-> v7_zf_lang(A)))) # label(t107_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5393 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v6_zf_lang(A) | v11_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v6_zf_lang(A) -> ((exists C (m2_subset_1(C,k5_numbers,k1_zf_lang) & A = k8_zf_lang(C,B))) <-> k24_zf_lang(A) = B)) & (-v6_zf_lang(A) -> ((exists C (k13_zf_lang(C,B) = A & m2_subset_1(C,k5_numbers,k1_zf_lang))) <-> B = k24_zf_lang(A)))))))) # label(d34_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5394 $T # label(t15_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5395 (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]. 62.17/59.64 5396 (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_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (A = k7_finseq_1(B,C) -> A = B))))))) # label(t46_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5397 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 62.17/59.64 5398 (all A all B (v1_zf_lang(B) & m1_finseq_1(B,k5_numbers) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_zf_lang(k12_zf_lang(A,B)) & m2_finseq_1(k12_zf_lang(A,B),k5_numbers))) # label(dt_k12_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5399 (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)),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]. 62.17/59.64 5400 (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_xreal_0(k3_finseq_1(B),k3_finseq_1(A)) & r1_zf_lang(A,B)))))) # label(t81_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5401 (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)))))))) # label(d25_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5402 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (v8_zf_lang(A) -> ((exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k10_zf_lang(B,C) = A)) -> B = k21_zf_lang(A)) & -(B = k22_zf_lang(A) & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> k10_zf_lang(C,B) != A))) & ((exists C (m2_finseq_1(C,k5_numbers) & A = k10_zf_lang(C,B) & v1_zf_lang(C))) -> k22_zf_lang(A) = B) & -(k21_zf_lang(A) = B & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> k10_zf_lang(B,C) != A)))))))) # label(t57_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5403 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v8_zf_lang(A) | v5_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (-v5_zf_lang(A) -> ((exists C (k10_zf_lang(C,B) = A & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) <-> k22_zf_lang(A) = B)) & (v5_zf_lang(A) -> (B = k22_zf_lang(A) <-> (exists C (v1_zf_lang(C) & k7_zf_lang(C,B) = A & m2_finseq_1(C,k5_numbers)))))))))) # label(d32_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5404 (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]. 62.17/59.64 5405 (all A all B (m1_subset_1(B,k1_zf_lang) & m1_subset_1(A,k1_zf_lang) -> m2_finseq_1(k5_zf_lang(A,B),k5_numbers))) # label(dt_k5_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5406 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> m2_finseq_1(k20_zf_lang(A),k5_numbers) & v1_zf_lang(k20_zf_lang(A)))) # label(dt_k20_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5407 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v7_zf_lang(A) -> k1_funct_1(A,np__2) = k18_zf_lang(A)))) # label(d28_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5408 (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) -> -r3_zf_lang(C,k4_zf_lang(A,B)))))))) # label(t88_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5409 (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]. 62.17/59.64 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 (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> k13_zf_lang(A,k15_zf_lang(B,C,D)) = k17_zf_lang(A,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]. 62.17/59.64 5411 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -(-v2_zf_lang(A) & -v5_zf_lang(A) & -v6_zf_lang(A) & -v4_zf_lang(A) & -v3_zf_lang(A)))) # label(t25_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5412 (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) -> C = D & A = B))))))))) # label(t51_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5413 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v5_zf_lang(A) <-> (exists B ((exists C (m2_finseq_1(C,k5_numbers) & A = k7_zf_lang(B,C) & v1_zf_lang(C))) & m2_finseq_1(B,k5_numbers) & v1_zf_lang(B)))))) # label(d13_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.64 5414 (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]. 62.17/59.65 5415 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> -(-v7_zf_lang(A) & -v5_zf_lang(A) & -v6_zf_lang(A) & -v4_zf_lang(A)))) # label(t26_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5416 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> -(v7_zf_lang(A) & r3_zf_lang(B,A)))))) # label(t93_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5417 (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 (m2_finseq_1(C,k5_numbers) & A = k13_zf_lang(B,C) & v1_zf_lang(C)))))))) # label(d23_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5418 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v7_zf_lang(A) -> k18_zf_lang(A) = k1_funct_1(A,np__2) & k1_funct_1(A,np__3) = k19_zf_lang(A)))) # label(t52_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5419 (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]. 62.17/59.65 5420 (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) -> (k11_zf_lang(C,D) = k11_zf_lang(A,B) -> C = A & B = D))))))))) # label(t49_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5421 (all A all B (m1_finseq_1(A,k5_numbers) & m1_finseq_1(B,k5_numbers) & v1_zf_lang(B) & v1_zf_lang(A) -> 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]. 62.17/59.65 5422 (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) -> -(k23_zf_lang(B) = A & (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> B != k13_zf_lang(A,D)))) & ((exists D (B = k13_zf_lang(A,D) & m2_finseq_1(D,k5_numbers) & v1_zf_lang(D))) -> k23_zf_lang(B) = A) & ((exists D (B = k13_zf_lang(D,C) & m2_subset_1(D,k5_numbers,k1_zf_lang))) -> C = k24_zf_lang(B)) & -((all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> B != k13_zf_lang(D,C))) & k24_zf_lang(B) = C)))))))) # label(t61_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5423 (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) -> A = C & B = D))))))))) # label(t50_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5424 (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) & A = k13_zf_lang(B,C) & m2_finseq_1(C,k5_numbers))) <-> k23_zf_lang(A) = B)) & (v6_zf_lang(A) -> ((exists C (m2_finseq_1(C,k5_numbers) & A = k8_zf_lang(B,C) & v1_zf_lang(C))) <-> k23_zf_lang(A) = B))))))) # label(d33_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5425 (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) -> 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]. 62.17/59.65 5426 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (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]. 62.17/59.65 5427 (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_finseq_1(k5_zf_lang(A,B)) & v1_zf_lang(k5_zf_lang(A,B)) & v1_finset_1(k5_zf_lang(A,B)) & v1_funct_1(k5_zf_lang(A,B)))) # label(fc3_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5428 (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]. 62.17/59.65 5429 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v6_zf_lang(A) -> k1_funct_1(A,np__1) = np__4))) # label(t39_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5430 (all A ((exists B (B = A & r1_xreal_0(np__5,B) & 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]. 62.17/59.65 5431 (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 (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (r1_zf_lang(B,k8_zf_lang(A,C)) <-> B = C))))))) # label(t73_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5432 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v8_zf_lang(A) | v5_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v5_zf_lang(A) -> (k21_zf_lang(A) = B <-> (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k7_zf_lang(B,C) = A)))) & (-v5_zf_lang(A) -> ((exists C (v1_zf_lang(C) & A = k10_zf_lang(B,C) & m2_finseq_1(C,k5_numbers))) <-> B = k21_zf_lang(A)))))))) # label(d31_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5433 (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]. 62.17/59.65 5434 (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]. 62.17/59.65 5435 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_zf_lang(k27_zf_lang(A)) & m2_finseq_1(k27_zf_lang(A),k5_numbers))) # label(dt_k27_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5436 (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) -> (r2_hidden(B,k29_zf_lang(C)) -> -r2_zf_lang(A,B) & -r3_zf_lang(A,B) & -r1_zf_lang(A,B) | r2_hidden(A,k29_zf_lang(C))))))))) # label(t111_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5437 $T # label(t99_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5438 (all A all B (v1_zf_lang(A) & m1_finseq_1(B,k5_numbers) & v1_zf_lang(B) & m1_finseq_1(A,k5_numbers) -> v1_relat_1(k7_zf_lang(A,B)) & v1_funct_1(k7_zf_lang(A,B)) & v1_finset_1(k7_zf_lang(A,B)) & v1_finseq_1(k7_zf_lang(A,B)) & v1_zf_lang(k7_zf_lang(A,B)))) # label(fc5_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5439 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) <-> r2_hidden(A,k9_zf_lang))) # label(t14_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5440 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 62.17/59.65 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) -> (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]. 62.17/59.65 5442 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (k3_finseq_1(A) = np__3 -> v7_zf_lang(A)))) # label(t30_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5443 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v10_zf_lang(A) -> -((all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> k12_zf_lang(B,C) != A)) & B = k27_zf_lang(A)) & -(B = k28_zf_lang(A) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> k12_zf_lang(C,B) != A))) & ((exists C (v1_zf_lang(C) & A = k12_zf_lang(C,B) & m2_finseq_1(C,k5_numbers))) -> B = k28_zf_lang(A)) & ((exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k12_zf_lang(B,C) = A)) -> k27_zf_lang(A) = B)))))) # label(t66_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5444 (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 (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]. 62.17/59.65 5445 (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]. 62.17/59.65 5446 (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]. 62.17/59.65 5447 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (v4_zf_lang(A) -> (k20_zf_lang(A) = B <-> r1_zf_lang(B,A))))))) # label(t75_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5448 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> ((exists B (m2_subset_1(B,k5_numbers,k1_zf_lang) & (exists C (A = k4_zf_lang(B,C) & m2_subset_1(C,k5_numbers,k1_zf_lang))))) <-> v2_zf_lang(A)))) # label(d10_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5449 (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) -> -(r3_zf_lang(A,k7_zf_lang(B,C)) & -r2_zf_lang(A,B) & -r2_zf_lang(A,C)))))))) # label(t91_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5450 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 62.17/59.65 5451 (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]. 62.17/59.65 5452 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> -(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]. 62.17/59.65 5453 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k12_zf_lang(A,B) = k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,A)))))) # label(d18_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 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) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> A != k10_zf_lang(B,C))))) & v8_zf_lang(A)) & ((exists B (m2_finseq_1(B,k5_numbers) & (exists C (k10_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) & v1_zf_lang(B))) -> v8_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) -> k11_zf_lang(B,C) != A)))) & 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) & (exists C (A = k12_zf_lang(B,C) & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) & m2_finseq_1(B,k5_numbers))) -> v10_zf_lang(A)) & ((exists B ((exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & A = k13_zf_lang(B,C))) & m2_subset_1(B,k5_numbers,k1_zf_lang))) -> v11_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) -> k13_zf_lang(B,C) != A)))) & v11_zf_lang(A)) & ((exists B (m2_finseq_1(B,k5_numbers) & (exists C (v1_zf_lang(C) & A = k11_zf_lang(B,C) & m2_finseq_1(C,k5_numbers))) & v1_zf_lang(B))) -> v9_zf_lang(A)))) # label(t22_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5455 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_relat_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)) & v1_funct_1(k6_zf_lang(A)))) # label(fc4_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5456 (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]. 62.17/59.65 5457 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (v9_zf_lang(A) -> ((exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k11_zf_lang(C,B) = A)) -> B = k26_zf_lang(A)) & -((all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> A != k11_zf_lang(C,B))) & k26_zf_lang(A) = B) & ((exists C (m2_finseq_1(C,k5_numbers) & k11_zf_lang(B,C) = A & v1_zf_lang(C))) -> B = k25_zf_lang(A)) & -((all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> k11_zf_lang(B,C) != A)) & B = k25_zf_lang(A))))))) # label(t64_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5458 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (np__3 = k1_funct_1(A,np__1) -> v5_zf_lang(A)))) # label(t44_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 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 (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]. 62.17/59.65 5460 (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]. 62.17/59.65 5461 $T # label(dt_k29_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5462 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> 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]. 62.17/59.65 5463 (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]. 62.17/59.65 5464 (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]. 62.17/59.65 5465 $T # label(t1_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5466 $T # label(t11_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5467 (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,k6_zf_lang(B)) <-> B = A))))) # label(t71_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5468 (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) & A = k12_zf_lang(B,C) & m2_finseq_1(C,k5_numbers))) & v1_zf_lang(B))) <-> v10_zf_lang(A)))) # label(d22_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5469 (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) -> C = A & B = D))))))))) # label(t48_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5470 (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]. 62.17/59.65 5471 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (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]. 62.17/59.65 5472 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v2_zf_lang(A) -> np__0 = k1_funct_1(A,np__1)))) # label(t35_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5473 (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) -> 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]. 62.17/59.65 5474 (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]. 62.17/59.65 5475 (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]. 62.17/59.65 5476 (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]. 62.17/59.65 5477 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> np__4 = k1_funct_1(k8_zf_lang(A,B),np__1))))) # label(t34_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5478 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v8_zf_lang(A) -> A = k10_zf_lang(k21_zf_lang(A),k22_zf_lang(A))))) # label(t59_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5479 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (v5_zf_lang(A) -> ((exists C (A = k7_zf_lang(B,C) & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) -> k21_zf_lang(A) = B) & ((exists C (m2_finseq_1(C,k5_numbers) & k7_zf_lang(C,B) = A & v1_zf_lang(C))) -> k22_zf_lang(A) = B) & -((all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> k7_zf_lang(C,B) != A)) & k22_zf_lang(A) = B) & -(B = k21_zf_lang(A) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> A != k7_zf_lang(B,C))))))))) # label(t56_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5480 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k5_zf_lang(A,B) = 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)))))) # label(d4_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5481 (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]. 62.17/59.65 5482 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m2_finseq_1(k24_zf_lang(A),k5_numbers) & v1_zf_lang(k24_zf_lang(A)))) # label(dt_k24_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5483 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v5_zf_lang(A) -> k7_zf_lang(k21_zf_lang(A),k22_zf_lang(A)) = A))) # label(t58_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5484 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> 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]. 62.17/59.65 5485 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> m2_subset_1(k18_zf_lang(A),k5_numbers,k1_zf_lang))) # label(dt_k18_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5486 (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 = k10_zf_lang(B,C))) & v1_zf_lang(B))) <-> v8_zf_lang(A)))) # label(d20_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5487 (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_zf_lang(A,B) & B != A <-> r3_zf_lang(A,B)))))) # label(d41_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5488 (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) -> (B = k20_zf_lang(A) <-> k6_zf_lang(B) = A)))))) # label(d30_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5489 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v4_zf_lang(A) -> k1_funct_1(A,np__1) = np__2))) # label(t37_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5490 $T # label(t2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5491 (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]. 62.17/59.65 5492 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -(-v7_zf_lang(A) & (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))))))) # label(t28_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5493 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 62.17/59.65 5494 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v3_zf_lang(A) -> k5_zf_lang(k18_zf_lang(A),k19_zf_lang(A)) = A))) # label(t54_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5495 (all A all B (m1_subset_1(B,k1_zf_lang) & m1_subset_1(A,k1_zf_lang) -> v1_relat_1(k4_zf_lang(A,B)) & v1_finset_1(k4_zf_lang(A,B)) & v1_zf_lang(k4_zf_lang(A,B)) & v1_finseq_1(k4_zf_lang(A,B)) & v1_funct_1(k4_zf_lang(A,B)))) # label(fc2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5496 (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) -> -r3_zf_lang(C,k5_zf_lang(A,B)))))))) # label(t89_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5497 (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]. 62.17/59.65 5498 $T # label(t20_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5499 $T # label(t9_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5500 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v9_zf_lang(A) <-> (exists B (v1_zf_lang(B) & (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k11_zf_lang(B,C) = A)) & m2_finseq_1(B,k5_numbers)))))) # label(d21_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5501 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> r2_zf_lang(A,A))) # label(t79_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5502 $T # label(t19_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5503 $T # label(t78_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5504 $T # label(t21_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5505 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> m2_subset_1(k19_zf_lang(A),k5_numbers,k1_zf_lang))) # label(dt_k19_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5506 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v7_zf_lang(A) <-> v2_zf_lang(A) | v3_zf_lang(A)))) # label(d15_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5507 (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 (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (k7_zf_lang(A,B) = k7_zf_lang(C,D) -> B = D & C = A))))))))) # label(t47_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5508 (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]. 62.17/59.65 5509 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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) & k5_zf_lang(B,C) = A))))))) # label(d11_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5510 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v10_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (B = k27_zf_lang(A) <-> (exists C (v1_zf_lang(C) & k12_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers))))))))) # label(d37_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5511 (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) -> k4_zf_lang(B,C) != A)))) & v2_zf_lang(A)) & ((exists B ((exists C (m2_subset_1(C,k5_numbers,k1_zf_lang) & k4_zf_lang(B,C) = A)) & m2_subset_1(B,k5_numbers,k1_zf_lang))) -> 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) & k5_zf_lang(B,C) = A)))) -> v3_zf_lang(A)) & -((all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> A != k6_zf_lang(B))) & v4_zf_lang(A)) & -(v5_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 != k7_zf_lang(B,C)))))) & -(v6_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)))))) & ((exists B ((exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k8_zf_lang(B,C) = A)) & m2_subset_1(B,k5_numbers,k1_zf_lang))) -> v6_zf_lang(A)) & ((exists B (m2_finseq_1(B,k5_numbers) & (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k7_zf_lang(B,C) = A)) & v1_zf_lang(B))) -> v5_zf_lang(A)) & ((exists B (A = k6_zf_lang(B) & m2_finseq_1(B,k5_numbers) & v1_zf_lang(B))) -> v4_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))))))) # label(t16_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 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 (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> k8_zf_lang(A,k8_zf_lang(B,C)) = k14_zf_lang(A,B,C) & k13_zf_lang(A,k13_zf_lang(B,C)) = k15_zf_lang(A,B,C))))))) # label(t23_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5513 $T # label(t80_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5514 (all A (m1_subset_1(A,k1_zf_lang) -> k3_zf_lang(A) = k5_finseq_1(A))) # label(redefinition_k3_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5515 (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) -> (C = k5_zf_lang(A,B) <-> r2_zf_lang(C,k5_zf_lang(A,B))))))))) # label(t98_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5516 (all A all B (m1_subset_1(A,k1_zf_lang) & m1_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> m2_finseq_1(k13_zf_lang(A,B),k5_numbers) & v1_zf_lang(k13_zf_lang(A,B)))) # label(dt_k13_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5517 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m2_subset_1(k23_zf_lang(A),k5_numbers,k1_zf_lang))) # label(dt_k23_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5518 (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 & A = C))))))))) # label(t6_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5519 $T # label(t4_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5520 (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) <-> -(k6_zf_lang(A) != B & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> k7_zf_lang(A,C) != B & B != k7_zf_lang(C,A))) & (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> B != k8_zf_lang(C,A))))))))) # label(d39_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5521 (all A all B (m1_finseq_1(B,k5_numbers) & v1_zf_lang(B) & m1_subset_1(A,k1_zf_lang) -> v1_relat_1(k8_zf_lang(A,B)) & v1_funct_1(k8_zf_lang(A,B)) & v1_finset_1(k8_zf_lang(A,B)) & v1_zf_lang(k8_zf_lang(A,B)) & v1_finseq_1(k8_zf_lang(A,B)))) # label(fc6_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5522 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> np__2 = k1_funct_1(k6_zf_lang(A),np__1))) # label(t32_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5523 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v9_zf_lang(A) -> A = k11_zf_lang(k25_zf_lang(A),k26_zf_lang(A))))) # label(t65_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5524 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v9_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> ((exists C (m2_finseq_1(C,k5_numbers) & A = k11_zf_lang(C,B) & v1_zf_lang(C))) <-> B = k26_zf_lang(A))))))) # label(d36_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5525 (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) -> (r1_zf_lang(B,A) <-> k21_zf_lang(A) = B | B = k22_zf_lang(A))))))) # label(t76_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5526 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k1_tarski(k4_zf_lang(A,B)) = k29_zf_lang(k4_zf_lang(A,B)))))) # label(t102_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5527 (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]. 62.17/59.65 5528 (all A all B (m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) -> m2_finseq_1(k4_zf_lang(A,B),k5_numbers))) # label(dt_k4_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5529 (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) -> A = C & B = D))))))))) # label(t7_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5530 (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]. 62.17/59.65 5531 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 62.17/59.65 5532 (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) -> B != k8_zf_lang(A,D)))) & -((all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> k8_zf_lang(D,C) != B)) & k24_zf_lang(B) = C) & ((exists D (B = k8_zf_lang(D,C) & m2_subset_1(D,k5_numbers,k1_zf_lang))) -> C = k24_zf_lang(B)) & ((exists D (B = k8_zf_lang(A,D) & 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]. 62.17/59.65 5533 (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 = B | C = A <-> r1_zf_lang(A,k7_zf_lang(B,C))))))))) # label(t72_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5534 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v5_zf_lang(A) -> np__3 = k1_funct_1(A,np__1)))) # label(t38_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5535 $T # label(t55_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5536 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> -(-(np__0 = k1_funct_1(A,np__1) & v2_zf_lang(A)) & -(np__1 = k1_funct_1(A,np__1) & v3_zf_lang(A)) & -(v4_zf_lang(A) & k1_funct_1(A,np__1) = np__2) & -(k1_funct_1(A,np__1) = np__3 & v5_zf_lang(A)) & -(k1_funct_1(A,np__1) = np__4 & v6_zf_lang(A))))) # label(t40_zf_lang) # label(axiom) # label(non_clause). [assumption]. 62.17/59.65 5537 (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) -> ((exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & A = k11_zf_lang(B,C))) <-> k25_zf_lang(A) = B)))))) # label(d35_zf_lang) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5538 (all A all B (m1_finseq_1(B,k5_numbers) & m1_subset_1(A,k1_zf_lang) -> m2_finseq_1(k8_zf_lang(A,B),k5_numbers))) # label(dt_k8_zf_lang) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5539 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (v2_zf_lang(A) -> (all C (m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(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,k18_zf_lang(A)) = k8_funct_2(k1_zf_lang,B,C,k19_zf_lang(A)))))))))) # label(t7_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5540 (all A (-v1_xboole_0(A) -> (v1_zf_model(A) <-> r2_zf_model(A,k7_zf_model) & r2_zf_model(A,k8_zf_model) & r2_zf_model(A,k9_zf_model) & r2_zf_model(A,k10_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))))) & v1_ordinal1(A)))) # label(d12_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5541 (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]. 78.79/76.26 5542 (all A all B all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_1_zf_model(B,C)) <-> (exists D (m1_subset_1(D,k3_zf_model(B)) & D = A & (all E (m2_relset_1(E,k1_zf_lang,B) & v1_funct_2(E,k1_zf_lang,B) & v1_funct_1(E) -> (D = E -> 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))))))))))) # label(fraenkel_a_2_1_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5543 $T # label(t24_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5544 (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) -> (k8_funct_2(k1_zf_lang,A,B,D) = k8_funct_2(k1_zf_lang,A,B,C) <-> r1_zf_model(A,B,k4_zf_lang(C,D))))))))))) # label(t12_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5545 (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 (m2_relset_1(E,k1_zf_lang,D) & v1_funct_2(E,k1_zf_lang,D) & v1_funct_1(E) -> (r1_zf_model(D,E,k15_zf_lang(B,C,A)) <-> (exists F (r1_zf_model(D,F,A) & (all G (m2_subset_1(G,k5_numbers,k1_zf_lang) -> -(k8_funct_2(k1_zf_lang,D,E,G) != k8_funct_2(k1_zf_lang,D,F,G) & G != C & B != G))) & 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]. 78.79/76.26 5546 (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 (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]. 78.79/76.26 5547 (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_subset_1(D,k5_numbers,k1_zf_lang) -> ((all E (m2_relset_1(E,k1_zf_lang,A) & v1_funct_2(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) -> D = F))) -> 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]. 78.79/76.26 5548 (exists 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) -> C = f1_s2_zf_model(k18_zf_lang(B),k19_zf_lang(B))) & -(v4_zf_lang(B) & (all D -(C = f3_s2_zf_model(D) & r2_hidden(k4_tarski(k20_zf_lang(B),D),A)))) & -((all D all E -(f4_s2_zf_model(D,E) = C & r2_hidden(k4_tarski(k22_zf_lang(B),E),A) & r2_hidden(k4_tarski(k21_zf_lang(B),D),A))) & v5_zf_lang(B)) & -(v6_zf_lang(B) & (all D -(f5_s2_zf_model(k23_zf_lang(B),D) = C & r2_hidden(k4_tarski(k24_zf_lang(B),D),A)))) & (v3_zf_lang(B) -> C = f2_s2_zf_model(k18_zf_lang(B),k19_zf_lang(B))))))) & r2_hidden(k4_tarski(f6_s2_zf_model,f7_s2_zf_model),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))))))) & (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))))) & (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (r2_hidden(k4_tarski(B,C),A) -> -(v6_zf_lang(B) & (all D -(f5_s2_zf_model(k23_zf_lang(B),D) = C & r2_hidden(k4_tarski(k24_zf_lang(B),D),A)))) & -((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)) & v5_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)) & (v3_zf_lang(B) -> C = f2_s2_zf_model(k18_zf_lang(B),k19_zf_lang(B))) & (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,f8_s2_zf_model),A))) -> f7_s2_zf_model = f8_s2_zf_model # label(s2_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5549 (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) -> (v2_zf_lang(D) -> E = k2_tarski(k18_zf_lang(D),k19_zf_lang(D))) & -(v6_zf_lang(D) & (all F -(E = k4_xboole_0(k3_tarski(k1_tarski(F)),k1_tarski(k23_zf_lang(D))) & r2_hidden(k4_tarski(k24_zf_lang(D),F),C)))) & -((all F all G -(E = k3_tarski(k2_tarski(F,G)) & 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 -(F = E & r2_hidden(k4_tarski(k20_zf_lang(D),F),C))) & v4_zf_lang(D)) & (v3_zf_lang(D) -> E = k2_tarski(k18_zf_lang(D),k19_zf_lang(D))))))) & (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),k2_tarski(D,E)),C) & r2_hidden(k4_tarski(k4_zf_lang(D,E),k2_tarski(D,E)),C))))))) <-> k1_zf_model(A) = B)))) # label(d1_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5550 (all A all B all C all D (-v1_xboole_0(B) & m2_subset_1(D,k5_numbers,k1_zf_lang) & m2_subset_1(C,k5_numbers,k1_zf_lang) -> (r2_hidden(A,a_3_1_zf_model(B,C,D)) <-> (exists E (m1_subset_1(E,k3_zf_model(B)) & (all F (v1_funct_1(F) & v1_funct_2(F,k1_zf_lang,B) & m2_relset_1(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))))) & A = E))))) # label(fraenkel_a_3_1_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5551 (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_0_zf_model(B,C,D)) <-> (exists E ((all F (v1_funct_2(F,k1_zf_lang,B) & m2_relset_1(F,k1_zf_lang,B) & v1_funct_1(F) -> (E = F -> k8_funct_2(k1_zf_lang,B,F,C) = k8_funct_2(k1_zf_lang,B,F,D)))) & E = A & m1_subset_1(E,k3_zf_model(B))))))) # label(fraenkel_a_3_0_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5552 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k3_zf_model(A)))) # label(fc1_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.26 5553 (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) -> (r2_hidden(B,k5_zf_model(C,A)) <-> r1_zf_model(A,B,C)))))))) # label(d4_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.27 5554 $T # label(dt_k4_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.27 5555 $T # label(dt_k3_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.27 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 (m1_subset_1(D,A) -> (exists E (v1_funct_2(E,k1_zf_lang,A) & m2_relset_1(E,k1_zf_lang,A) & (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (C != F -> k8_funct_2(k1_zf_lang,A,E,F) = k8_funct_2(k1_zf_lang,A,B,F)))) & k8_funct_2(k1_zf_lang,A,E,C) = D & v1_funct_1(E))))))))))) # label(t21_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.27 5557 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (v4_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(k20_zf_lang(A),B)) <-> r2_hidden(C,k5_zf_model(A,B)))))))))) # label(t9_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.27 5558 (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_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (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,k11_zf_lang(C,D))))))))))) # label(t18_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.27 5559 (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]. 78.79/76.27 5560 (all A (-v1_xboole_0(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_funct_1(D) & m2_relset_1(D,k1_zf_lang,A) & v1_funct_2(D,k1_zf_lang,A) -> (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]. 78.79/76.27 5561 (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 (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,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]. 78.79/76.27 5562 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C ((exists 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))))) & (all E (m2_finseq_1(E,k5_numbers) & v1_zf_lang(E) -> (all F (r2_hidden(k4_tarski(E,F),D) -> -(v5_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(k22_zf_lang(E),H),D) & r2_hidden(k4_tarski(k21_zf_lang(E),G),D)))) & -((all G -(r2_hidden(k4_tarski(k24_zf_lang(E),G),D) & F = a_3_2_zf_model(B,E,G))) & v6_zf_lang(E)) & -(v4_zf_lang(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)))))) & (v3_zf_lang(E) -> a_2_1_zf_model(B,E) = F) & (v2_zf_lang(E) -> a_2_0_zf_model(B,E) = F))))) & r2_hidden(k4_tarski(A,C),D))) <-> C = k4_zf_model(A,B))))))) # label(d3_zf_model) # label(axiom) # label(non_clause). [assumption]. 78.79/76.27 5563 (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) -> (r1_zf_model(D,E,k14_zf_lang(B,C,A)) <-> (all F (v1_funct_1(F) & m2_relset_1(F,k1_zf_lang,D) & v1_funct_2(F,k1_zf_lang,D) -> ((all G (m2_subset_1(G,k5_numbers,k1_zf_lang) -> -(k8_funct_2(k1_zf_lang,D,F,G) != k8_funct_2(k1_zf_lang,D,E,G) & G != C & G != B))) -> r1_zf_model(D,F,A))))))))))))))) # label(t22_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.61 5564 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> k2_zf_model(A) = k1_zf_model(A))) # label(redefinition_k2_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.61 5565 (all A (-v1_xboole_0(A) -> (all B (B = k3_zf_model(A) <-> (all C (m2_relset_1(C,k1_zf_lang,A) & v1_funct_2(C,k1_zf_lang,A) & v1_funct_1(C) <-> r2_hidden(C,B))))))) # label(d2_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.61 5566 (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_1(C) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,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))) <-> r2_hidden(C,k5_zf_model(A,B)))))))))) # label(t8_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.61 5567 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> 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]. 83.14/80.61 5568 (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]. 83.14/80.61 5569 (all A (-v1_xboole_0(A) -> (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) -> (-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]. 83.14/80.61 5570 (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 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(A) & p1_s4_zf_model(B) -> p1_s4_zf_model(f4_s4_zf_model(A,B)))) & (all A (p1_s4_zf_model(A) -> p1_s4_zf_model(f3_s4_zf_model(A)))) & (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (B = f6_s4_zf_model(A) <-> (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(k4_zf_lang(D,E),f1_s4_zf_model(D,E)),C) & r2_hidden(k4_tarski(k5_zf_lang(D,E),f2_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) -> -((all F -(f5_s4_zf_model(k23_zf_lang(D),F) = E & r2_hidden(k4_tarski(k24_zf_lang(D),F),C))) & v6_zf_lang(D)) & -(v5_zf_lang(D) & (all F all G -(f4_s4_zf_model(F,G) = E & r2_hidden(k4_tarski(k21_zf_lang(D),F),C) & r2_hidden(k4_tarski(k22_zf_lang(D),G),C)))) & -(v4_zf_lang(D) & (all F -(f3_s4_zf_model(F) = E & r2_hidden(k4_tarski(k20_zf_lang(D),F),C)))) & (v3_zf_lang(D) -> E = f2_s4_zf_model(k18_zf_lang(D),k19_zf_lang(D))) & (v2_zf_lang(D) -> E = f1_s4_zf_model(k18_zf_lang(D),k19_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]. 83.14/80.61 5571 (all A all B (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) & -v1_xboole_0(B) -> k5_zf_model(A,B) = k4_zf_model(A,B))) # label(redefinition_k5_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.61 5572 (all A all B all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_0_zf_model(B,C)) <-> (exists D ((all E (v1_funct_2(E,k1_zf_lang,B) & m2_relset_1(E,k1_zf_lang,B) & v1_funct_1(E) -> (E = D -> k8_funct_2(k1_zf_lang,B,E,k18_zf_lang(C)) = k8_funct_2(k1_zf_lang,B,E,k19_zf_lang(C))))) & D = A & m1_subset_1(D,k3_zf_model(B))))))) # label(fraenkel_a_2_0_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5573 (all A all B all C all D (-v1_xboole_0(B) & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (r2_hidden(A,a_3_2_zf_model(B,C,D)) <-> (exists E (m1_subset_1(E,k3_zf_model(B)) & A = E & (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,G,I) != k8_funct_2(k1_zf_lang,B,H,I) -> k23_zf_lang(C) = I))) -> r2_hidden(H,F)))) & r2_hidden(G,F))))))))) # label(fraenkel_a_3_2_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5574 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all 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_s3_zf_model(D,E)),C) & r2_hidden(k4_tarski(k4_zf_lang(D,E),f1_s3_zf_model(D,E)),C))))) & r2_hidden(k4_tarski(A,B),C) & (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (all E (r2_hidden(k4_tarski(D,E),C) -> -(v5_zf_lang(D) & (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)))) & -(v6_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)))) & -(v4_zf_lang(D) & (all F -(f3_s3_zf_model(F) = E & r2_hidden(k4_tarski(k20_zf_lang(D),F),C)))) & (v3_zf_lang(D) -> E = f2_s3_zf_model(k18_zf_lang(D),k19_zf_lang(D))) & (v2_zf_lang(D) -> f1_s3_zf_model(k18_zf_lang(D),k19_zf_lang(D)) = E))))))) <-> B = f7_s3_zf_model(A))))) -> (v2_zf_lang(f6_s3_zf_model) -> f7_s3_zf_model(f6_s3_zf_model) = f1_s3_zf_model(k18_zf_lang(f6_s3_zf_model),k19_zf_lang(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)) & (v5_zf_lang(f6_s3_zf_model) -> (all A all B (A = f7_s3_zf_model(k21_zf_lang(f6_s3_zf_model)) & B = f7_s3_zf_model(k22_zf_lang(f6_s3_zf_model)) -> f4_s3_zf_model(A,B) = 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)) & (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]. 83.14/80.65 5575 $T # label(dt_k1_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5576 (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) -> (k8_funct_2(k1_zf_lang,A,D,C) = k8_funct_2(k1_zf_lang,A,D,B) <-> r2_hidden(D,k5_zf_model(k4_zf_lang(B,C),A))))))))))) # label(t2_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5577 (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) -> ((exists E (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) -> D = F))) & r1_zf_model(A,E,C) & m2_relset_1(E,k1_zf_lang,A) & v1_funct_2(E,k1_zf_lang,A))) <-> r1_zf_model(A,B,k13_zf_lang(D,C))))))))))) # label(t20_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5578 (all A (-v1_xboole_0(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> ((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))) <-> r2_zf_model(A,B)))))) # label(d5_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5579 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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) -> (r2_hidden(C,k5_zf_model(A,B)) <-> r2_hidden(C,k5_zf_model(k24_zf_lang(A),B)) & (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,D,E) != k8_funct_2(k1_zf_lang,B,C,E) -> k23_zf_lang(A) = E))) -> r2_hidden(D,k5_zf_model(k24_zf_lang(A),B))))))))))))) # label(t11_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5580 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> m2_finseq_1(k11_zf_model(A),k5_numbers) & v1_zf_lang(k11_zf_model(A)))) # label(dt_k11_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 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]. 83.14/80.65 5582 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v2_zf_lang(A) -> k2_zf_model(A) = k2_tarski(k18_zf_lang(A),k19_zf_lang(A))) & (v4_zf_lang(A) -> k2_zf_model(A) = k2_zf_model(k20_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)))) & (v6_zf_lang(A) -> k2_zf_model(A) = k4_xboole_0(k2_zf_model(k24_zf_lang(A)),k1_tarski(k23_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]. 83.14/80.65 5583 (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]. 83.14/80.65 5584 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (v5_zf_lang(A) -> (all C (m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) & v1_funct_1(C) -> (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]. 83.14/80.65 5585 (exists A exists 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(k4_tarski(k4_zf_lang(C,D),f1_s1_zf_model(C,D)),B) & r2_hidden(k4_tarski(k5_zf_lang(C,D),f2_s1_zf_model(C,D)),B))))) & r2_hidden(k4_tarski(f6_s1_zf_model,A),B) & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (r2_hidden(k4_tarski(C,D),B) -> (v3_zf_lang(C) -> D = f2_s1_zf_model(k18_zf_lang(C),k19_zf_lang(C))) & -(v4_zf_lang(C) & (all E -(f3_s1_zf_model(E) = D & r2_hidden(k4_tarski(k20_zf_lang(C),E),B)))) & -(v6_zf_lang(C) & (all E -(r2_hidden(k4_tarski(k24_zf_lang(C),E),B) & D = f5_s1_zf_model(k23_zf_lang(C),E)))) & -(v5_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)))) & (v2_zf_lang(C) -> D = f1_s1_zf_model(k18_zf_lang(C),k19_zf_lang(C))))))))) # label(s1_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5586 (all A (-v1_xboole_0(A) -> (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_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(C,A)) & (all E (m2_relset_1(E,k1_zf_lang,A) & v1_funct_2(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,D,F) != k8_funct_2(k1_zf_lang,A,E,F) -> B = F))) -> r2_hidden(E,k5_zf_model(C,A))))) <-> r2_hidden(D,k5_zf_model(k8_zf_lang(B,C),A))))))))))) # label(t6_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5587 (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 (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]. 83.14/80.65 5588 (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,D) & r1_zf_model(A,B,C) <-> r1_zf_model(A,B,k7_zf_lang(C,D))))))))))) # label(t15_zf_model) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5589 $T # label(dt_k1_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5590 (all A all B all C all D (v3_ordinal1(D) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) & -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))))))))) & E = A))))) # label(fraenkel_a_3_0_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5591 (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]. 83.14/80.65 5592 (all A all B (r2_zf_colla(A,B) <-> (exists C (r1_zf_colla(C,A,B) & v1_funct_1(C) & v1_relat_1(C))))) # label(d3_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5593 (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]. 83.14/80.65 5594 (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]. 83.14/80.65 5595 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (m1_subset_1(C,A) -> k9_relat_1(B,C) = k1_funct_1(B,C))) & A = k1_relat_1(B) -> v1_ordinal1(k2_relat_1(B))))))) # label(t12_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5596 (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]. 83.14/80.65 5597 $T # label(t11_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5598 (all A all B all C (-v1_xboole_0(B) & v3_ordinal1(C) -> ((exists D (m1_subset_1(D,B) & A = D & (all E (m1_subset_1(E,B) -> -((all F (v3_ordinal1(F) -> -(r2_hidden(E,k1_zf_colla(B,F)) & r2_hidden(F,C)))) & r2_hidden(E,D)))))) <-> r2_hidden(A,a_2_1_zf_colla(B,C))))) # label(fraenkel_a_2_1_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5599 (all A all B all C (-v1_xboole_0(B) & v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) -> ((exists D ((all E (m1_subset_1(E,B) -> -(r2_hidden(E,D) & (all F (v3_ordinal1(F) -> -(r2_hidden(E,k3_tarski(k1_tarski(k1_funct_1(C,F)))) & r2_hidden(F,k1_relat_1(C)))))))) & A = D & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_0_zf_colla(B,C))))) # label(fraenkel_a_2_0_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5600 (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]. 83.14/80.65 5601 (all A (-v1_xboole_0(A) -> (all B (v3_ordinal1(B) -> (all C (C = k1_zf_colla(A,B) <-> (exists D (v1_relat_1(D) & v5_ordinal1(D) & B = k1_relat_1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(E,B) -> k1_funct_1(D,E) = a_3_0_zf_colla(A,D,E)))) & C = a_2_0_zf_colla(A,D) & v1_funct_1(D))))))))) # label(d1_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5602 (all A (-v1_xboole_0(A) -> -((all B -(v1_ordinal1(B) & r2_zf_colla(A,B))) & r2_zf_model(A,k6_zf_model)))) # label(t14_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5603 (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 (v3_ordinal1(E) & r2_hidden(E,B) & r2_hidden(C,k1_zf_colla(A,E))))))))))))) # label(t6_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5604 (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]. 83.14/80.65 5605 $T # label(t10_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5606 (all A (-v1_xboole_0(A) -> (exists B (A = k1_zf_colla(A,B) & v3_ordinal1(B))))) # label(t8_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5607 (all A (-v1_xboole_0(A) -> (exists B ((all C (m1_subset_1(C,A) -> k1_funct_1(B,C) = k9_relat_1(B,C))) & A = k1_relat_1(B) & v1_funct_1(B) & v1_relat_1(B))))) # label(t9_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5608 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v2_funct_1(A) & (all D all E (r2_hidden(D,B) & r2_hidden(E,B) -> -((all F -(r2_hidden(D,F) & F = E)) & (exists F (r2_hidden(k1_funct_1(A,D),F) & F = k1_funct_1(A,E)))) & -((exists F (F = E & r2_hidden(D,F))) & (all F -(r2_hidden(k1_funct_1(A,D),F) & k1_funct_1(A,E) = F))))) & C = k2_relat_1(A) & k1_relat_1(A) = B <-> r1_zf_colla(A,B,C))))) # label(d2_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5609 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> ((all C (m1_subset_1(C,A) -> -r2_hidden(C,B))) <-> r2_hidden(B,k1_zf_colla(A,k1_xboole_0))))))) # label(t2_zf_colla) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5610 (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]. 83.14/80.65 5611 $T # label(t168_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5612 $T # label(t63_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5613 (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]. 83.14/80.65 5614 $T # label(t11_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5615 $T # label(t172_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5616 (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]. 83.14/80.65 5617 (all A (-v1_xboole_0(A) -> (-r2_hidden(k1_xboole_0,A) -> (all B (v1_funct_2(B,A,k3_tarski(A)) & m2_relset_1(B,A,k3_tarski(A)) & v1_funct_1(B) -> (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]. 83.14/80.65 5618 (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]. 83.14/80.65 5619 $T # label(t10_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5620 (all A all B all C all D (v1_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) & v4_relat_2(D) -> (r2_hidden(B,A) & r2_hidden(k4_tarski(C,B),D) & r2_hidden(k4_tarski(B,C),D) & r2_hidden(C,A) -> B = C))) # label(t13_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5621 $T # label(t123_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5622 $T # label(t41_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5623 (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]. 83.14/80.65 5624 $T # label(t31_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5625 (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]. 83.14/80.65 5626 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_hidden(A,k1_orders_1(B)) <-> m1_subset_1(A,k1_zfmisc_1(B))))))) # label(t6_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5627 $T # label(t103_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5628 $T # label(t43_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5629 (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]. 83.14/80.65 5630 $T # label(t60_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5631 $T # label(t148_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5632 (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]. 83.14/80.65 5633 (all A (v1_relat_1(A) -> (all 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)) <-> r8_orders_1(A,B))))) # label(d13_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5634 (all A (v1_relat_1(A) -> (all B (r4_orders_1(A,B) <-> (all C -((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)) & r1_tarski(C,B))))))) # label(d9_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5635 (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]. 83.14/80.65 5636 (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]. 83.14/80.65 5637 (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]. 83.14/80.65 5638 (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]. 83.14/80.65 5639 $T # label(t144_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5640 (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]. 83.14/80.65 5641 $T # label(t49_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5642 $T # label(t33_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5643 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) & r8_relat_2(A,B) <-> r1_orders_1(A,B))))) # label(d6_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5644 $T # label(t44_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5645 $T # label(t21_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5646 (all A (-v1_xboole_0(A) -> (exists B m1_orders_1(B,A)))) # label(existence_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5647 (all A (v1_relat_1(A) -> (all B all C (v1_relat_2(A) & r1_tarski(C,k3_relat_1(A)) & r9_orders_1(A,B) & r2_hidden(B,C) -> r5_orders_1(A,C))))) # label(t162_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5648 (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]. 83.14/80.65 5649 $T # label(t42_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5650 $T # label(t84_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5651 $T # label(t121_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5652 $T # label(t71_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5653 $T # label(t72_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5654 (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]. 83.14/80.65 5655 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) & r6_relat_2(A,B) & r8_relat_2(A,B) & r1_relat_2(A,B) <-> r3_orders_1(A,B))))) # label(d8_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5656 $T # label(t101_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5657 $T # label(t69_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5658 (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]. 83.14/80.65 5659 $T # label(t52_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5660 (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]. 83.14/80.65 5661 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k3_relat_1(B) = A)) # label(t97_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5662 $T # label(t87_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5663 $T # label(t73_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5664 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> v2_orders_1(A) & v3_orders_1(A) & v1_orders_1(A)))) # label(t107_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5665 $T # label(t88_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5666 $T # label(t1_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5667 $T # label(t77_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5668 (all A -(k1_xboole_0 != A & (all B -(r1_tarski(B,A) & (all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(D,C))))) & v6_ordinal1(B))) & (all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & r1_tarski(B,C) & B != C)))))) # label(t175_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5669 $T # label(t89_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5670 (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]. 83.14/80.65 5671 (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]. 83.14/80.65 5672 (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]. 83.14/80.65 5673 (all A all B (v4_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v1_relat_2(B) -> A = k3_relat_1(B))) # label(t100_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5674 $T # label(t59_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5675 $T # label(t79_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5676 $T # label(t36_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5677 (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]. 83.14/80.65 5678 $T # label(t53_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5679 (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]. 83.14/80.65 5680 $T # label(t18_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5681 $T # label(t8_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5682 $T # label(t153_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5683 (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]. 83.14/80.65 5684 $T # label(t35_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5685 $T # label(t66_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5686 $T # label(t51_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5687 (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]. 83.14/80.65 5688 (all A (-((all B -(r2_hidden(B,A) & B != k1_xboole_0)) & k1_xboole_0 != k3_tarski(A)) & -(k1_xboole_0 = k3_tarski(A) & (exists B (r2_hidden(B,A) & B != k1_xboole_0))))) # label(t91_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5689 $T # label(t45_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.14/80.65 5690 $T # label(t102_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5691 $T # label(t2_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5692 $T # label(t39_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5693 $T # label(t48_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5694 $T # label(t37_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5695 $T # label(t82_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5696 $T # label(t28_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5697 (all A (m1_subset_1(A,f1_s1_orders_1) -> p1_s1_orders_1(A,A))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (p1_s1_orders_1(A,B) & p1_s1_orders_1(B,A) -> A = B))))) & (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) -> (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)))))) & (all B (m1_subset_1(B,f1_s1_orders_1) -> (exists C (r2_hidden(C,A) & -p1_s1_orders_1(C,B) & m1_subset_1(C,f1_s1_orders_1))))) & r1_tarski(A,f1_s1_orders_1))) -> (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]. 83.20/80.68 5698 (all A (v1_orders_1(k6_partfun1(A)) & v2_orders_1(k6_partfun1(A)))) # label(t120_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5699 $T # label(t56_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5700 $T # label(t61_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5701 (all A (v1_relat_1(A) -> (all B -(r5_orders_1(A,B) & B = k1_xboole_0)))) # label(t150_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5702 (all A (v1_relat_1(A) -> k2_wellord1(A,k1_xboole_0) = k1_xboole_0)) # label(t194_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5703 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,k3_relat_1(A)) -> C = B | r2_hidden(k4_tarski(B,C),A))) & r2_hidden(B,k3_relat_1(A)) <-> r9_orders_1(A,B))))) # label(d14_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5704 $T # label(t78_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5705 (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]. 83.20/80.68 5706 (all A (v1_relat_1(A) -> (all B (r9_orders_1(A,B) <-> r8_orders_1(k4_relat_1(A),B))))) # label(t165_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5707 (all A (v1_relat_1(A) -> (all B -(B = k3_relat_1(A) & (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]. 83.20/80.68 5708 $T # label(t58_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5709 (all A (v1_relat_1(A) -> (all B (r3_orders_1(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) & v4_relat_2(k2_wellord1(A,B)) & v1_relat_2(k2_wellord1(A,B)))))) # label(t142_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5710 (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]. 83.20/80.68 5711 (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]. 83.20/80.68 5712 (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]. 83.20/80.68 5713 $T # label(t85_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5714 (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]. 83.20/80.68 5715 (all A (v1_relat_1(A) -> (all B (r2_hidden(B,k3_relat_1(A)) & (all C -(r2_hidden(k4_tarski(B,C),A) & C != B & r2_hidden(C,k3_relat_1(A)))) <-> r6_orders_1(A,B))))) # label(d11_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5716 $T # label(t23_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5717 $T # label(t154_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5718 (all A (v1_relat_1(A) -> (all B -(k3_relat_1(A) = B & (all C -r7_orders_1(A,C)) & r5_orders_1(A,B) & r2_orders_1(A,B))))) # label(t174_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5719 (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]. 83.20/80.68 5720 $T # label(t156_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5721 $T # label(t15_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5722 (all A -((all B -((all C -(r2_hidden(C,A) & B != C & r1_tarski(C,B))) & r2_hidden(B,A))) & (all B -((all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(C,D))))) & v6_ordinal1(B) & r1_tarski(B,A))) & k1_xboole_0 != A)) # label(t176_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5723 (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]. 83.20/80.68 5724 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B) & v8_relat_2(k2_wellord1(A,B)))))) # label(t143_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5725 $T # label(t80_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5726 $T # label(t9_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5727 $T # label(t32_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5728 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> r1_orders_1(A,B) & r2_orders_1(A,B))))) # label(t125_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5729 $T # label(t90_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5730 $T # label(t34_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5731 (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]. 83.20/80.68 5732 $T # label(t54_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5733 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)) & v8_relat_2(k2_wellord1(A,B)) & v1_partfun1(k2_wellord1(A,B),B,B) & m2_relset_1(k2_wellord1(A,B),B,B))))) # label(t141_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5734 (all A (v1_relat_1(A) -> (all B all C (r2_hidden(B,C) & r8_orders_1(A,B) & r1_tarski(C,k3_relat_1(A)) & v1_relat_2(A) -> r4_orders_1(A,C))))) # label(t161_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5735 $T # label(t30_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5736 $T # label(t17_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5737 (all A all B all C (v4_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v1_relat_2(C) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t12_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5738 $T # label(t19_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5739 (all A (-v1_xboole_0(A) -> r2_hidden(A,k1_orders_1(A)))) # label(t7_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5740 (all A (v1_relat_1(A) -> (all B (r4_orders_1(A,B) <-> r5_orders_1(k4_relat_1(A),B))))) # label(t151_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5741 $T # label(t86_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5742 $T # label(t62_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5743 (all A (v1_relat_1(A) -> (all B (v6_relat_2(A) & r6_orders_1(A,B) -> r8_orders_1(A,B))))) # label(t160_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5744 $T # label(t169_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5745 (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]. 83.20/80.68 5746 (all A (v1_relat_1(A) -> (all B -(k3_relat_1(A) = B & (all C -r6_orders_1(A,C)) & r4_orders_1(A,B) & r2_orders_1(A,B))))) # label(t173_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5747 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v1_orders_1(A)))) # label(t109_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5748 $T # label(t117_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5749 $T # label(t64_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5750 $T # label(t57_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5751 $T # label(dt_k1_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5752 (all A (-v1_xboole_0(A) -> (all B (m1_orders_1(B,A) -> m2_relset_1(B,A,k3_tarski(A)) & v1_funct_2(B,A,k3_tarski(A)) & v1_funct_1(B))))) # label(dt_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5753 $T # label(t46_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5754 (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]. 83.20/80.68 5755 (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]. 83.20/80.68 5756 (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]. 83.20/80.68 5757 (all A (r1_orders_1(k6_partfun1(A),A) & r2_orders_1(k6_partfun1(A),A))) # label(t146_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5758 (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]. 83.20/80.68 5759 $T # label(t16_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5760 $T # label(t20_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5761 $T # label(t55_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5762 (all A (v1_relat_1(A) -> (v4_relat_2(A) & v6_relat_2(A) & v8_relat_2(A) & v1_relat_2(A) <-> v3_orders_1(A)))) # label(d5_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5763 (all A -((all B (v6_ordinal1(B) & r1_tarski(B,A) -> r2_hidden(k3_tarski(B),A) | B = k1_xboole_0)) & (all B -(r2_hidden(B,A) & (all C -(r1_tarski(B,C) & B != C & r2_hidden(C,A))))) & A != k1_xboole_0)) # label(t177_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5764 (all A (v1_relat_1(A) -> (all B (r6_orders_1(A,B) <-> r7_orders_1(k4_relat_1(A),B))))) # label(t164_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5765 (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]. 83.20/80.68 5766 $T # label(t81_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5767 $T # label(t27_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5768 (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]. 83.20/80.68 5769 (all A -(k1_xboole_0 != A & (all B (v6_ordinal1(B) & r1_tarski(B,A) -> r2_hidden(k1_setfam_1(B),A) | B = k1_xboole_0)) & (all B -(r2_hidden(B,A) & (all C -(r1_tarski(C,B) & C != B & r2_hidden(C,A))))))) # label(t178_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5770 $T # label(t65_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5771 $T # label(t3_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5772 $T # label(t25_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.68 5773 (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]. 83.20/80.70 5774 $T # label(t167_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.70 5775 $T # label(t70_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.70 5776 $T # label(t47_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.70 5777 (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]. 83.20/80.70 5778 $T # label(t24_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.70 5779 $T # label(t40_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.70 5780 (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]. 83.20/80.70 5781 $T # label(t26_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.70 5782 $T # label(t147_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5783 $T # label(t76_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5784 (all A (v1_relat_1(A) -> (all B ((all C -(v3_orders_1(k2_wellord1(A,C)) & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),A))) & r2_hidden(D,B))) & r1_tarski(C,B))) <-> r5_orders_1(A,B))))) # label(d10_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5785 $T # label(t38_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5786 (all A all B (v1_relat_1(B) -> (r6_relat_2(B,A) & r1_relat_2(B,A) <-> r7_relat_2(B,A)))) # label(t92_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5787 $T # label(t122_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5788 $T # label(t116_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5789 (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]. 83.20/80.71 5790 (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]. 83.20/80.71 5791 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r2_orders_1(A,B) -> r2_orders_1(A,C))))) # label(t131_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5792 $T # label(t29_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5793 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) -> (v6_relat_2(B) -> v3_orders_1(B)))) # label(t112_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5794 (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]. 83.20/80.71 5795 (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]. 83.20/80.71 5796 (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]. 83.20/80.71 5797 (all A all B all C all D all E (v4_relat_2(E) & v8_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v1_relat_2(E) -> (r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(k4_tarski(B,C),E) -> r2_hidden(k4_tarski(B,D),E)))) # label(t14_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5798 $T # label(t67_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5799 $T # label(t145_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5800 $T # label(t171_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5801 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_orders_1(A)))) # label(fc1_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5802 (all A all B (v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> r2_orders_1(B,A))) # label(t140_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5803 (all A (m1_subset_1(A,f1_s2_orders_1) -> (all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> (p1_s2_orders_1(A,B) & p1_s2_orders_1(B,C) -> p1_s2_orders_1(A,C)))))))) & (all A -(r1_tarski(A,f1_s2_orders_1) & (all B (m1_subset_1(B,f1_s2_orders_1) -> (exists C (m1_subset_1(C,f1_s2_orders_1) & r2_hidden(C,A) & -p1_s2_orders_1(B,C))))) & (all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> -(-p1_s2_orders_1(C,B) & -p1_s2_orders_1(B,C) & r2_hidden(C,A) & r2_hidden(B,A)))))))) & (all 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 (m1_subset_1(A,f1_s2_orders_1) -> p1_s2_orders_1(A,A))) -> (exists A (m1_subset_1(A,f1_s2_orders_1) & (all B (m1_subset_1(B,f1_s2_orders_1) -> -(p1_s2_orders_1(B,A) & A != B))))) # label(s2_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5804 (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]. 83.20/80.71 5805 (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]. 83.20/80.71 5806 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(k4_tarski(C,B),A) & B != C & r2_hidden(C,k3_relat_1(A)))) & r2_hidden(B,k3_relat_1(A)) <-> r7_orders_1(A,B))))) # label(d12_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5807 $T # label(t83_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5808 $T # label(t155_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5809 (all A all B (m2_relset_1(B,A,A) -> (r1_relat_2(B,A) -> A = k3_relat_1(B) & A = k4_relset_1(A,A,B)))) # label(t98_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5810 $T # label(t170_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5811 $T # label(t50_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5812 $T # label(t118_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5813 (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) -> k4_relset_1(A,A,B) = A & k5_relset_1(A,A,B) = A)) # label(t99_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5814 $T # label(t68_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5815 (all A (v1_relat_1(A) -> (v4_relat_2(A) & v8_relat_2(A) & v1_relat_2(A) <-> v2_orders_1(A)))) # label(d4_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5816 $T # label(t75_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5817 $T # label(t22_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5818 $T # label(t74_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5819 (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]. 83.20/80.71 5820 (all A (v1_relat_1(A) -> (all B (v1_relat_2(A) & r1_tarski(B,k3_relat_1(A)) -> k3_relat_1(k2_wellord1(A,B)) = B)))) # label(t181_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5821 (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]. 83.20/80.71 5822 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B -((all C -(r1_tarski(C,k1_relat_1(A)) & k9_relat_1(A,C) = B & v1_finset_1(C))) & r1_tarski(B,k2_relat_1(A)) & v1_finset_1(B))))) # label(t195_orders_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5823 (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]. 83.20/80.71 5824 (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))) -> 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)) | B = k1_xboole_0))) # label(t19_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5825 (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]. 83.20/80.71 5826 (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 (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_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]. 83.20/80.71 5827 (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]. 83.20/80.71 5828 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5829 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5830 (all A (v1_relat_2(k1_eqrel_1(A)) & v3_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v8_relat_2(k1_eqrel_1(A)) & v1_relat_1(k1_eqrel_1(A)))) # label(fc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5831 (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]. 83.20/80.71 5832 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & m1_relset_1(B,A,A) -> B = k5_eqrel_1(A,B,B))) # label(idempotence_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5833 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5834 (all A all B all C all D (v3_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) -> (r2_hidden(k4_tarski(B,C),D) -> r2_hidden(k4_tarski(C,B),D)))) # label(t12_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5835 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(k4_tarski(D,B),C) <-> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B)))))) # label(t44_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5836 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5837 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5838 (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) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> -(B != k1_eqrel_1(A) & k1_eqrel_1(A) != C & k1_eqrel_1(A) = k3_eqrel_1(A,B,C)))))) # label(t38_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5839 (all A all B (-v1_xboole_0(A) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(B) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5840 (all A k1_eqrel_1(A) = k2_zfmisc_1(A,A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5841 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> -((exists C r2_hidden(C,A)) & k1_xboole_0 = B))) # label(t14_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5842 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5843 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5844 (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]. 83.20/80.71 5845 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> ((exists C A = k6_eqrel_1(A,B,C)) -> k1_eqrel_1(A) = B))) # label(t35_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5846 (all A all B (m2_relset_1(B,A,A) -> (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) <-> A = k3_relat_1(B) & v8_relat_2(B) & v3_relat_2(B) & v1_relat_2(B)))) # label(t16_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5847 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) -> k7_eqrel_1(A,B) = k8_eqrel_1(A,B))) # label(redefinition_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5848 (all A all B (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & -v1_xboole_0(A) -> -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]. 83.20/80.71 5849 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & m1_relset_1(B,A,A) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))) # label(commutativity_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5850 (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 (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))))) <-> k7_eqrel_1(A,B) = C))))) # label(d5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5851 (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 (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> B = k5_eqrel_1(A,B,k4_eqrel_1(A,B,C)))))) # label(t25_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5852 (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) -> k3_xboole_0(B,C) = k4_eqrel_1(A,B,C))) # label(redefinition_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5853 (all A all B all C (v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & 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]. 83.20/80.71 5854 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != A -> (k5_setfam_1(A,B) = A & (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)) -> -(D != C & -r1_xboole_0(C,D) & r2_hidden(D,B))))))) <-> m1_eqrel_1(B,A))) & (k1_xboole_0 = A -> (m1_eqrel_1(B,A) <-> B = k1_xboole_0)))) # label(d6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5855 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5856 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k4_eqrel_1(A,k6_partfun1(A),B) = k6_partfun1(A))) # label(t17_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5857 (all A all B all C (m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> (all D (r2_hidden(D,A) -> (k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) <-> r2_hidden(B,k6_eqrel_1(A,C,D))))))) # label(t31_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5858 (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 (v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & 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]. 83.20/80.71 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 all D -(r2_hidden(D,A) & k6_eqrel_1(A,B,D) != k6_eqrel_1(A,B,C) & -r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) & r2_hidden(C,A))))) # label(t32_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5860 (all A (v1_relat_1(k1_eqrel_1(A)) & v1_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A))) # label(fc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5861 (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 k6_eqrel_1(A,B,C) = k10_relset_1(A,A,B,k1_tarski(C))))) # label(d4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5862 (all A all B all C all D (v1_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v3_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]. 83.20/80.71 5863 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_eqrel_1(A,B,B) = B)) # label(idempotence_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5864 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5865 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_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]. 83.20/80.71 5866 (all A all B all C all D all E (v1_relat_2(E) & v3_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v8_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]. 83.20/80.71 5867 (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]. 83.20/80.71 5868 (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]. 83.20/80.71 5869 (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]. 83.20/80.71 5870 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5871 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(B) -> m1_eqrel_1(k8_eqrel_1(A,B),A))) # label(dt_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5872 (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 (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> (all D (v3_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v8_relat_2(D) -> (r1_tarski(k3_eqrel_1(A,B,C),D) & (all E (v3_relat_2(E) & v8_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) -> (r1_tarski(k3_eqrel_1(A,B,C),E) -> r1_tarski(D,E)))) <-> k5_eqrel_1(A,B,C) = D))))))) # label(d3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5873 (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]. 83.20/80.71 5874 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k2_xboole_0(B,C) = k3_eqrel_1(A,B,C))) # label(redefinition_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5875 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5876 (all A all B (m2_relset_1(B,A,A) -> B = k2_eqrel_1(A,k1_eqrel_1(A),B))) # label(t18_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5877 (all A (v8_relat_2(k1_eqrel_1(A)) & m2_relset_1(k1_eqrel_1(A),A,A) & v1_partfun1(k1_eqrel_1(A),A,A) & v3_relat_2(k1_eqrel_1(A)))) # label(t7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5878 (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]. 83.20/80.71 5879 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5880 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k2_eqrel_1(A,B,C) = k2_eqrel_1(A,C,B))) # label(commutativity_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5881 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> v3_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) & v8_relat_2(k4_eqrel_1(A,B,C)))) # label(dt_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5882 (all A (r1_relat_2(k6_partfun1(A),A) & r8_relat_2(k6_partfun1(A),A) & r3_relat_2(k6_partfun1(A),A))) # label(t4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5883 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5884 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> (all D (v3_relat_2(D) & v8_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) -> (D = k3_eqrel_1(A,B,C) -> (all E -(r2_hidden(E,A) & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,C,E) & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,B,E)))))))))) # label(t37_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5885 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> m1_eqrel_1(k7_eqrel_1(A,B),A))) # label(t42_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5886 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k4_eqrel_1(A,B,C) = k4_eqrel_1(A,C,B))) # label(commutativity_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5887 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5888 (all A all B all C (v1_partfun1(B,A,A) & 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) & v8_relat_2(B) & v3_relat_2(B) -> v8_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) & v3_relat_2(k5_eqrel_1(A,B,C)))) # label(dt_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5889 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,B,B) & m2_relset_1(C,B,B) & v8_relat_2(C) -> -((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]. 83.20/80.71 5890 (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]. 83.20/80.71 5891 (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]. 83.20/80.71 5892 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5893 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_eqrel_1(A,B,C) = k3_eqrel_1(A,C,B))) # label(commutativity_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5894 (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]. 83.20/80.71 5895 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5896 (all A all B all C (m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> B = k4_eqrel_1(A,B,B))) # label(idempotence_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5897 (all A all B (m1_eqrel_1(B,A) -> (exists C (v3_relat_2(C) & v8_relat_2(C) & B = k7_eqrel_1(A,C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A))))) # label(t43_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5898 (all A (v3_relat_2(k6_partfun1(A)) & v8_relat_2(k6_partfun1(A)) & m2_relset_1(k6_partfun1(A),A,A) & v1_partfun1(k6_partfun1(A),A,A))) # label(t6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5899 (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]. 83.20/80.71 5900 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5901 (all A all B all C all D (v3_relat_2(D) & v8_relat_2(D) & v1_partfun1(D,B,B) & m2_relset_1(D,B,B) -> (all E (v3_relat_2(E) & v8_relat_2(E) & m2_relset_1(E,B,B) & v1_partfun1(E,B,B) -> (r2_hidden(A,B) -> (r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E)) <-> (exists 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)))) & C = k1_funct_1(F,k3_finseq_1(F)) & A = k1_funct_1(F,np__1) & r1_xreal_0(np__1,k3_finseq_1(F)) & v1_finseq_1(F) & v1_funct_1(F) & v1_relat_1(F))))))))) # label(t36_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5902 (all A (r2_hidden(A,f1_s1_eqrel_1) -> p1_s1_eqrel_1(A,A))) & (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))) -> (exists A (v3_relat_2(A) & m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & (all B all C (r2_hidden(B,f1_s1_eqrel_1) & r2_hidden(C,f1_s1_eqrel_1) & p1_s1_eqrel_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))) & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v8_relat_2(A))) # label(s1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5903 (all A all B (m2_relset_1(B,A,A) -> (exists C (r1_tarski(B,C) & (all D (v3_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v8_relat_2(D) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C))))) # label(t20_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5904 (all A all B all C all D (k2_tarski(A,C) = k1_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) & 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]. 83.20/80.71 5905 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k5_funct_5(A)) & v1_relat_1(k5_funct_5(A)))) # label(dt_k5_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5906 (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]. 83.20/80.71 5907 (all A (k1_xboole_0 = k1_funct_5(A) <-> k2_funct_5(A) = k1_xboole_0)) # label(t19_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5908 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k5_funct_5(A)),k4_partfun1(k1_funct_5(k1_relat_1(A)),k2_relat_1(A))) & r1_tarski(k2_relat_1(k3_funct_5(A)),k4_partfun1(k2_funct_5(k1_relat_1(A)),k2_relat_1(A))))) # label(t43_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5909 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> r2_hidden(B,k1_relat_1(k5_funct_5(C))) & v1_relat_1(k1_funct_1(k5_funct_5(C),B)) & v1_funct_1(k1_funct_1(k5_funct_5(C),B))))) # label(t28_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5910 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> C = k3_funct_5(k4_funct_5(C)) & C = k5_funct_5(k6_funct_5(C)) | A = k1_xboole_0))) # label(t55_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5911 (all A (k1_xboole_0 = k1_funct_5(A) | k2_funct_5(A) = k1_xboole_0 -> (all B all C -r2_hidden(k4_tarski(B,C),A)))) # label(t18_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5912 (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_funct_2(C,k2_tarski(A,B))) = k1_card_1(k1_zfmisc_1(C)))) # label(t72_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5913 (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]. 83.20/80.71 5914 (all A all B (r1_tarski(k4_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k4_xboole_0(A,B))) & r1_tarski(k4_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k4_xboole_0(A,B))))) # label(t8_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5915 (all A all B all C all D (k1_card_1(A) = k1_card_1(B) & k1_card_1(C) = k1_card_1(D) -> k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)))) # label(t68_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5916 (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(k3_funct_5(B))) & C = k1_funct_1(k3_funct_5(B),A) -> r1_tarski(k1_relat_1(C),k2_funct_5(k1_relat_1(B))) & r1_tarski(k2_relat_1(C),k2_relat_1(B)) & (all D (r2_hidden(D,k1_relat_1(C)) -> r2_hidden(k4_tarski(A,D),k1_relat_1(B)) & k1_funct_1(B,k4_tarski(A,D)) = k1_funct_1(C,D))) & 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)))))))))) # label(t38_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5917 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> 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]. 83.20/80.71 5918 (all A all B (r2_wellord2(A,k1_funct_2(k1_tarski(B),A)) & k1_card_1(A) = k1_card_1(k1_funct_2(k1_tarski(B),A)))) # label(t65_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5919 (all A all B (r1_tarski(k5_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k5_xboole_0(A,B))) & r1_tarski(k5_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k5_xboole_0(A,B))))) # label(t9_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5920 $T # label(t22_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5921 (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]. 83.20/80.71 5922 (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]. 83.20/80.71 5923 (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]. 83.20/80.71 5924 (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]. 83.20/80.71 5925 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k4_funct_5(A) = B <-> (all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (v1_funct_1(E) & (exists F (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = E & r2_hidden(F,k1_relat_1(E)) & C = k4_tarski(D,F))) & v1_relat_1(E))))) & (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(C,k1_relat_1(B)) & k1_funct_1(A,k1_mcart_1(C)) = D -> k1_funct_1(B,C) = k1_funct_1(D,k2_mcart_1(C)))))))))) # label(d4_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5926 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k3_funct_5(C) = k3_funct_5(D) & k1_relat_1(D) = k2_zfmisc_1(A,B) & k2_zfmisc_1(A,B) = k1_relat_1(C) -> D = C))))) # label(t51_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5927 (all A all B (-(k1_xboole_0 = k2_zfmisc_1(B,A) & k1_xboole_0 = k2_zfmisc_1(A,B) & k1_xboole_0 = A) -> B = k1_funct_5(k2_zfmisc_1(B,A)) & k2_funct_5(k2_zfmisc_1(A,B)) = B)) # label(t11_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5928 (all A all B (B = k1_funct_5(A) <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))) # label(d1_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5929 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k4_funct_5(D) = k4_funct_5(C) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> k1_xboole_0 = A | C = D))))) # label(t53_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5930 (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)) & r2_hidden(B,k1_relat_1(D)) & D = k1_funct_1(C,A) -> 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(k4_funct_5(C),k4_tarski(A,B)) = k1_funct_1(D,B)))))) # label(t45_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5931 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k1_relat_1(k4_funct_5(C)),k2_zfmisc_1(k1_relat_1(C),A)) & r1_tarski(k1_relat_1(k6_funct_5(C)),k2_zfmisc_1(A,k1_relat_1(C)))))) # label(t44_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5932 (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(k4_tarski(A,B),k1_relat_1(C)) & D = k1_funct_1(k3_funct_5(C),A) -> k1_funct_1(C,k4_tarski(A,B)) = k1_funct_1(D,B) & r2_hidden(B,k1_relat_1(D))))))) # label(t27_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5933 (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]. 83.20/80.71 5934 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k3_funct_5(D) = k3_funct_5(C) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> D = C))))) # label(t59_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5935 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k3_funct_5(A) <-> k1_relat_1(B) = k1_funct_5(k1_relat_1(A)) & (all C -((all D (v1_funct_1(D) & v1_relat_1(D) -> -(k1_relat_1(D) = k2_funct_5(k3_xboole_0(k1_relat_1(A),k2_zfmisc_1(k1_tarski(C),k2_funct_5(k1_relat_1(A))))) & (all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(D,E) = k1_funct_1(A,k4_tarski(C,E)))) & k1_funct_1(B,C) = D))) & r2_hidden(C,k1_funct_5(k1_relat_1(A)))))))))) # label(d3_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5936 (all A all B all C (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_funct_5(C)) & r2_hidden(B,k2_funct_5(C)))) # label(t4_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5937 (all A all B (k2_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(B) & k1_tarski(A) = k1_funct_5(k1_tarski(k4_tarski(A,B))))) # label(t15_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5938 (all A k1_funct_2(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t64_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5939 (all A all B all C (B != A -> k1_card_1(k1_funct_2(k2_tarski(A,B),C)) = k1_card_1(k2_zfmisc_1(C,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]. 83.20/80.71 5940 (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]. 83.20/80.71 5941 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> v1_relat_1(k1_funct_1(k5_funct_5(B),A)) & v1_funct_1(k1_funct_1(k5_funct_5(B),A))))) # label(t40_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5942 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k6_funct_5(A)) & v1_relat_1(k6_funct_5(A)))) # label(dt_k6_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5943 (all A all B k1_tarski(k2_funcop_1(A,B)) = k1_funct_2(A,k1_tarski(B))) # label(t66_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5944 (all A all B all C (r1_xboole_0(A,B) -> r2_wellord2(k1_funct_2(k2_xboole_0(A,B),C),k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) & k1_card_1(k1_funct_2(k2_xboole_0(A,B),C)) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))))) # label(t69_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5945 $T # label(t14_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5946 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -(r2_hidden(B,k1_relat_1(A)) & v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) -> k4_funct_5(A) = k1_xboole_0 & k6_funct_5(A) = k1_xboole_0))) # label(t35_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5947 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> r1_tarski(k2_relat_1(k3_funct_5(C)),k1_funct_2(B,k2_relat_1(C))) & r1_tarski(k2_relat_1(k5_funct_5(C)),k1_funct_2(A,k2_relat_1(C)))))) # label(t42_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5948 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 83.20/80.71 5949 (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]. 83.20/80.71 5950 (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)) -> C = k6_funct_5(k5_funct_5(C)) & C = k4_funct_5(k3_funct_5(C))))) # label(t57_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5951 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_funct_1(k5_funct_5(C),B) = D & 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]. 83.20/80.71 5952 $T # label(dt_k2_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5953 (all A all B all C (k1_card_1(k1_funct_2(A,k1_funct_2(B,C))) = k1_card_1(k1_funct_2(k2_zfmisc_1(A,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]. 83.20/80.71 5954 (all A all B all C all D (r2_wellord2(C,D) & r2_wellord2(A,B) -> r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D)) & k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)))) # label(t67_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5955 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & k5_funct_5(D) = k5_funct_5(C) -> D = C))))) # label(t60_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5956 (all A (v1_funct_1(A) & v1_relat_1(A) -> k2_funct_4(k4_funct_5(A)) = k6_funct_5(A))) # label(d6_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5957 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> B = k1_relat_1(k5_funct_5(C)) & k1_relat_1(k3_funct_5(C)) = A | k2_zfmisc_1(A,B) = k1_xboole_0))) # label(t31_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5958 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(k5_funct_5(A)) = k2_funct_5(k1_relat_1(A)))) # label(t30_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5959 (all A all B (v1_funct_1(B) & v1_relat_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]. 83.20/80.71 5960 (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)) -> k1_funct_1(D,B) = k1_funct_1(k6_funct_5(C),k4_tarski(B,A)) & r2_hidden(k1_funct_1(D,B),k2_relat_1(k6_funct_5(C))) & r2_hidden(k4_tarski(B,A),k1_relat_1(k6_funct_5(C)))))))) # label(t46_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.71 5961 (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]. 83.20/80.71 5962 (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(C),k4_partfun1(A,B)) & r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) & k4_funct_5(C) = k4_funct_5(D) -> C = D | r2_hidden(k1_xboole_0,k2_relat_1(D)) | r2_hidden(k1_xboole_0,k2_relat_1(C))))))) # label(t61_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5963 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> r2_hidden(A,k1_relat_1(k3_funct_5(C))) & v1_funct_1(k1_funct_1(k3_funct_5(C),A)) & v1_relat_1(k1_funct_1(k3_funct_5(C),A))))) # label(t26_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5964 $T # label(t3_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5965 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_5(k1_relat_1(A)) = k2_funct_5(k1_relat_1(k2_funct_4(A))) & k1_funct_5(k1_relat_1(k2_funct_4(A))) = k2_funct_5(k1_relat_1(A)))) # label(t20_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5966 $T # label(dt_k1_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5967 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_funct_5(A),k1_funct_5(B)) & r1_tarski(k2_funct_5(A),k2_funct_5(B)))) # label(t5_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5968 (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(k2_relat_1(C),k4_partfun1(A,B)) & k6_funct_5(C) = k6_funct_5(D) & r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(D)) | D = C | r2_hidden(k1_xboole_0,k2_relat_1(C))))))) # label(t62_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5969 $T # label(t24_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5970 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> C = k6_funct_5(k5_funct_5(C)) & k4_funct_5(k3_funct_5(C)) = C))) # label(t56_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5971 (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]. 83.20/80.72 5972 (all A (v1_funct_1(A) & v1_relat_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]. 83.20/80.72 5973 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> r1_tarski(k2_relat_1(k6_funct_5(C)),B) & r1_tarski(k2_relat_1(k4_funct_5(C)),B)))) # label(t48_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5974 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),k1_relat_1(A))) -> k1_xboole_0 = k3_funct_5(A) & k5_funct_5(A) = k1_xboole_0))) # label(t34_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5975 (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(k2_relat_1(C),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & k6_funct_5(D) = k6_funct_5(C) -> k1_xboole_0 = A | D = C))))) # label(t54_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5976 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k2_zfmisc_1(A,B) = k1_relat_1(D) & k5_funct_5(D) = k5_funct_5(C) & k1_relat_1(C) = k2_zfmisc_1(A,B) -> C = D))))) # label(t52_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5977 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> -(k1_relat_1(D) = k2_zfmisc_1(A,B) & (all E (v1_funct_1(E) & v1_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)))) & k1_relat_1(E) = A & E = k1_funct_1(k5_funct_5(D),C)))) & r2_hidden(C,B) & k2_zfmisc_1(A,B) != k1_xboole_0))) # label(t39_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5978 $T # label(t23_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5979 (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(k5_funct_5(B))) & C = k1_funct_1(k5_funct_5(B),A) -> k1_relat_1(C) = k1_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_funct_5(k1_relat_1(B)),k1_tarski(A)))) & r1_tarski(k1_relat_1(C),k1_funct_5(k1_relat_1(B))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(B,k4_tarski(D,A)) = k1_funct_1(C,D) & r2_hidden(k4_tarski(D,A),k1_relat_1(B)))) & r1_tarski(k2_relat_1(C),k2_relat_1(B))))))) # label(t41_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5980 (all A all B (B = k2_funct_5(A) <-> (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]. 83.20/80.72 5981 $T # label(t2_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5982 $T # label(t25_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5983 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> -(k2_zfmisc_1(A,B) != k1_xboole_0 & k1_relat_1(D) = k2_zfmisc_1(A,B) & r2_hidden(C,A) & (all E (v1_funct_1(E) & v1_relat_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)))))) # label(t36_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5984 (all A ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k1_funct_5(A) = k1_xboole_0 & k2_funct_5(A) = k1_xboole_0)) # label(t17_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5985 (all A (v1_relat_1(A) & v1_funct_1(A) -> k5_funct_5(A) = k3_funct_5(k2_funct_4(A)))) # label(d5_funct_5) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5986 (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]. 83.20/80.72 5987 (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]. 83.20/80.72 5988 (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]. 83.20/80.72 5989 (all A all B (k1_card_1(k2_zfmisc_1(B,A)) = k1_card_1(k2_zfmisc_1(A,B)) & r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)))) # label(t11_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5990 (all A all B all C all D all E all F all G all H (r2_wellord2(C,D) & r2_wellord2(A,B) -> 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(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)))) | F = E)) # label(t23_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5991 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> k2_card_2(k2_card_2(A,B),C) = k2_card_2(A,k2_card_2(B,C)))))))) # label(t35_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5992 (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]. 83.20/80.72 5993 $T # label(t66_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5994 (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]. 83.20/80.72 5995 $T # label(t9_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5996 (all A all B (v1_finset_1(B) -> v1_finset_1(A) | -r2_hidden(k1_card_1(A),k1_card_1(B)) & -r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t68_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5997 (all A all B (v1_card_1(B) & v1_card_1(A) -> v1_card_1(k3_card_2(A,B)))) # label(dt_k3_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 5998 (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]. 83.20/80.72 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]. 83.20/80.72 6000 (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]. 83.20/80.72 6001 (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]. 83.20/80.72 6002 (all A all B (B != A -> k4_card_1(k2_tarski(A,B)) = np__2)) # label(t76_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6003 (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]. 83.20/80.72 6004 $T # label(t30_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6005 (all A all B (r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(k1_card_1(A),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(k1_card_1(A),k1_card_1(B))) = k1_card_1(k2_zfmisc_1(A,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(k1_card_1(A),B)) = k1_card_1(k2_zfmisc_1(A,B)) & r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(A,k1_card_1(B))))) # label(t14_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6006 (all A (v1_card_1(A) -> k2_card_2(A,np__1) = A)) # label(t33_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6007 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> r1_xreal_0(k4_card_1(A),k4_card_1(B))))))) # label(t57_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6008 (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]. 83.20/80.72 6009 (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]. 83.20/80.72 6010 (all A (v1_card_1(A) -> np__0 = k2_card_2(A,np__0))) # label(t32_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6011 (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]. 83.20/80.72 6012 $T # label(t1_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6013 (all A all B all C (k1_card_1(k2_zfmisc_1(A,k2_zfmisc_1(B,C))) = k1_card_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & r2_wellord2(k2_zfmisc_1(k2_zfmisc_1(A,B),C),k2_zfmisc_1(A,k2_zfmisc_1(B,C))))) # label(t12_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6014 (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]. 83.20/80.72 6015 $T # label(t34_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6016 (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]. 83.20/80.72 6017 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (-r1_xreal_0(k4_card_1(B),k4_card_1(A)) <-> r2_hidden(k1_card_1(A),k1_card_1(B))))))) # label(t58_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6018 $T # label(t56_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6019 (all A all B all C -(C != A & C != B & k4_card_1(k1_enumset1(A,B,C)) != np__3 & B != A)) # label(t77_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6020 (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]. 83.20/80.72 6021 $T # label(t55_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6022 (all A all B (v1_card_1(B) & v1_card_1(A) -> k1_card_2(A,B) = k1_card_2(B,A))) # label(commutativity_k1_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6023 (all A all B (k1_card_1(k2_xboole_0(k2_zfmisc_1(A,k1_tarski(np__0)),k2_zfmisc_1(B,k1_tarski(np__1)))) = k1_card_1(k2_xboole_0(k2_zfmisc_1(B,k1_tarski(np__0)),k2_zfmisc_1(A,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]. 83.20/80.72 6024 (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]. 83.20/80.72 6025 (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]. 83.20/80.72 6026 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> k1_card_2(A,k1_card_2(B,C)) = k1_card_2(k1_card_2(A,B),C))))))) # label(t31_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6027 (all A all B all C all D (B != A -> k1_card_2(k1_card_1(C),k1_card_1(D)) = k1_card_1(k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B)))))) # label(t28_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6028 (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]. 83.20/80.72 6029 (all A all B (r2_wellord2(A,k2_zfmisc_1(A,k1_tarski(B))) & k1_card_1(A) = k1_card_1(k2_zfmisc_1(A,k1_tarski(B))))) # label(t13_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6030 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r1_xboole_0(A,B) -> k4_card_1(k2_xboole_0(A,B)) = k1_nat_1(k4_card_1(A),k4_card_1(B))))))) # label(t53_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6031 $T # label(t21_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6032 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> k2_card_2(A,k1_card_2(B,C)) = k1_card_2(k2_card_2(A,B),k2_card_2(A,C)))))))) # label(t37_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6033 (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]. 83.20/80.72 6034 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k3_card_2(A,B) = k1_card_1(k1_funct_2(B,A)))))) # label(d3_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6035 (all A (v1_card_1(A) -> k3_card_2(np__1,A) = np__1 & A = k3_card_2(A,np__1))) # label(t40_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6036 (all A all B all C all D (r2_wellord2(A,B) & r2_wellord2(C,D) -> k1_card_1(k2_zfmisc_1(B,D)) = k1_card_1(k2_zfmisc_1(A,C)) & r2_wellord2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t15_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6037 (all A (v1_relat_1(A) & v1_funct_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]. 83.20/80.72 6038 (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]. 83.20/80.72 6039 (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]. 83.20/80.72 6040 (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]. 83.20/80.72 6041 (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]. 83.20/80.72 6042 (all A (v1_card_1(A) -> (np__0 != A -> k3_card_2(np__0,A) = np__0))) # label(t39_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6043 (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]. 83.20/80.72 6044 (all A (v1_card_1(A) -> k1_card_2(A,np__0) = A)) # label(t29_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6045 (all A k1_card_1(k1_zfmisc_1(A)) = k3_card_2(np__2,k1_card_1(A))) # label(t44_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6046 (all A all B all C all D -(A != C & C != B & D != B & k4_card_1(k2_enumset1(A,B,C,D)) != np__4 & C != D & A != D & A != B)) # label(t78_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6047 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k1_card_2(A,B) = k1_card_1(k14_ordinal2(A,B)))))) # label(d1_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6048 (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]. 83.20/80.72 6049 (all A all B (v1_card_1(B) & v1_card_1(A) -> v1_card_1(k1_card_2(A,B)))) # label(dt_k1_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6050 (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]. 83.20/80.72 6051 (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]. 83.20/80.72 6052 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k1_card_1(k14_ordinal2(A,B)) = k1_card_2(k1_card_1(A),k1_card_1(B)))))) # label(t24_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6053 (all A (k1_card_1(A) = np__0 -> k1_xboole_0 = A)) # label(t59_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6054 (all A (v1_card_1(A) -> k3_card_2(A,np__0) = np__1)) # label(t38_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6055 (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]. 83.20/80.72 6056 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C all D (C != 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)))) & r2_wellord2(k14_ordinal2(A,B),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]. 83.20/80.72 6057 (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]. 83.20/80.72 6058 (all A all B (r1_xboole_0(A,B) -> k1_card_2(k1_card_1(A),k1_card_1(B)) = k1_card_1(k2_xboole_0(A,B)))) # label(t48_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6059 (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) -> r2_hidden(k3_tarski(A),A) | A = k1_xboole_0)) # label(t81_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6060 (all A ((exists B A = k1_tarski(B)) <-> np__1 = k1_card_1(A))) # label(t60_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6061 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k1_card_1(k1_nat_1(A,B)) = k1_card_2(k1_card_1(A),k1_card_1(B)))))) # label(t51_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6062 (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]. 83.20/80.72 6063 $T # label(t10_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6064 $T # label(t8_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6065 (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]. 83.20/80.72 6066 (all A (v1_finset_1(A) -> r2_wellord2(A,k1_card_1(k4_card_1(A))) & r2_wellord2(A,k2_finseq_1(k4_card_1(A))) & r2_wellord2(A,k4_card_1(A)))) # label(t61_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6067 (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]. 83.20/80.72 6068 (all A all B all C (r2_hidden(A,k1_funct_2(B,C)) -> r2_wellord2(A,B) & k1_card_1(A) = k1_card_1(B))) # label(t7_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6069 (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]. 83.20/80.72 6070 (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]. 83.20/80.72 6071 (all A (v1_finset_1(A) -> -((all B all C -(A = k2_tarski(B,C) & C != B)) & np__2 = k4_card_1(A)))) # label(t79_card_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6072 $T # label(t62_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6073 $T # label(d2_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6074 (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]. 83.20/80.72 6075 $T # label(t51_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6076 $T # label(t22_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6077 (all A 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) -> (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]. 83.20/80.72 6078 (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_finset_1(k3_xboole_0(B,A)) & -v1_xboole_0(k3_xboole_0(A,B)) & v1_trees_1(k3_xboole_0(A,B)) & v1_finset_1(k3_xboole_0(A,B)) & v1_trees_1(k3_xboole_0(B,A)) & -v1_xboole_0(k3_xboole_0(B,A)))))) # label(t53_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6079 (all A (v1_trees_1(A) & -v1_xboole_0(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]. 83.20/80.72 6080 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (m1_trees_1(B,A) <-> m1_subset_1(B,A))))) # label(redefinition_m1_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6081 (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]. 83.20/80.72 6082 $T # label(dt_k1_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6083 $T # label(t43_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6084 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (C = k7_relat_1(B,k2_finseq_1(A)) -> r1_xreal_0(k3_finseq_1(C),A)))))))) # label(t1_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6085 (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]. 83.20/80.72 6086 (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]. 83.20/80.72 6087 $T # label(t65_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6088 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (v1_trees_1(B) & -v1_xboole_0(B) -> (m3_trees_1(B,A) <-> (exists C (m1_trees_1(C,A) & k4_trees_1(A,C) = B))))))) # label(d11_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6089 (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) -> (-(-(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]. 83.20/80.72 6090 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) -> -(r2_hidden(B,k2_trees_1(A)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(k12_finseq_1(k5_numbers,C) = B & -r1_xreal_0(A,C)))) & B != k1_xboole_0))))) # label(t57_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6091 (all A k1_trees_1(k9_finseq_1(A)) = k1_tarski(k1_xboole_0)) # label(t40_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6092 (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]. 83.20/80.72 6093 (all A k1_xboole_0 != k9_finseq_1(A)) # label(t4_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6094 (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) -> r1_tarski(k1_trees_1(A),k1_trees_1(B))))))) # label(t41_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6095 $T # label(t10_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6096 (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) -> 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]. 83.20/80.72 6097 (all A (v1_finset_1(A) & v1_trees_1(A) & -v1_xboole_0(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]. 83.20/80.72 6098 $T # label(d3_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6099 (all A all B all C (-v1_xboole_0(C) & v1_trees_1(C) & v1_finset_1(C) & m1_subset_1(B,A) & v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k5_trees_1(A,B,C)) & v1_finset_1(k5_trees_1(A,B,C)) & v1_trees_1(k5_trees_1(A,B,C)))) # label(fc2_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6100 $T # label(t18_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6101 $T # label(t13_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6102 (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) -> (-r3_xboole_0(A,B) -> v2_trees_1(k2_tarski(A,B))))))) # label(t71_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6103 $T # label(t58_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6104 $T # label(t20_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6105 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B = k7_trees_1(A) <-> (exists C (k4_card_1(C) = B & (all D (m4_trees_1(D,A) -> r1_xreal_0(k4_card_1(D),k4_card_1(C)))) & m4_trees_1(C,A)))))))) # label(d16_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6106 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_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]. 83.20/80.72 6107 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> ((all C (m2_finseq_1(C,k5_numbers) -> ((all D (m2_finseq_1(D,k5_numbers) -> -(r2_xboole_0(C,D) & r2_hidden(D,A)))) & r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> B = k3_trees_1(A)))))) # label(d8_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6108 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> k4_trees_1(A,k6_finseq_1(k5_numbers)) = A)) # label(t60_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6109 (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]. 83.20/80.72 6110 (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]. 83.20/80.72 6111 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> (all B (m4_trees_1(B,A) -> v1_finset_1(B))))) # label(cc1_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6112 $T # label(t69_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6113 (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]. 83.20/80.72 6114 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> m4_trees_1(k1_tarski(k1_xboole_0),A) & m4_trees_1(k1_xboole_0,A))) # label(t73_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6115 (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]. 83.20/80.72 6116 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> k4_card_1(k1_trees_1(A)) = k3_finseq_1(A))) # label(t68_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6117 (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) -> (-(k1_xboole_0 = A & -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]. 83.20/80.72 6118 $T # label(t54_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6119 (all 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) -> -(k9_finseq_1(A) = k7_finseq_1(B,C) & -(k9_finseq_1(A) = C & B = k1_xboole_0) & -(C = k1_xboole_0 & B = k9_finseq_1(A))))))) # label(t6_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6120 (all A (v1_trees_1(A) <-> (all B (m2_finseq_1(B,k5_numbers) -> (r2_hidden(B,A) -> r1_tarski(k1_trees_1(B),A)))) & (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) -> (r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C)),A) & r1_xreal_0(D,C) -> r2_hidden(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,D)),A)))))))) & r1_tarski(A,k13_finseq_1(k5_numbers)))) # label(d5_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6121 (all A (m2_finseq_1(A,k5_numbers) -> (all B (v1_trees_1(B) & -v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (r2_hidden(k7_finseq_1(A,C),B) -> r2_hidden(A,B)))))))) # label(t46_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6122 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_nat_1(A,np__1) = k7_trees_1(k2_trees_1(k1_nat_1(A,np__1))))) # label(t83_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6123 (all A (v1_finseq_1(A) & v1_funct_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]. 83.20/80.72 6124 $T # label(t76_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6125 (all A (-v1_xboole_0(A) & v1_trees_1(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]. 83.20/80.72 6126 (all A all B all C (-v1_xboole_0(C) & v1_trees_1(C) & m2_finseq_1(B,k5_numbers) -> ((exists D (m1_trees_1(D,C) & D = D & A = k8_finseq_1(k5_numbers,B,D))) <-> r2_hidden(A,a_2_1_trees_1(B,C))))) # label(fraenkel_a_2_1_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6127 (all A (v1_finset_1(A) & v1_trees_1(A) & -v1_xboole_0(A) -> r1_xreal_0(np__1,k7_trees_1(A)))) # label(t78_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6128 $T # label(t34_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6129 (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]. 83.20/80.72 6130 (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 (v1_relat_1(C) & v1_funct_1(C) & B = k7_finseq_1(A,C) & v1_finseq_1(C))) <-> r1_tarski(A,B)))))) # label(t8_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6131 $T # label(t59_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6132 (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_funct_1(D) & r2_xboole_0(D,A) & C = D & v1_finseq_1(D) & v1_relat_1(D))) <-> r2_hidden(C,B))))))) # label(d4_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6133 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> m1_subset_1(k3_trees_1(A),k1_zfmisc_1(A)))) # label(dt_k3_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6134 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> (all B (m1_trees_1(B,A) -> -(r1_xreal_0(k6_trees_1(A),k6_trees_1(k4_trees_1(A,B))) & k1_xboole_0 != B))))) # label(t85_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6135 (all A (v2_trees_1(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) -> -(r2_hidden(B,A) & r2_hidden(C,A) & B != C & r3_xboole_0(B,C)))))) & (all B (r2_hidden(B,A) -> v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B))))) # label(d13_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6136 (all A all B (A = B <-> r1_tarski(k9_finseq_1(A),k9_finseq_1(B)))) # label(t16_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6137 (exists A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A))) # label(rc2_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6138 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (m2_finseq_1(B,k5_numbers) -> (all C (-v1_xboole_0(C) & v1_trees_1(C) -> (r2_hidden(B,A) -> (all D (v1_trees_1(D) & -v1_xboole_0(D) -> ((all E (m2_finseq_1(E,k5_numbers) -> (r2_hidden(E,D) <-> -((all F (m2_finseq_1(F,k5_numbers) -> -(r2_hidden(F,C) & E = k8_finseq_1(k5_numbers,B,F)))) & -(r2_hidden(E,A) & -r2_xboole_0(B,E)))))) <-> D = k5_trees_1(A,B,C))))))))))) # label(d12_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6139 (all 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_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]. 83.20/80.72 6140 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_trees_1(B)) -> v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A)))) # label(t35_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6141 (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]. 83.20/80.72 6142 $T # label(d6_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6143 (all A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> (all B (v1_finset_1(B) & v1_trees_1(B) & -v1_xboole_0(B) -> v1_trees_1(k2_xboole_0(A,B)) & v1_finset_1(k2_xboole_0(A,B)) & -v1_xboole_0(k2_xboole_0(A,B)))))) # label(t52_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6144 $T # label(t29_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6145 $T # label(t77_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6146 $T # label(t9_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6147 (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]. 83.20/80.72 6148 (all A (v1_trees_1(A) & -v1_xboole_0(A) -> r2_hidden(k6_finseq_1(k5_numbers),A) & r2_hidden(k1_xboole_0,A))) # label(t47_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6149 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r3_xboole_0(A,B) & k4_card_1(B) = k4_card_1(A) -> A = B))))) # label(t19_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6150 $T # label(t7_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6151 (all A (v1_trees_1(A) & v1_finset_1(A) & -v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B = k6_trees_1(A) <-> (all C (m2_finseq_1(C,k5_numbers) -> (r2_hidden(C,A) -> r1_xreal_0(k3_finseq_1(C),B)))) & (exists C (m2_finseq_1(C,k5_numbers) & r2_hidden(C,A) & k3_finseq_1(C) = B))))))) # label(d15_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6152 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (v1_trees_1(B) & -v1_xboole_0(B) -> -v1_xboole_0(k3_xboole_0(A,B)) & v1_trees_1(k3_xboole_0(A,B)))))) # label(t50_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6153 (all A (-v1_xboole_0(A) & v1_trees_1(A) -> (all B (m2_trees_1(B,A) -> m1_trees_1(B,A))))) # label(dt_m2_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6154 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_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]. 83.20/80.72 6155 (all A (-v1_xboole_0(A) & v1_trees_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(B,A) & r1_tarski(C,B) -> r2_hidden(C,A)))))))) # label(t45_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6156 (all A (-v1_xboole_0(A) & v1_trees_1(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]. 83.20/80.72 6157 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_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]. 83.20/80.72 6158 (exists A (v1_trees_1(A) & -v1_xboole_0(A))) # label(rc1_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6159 $T # label(t61_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6160 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists C (-r1_xreal_0(B,C) & A = k12_finseq_1(k5_numbers,C) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_0_trees_1(B))))) # label(fraenkel_a_1_0_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6161 (all A (m1_subset_1(A,k5_numbers) -> -v1_xboole_0(k2_trees_1(A)) & v1_trees_1(k2_trees_1(A)) & v1_finset_1(k2_trees_1(A)))) # label(dt_k2_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6162 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> v1_finset_1(k1_trees_1(A)))) # label(fc3_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6163 (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) -> -(r2_xboole_0(B,A) & r1_tarski(A,B)))))) # label(t28_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6164 (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]. 83.20/80.72 6165 (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) -> (C = k7_relat_1(B,k2_finseq_1(A)) -> r1_xreal_0(k3_finseq_1(C),k3_finseq_1(B))))))))) # label(t2_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6166 $T # label(t14_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6167 (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) -> ((exists C (A = k7_relat_1(B,k2_finseq_1(C)) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r1_tarski(A,B)))))) # label(d1_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6168 (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]. 83.20/80.72 6169 $T # label(t17_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6170 (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) -> (k3_finseq_1(A) = k3_finseq_1(B) & r1_tarski(A,B) -> B = A))))) # label(t15_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6171 $T # label(t21_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6172 (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) -> (r2_hidden(A,k1_trees_1(B)) <-> r2_xboole_0(A,B)))))) # label(t36_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6173 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> -((all D (v1_funct_1(D) & v1_finseq_1(D) & v1_relat_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]. 83.20/80.72 6174 (all A all B (-v1_xboole_0(A) & v1_trees_1(A) & m1_finseq_1(B,k5_numbers) -> v1_trees_1(k4_trees_1(A,B)) & -v1_xboole_0(k4_trees_1(A,B)))) # label(dt_k4_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6175 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> (k6_trees_1(A) = np__0 -> A = k2_trees_1(np__0)))) # label(t80_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6176 $T # label(t72_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6177 (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) -> k4_trees_1(k5_trees_1(B,A,C),A) = C))))))) # label(t66_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6178 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k2_trees_1(A) = k2_xboole_0(a_1_0_trees_1(A),k1_tarski(k1_xboole_0)))) # label(d7_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6179 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> np__1 = k6_trees_1(k2_trees_1(k1_nat_1(A,np__1))))) # label(t81_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6180 (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) -> -(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]. 83.20/80.72 6181 $T # label(t63_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6182 (all A (v1_trees_1(A) & -v1_xboole_0(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(k8_finseq_1(k5_numbers,B,D),A) <-> r2_hidden(D,C)))) <-> k4_trees_1(A,B) = C)))))))) # label(d9_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6183 (all A all B (A = B <-> r3_xboole_0(k9_finseq_1(A),k9_finseq_1(B)))) # label(t23_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6184 (all A all B all C (-v1_xboole_0(A) & v1_trees_1(A) & m1_finseq_1(B,k5_numbers) & v1_trees_1(C) & -v1_xboole_0(C) -> -v1_xboole_0(k5_trees_1(A,B,C)) & v1_trees_1(k5_trees_1(A,B,C)))) # label(dt_k5_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6185 (exists A v2_trees_1(A)) # label(rc3_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6186 (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) -> -(r2_xboole_0(A,B) & r2_xboole_0(B,A)))))) # label(t26_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6187 $T # label(t11_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.72 6188 (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) -> (A = k7_finseq_1(B,A) | k7_finseq_1(A,B) = A -> B = k1_xboole_0))))) # label(t5_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6189 (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_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]. 83.20/80.73 6190 $T # label(t12_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6191 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> m2_subset_1(k7_trees_1(A),k1_numbers,k5_numbers))) # label(dt_k7_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6192 (all A all B all C (v1_trees_1(C) & -v1_xboole_0(C) & m2_finseq_1(B,k5_numbers) -> (r2_hidden(A,a_2_0_trees_1(B,C)) <-> (exists D (-r2_xboole_0(B,D) & A = D & m1_trees_1(D,C)))))) # label(fraenkel_a_2_0_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6193 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_trees_1(A) & v1_finset_1(A) -> -v1_xboole_0(k4_trees_1(A,B)) & v1_trees_1(k4_trees_1(A,B)) & v1_finset_1(k4_trees_1(A,B)))) # label(fc1_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6194 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(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_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> p1_s1_trees_1(A))) # label(s1_trees_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6195 (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]. 83.20/80.73 6196 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(A,k4_finseq_1(k7_finseq_1(B,C)))))))))) # label(t18_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6197 (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 (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_2(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]. 83.20/80.73 6198 (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]. 83.20/80.73 6199 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6200 (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_finseq_1(E) & v1_funct_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,A) -> (E = k4_funcop_1(F,G,D) -> k3_finseq_1(G) = k3_finseq_1(E)))))))))))))))) # label(t98_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6201 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (all J (m2_finseq_1(J,B) -> (k10_finseq_1(D,E) = I & J = k10_finseq_1(F,G) -> k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G)) = k3_funcop_1(H,I,J)))))))))))))))))))))) # label(t89_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6202 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6203 (all A (m1_finseq_2(k3_finseq_2(A),A) & -v1_xboole_0(k3_finseq_2(A)))) # label(dt_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 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]. 83.20/80.73 6205 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k4_finseq_1(B),k4_finseq_1(B)) & m2_relset_1(C,k4_finseq_1(B),k4_finseq_1(B)) -> 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]. 83.20/80.73 6206 (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]. 83.20/80.73 6207 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6208 (all A all B all C (v4_ordinal2(B) -> (r2_hidden(A,a_2_0_finseq_2(B,C)) <-> (exists D (B = k3_finseq_1(D) & A = D & m2_finseq_2(D,C,k3_finseq_2(C))))))) # label(fraenkel_a_2_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6209 (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]. 83.20/80.73 6210 (all A (v4_ordinal2(A) -> A = k3_finseq_1(k1_finseq_2(A)))) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6211 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6212 (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]. 83.20/80.73 6213 (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]. 83.20/80.73 6214 (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]. 83.20/80.73 6215 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k5_relat_1(A,C) = B & r1_tarski(k2_relat_1(A),k1_relat_1(C)) -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t33_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6216 (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]. 83.20/80.73 6217 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (k11_finseq_1(D,E,F) = I -> 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]. 83.20/80.73 6218 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (np__0 != A -> (all B (m1_subset_1(B,k2_finseq_1(A)) -> B = k1_funct_1(k1_finseq_2(A),B)))))) # label(t57_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6219 (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]. 83.20/80.73 6220 (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) -> (k3_finseq_1(B) = A & (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)))) & A = k3_finseq_1(C) -> B = C))))))) # label(t10_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6221 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (m2_finseq_1(D,A) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (C = k1_partfun1(k5_numbers,A,A,B,D,E) -> k3_finseq_1(C) = k3_finseq_1(D)))))))))) # label(t37_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6222 (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]. 83.20/80.73 6223 (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]. 83.20/80.73 6224 (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]. 83.20/80.73 6225 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> a_3_0_finseq_2(A,B,C) = k4_finseq_2(k1_nat_1(A,B),C))))))) # label(t125_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6226 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(k1_funct_1(A,C),B)))) -> m2_finseq_1(A,B))))) # label(t14_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6227 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> k4_funcop_1(E,k6_finseq_1(A),D) = k6_finseq_1(C))))))))))) # label(t99_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6228 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> -(k3_finseq_1(C) = k1_nat_1(A,B) & (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> (all E (v1_relat_1(E) & v1_finseq_1(E) & v1_funct_1(E) -> -(B = k3_finseq_1(E) & k7_finseq_1(D,E) = C & k3_finseq_1(D) = A)))))))))))) # label(t25_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6229 (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) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> (r1_xreal_0(A,k3_finseq_1(B)) & C = k5_relat_1(D,B) & k2_finseq_1(A) = k2_relat_1(D) -> A = k3_finseq_1(C)))))))))) # label(t45_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6230 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C k2_finseq_2(k1_nat_1(A,B),C) = k7_finseq_1(k2_finseq_2(A,C),k2_finseq_2(B,C))))))) # label(t143_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6231 (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]. 83.20/80.73 6232 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (r1_tarski(A,C) & r1_tarski(B,C) & k3_finseq_1(B) = k3_finseq_1(A) -> B = A))))))) # label(t149_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6233 (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) -> k8_finseq_1(A,C,k12_finseq_1(A,D)) != B))))))))) # label(t22_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 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 (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (m2_finseq_1(H,A) -> (k10_finseq_1(D,E) = H -> 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]. 83.20/80.73 6235 (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]. 83.20/80.73 6236 (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]. 83.20/80.73 6237 (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]. 83.20/80.73 6238 (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]. 83.20/80.73 6239 (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]. 83.20/80.73 6240 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) -> 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]. 83.20/80.73 6241 (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]. 83.20/80.73 6242 (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]. 83.20/80.73 6243 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r2_hidden(A,k2_finseq_1(B)) & k1_nat_1(B,np__1) != A & r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1)))))))) # label(t8_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6244 (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) & m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B)) -> (r1_xreal_0(B,k3_finseq_1(D)) -> B = np__0 & np__0 != A | 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]. 83.20/80.73 6245 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k3_square_1(B,C) = A -> k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(C)) = k2_finseq_1(A)))))))) # label(t2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6246 (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]. 83.20/80.73 6247 (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]. 83.20/80.73 6248 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__1,A) = a_1_0_finseq_2(A))) # label(t116_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6249 (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]. 83.20/80.73 6250 (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]. 83.20/80.73 6251 (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]. 83.20/80.73 6252 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k5_numbers,B) & m2_relset_1(C,k5_numbers,B) & v1_funct_1(C) -> m2_finseq_1(k2_partfun1(k5_numbers,B,C,k2_finseq_1(A)),B))))))) # label(t31_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6253 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6254 (all A (v4_ordinal2(A) -> (all B k3_finseq_1(k2_finseq_2(A,B)) = A))) # label(t69_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6255 (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,B) -> (k12_finseq_1(B,E) = G -> k5_funcop_1(F,D,G) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E))))))))))))))))) # label(t94_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6256 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6257 (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]. 83.20/80.73 6258 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (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]. 83.20/80.73 6259 (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 & D = k8_finseq_1(B,D,C))))))))) # label(t115_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6260 (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]. 83.20/80.73 6261 (all A all B all C (m2_finseq_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> m2_finseq_1(k1_partfun1(k5_numbers,A,A,B,C,D),B))))) # label(t36_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6262 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -(k3_finseq_1(B) = k1_nat_1(A,np__1) & (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D B != k7_finseq_1(C,k9_finseq_1(D)))))))))) # label(t21_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6263 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> m2_finseq_2(k1_partfun1(k5_numbers,B,B,C,D,E),C,k4_finseq_2(A,C)))))))))))) # label(t133_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6264 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> np__0 = k3_square_1(A,np__0) & A = k4_square_1(A,np__0) & A = k4_square_1(np__0,A) & np__0 = k3_square_1(np__0,A))) # label(t6_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6265 (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]. 83.20/80.73 6266 (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 (m2_relset_1(C,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(C,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(C) -> (r1_xreal_0(A,k3_finseq_1(B)) -> v1_funct_1(k5_relat_1(C,B)) & v1_finseq_1(k5_relat_1(C,B)) & v1_relat_1(k5_relat_1(C,B))))))))) # label(t43_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6267 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,k2_finseq_1(B)) -> k1_funct_1(k1_finseq_2(B),A) = A))))) # label(t56_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6268 (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]. 83.20/80.73 6269 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__2,A) = a_1_1_finseq_2(A))) # label(t119_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6270 (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 (m2_relset_1(G,D,E) & v1_funct_2(G,D,E) & v1_funct_1(G) -> (F = k11_finseq_1(A,B,C) -> k1_partfun1(k5_numbers,D,D,E,F,G) = k11_finseq_1(k1_funct_1(G,A),k1_funct_1(G,B),k1_funct_1(G,C))))))))))) # label(t41_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6271 (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_2(C,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(C) -> (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]. 83.20/80.73 6272 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (B = k7_relat_1(C,k2_finseq_1(A)) & r1_xreal_0(k3_finseq_1(C),A) -> B = C))))))) # label(t23_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6273 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> (all C (m2_finseq_2(C,A,B) -> m2_finseq_1(C,A))))) # label(dt_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6274 (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_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(A),k2_relat_1(B)),k1_relat_1(D)) & C = k3_funcop_1(D,A,B) -> k3_square_1(k3_finseq_1(A),k3_finseq_1(B)) = k3_finseq_1(C)))))))))) # label(t79_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6275 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,C) -> (all F (m2_relset_1(F,k2_zfmisc_1(B,C),D) & v1_funct_2(F,k2_zfmisc_1(B,C),D) & v1_funct_1(F) -> (all G (m2_finseq_2(G,B,k4_finseq_2(A,B)) -> m2_finseq_2(k4_funcop_1(F,G,E),D,k4_finseq_2(A,D)))))))))))))))) # label(t142_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6276 (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(k2_relat_1(B),k1_tarski(A)),k1_relat_1(C)) -> v1_relat_1(k4_funcop_1(C,B,A)) & v1_funct_1(k4_funcop_1(C,B,A)) & v1_finseq_1(k4_funcop_1(C,B,A))))))) # label(t82_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6277 (all A all B all C all D (m2_subset_1(B,k1_numbers,k5_numbers) & -v1_xboole_0(D) & m2_subset_1(C,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]. 83.20/80.73 6278 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6279 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) -> k6_xcmplx_0(B,A) = k2_square_1(np__0,k6_xcmplx_0(B,A))))))) # label(t4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6280 (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]. 83.20/80.73 6281 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (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]. 83.20/80.73 6282 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6283 (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) -> -(k1_nat_1(A,B) = k3_finseq_1(D) & (all E (m2_finseq_1(E,C) -> (all F (m2_finseq_1(F,C) -> -(k3_finseq_1(E) = A & k3_finseq_1(F) = B & k8_finseq_1(C,E,F) = D)))))))))))))) # label(t26_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6284 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (-v1_xboole_0(C) & m1_finseq_2(C,B) -> -v1_xboole_0(C) & m1_finseq_2(C,A))))))) # label(t107_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6285 (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]. 83.20/80.73 6286 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k4_funcop_1(D,B,A) = C & r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(D)) -> k3_finseq_1(C) = k3_finseq_1(B)))))))) # label(t83_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6287 (all A (v4_ordinal2(A) -> v1_finseq_1(k1_finseq_2(A)) & v1_funct_1(k1_finseq_2(A)) & v1_relat_1(k1_finseq_2(A)))) # label(dt_k1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6288 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_funct_2(D,k5_numbers,B) & m2_relset_1(D,k5_numbers,B) & v1_funct_1(D) -> (k2_partfun1(k5_numbers,B,D,k2_finseq_1(A)) = C -> k3_finseq_1(C) = A))))))))) # label(t32_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6289 (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]. 83.20/80.73 6290 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_1(D) & 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)) -> (k5_relat_1(D,B) = C & r1_xreal_0(A,k3_finseq_1(B)) -> A = k3_finseq_1(C)))))))))) # label(t47_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6291 (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) -> k6_finseq_1(B) = k1_partfun1(k5_numbers,A,A,B,k6_finseq_1(A),C))))) # label(t38_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6292 (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]. 83.20/80.73 6293 (all A k1_xboole_0 = k2_finseq_2(np__0,A)) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6294 (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]. 83.20/80.73 6295 (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]. 83.20/80.73 6296 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_relat_1(k3_funcop_1(C,A,B)) & v1_finseq_1(k3_funcop_1(C,A,B)) & v1_funct_1(k3_funcop_1(C,A,B))))))))) # label(t78_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6297 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> (exists C m2_finseq_2(C,A,B)))) # label(existence_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6298 (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) & B = k12_finseq_1(A,C))))))) # label(t117_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6299 (all A k2_finseq_2(np__2,A) = k10_finseq_1(A,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6300 (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]. 83.20/80.73 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 (v1_relat_1(E) & v1_finseq_1(E) & v1_funct_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(E) = k3_finseq_1(G)))))))))))))))) # label(t92_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6302 (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) -> (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]. 83.20/80.73 6303 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (v1_funct_1(G) & 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,B) -> (H = k10_finseq_1(E,F) -> k10_finseq_1(k2_binop_1(A,B,C,G,D,E),k2_binop_1(A,B,C,G,D,F)) = k5_funcop_1(G,D,H)))))))))))))))))) # label(t95_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6304 (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) -> (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]. 83.20/80.73 6305 (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]. 83.20/80.73 6306 (all A all B (-v1_xboole_0(B) -> ((exists C exists D (m1_subset_1(D,B) & A = k10_finseq_1(C,D) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_1_finseq_2(B))))) # label(fraenkel_a_1_1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6307 (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]. 83.20/80.73 6308 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6309 (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)) -> k1_funct_1(k2_finseq_2(A,C),D) = C))))))))) # label(t71_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6310 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,A) -> (all H (m2_finseq_1(H,B) -> (k12_finseq_1(B,E) = H & k12_finseq_1(A,D) = G -> k3_funcop_1(F,G,H) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E))))))))))))))))))) # label(t88_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6311 (exists A (m2_finseq_1(A,f2_s1_finseq_2) & f1_s1_finseq_2 = k3_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_2)) -> f3_s1_finseq_2(B) = k1_funct_1(A,B)))))) # label(s1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6312 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_2(B,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(B,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(B) -> v1_funct_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))))) # label(t44_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6313 (all A (v4_ordinal2(A) -> (all B k4_finseq_1(k2_finseq_2(A,B)) = k2_finseq_1(A)))) # label(t68_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6314 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_3_finseq_2(B)) <-> (exists C (k4_finseq_2(C,B) = A & m2_subset_1(C,k1_numbers,k5_numbers)))))) # label(fraenkel_a_1_3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6315 (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 (k11_finseq_1(C,D,E) = B & m1_subset_1(E,A))))))))))) # label(t123_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6316 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6317 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> k7_relat_1(B,k2_finseq_1(A)) = k5_relat_1(k1_finseq_2(A),B))))) # label(t63_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6318 (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]. 83.20/80.73 6319 (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_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,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]. 83.20/80.73 6320 (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 (v1_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) -> (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]. 83.20/80.73 6321 (all A all B k2_relat_1(k10_finseq_1(A,B)) = k2_tarski(A,B)) # label(t147_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6322 (all A k11_finseq_1(A,A,A) = k2_finseq_2(np__3,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6323 (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]. 83.20/80.73 6324 (all A k13_finseq_1(A) = k3_finseq_2(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6325 (all A (v4_ordinal2(A) -> v1_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)) & v3_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(k1_finseq_2(A)))) # label(t65_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6326 (all A k9_finseq_1(A) = k2_finseq_2(np__1,A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6327 (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]. 83.20/80.73 6328 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & A = k12_finseq_1(B,C))) <-> r2_hidden(A,a_1_0_finseq_2(B))))) # label(fraenkel_a_1_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6329 (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) -> (k9_finseq_1(A) = D -> k9_finseq_1(k1_funct_1(E,A)) = k1_partfun1(k5_numbers,B,B,C,D,E)))))))))) # label(t39_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6330 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))) = k1_nat_1(k3_finseq_1(B),np__1))) # label(t19_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6331 (all A exists B (-v1_xboole_0(B) & m1_finseq_2(B,A))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6332 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(C,A))))))) # label(t27_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6333 (all A (v1_funct_1(A) & v1_relat_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)) -> k11_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C),k1_funct_1(A,D)) = k5_relat_1(k11_finseq_1(B,C,D),A))))) # label(t146_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6334 (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)))))))) & p1_s2_finseq_2(k6_finseq_1(f1_s2_finseq_2)) -> (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]. 83.20/80.73 6335 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_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]. 83.20/80.73 6336 (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]. 83.20/80.73 6337 (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) & m2_relset_1(J,k2_zfmisc_1(A,B),C) & v1_funct_2(J,k2_zfmisc_1(A,B),C) -> (all K (m2_finseq_1(K,A) -> (all L (m2_finseq_1(L,B) -> (L = k11_finseq_1(G,H,I) & k11_finseq_1(D,E,F) = K -> 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]. 83.20/80.73 6338 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (k2_finseq_1(A) = B -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (m2_finseq_1(D,B) -> (r1_xreal_0(A,k3_finseq_1(C)) -> 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(t34_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6339 (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]. 83.20/80.73 6340 (all A all B all C k1_enumset1(A,B,C) = k2_relat_1(k11_finseq_1(A,B,C))) # label(t148_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6341 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -(r2_hidden(A,k2_relat_1(B)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(A = k1_funct_1(B,C) & r2_hidden(C,k4_finseq_1(B)))))))) # label(t11_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6342 (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]. 83.20/80.73 6343 (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]. 83.20/80.73 6344 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(k1_nat_1(A,np__1),B)) -> (exists D ((exists E (k8_finseq_1(B,D,k12_finseq_1(B,E)) = C & m1_subset_1(E,B))) & m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t137_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6345 (all A all B (-v1_xboole_0(B) -> ((exists C exists D exists E (k11_finseq_1(C,D,E) = A & m1_subset_1(E,B) & m1_subset_1(D,B) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_2_finseq_2(B))))) # label(fraenkel_a_1_2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6346 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__2,A)) -> (exists C ((exists D (m1_subset_1(D,A) & k10_finseq_1(C,D) = B)) & m1_subset_1(C,A))))))) # label(t120_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6347 (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]. 83.20/80.73 6348 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_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,B) -> (k11_finseq_1(E,F,G) = I -> k5_funcop_1(H,D,I) = k11_finseq_1(k2_binop_1(A,B,C,H,D,E),k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,D,G))))))))))))))))))))) # label(t96_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6349 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6350 (all A (m1_finseq_2(k13_finseq_1(A),A) & -v1_xboole_0(k13_finseq_1(A)))) # label(t104_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6351 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m2_finseq_2(D,C,k4_finseq_2(A,C)) -> m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t129_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6352 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_finseq_1(E,C) -> (all F (v1_funct_1(F) & v1_funct_2(F,C,D) & m2_relset_1(F,C,D) -> (k10_finseq_1(A,B) = E -> k1_partfun1(k5_numbers,C,C,D,E,F) = k10_finseq_1(k1_funct_1(F,A),k1_funct_1(F,B))))))))))) # label(t40_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 6353 (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_finseq_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_finseq_1(G) = k3_finseq_1(F) & k3_funcop_1(E,F,G) = D -> k3_finseq_1(D) = k3_finseq_1(F) & k3_finseq_1(D) = k3_finseq_1(G)))))))))))))))) # label(t86_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.73 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) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(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]. 83.20/80.73 6355 (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)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(D) -> (k2_relat_1(D) = k2_finseq_1(A) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B))))))))))) # label(t134_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.74 6356 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (k4_finseq_2(B,C) = k4_finseq_2(A,C) -> A = B))))))) # label(t130_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.74 6357 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) -> k2_square_1(np__0,k6_xcmplx_0(A,B)) = np__0))))) # label(t3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.74 6358 (all A all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> (k7_finseq_1(C,k9_finseq_1(A)) = k7_finseq_1(D,k9_finseq_1(B)) -> D = C & A = B))))) # label(t20_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.74 6359 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_finseq_1(E,A) -> (all F (m2_finseq_1(F,B) -> k3_funcop_1(D,k6_finseq_1(A),F) = k6_finseq_1(C) & k6_finseq_1(C) = k3_funcop_1(D,E,k6_finseq_1(B)))))))))))))) # label(t87_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.74 6360 (all A (v4_ordinal2(A) -> (all B k2_finseq_2(A,B) = k2_funcop_1(k2_finseq_1(A),B)))) # label(d2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.74 6361 (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_funct_1(D) & v1_finseq_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_finseq_1(D) = k3_square_1(k3_finseq_1(F),k3_finseq_1(G))))))))))))))))) # label(t85_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.74 6362 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v3_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) -> (k5_relat_1(C,A) = B -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t48_finseq_2) # label(axiom) # label(non_clause). [assumption]. 83.20/80.74 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,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) -> (G = k12_finseq_1(A,D) -> 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]. 83.20/80.74 6364 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(f3_s11_recdef_1,k1_nat_1(A,np__1)) = f2_s11_recdef_1(A,k1_funct_1(f3_s11_recdef_1,A)))) & f1_s11_recdef_1 = k1_funct_1(f4_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_relat_1(f4_s11_recdef_1) = k5_numbers -> f4_s11_recdef_1 = f3_s11_recdef_1 # label(s11_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6365 (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = k5_numbers & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> f2_s3_recdef_1(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_nat_1(B,np__1)))) & f1_s3_recdef_1 = k1_funct_1(A,np__0))) # label(s3_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6366 f2_s12_recdef_1 = k8_funct_2(k5_numbers,f1_s12_recdef_1,f4_s12_recdef_1,np__0) & (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)))) & 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) -> k8_funct_2(k5_numbers,f1_s12_recdef_1,f4_s12_recdef_1,k1_nat_1(A,np__1)) = f3_s12_recdef_1(A,k8_funct_2(k5_numbers,f1_s12_recdef_1,f4_s12_recdef_1,A)))) -> f4_s12_recdef_1 = f5_s12_recdef_1 # label(s12_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6367 k3_finseq_1(f4_s15_recdef_1) = f3_s15_recdef_1 & (f3_s15_recdef_1 = np__0 | k1_funct_1(f4_s15_recdef_1,np__1) = f2_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(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)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,A) -> r1_xreal_0(f3_s15_recdef_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)))))) & (f2_s15_recdef_1 = k1_funct_1(f5_s15_recdef_1,np__1) | np__0 = f3_s15_recdef_1) & 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) -> 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,C) & p1_s15_recdef_1(A,B,D) -> D = C)))))))))) -> f4_s15_recdef_1 = f5_s15_recdef_1 # label(s15_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6368 (exists A (v1_relat_1(A) & v1_funct_1(A) & k3_finseq_1(f1_s17_recdef_1) = k3_finseq_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_s17_recdef_1),B) | k1_funct_1(A,k1_nat_1(B,np__1)) = 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,np__1) = k1_funct_1(f1_s17_recdef_1,np__1) & k1_funct_1(A,k3_finseq_1(A)) = f3_s17_recdef_1 & v1_finseq_1(A))) & (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & f4_s17_recdef_1 = k1_funct_1(A,k3_finseq_1(A)) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,B) -> k1_funct_1(A,k1_nat_1(B,np__1)) = f2_s17_recdef_1(k1_funct_1(f1_s17_recdef_1,k1_nat_1(B,np__1)),k1_funct_1(A,B)) | r1_xreal_0(k3_finseq_1(f1_s17_recdef_1),B)))) & k1_funct_1(A,np__1) = k1_funct_1(f1_s17_recdef_1,np__1) & k3_finseq_1(f1_s17_recdef_1) = k3_finseq_1(A))) -> f3_s17_recdef_1 = f4_s17_recdef_1 # label(s17_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6369 (all A all B -(A != B & (exists C (v1_relat_1(C) & v1_finseq_1(C) & B = 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_funct_1(C))) & (exists C (v1_relat_1(C) & v1_finseq_1(C) & (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) & k1_funct_1(C,k3_finseq_1(C)) = A & v1_funct_1(C))))) # label(s23_recdef_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6370 (exists A exists B (v1_relat_1(B) & k1_funct_1(B,k3_finseq_1(B)) = A & k3_finseq_1(B) = k3_finseq_1(f1_s23_recdef_1) & k1_funct_1(f1_s23_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_s23_recdef_1(k1_funct_1(f1_s23_recdef_1,k1_nat_1(C,np__1)),k1_funct_1(B,C)) | r1_xreal_0(k3_finseq_1(f1_s23_recdef_1),C)))) & v1_finseq_1(B) & v1_funct_1(B))) # label(s23_recdef_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6371 (all A (m1_subset_1(A,f1_s21_recdef_1) -> (all B (m1_subset_1(B,f1_s21_recdef_1) -> -((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) & k8_funct_2(k5_numbers,f1_s21_recdef_1,C,f3_s21_recdef_1) = B & 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)))))) & A != B & (exists C (m2_relset_1(C,k5_numbers,f1_s21_recdef_1) & k8_funct_2(k5_numbers,f1_s21_recdef_1,C,f3_s21_recdef_1) = A & 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)))) & v1_funct_2(C,k5_numbers,f1_s21_recdef_1) & v1_funct_1(C)))))))) # label(s21_recdef_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6372 (exists A (m1_subset_1(A,f1_s21_recdef_1) & (exists B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,f1_s21_recdef_1) & f2_s21_recdef_1 = k8_funct_2(k5_numbers,f1_s21_recdef_1,B,np__0) & (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,f3_s21_recdef_1) = A & m2_relset_1(B,k5_numbers,f1_s21_recdef_1))))) # label(s21_recdef_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6373 (all A all B all C (m1_subset_1(C,A) & m1_relset_1(B,A,k5_numbers) & v1_funct_1(B) -> k1_recdef_1(A,B,C) = k1_funct_1(B,C))) # label(redefinition_k1_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6374 (exists A exists B (v1_funct_1(B) & k1_funct_1(B,k3_finseq_1(B)) = A & 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)))) & k3_finseq_1(f1_s8_recdef_1) = k3_finseq_1(B) & v1_finseq_1(B) & v1_relat_1(B))) # label(s8_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6375 (all A all B -(A != B & (exists C (v1_relat_1(C) & v1_funct_1(C) & k5_numbers = k1_relat_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)))) & f1_s19_recdef_1 = k1_funct_1(C,np__0) & B = k1_funct_1(C,f2_s19_recdef_1))) & (exists C (v1_relat_1(C) & v1_funct_1(C) & (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_funct_1(C,np__0) = f1_s19_recdef_1 & k5_numbers = k1_relat_1(C) & k1_funct_1(C,f2_s19_recdef_1) = A)))) # label(s19_recdef_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 83.20/80.75 6376 (exists A exists B (k1_funct_1(B,f2_s19_recdef_1) = A & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> f3_s19_recdef_1(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_nat_1(C,np__1)))) & f1_s19_recdef_1 = k1_funct_1(B,np__0) & k1_relat_1(B) = k5_numbers & v1_funct_1(B) & v1_relat_1(B))) # label(s19_recdef_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 83.29/80.79 6377 (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))))))) & (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,C) & p1_s20_recdef_1(A,B,D) -> C = D))))))))) -> (exists A (m1_subset_1(A,f1_s20_recdef_1) & (exists B (A = k8_funct_2(k5_numbers,f1_s20_recdef_1,B,f3_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) & m2_relset_1(B,k5_numbers,f1_s20_recdef_1) & v1_funct_2(B,k5_numbers,f1_s20_recdef_1) & v1_funct_1(B))))) & (all A (m1_subset_1(A,f1_s20_recdef_1) -> (all B (m1_subset_1(B,f1_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) & 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))))) & A = k8_funct_2(k5_numbers,f1_s20_recdef_1,C,f3_s20_recdef_1) & v1_funct_1(C))) & (exists C (v1_funct_2(C,k5_numbers,f1_s20_recdef_1) & m2_relset_1(C,k5_numbers,f1_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))))) & B = k8_funct_2(k5_numbers,f1_s20_recdef_1,C,f3_s20_recdef_1) & v1_funct_1(C))) & A != B))))) # label(s20_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.29/80.79 6378 (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 (r1_xreal_0(np__1,A) & k1_funct_1(f1_s22_recdef_1,k1_nat_1(A,np__1)) = E & p1_s22_recdef_1(E,B,C) & p1_s22_recdef_1(E,B,D) -> r1_xreal_0(k3_finseq_1(f1_s22_recdef_1),A) | D = C)))) -> (all A all B -((exists C (A = k1_funct_1(C,k3_finseq_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)))))) & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))) & A != B & (exists C (v1_relat_1(C) & v1_finseq_1(C) & k1_funct_1(C,k3_finseq_1(C)) = B & k3_finseq_1(C) = k3_finseq_1(f1_s22_recdef_1) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(np__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))) | r1_xreal_0(k3_finseq_1(f1_s22_recdef_1),D)))) & k1_funct_1(C,np__1) = k1_funct_1(f1_s22_recdef_1,np__1) & v1_funct_1(C))))) & (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & k3_finseq_1(f1_s22_recdef_1) = k3_finseq_1(B) & k1_funct_1(B,np__1) = k1_funct_1(f1_s22_recdef_1,np__1) & (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,k3_finseq_1(B)) = A)) # label(s22_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.29/80.79 6379 (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) -> C = D))))))))) & f2_s10_recdef_1 = k8_funct_2(k5_numbers,f1_s10_recdef_1,f4_s10_recdef_1,np__0) & k8_funct_2(k5_numbers,f1_s10_recdef_1,f3_s10_recdef_1,np__0) = f2_s10_recdef_1 -> f4_s10_recdef_1 = f3_s10_recdef_1 # label(s10_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.79 6380 (exists A (v1_funct_1(A) & f2_s4_recdef_1 = k8_funct_2(k5_numbers,f1_s4_recdef_1,A,np__0) & (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)))) & m2_relset_1(A,k5_numbers,f1_s4_recdef_1) & v1_funct_2(A,k5_numbers,f1_s4_recdef_1))) # label(s4_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.79 6381 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C all D (p1_s18_recdef_1(A,B,D) & p1_s18_recdef_1(A,B,C) -> C = D)))) & (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_relat_1(B) & v1_funct_1(B) & A = k1_funct_1(B,f2_s18_recdef_1) & k1_relat_1(B) = k5_numbers & (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)) & (all A all B -(A != B & (exists C (k1_funct_1(C,f2_s18_recdef_1) = B & k5_numbers = k1_relat_1(C) & (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_funct_1(C,np__0) = f1_s18_recdef_1 & v1_funct_1(C) & v1_relat_1(C))) & (exists C (v1_funct_1(C) & A = k1_funct_1(C,f2_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))))) & f1_s18_recdef_1 = k1_funct_1(C,np__0) & k1_relat_1(C) = k5_numbers & v1_relat_1(C))))) # label(s18_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.79 6382 (all A all B all C (v1_funct_1(B) & m1_subset_1(C,A) & m1_relset_1(B,A,k5_numbers) -> m2_subset_1(k1_recdef_1(A,B,C),k1_numbers,k5_numbers))) # label(dt_k1_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.79 6383 (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,C) & p1_s5_recdef_1(A,B,D) -> D = C))))) & (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 exists C p1_s5_recdef_1(A,B,C))))) -> (exists A (v1_finseq_1(A) & k3_finseq_1(A) = f2_s5_recdef_1 & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,B) -> p1_s5_recdef_1(B,k1_funct_1(A,B),k1_funct_1(A,k1_nat_1(B,np__1))) | r1_xreal_0(f2_s5_recdef_1,B)))) & (np__0 = f2_s5_recdef_1 | k1_funct_1(A,np__1) = f1_s5_recdef_1) & v1_funct_1(A) & v1_relat_1(A))) # label(s5_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.79 6384 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & k3_finseq_1(A) = k3_finseq_1(f1_s16_recdef_1) & k1_funct_1(f1_s16_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) -> 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,k3_finseq_1(A)) = f2_s16_recdef_1)) & (exists A (v1_finseq_1(A) & k1_funct_1(f1_s16_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) -> 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)))))) & k3_finseq_1(f1_s16_recdef_1) = k3_finseq_1(A) & k1_funct_1(A,k3_finseq_1(A)) = f3_s16_recdef_1 & v1_funct_1(A) & v1_relat_1(A))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C all D all E (k1_funct_1(f1_s16_recdef_1,k1_nat_1(A,np__1)) = E & p1_s16_recdef_1(E,B,C) & p1_s16_recdef_1(E,B,D) & r1_xreal_0(np__1,A) -> C = D | r1_xreal_0(k3_finseq_1(f1_s16_recdef_1),A))))) -> f2_s16_recdef_1 = f3_s16_recdef_1 # label(s16_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6385 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C all D all E (r1_xreal_0(np__1,A) & p1_s7_recdef_1(E,B,D) & p1_s7_recdef_1(E,B,C) & E = k1_funct_1(f1_s7_recdef_1,k1_nat_1(A,np__1)) -> r1_xreal_0(k3_finseq_1(f1_s7_recdef_1),A) | C = D)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B -(r1_xreal_0(np__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(k3_finseq_1(f1_s7_recdef_1),A))))) -> (exists A exists B ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) -> r1_xreal_0(k3_finseq_1(f1_s7_recdef_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)))))) & k1_funct_1(f1_s7_recdef_1,np__1) = k1_funct_1(B,np__1) & k3_finseq_1(B) = k3_finseq_1(f1_s7_recdef_1) & k1_funct_1(B,k3_finseq_1(B)) = A & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(s7_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6386 (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 (m1_subset_1(C,f1_s6_recdef_1) & p1_s6_recdef_1(A,B,C)))))))) -> (exists A (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)))) & (k1_funct_1(A,np__1) = f2_s6_recdef_1 | np__0 = f3_s6_recdef_1) & m2_finseq_1(A,f1_s6_recdef_1))) # label(s6_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6387 k5_numbers = k1_relat_1(f2_s9_recdef_1) & 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) & k1_funct_1(f3_s9_recdef_1,np__0) = f1_s9_recdef_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)))) & (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))))) -> f2_s9_recdef_1 = f3_s9_recdef_1 # label(s9_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6388 f1_s13_recdef_1 = k8_funct_2(k5_numbers,k1_numbers,f3_s13_recdef_1,np__0) & (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 & (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)))) -> f3_s13_recdef_1 = f4_s13_recdef_1 # label(s13_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6389 (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,D) & p1_s1_recdef_1(A,B,C) -> D = C)))) -> (exists A (v1_relat_1(A) & (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))))) & k1_funct_1(A,np__0) = f1_s1_recdef_1 & k5_numbers = k1_relat_1(A) & v1_funct_1(A))) # label(s1_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6390 k3_finseq_1(f3_s14_recdef_1) = f2_s14_recdef_1 & (k1_funct_1(f3_s14_recdef_1,np__1) = f1_s14_recdef_1 | f2_s14_recdef_1 = np__0) & (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)))))) & (f2_s14_recdef_1 = np__0 | k1_funct_1(f4_s14_recdef_1,np__1) = f1_s14_recdef_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(f3_s14_recdef_1,A),k1_funct_1(f3_s14_recdef_1,k1_nat_1(A,np__1)))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,A) -> (all B all C all D (p1_s14_recdef_1(A,B,D) & p1_s14_recdef_1(A,B,C) -> C = D)) | r1_xreal_0(f2_s14_recdef_1,A)))) -> f4_s14_recdef_1 = f3_s14_recdef_1 # label(s14_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6391 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_subset_1(B,f1_s2_recdef_1) -> (exists C (m1_subset_1(C,f1_s2_recdef_1) & p1_s2_recdef_1(A,B,C))))))) -> (exists 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) & v1_funct_1(A))) # label(s2_recdef_1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6392 (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]. 83.32/80.80 6393 (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]. 83.32/80.80 6394 (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]. 83.32/80.80 6395 (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]. 83.32/80.80 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]. 83.32/80.80 6397 (all A exists B (k3_classes1(A,B) = k1_classes1(A) & v3_ordinal1(B))) # label(t22_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6398 (all A v1_ordinal1(k5_classes1(A))) # label(t58_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6399 (all A (v3_ordinal1(A) -> k6_classes1(A) = A)) # label(t81_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6400 (all A (v1_ordinal1(A) -> A = k5_classes1(A))) # label(t62_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6401 (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]. 83.32/80.80 6402 (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]. 83.32/80.80 6403 $T # label(t57_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6404 (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]. 83.32/80.80 6405 (all A all B all C all D (v3_ordinal1(D) -> (r1_tarski(A,B) & r2_hidden(B,k3_classes1(C,D)) -> r2_hidden(A,k3_classes1(C,k1_ordinal1(D)))))) # label(t14_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6406 (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]. 83.32/80.80 6407 (all A r2_hidden(A,k1_classes1(A))) # label(t5_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6408 (all A exists B (v3_ordinal1(B) & k1_classes1(A) = k3_classes1(A,B) & (all C (v3_ordinal1(C) -> -(r2_hidden(C,B) & k3_classes1(A,C) = k1_classes1(A)))))) # label(t23_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6409 (all A (v2_classes1(A) <-> (all B (r2_hidden(B,A) -> r2_hidden(k1_zfmisc_1(B),A))) & (all B -(r1_tarski(B,A) & -r2_hidden(B,A) & -r2_tarski(B,A))) & v1_classes1(A))) # label(d2_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6410 (all A all B all C all D (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v3_ordinal1(D) -> (r2_hidden(A,a_3_0_classes1(B,C,D)) <-> (exists E (E = A & (exists F (m1_subset_1(F,k1_classes1(B)) & r2_hidden(F,k1_funct_1(C,D)) & r1_tarski(E,F))) & m1_subset_1(E,k1_classes1(B))))))) # label(fraenkel_a_3_0_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6411 (all A (k6_classes1(A) = k1_xboole_0 <-> A = k1_xboole_0)) # label(t79_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6412 (all A all B (v1_ordinal1(A) & v1_ordinal1(B) -> v1_ordinal1(k2_xboole_0(A,B)))) # label(t55_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6413 (all A all B -(r2_tarski(A,k1_classes1(B)) & r2_hidden(A,k1_classes1(B)))) # label(t29_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6414 (all A all B ((all C (r1_tarski(A,C) & v1_ordinal1(C) -> r1_tarski(B,C))) & v1_ordinal1(B) & r1_tarski(A,B) -> k5_classes1(A) = B)) # label(t61_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6415 (all A all B all C (v3_ordinal1(C) -> (v4_ordinal1(C) -> k1_xboole_0 = C | ((exists D (v3_ordinal1(D) & r2_hidden(D,C) & r2_hidden(B,k3_classes1(A,D)))) <-> r2_hidden(B,k3_classes1(A,C)))))) # label(t16_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6416 (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]. 83.32/80.80 6417 (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]. 83.32/80.80 6418 (all A all B all C (v3_ordinal1(C) -> ((exists D (m1_subset_1(D,k1_classes1(B)) & (exists E (r1_tarski(D,E) & r2_hidden(E,k3_classes1(B,C)) & m1_subset_1(E,k1_classes1(B)))) & D = A)) <-> r2_hidden(A,a_2_0_classes1(B,C))))) # label(fraenkel_a_2_0_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6419 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,k3_classes1(B,k1_ordinal1(C))) <-> -((all D -(r2_hidden(D,k3_classes1(B,C)) & (r1_tarski(A,D) | k1_zfmisc_1(D) = A))) & -(r1_tarski(A,k3_classes1(B,C)) & r2_hidden(A,k1_classes1(B))))))) # label(t13_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6420 $T # label(dt_k2_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6421 (all A all B (r1_classes1(A,B) & (all C (r1_classes1(A,C) -> r1_tarski(B,C))) <-> B = k1_classes1(A))) # label(d4_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6422 (all 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))) <-> v2_classes1(A))) # label(t2_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6423 (all A all B all C (r2_hidden(B,k1_classes1(A)) & r2_hidden(C,k1_classes1(A)) -> r2_hidden(k2_tarski(B,C),k1_classes1(A)) & r2_hidden(k1_tarski(B),k1_classes1(A)))) # label(t30_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6424 (all A all B all C (r1_tarski(C,k1_classes1(B)) & r1_tarski(A,k1_classes1(B)) -> r1_tarski(k2_zfmisc_1(A,C),k1_classes1(B)))) # label(t32_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6425 $T # label(t1_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6426 (all A all B (v3_ordinal1(B) -> (v4_ordinal1(B) -> k1_xboole_0 = B | a_2_2_classes1(A,B) = k3_classes1(A,B)))) # label(t12_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6427 (all A all B all C (r2_hidden(A,k1_classes1(B)) & r1_tarski(C,A) -> r2_hidden(C,k1_classes1(B)))) # label(t6_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6428 $T # label(dt_k1_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6429 (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]. 83.32/80.80 6430 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(B,k4_classes1(C)) & r1_tarski(A,B) -> r2_hidden(A,k4_classes1(C))))) # label(t47_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6431 (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]. 83.32/80.80 6432 (all A v3_ordinal1(k6_classes1(A))) # label(dt_k6_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6433 (all A all B all C all D (v3_ordinal1(D) -> (r2_hidden(A,k3_classes1(B,D)) & v4_ordinal1(D) -> -r1_tarski(C,A) & C != k1_zfmisc_1(A) | r2_hidden(C,k3_classes1(B,D)) | D = k1_xboole_0))) # label(t17_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6434 (all A all B -(r2_hidden(A,k1_classes1(B)) & (all C (v3_ordinal1(C) -> -(-r2_hidden(A,k3_classes1(B,C)) & r2_hidden(A,k3_classes1(B,k1_ordinal1(C)))))) & A != B)) # label(t24_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6435 (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]. 83.32/80.80 6436 (all A all B (v3_ordinal1(B) -> (all C (C = k2_classes1(A,B) <-> (exists D (v1_funct_1(D) & v5_ordinal1(D) & k1_relat_1(D) = k1_ordinal1(B) & k1_funct_1(D,k1_xboole_0) = k1_tarski(A) & (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)) -> E = k1_xboole_0 | k1_funct_1(D,E) = k3_xboole_0(k3_tarski(k2_relat_1(k2_ordinal1(D,E))),k1_classes1(A))))) & k1_ordinal2(D) = C & v1_relat_1(D))))))) # label(d5_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6437 (all A all B (r2_hidden(A,B) & v2_classes1(B) <-> r1_classes1(A,B))) # label(d3_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6438 (all A all B (B = k5_classes1(A) <-> (all C (r2_hidden(C,B) <-> (exists D ((exists E (m2_subset_1(E,k1_numbers,k5_numbers) & 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)))) & k1_relat_1(D) = k5_numbers & r2_hidden(C,k1_funct_1(D,E)))) & v1_funct_1(D) & v1_relat_1(D))))))) # label(d7_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6439 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) <-> r2_hidden(k1_tarski(A),k4_classes1(k1_ordinal1(B)))))) # label(t49_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6440 (all A -v1_xboole_0(k1_classes1(A))) # label(fc1_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6441 (all A (v3_ordinal1(A) -> r1_tarski(k3_tarski(k4_classes1(A)),k4_classes1(A)))) # label(t40_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6442 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k1_xboole_0 != B -> v1_ordinal1(k3_classes1(A,B))))))) # label(t25_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6443 (all A (v1_ordinal1(A) -> v1_ordinal1(k1_classes1(A)))) # label(t27_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6444 (all A (v1_ordinal1(A) -> r1_tarski(k3_tarski(A),A))) # label(t54_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6445 (all A all B all C all D (v1_relat_1(C) & v5_ordinal1(C) & v3_ordinal1(D) & v1_funct_1(C) -> (r2_hidden(A,a_3_1_classes1(B,C,D)) <-> (exists E (m1_subset_1(E,k1_classes1(B)) & r2_hidden(E,k1_funct_1(C,D)) & A = k1_zfmisc_1(E)))))) # label(fraenkel_a_3_1_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6446 (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]. 83.32/80.80 6447 (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]. 83.32/80.80 6448 (all A (v3_ordinal1(A) -> A = k6_classes1(k4_classes1(A)))) # label(t72_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6449 $T # label(t4_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6450 (all A all B (v3_ordinal1(B) -> (r1_tarski(k1_zfmisc_1(A),k4_classes1(k1_ordinal1(B))) <-> r1_tarski(A,k4_classes1(B))))) # label(t46_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6451 (all A all B (v3_ordinal1(B) -> -(k6_classes1(A) = k1_ordinal1(B) & (all C -(k6_classes1(C) = B & r2_hidden(C,A)))))) # label(t80_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6452 (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]. 83.32/80.80 6453 (all A exists B (k3_classes1(A,B) = k3_classes1(A,k1_ordinal1(B)) & v3_ordinal1(B))) # label(t20_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6454 $T # label(dt_k4_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6455 (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]. 83.32/80.80 6456 (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]. 83.32/80.80 6457 $T # label(t3_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6458 (all A all B all C (v3_ordinal1(C) -> ((exists D (m1_subset_1(D,k1_classes1(B)) & (exists E (r2_hidden(E,C) & r2_hidden(D,k3_classes1(B,E)) & v3_ordinal1(E))) & D = A)) <-> r2_hidden(A,a_2_2_classes1(B,C))))) # label(fraenkel_a_2_2_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6459 (all A all B (v3_ordinal1(B) -> (k3_classes1(A,k1_ordinal1(B)) = k3_classes1(A,B) -> k1_classes1(A) = k3_classes1(A,B)))) # label(t21_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6460 (all A (v3_ordinal1(A) -> A = k5_classes1(A))) # label(t64_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6461 (all A (v3_ordinal1(A) -> (all B (r2_hidden(B,k4_classes1(A)) -> r2_hidden(k1_card_1(B),k1_card_1(k4_classes1(A))) & -r2_tarski(B,k4_classes1(A)))))) # label(t45_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6462 (all A all B (v3_ordinal1(B) -> (v1_ordinal1(A) & k3_xboole_0(k4_classes1(k1_ordinal1(B)),k1_classes1(A)) = k3_xboole_0(k4_classes1(B),k1_classes1(A)) -> r1_tarski(k1_classes1(A),k4_classes1(B))))) # label(t52_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6463 $T # label(dt_k5_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6464 $T # label(t70_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6465 (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]. 83.32/80.80 6466 (all A (v3_ordinal1(A) -> (all B (B = k4_classes1(A) <-> (exists C ((all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_zfmisc_1(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 | k3_tarski(k2_relat_1(k2_ordinal1(C,D))) = k1_funct_1(C,D)))) & k1_funct_1(C,k1_xboole_0) = k1_xboole_0 & k1_ordinal1(A) = k1_relat_1(C) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))))))) # label(d6_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6467 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> (all B ((exists C (v3_ordinal1(C) & r2_hidden(C,A) & r2_hidden(B,k4_classes1(C)))) <-> r2_hidden(B,k4_classes1(A)))) | A = k1_xboole_0))) # label(t35_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6468 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(k1_ordinal1(B))) <-> r1_tarski(A,k4_classes1(B))))) # label(t36_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6469 (all A (v3_ordinal1(A) -> k1_zfmisc_1(k4_classes1(A)) = k4_classes1(k1_ordinal1(A)))) # label(t34_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6470 (all A exists B (v3_ordinal1(B) & r1_tarski(A,k4_classes1(B)))) # label(t69_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6471 (all A (v3_ordinal1(A) -> r1_tarski(A,k4_classes1(A)))) # label(t44_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6472 (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]. 83.32/80.80 6473 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(t37_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6474 (all A (v3_ordinal1(A) -> r1_tarski(k4_classes1(A),k4_classes1(k1_ordinal1(A))))) # label(t39_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6475 (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]. 83.32/80.80 6476 (all A r1_tarski(A,k5_classes1(A))) # label(t59_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6477 (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]. 83.32/80.80 6478 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,k4_classes1(B)) <-> r1_ordinal1(k6_classes1(A),B)))) # label(t73_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6479 (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]. 83.32/80.80 6480 (all A all B (r1_tarski(A,k1_classes1(B)) & r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))) -> r2_hidden(A,k1_classes1(B)))) # label(t9_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6481 (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]. 83.32/80.80 6482 (all A k1_ordinal1(k6_classes1(A)) = k6_classes1(k1_zfmisc_1(A))) # label(t71_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6483 (all A all B (v3_ordinal1(B) -> (r1_ordinal1(B,k6_classes1(A)) <-> (all C (v3_ordinal1(C) -> -(r2_hidden(C,B) & (all D -(r2_hidden(D,A) & r1_ordinal1(C,k6_classes1(D)))))))))) # label(t78_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6484 (all A k5_classes1(k5_classes1(A)) = k5_classes1(A)) # label(t66_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6485 (all A (v1_classes1(A) <-> (all B all C (r1_tarski(C,B) & r2_hidden(B,A) -> r2_hidden(C,A))))) # label(d1_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6486 (all A all B all C (v3_ordinal1(C) -> ((exists D (m1_subset_1(D,k1_classes1(B)) & A = k1_zfmisc_1(D) & r2_hidden(D,k3_classes1(B,C)))) <-> r2_hidden(A,a_2_1_classes1(B,C))))) # label(fraenkel_a_2_1_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6487 (all A k1_tarski(A) = k3_classes1(A,k1_xboole_0)) # label(t10_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6488 (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]. 83.32/80.80 6489 (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]. 83.32/80.80 6490 (all A all B (v3_ordinal1(B) -> k3_classes1(A,B) = k2_classes1(A,B))) # label(redefinition_k3_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6491 (all A (r2_hidden(k3_classes1(A,k1_xboole_0),k3_classes1(A,k4_ordinal2)) & k3_classes1(A,k1_xboole_0) != k3_classes1(A,k4_ordinal2))) # label(t26_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6492 (all A all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r1_tarski(A,k4_classes1(C)) -> r1_ordinal1(B,C)))) & r1_tarski(A,k4_classes1(B)) <-> k6_classes1(A) = B))) # label(d8_classes1) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6493 $T # label(t1_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6494 $T # label(t2_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6495 (all A all B all C (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) & v1_setfam_1(B) -> v1_fraenkel(k4_card_3(C)) & -v1_xboole_0(k4_card_3(C)))) # label(fc4_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6496 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(A)))) # label(t55_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6497 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & D = k1_funct_1(E,A) & v1_funct_1(E) & v1_relat_1(E))))) <-> k5_card_3(A,B) = C)) # label(d6_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6498 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 83.32/80.80 6499 (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]. 83.32/80.80 6500 (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]. 83.32/80.80 6501 (all A -(v6_ordinal1(A) & (all B -((all C -(r1_tarski(C,B) & (all D -((all E (r2_hidden(E,C) -> r1_tarski(D,E))) & r2_hidden(D,C))) & k1_xboole_0 != C)) & k3_tarski(A) = k3_tarski(B) & r1_tarski(B,A))))) # label(t61_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6502 (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s4_card_3 & (all B (r2_hidden(B,f1_s4_card_3) -> (all C (p1_s4_card_3(B,C) & r2_hidden(C,f2_s4_card_3(B)) <-> r2_hidden(C,k1_funct_1(A,B)))))) & v1_relat_1(A))) # label(s4_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6503 (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]. 83.32/80.80 6504 (all A all B all C (p1_s3_card_3(B,C) & p1_s3_card_3(A,B) -> p1_s3_card_3(A,C))) & (all A all B (p1_s3_card_3(A,B) | p1_s3_card_3(B,A))) & f1_s3_card_3 != k1_xboole_0 -> (exists A ((all B (r2_hidden(B,f1_s3_card_3) -> p1_s3_card_3(A,B))) & r2_hidden(A,f1_s3_card_3))) # label(s3_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6505 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(C)) -> r1_xboole_0(k1_funct_1(k2_card_3(C),A),k1_funct_1(k2_card_3(C),B)) | A = B))) # label(t13_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6506 (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]. 83.32/80.80 6507 $T # label(t23_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6508 $T # label(t41_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6509 (all A all B k1_funct_2(A,B) = k4_card_3(k2_funcop_1(A,B))) # label(t20_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6510 $T # label(t5_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6511 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (v1_card_3(B) & v1_funct_1(B) & v1_relat_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]. 83.32/80.80 6512 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_card_3(k7_relat_1(A,B)))) # label(fc1_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6513 $T # label(dt_k3_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6514 (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]. 83.32/80.80 6515 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_card_3(B) & v1_funct_1(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]. 83.32/80.80 6516 (all A all B k2_card_3(k2_funcop_1(k1_tarski(A),B)) = k2_funcop_1(k1_tarski(A),k2_zfmisc_1(B,k1_tarski(A)))) # label(t12_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6517 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k5_card_3(A,k1_tarski(B)) = k1_tarski(k1_funct_1(B,A)))) # label(t25_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6518 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A))) # label(rc1_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6519 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (k7_card_3(A) = np__0 <-> r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(t44_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6520 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_card_3(A) = k3_tarski(k2_relat_1(A)))) # label(d4_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6521 (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]. 83.32/80.80 6522 (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 A != k4_tarski(C,D))))) # label(t32_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6523 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k4_card_3(B)) <-> (all C (r2_hidden(C,k1_relat_1(B)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = k1_relat_1(B)))))) # label(t18_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6524 (all A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) -> v1_fraenkel(k4_card_3(A)) & -v1_xboole_0(k4_card_3(A)))) # label(fc5_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6525 (all A (v1_relat_1(A) & v1_funct_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]. 83.32/80.80 6526 (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]. 83.32/80.80 6527 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> A = k1_card_3(A))) # label(t8_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6528 (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]. 83.32/80.80 6529 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_card_3(B) & v1_relat_1(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]. 83.32/80.80 6530 (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]. 83.32/80.80 6531 (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]. 83.32/80.80 6532 (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]. 83.32/80.80 6533 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_card_3(A)) & v1_funct_1(k2_card_3(A)))) # label(dt_k2_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6534 (all A (v1_card_1(A) -> np__0 = k6_card_3(k2_funcop_1(k1_xboole_0,A)))) # label(t48_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6535 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_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]. 83.32/80.80 6536 (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]. 83.32/80.80 6537 $T # label(t42_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6538 (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]. 83.32/80.80 6539 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> v1_card_1(k6_card_3(A)))) # label(dt_k6_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6540 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_card_3(B) & v1_funct_1(B) -> (B = k1_card_3(A) <-> (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)))))) # label(d2_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6541 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> k1_card_1(k3_card_3(k2_card_3(A))) = k6_card_3(A))) # label(d7_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6542 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k1_card_1(k1_funct_1(A,B)))))) # label(t39_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6543 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k7_card_3(k2_funcop_1(A,B)) = k3_card_2(B,A))))) # label(t53_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6544 (all A (v1_relat_1(A) & v1_funct_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]. 83.32/80.80 6545 (all A k1_xboole_0 = k5_card_3(A,k1_xboole_0)) # label(t24_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6546 (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]. 83.32/80.80 6547 (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]. 83.32/80.80 6548 $T # label(t7_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6549 $T # label(dt_k5_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6550 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_card_3(A,k4_card_3(B)) | k4_card_3(B) = k1_xboole_0))) # label(t22_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6551 (exists A (v1_funct_1(A) & f1_s1_card_3 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s1_card_3) -> k1_funct_1(A,B) = f2_s1_card_3(B))) & v1_card_3(A) & v1_relat_1(A))) # label(s1_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6552 (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)) & k1_xboole_0 != f1_s2_card_3 -> (exists A ((all B -(p1_s2_card_3(B,A) & A != B & r2_hidden(B,f1_s2_card_3))) & r2_hidden(A,f1_s2_card_3))) # label(s2_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6553 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k2_card_3(A) <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B)))))) # label(d3_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6554 (all A all B k3_card_3(k2_card_3(k2_funcop_1(A,B))) = k2_zfmisc_1(B,A)) # label(t36_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6555 (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]. 83.32/80.80 6556 $T # label(dt_k4_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.80 6557 (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]. 83.32/80.81 6558 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_card_3(B) & v1_relat_1(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]. 83.32/80.81 6559 (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]. 83.32/80.81 6560 (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]. 83.32/80.81 6561 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> v1_card_1(k7_card_3(A)))) # label(dt_k7_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6562 $T # label(t21_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6563 $T # label(t4_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6564 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = k1_relat_1(B) -> r1_tarski(k4_card_3(A),k4_card_3(B))))))) # label(t38_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6565 $T # label(t6_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6566 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (B = k4_card_3(A) <-> (all C (r2_hidden(C,B) <-> (exists 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) & C = D & v1_funct_1(D) & v1_relat_1(D))))))))) # label(d5_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6567 (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]. 83.32/80.81 6568 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k3_card_3(k2_card_3(B))) <-> r2_hidden(k1_mcart_1(A),k1_funct_1(B,k2_mcart_1(A))) & A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) & r2_hidden(k2_mcart_1(A),k1_relat_1(B))))) # label(t33_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6569 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_card_3(B) & v1_funct_1(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]. 83.32/80.81 6570 (all A all B B = k3_card_3(k2_funcop_1(k1_tarski(A),B))) # label(t17_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6571 (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]. 83.32/80.81 6572 (all A (v1_funct_1(A) & v1_relat_1(A) -> (r2_hidden(k1_xboole_0,k2_relat_1(A)) <-> k1_xboole_0 = k4_card_3(A)))) # label(t37_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6573 (all A all B (v1_card_1(B) -> v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_card_3(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc2_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6574 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k1_card_1(k1_funct_1(k2_card_3(A),B)))))) # label(t40_card_3) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6575 (all A all B (v2_classes1(A) -> r1_tarski(k1_funct_2(B,A),A) | -(r2_hidden(B,A) & r1_tarski(B,A)) & -(r2_hidden(k1_card_1(B),k1_card_1(A)) & r1_tarski(B,A)) & -(r2_hidden(B,A) & v1_ordinal1(A)))) # label(t23_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6576 (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]. 83.32/80.81 6577 (all A (v1_ordinal1(A) -> k1_classes1(A) = k4_classes1(k1_card_1(k1_classes1(A))))) # label(t46_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6578 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(k1_classes1(B))) -> r2_hidden(k1_card_1(k4_classes1(A)),k1_card_1(k1_classes1(B))) & r2_hidden(k4_classes1(A),k1_classes1(B)))))) # label(t27_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6579 (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]. 83.32/80.81 6580 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> (v4_ordinal1(k1_relat_1(A)) & (all B (v3_ordinal1(B) -> (r2_hidden(B,k1_relat_1(A)) -> k4_classes1(B) = k1_funct_1(A,B)))) -> k3_card_3(A) = k4_classes1(k1_relat_1(A))))) # label(t25_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6581 $T # label(t48_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6582 (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(k12_classes2(A,B,C),A))) # label(dt_k12_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6583 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k11_classes2(A,B,C),A))) # label(dt_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6584 (all A (v3_ordinal1(A) -> (all B (v2_classes1(B) & r2_hidden(A,B) -> r1_tarski(A,B) & r2_hidden(k1_ordinal1(A),B))))) # label(t6_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6585 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k16_classes2(B) = k16_classes2(A) -> B = A))))) # label(t81_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6586 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k8_classes2(A,C,B) = k8_classes2(A,B,C))) # label(commutativity_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6587 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r1_tarski(k16_classes2(A),k16_classes2(B))))))) # label(t82_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6588 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (exists B (m1_subset_1(B,A) & -v1_xboole_0(B))))) # label(rc2_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6589 (exists A (-v1_xboole_0(A) & v1_classes1(A) & v2_classes1(A) & v1_classes2(A) & v1_ordinal1(A))) # label(rc1_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6590 (all A all B (r2_hidden(B,A) & v1_classes1(A) -> r2_hidden(k1_card_1(B),k1_card_1(A)) & -r2_wellord2(B,A))) # label(t1_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6591 (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]. 83.32/80.81 6592 (all A (v1_classes2(k15_classes2(A)) & -v1_xboole_0(k15_classes2(A)))) # label(dt_k15_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6593 (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]. 83.32/80.81 6594 (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]. 83.32/80.81 6595 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k5_classes2(A,B,C) = k2_tarski(B,C))) # label(redefinition_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6596 (all A (v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(fc1_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6597 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)))) # label(fc3_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6598 (all A all B (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k1_classes2(A,B),A))) # label(dt_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6599 (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]. 83.32/80.81 6600 (all A (v2_classes1(A) -> v4_ordinal1(k1_card_1(A)))) # label(t20_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6601 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(fc4_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6602 (all A (v3_ordinal1(A) -> (all B (v2_classes1(B) & r2_hidden(A,k2_ordinal2(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]. 83.32/80.81 6603 (all A all B all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k2_tarski(A,B),C) & r2_hidden(k4_tarski(A,B),C)))) # label(t64_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6604 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> (r2_hidden(A,B) -> r2_hidden(k1_setfam_1(A),B) & r2_hidden(k3_tarski(A),B) & r2_hidden(k1_zfmisc_1(A),B)))) # label(t65_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6605 (all A (v2_classes1(A) -> v4_ordinal1(k1_card_1(A)) & k1_xboole_0 != k1_card_1(A) & k1_card_1(A) != np__0 | A = k1_xboole_0)) # label(t21_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6606 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k4_tarski(B,C) = k6_classes2(A,B,C))) # label(redefinition_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6607 (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]. 83.32/80.81 6608 (all A all B (r2_hidden(A,k1_classes1(B)) & v1_ordinal1(A) -> r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))))) # label(t44_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6609 (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]. 83.32/80.81 6610 (all A all B (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k2_classes2(A,B) = k1_zfmisc_1(B))) # label(redefinition_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6611 (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]. 83.32/80.81 6612 (all A v2_classes1(k4_classes1(k1_card_1(k1_classes1(A))))) # label(t40_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6613 (all A (v3_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t53_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6614 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,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]. 83.32/80.81 6615 (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]. 83.32/80.81 6616 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> (all C (-v1_xboole_0(C) & v1_classes2(C) -> (r2_hidden(A,B) & r2_hidden(B,C) -> r2_hidden(A,C)))))))) # label(t59_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6617 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r2_hidden(k1_xboole_0,A))) # label(t62_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6618 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,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]. 83.32/80.81 6619 $T # label(t2_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6620 (all A (v1_ordinal1(A) -> v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)))) # label(fc6_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6621 (all A all B (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k1_classes2(A,B) = k1_tarski(B))) # label(redefinition_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6622 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> r3_xboole_0(A,B))))) # label(t58_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6623 (all A (v1_classes2(A) -> v2_classes1(A) & v1_classes1(A) & v1_ordinal1(A))) # label(cc2_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6624 (all A all B all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k3_xboole_0(A,B),C) & r2_hidden(k5_xboole_0(A,B),C) & r2_hidden(k4_xboole_0(A,B),C) & r2_hidden(k2_xboole_0(A,B),C)))) # label(t66_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6625 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k9_classes2(A,B,C),A))) # label(dt_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6626 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k7_classes2(A,B,C),A))) # label(dt_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6627 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k4_classes2(A,B),A))) # label(dt_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6628 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r1_tarski(k13_classes2,A) & r1_tarski(k16_classes2(k1_xboole_0),A) & r1_tarski(k1_classes1(k1_xboole_0),A))) # label(t79_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6629 $T # label(t72_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6630 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) -> (v4_ordinal1(A) & (all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k1_funct_1(B,C) = k16_classes2(C)))) & k1_relat_1(B) = A -> k16_classes2(A) = k15_classes2(k3_card_3(B)) | k1_xboole_0 = A))))) # label(t78_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6631 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(A,B) -> r2_hidden(k1_tarski(A),B)))) # label(t63_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6632 (all A (v4_ordinal1(k1_card_1(k1_classes1(A))) & k1_card_1(k1_classes1(A)) != k1_xboole_0 & k1_card_1(k1_classes1(A)) != np__0)) # label(t22_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6633 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k5_classes2(A,B,C) = k5_classes2(A,C,B))) # label(commutativity_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6634 $T # label(t49_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6635 (all A (v1_ordinal1(A) & v2_classes1(A) -> k4_classes1(k1_card_1(A)) = A)) # label(t32_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6636 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(fc7_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6637 $T # label(t60_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6638 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> -v1_xboole_0(k2_classes2(A,B)) & m1_subset_1(k2_classes2(A,B),A))) # label(dt_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6639 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> r2_hidden(B,A) | r1_tarski(A,B))))) # label(t57_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6640 (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]. 83.32/80.81 6641 (all A k1_card_1(k4_classes1(k1_card_1(k1_classes1(A)))) = k1_card_1(k1_classes1(A))) # label(t36_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6642 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k6_classes2(A,B,C),A))) # label(dt_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6643 (all A all B (v2_classes1(A) & r2_hidden(B,k1_card_1(A)) -> r2_hidden(B,A))) # label(t14_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6644 (all A all B (r2_hidden(B,A) & v1_ordinal1(B) & v1_classes1(A) -> r1_tarski(B,A))) # label(t8_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6645 (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,B) = B)) # label(idempotence_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6646 $T # label(t73_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6647 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k7_classes2(A,C,B) = k7_classes2(A,B,C))) # label(commutativity_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6648 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k8_classes2(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6649 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k10_classes2(A,B,C) = k5_xboole_0(B,C))) # label(redefinition_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6650 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k8_classes2(A,B,C),A))) # label(dt_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6651 (all A (v1_classes2(A) <-> v2_classes1(A) & v1_ordinal1(A))) # label(d1_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6652 (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]. 83.32/80.81 6653 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> -v1_xboole_0(k2_xboole_0(A,B)) & v1_classes2(k2_xboole_0(A,B)) & v1_classes2(k3_xboole_0(A,B)) & -v1_xboole_0(k3_xboole_0(A,B)))))) # label(t61_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6654 (all A (v1_card_1(A) -> (all B (r2_hidden(A,B) & v2_classes1(B) -> r1_tarski(A,B))))) # label(t18_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6655 (all A all B all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(B,C) & r2_hidden(A,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]. 83.32/80.81 6656 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k3_tarski(B) = k3_classes2(A,B))) # label(redefinition_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6657 (all A (v1_classes2(A) & -v1_xboole_0(A) -> A = k4_classes1(k2_ordinal2(A)))) # label(t54_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6658 $T # label(t47_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6659 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k10_classes2(A,C,B) = k10_classes2(A,B,C))) # label(commutativity_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 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(k5_classes2(A,B,C),A))) # label(dt_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6661 (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]. 83.32/80.81 6662 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k3_classes2(A,B),A))) # label(dt_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6663 $T # label(dt_k16_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6664 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v4_ordinal1(k2_ordinal2(A)) & k2_ordinal2(A) != k1_xboole_0)) # label(t55_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6665 (all A (v3_ordinal1(A) -> k1_classes1(k16_classes2(A)) = k16_classes2(k1_ordinal1(A)))) # label(t76_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6666 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v1_ordinal1(k2_ordinal2(A)) & v3_ordinal1(k2_ordinal2(A)) & v2_ordinal1(k2_ordinal2(A)))) # label(fc2_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6667 (all A all B (-(-(r1_tarski(A,k1_classes1(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))) & -(v1_ordinal1(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]. 83.32/80.81 6668 (all A (v3_ordinal1(A) -> (all B -((all C -(A = k6_classes1(C) & r2_hidden(C,B))) & r2_hidden(A,k6_classes1(B)) & v1_ordinal1(B))))) # label(t41_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6669 (all A (v2_classes1(A) -> r1_tarski(k4_classes1(k1_card_1(A)),A))) # label(t28_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6670 (all A (v2_classes1(A) -> k2_ordinal2(A) = k1_card_1(A))) # label(t10_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6671 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> (k15_classes2(A) = B <-> r1_tarski(A,B) & (all C (-v1_xboole_0(C) & v1_classes2(C) -> (r1_tarski(A,C) -> r1_tarski(B,C))))))) # label(d4_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6672 (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]. 83.32/80.81 6673 $T # label(t74_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6674 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> -(-r2_hidden(B,A) & B != A & -r2_hidden(A,B)))))) # label(t56_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6675 (all A r1_tarski(k4_classes1(k1_card_1(k1_classes1(A))),k1_classes1(A))) # label(t29_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6676 (all A all B (r2_hidden(B,A) & v1_ordinal1(B) & v2_classes1(A) -> r2_hidden(B,k4_classes1(k1_card_1(A))))) # label(t43_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6677 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k7_classes2(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6678 (all A (v2_classes1(A) -> v1_classes1(A))) # label(cc1_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6679 (all A v1_ordinal1(k5_classes1(A))) # label(fc5_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6680 (all A (v1_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t51_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6681 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k1_classes1(A)) & v1_classes2(k1_classes1(A)))) # label(t52_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6682 (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]. 83.32/80.81 6683 (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]. 83.32/80.81 6684 $T # label(t68_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6685 (all A (v3_ordinal1(A) -> v1_classes2(k16_classes2(A)) & v2_classes1(k16_classes2(A)) & v1_classes1(k16_classes2(A)) & -v1_xboole_0(k16_classes2(A)) & v1_ordinal1(k16_classes2(A)))) # label(fc8_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6686 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v3_ordinal1(k2_ordinal2(A)))) # label(t50_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6687 (all A all B -(-r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))) & -r2_wellord2(A,k4_classes1(k1_card_1(k1_classes1(B)))) & r1_tarski(A,k4_classes1(k1_card_1(k1_classes1(B)))))) # label(t38_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6688 (all A (v2_classes1(A) -> v2_classes1(k4_classes1(k1_card_1(A))))) # label(t39_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6689 (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(k10_classes2(A,B,C),A))) # label(dt_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6690 (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]. 83.32/80.81 6691 (all A all B (r2_hidden(B,A) & v2_classes1(A) -> r1_tarski(k1_classes1(B),A))) # label(t5_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6692 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k7_classes2(A,B,B) = B)) # label(idempotence_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6693 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k16_classes2(A),k16_classes2(B)) <-> r2_hidden(A,B)))))) # label(t80_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6694 (all A all B all C (r2_hidden(B,A) & r2_hidden(C,A) & v2_classes1(A) -> r2_hidden(k2_tarski(B,C),A) & r2_hidden(k1_tarski(B),A))) # label(t3_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6695 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k2_zfmisc_1(B,C) = k11_classes2(A,B,C))) # label(redefinition_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6696 (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]. 83.32/80.81 6697 (all A k1_card_1(k1_classes1(A)) = k2_ordinal2(k1_classes1(A))) # label(t11_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6698 (all A (v1_ordinal1(A) & v2_classes1(A) -> v1_classes2(A))) # label(cc3_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6699 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & k1_funct_1(C,k1_xboole_0) = k13_classes2 & (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))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | k15_classes2(k3_card_3(k2_ordinal1(C,D))) = k1_funct_1(C,D)))) & v5_ordinal1(C) & v1_funct_1(C))) <-> B = k16_classes2(A))))) # label(d5_classes2) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6700 (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]. 83.32/80.81 6701 (all A all B all C (-v1_xboole_0(A) & m1_ordinal4(C,A) & m1_ordinal4(B,A) & v1_classes2(A) -> k7_ordinal4(A,B,C) = k14_ordinal2(B,C))) # label(redefinition_k7_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6702 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) -> v1_ordinal1(k1_ordinal2(A)) & v3_ordinal1(k1_ordinal2(A)) & v2_ordinal1(k1_ordinal2(A)))) # label(fc1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6703 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) -> k14_ordinal2(B,C) = k1_funct_1(A,C)))) -> v2_ordinal2(A)))))) # label(t18_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6704 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_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_funct_1(D) & v5_ordinal1(D) & v1_ordinal2(D) & v1_relat_1(D) -> (k1_relat_1(D) = k1_relat_1(A) & (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))))) & r1_ordinal2(B,D) & r1_ordinal2(B,C) & k1_relat_1(C) = k1_relat_1(A) -> r1_ordinal2(B,A)))))))))) # label(t7_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6705 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k4_ordinal2,A) & v4_ordinal1(B) -> k1_xboole_0 = B | (all C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> (B = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,B) -> k16_ordinal2(A,D) = k1_funct_1(C,D)))) -> k16_ordinal2(A,B) = k8_ordinal2(C))))))))) # label(t26_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6706 (exists A (m2_ordinal4(A,f1_s2_ordinal4) & (all B (m1_ordinal4(B,f1_s2_ordinal4) -> k1_funct_1(A,B) = f2_s2_ordinal4(B))))) # label(s2_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6707 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> -(v2_ordinal2(A) & (all C (v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> -(v2_ordinal2(C) & C = k5_relat_1(B,A)))) & v2_ordinal2(B)))))) # label(t13_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6708 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (exists B (m1_ordinal4(B,A) & v1_ordinal1(B) & v2_ordinal1(B) & -v1_xboole_0(B) & v3_ordinal1(B))))) # label(rc1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6709 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all C (v1_relat_1(C) & v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k16_ordinal2(B,D)))) -> r1_ordinal2(k16_ordinal2(B,A),C))))))))) # label(t21_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6710 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) -> (v2_ordinal2(A) & v4_ordinal1(k1_relat_1(A)) -> v4_ordinal1(k8_ordinal2(A))))) # label(t16_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6711 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(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) -> (r1_ordinal2(C,A) & r1_ordinal2(D,B) & k1_relat_1(A) = k1_relat_1(B) -> (exists E (v3_ordinal1(E) & -r1_ordinal1(k1_funct_1(A,E),k1_funct_1(B,E)) & r2_hidden(E,k1_relat_1(A)))) & (exists E (r2_hidden(E,k1_relat_1(A)) & -r2_hidden(k1_funct_1(A,E),k1_funct_1(B,E)) & v3_ordinal1(E))) | r1_ordinal1(C,D)))))))))) # label(t6_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6712 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v3_ordinal1(B) -> (m1_ordinal4(B,A) <-> r2_hidden(B,A)))))) # label(d2_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6713 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k4_ordinal2 = k3_ordinal4(A) & k2_ordinal4(A) = k1_xboole_0)) # label(t35_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6714 (all A all B all C (v1_classes2(A) & m2_ordinal4(B,A) & m1_ordinal4(C,A) & -v1_xboole_0(A) -> k1_funct_1(B,C) = k4_ordinal4(A,B,C))) # label(redefinition_k4_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6715 (all A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_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]. 83.32/80.81 6716 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> (k1_ordinal1(B) = k1_relat_1(A) -> r1_ordinal2(k1_ordinal2(A),A) & k1_ordinal2(A) = k12_ordinal2(A)))))) # label(t1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6717 (all A (v3_ordinal1(A) -> (k1_xboole_0 != A -> k16_ordinal2(k1_xboole_0,A) = k1_xboole_0))) # label(t20_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6718 (all A all B (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_relat_1(k1_ordinal4(A,B)) & v1_funct_1(k1_ordinal4(A,B)) & v5_ordinal1(k1_ordinal4(A,B)))) # label(dt_k1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6719 (all A all B (m1_ordinal4(B,A) & v1_classes2(A) & -v1_xboole_0(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]. 83.32/80.81 6720 $T # label(t34_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6721 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_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]. 83.32/80.81 6722 $T # label(t33_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6723 (all A all B all C (-v1_xboole_0(A) & m2_ordinal4(C,A) & m2_ordinal4(B,A) & v1_classes2(A) -> k5_ordinal4(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k5_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6724 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(A != k1_xboole_0 & k16_ordinal2(A,B) = k1_xboole_0))))) # label(t22_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6725 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k4_ordinal2,A) -> B = k1_xboole_0 | r2_hidden(k4_ordinal2,k16_ordinal2(A,B))))))) # label(t29_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6726 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k3_ordinal4(A) = k4_ordinal2)) # label(d5_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6727 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> (v3_ordinal2(A) & k5_relat_1(A,B) = C & v3_ordinal2(B) & v2_ordinal2(A) -> v3_ordinal2(C)))))))) # label(t17_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6728 (all A all B (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_funct_1(k1_ordinal4(A,B)) & v1_ordinal2(k1_ordinal4(A,B)) & v5_ordinal1(k1_ordinal4(A,B)) & v1_relat_1(k1_ordinal4(A,B)))) # label(fc2_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6729 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) -> k15_ordinal2(C,B) = k1_funct_1(A,C)))) -> B = k1_xboole_0 | v2_ordinal2(A)))))) # label(t19_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6730 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) -> (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k14_ordinal2(k1_relat_1(A),k1_relat_1(B)) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,k14_ordinal2(k1_relat_1(A),D)) = k1_funct_1(B,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(A,D) = k1_funct_1(C,D)))) <-> k1_ordinal4(A,B) = C))))))) # label(d1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6731 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (m2_ordinal4(B,A) <-> r1_tarski(k2_relat_1(B),k2_ordinal2(A)) & k2_ordinal2(A) = k1_relat_1(B)))))) # label(d3_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6732 (all A (-v1_xboole_0(A) & v1_classes2(A) -> k2_ordinal4(A) = k1_xboole_0)) # label(d4_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6733 (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]. 83.32/80.81 6734 $T # label(t2_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6735 (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]. 83.32/80.81 6736 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(B,C) -> k1_xboole_0 = A | r1_ordinal1(k16_ordinal2(A,B),k16_ordinal2(A,C))))))))) # label(t27_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6737 (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]. 83.32/80.81 6738 (all A all B all C (-v1_xboole_0(A) & m1_ordinal4(C,A) & m2_ordinal4(B,A) & v1_classes2(A) -> m1_ordinal4(k4_ordinal4(A,B,C),A))) # label(dt_k4_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6739 (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]. 83.32/80.81 6740 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> (r1_tarski(k2_relat_1(A),B) & r2_hidden(k1_relat_1(A),B) -> r2_hidden(k8_ordinal2(A),B)))))) # label(t37_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6741 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) -> (all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(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]. 83.32/80.81 6742 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -v1_xboole_0(k3_ordinal4(A)) & m1_ordinal4(k3_ordinal4(A),A))) # label(dt_k3_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6743 (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) -> (r1_ordinal1(B,C) & r2_hidden(C,k1_relat_1(A)) & v2_ordinal2(A) -> r1_ordinal1(k1_funct_1(A,B),k1_funct_1(A,C))))))))) # label(t9_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6744 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) & v1_ordinal2(D) & v5_ordinal1(D) -> (v2_ordinal2(C) & A = k5_relat_1(C,D) & 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]. 83.32/80.81 6745 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) -> k16_ordinal2(B,C) = k1_funct_1(A,C)))) & r2_hidden(k4_ordinal2,B) -> v2_ordinal2(A)))))) # label(t25_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 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]. 83.32/80.81 6747 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(k4_ordinal2,A) & r2_hidden(B,C) -> r2_hidden(k16_ordinal2(A,B),k16_ordinal2(A,C))))))))) # label(t24_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6748 (all A all B all C (m1_ordinal4(B,A) & m1_ordinal4(C,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]. 83.32/80.81 6749 (all A all B all C (m1_ordinal4(C,A) & m1_ordinal4(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_ordinal4(k7_ordinal4(A,B,C),A))) # label(dt_k7_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.81 6750 (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) -> (r1_ordinal2(B,A) -> r1_ordinal2(k14_ordinal2(C,B),k1_ordinal3(C,A))))))))) # label(t4_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6751 (all A all B all C (m2_ordinal4(B,A) & m2_ordinal4(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> m2_ordinal4(k5_ordinal4(A,B,C),A))) # label(dt_k5_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6752 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (exists B m1_ordinal4(B,A)))) # label(existence_m1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6753 (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)) -> k12_ordinal2(A) = k8_ordinal2(A) & r1_ordinal2(k8_ordinal2(A),A) | k1_xboole_0 = k1_relat_1(A)))) # label(t8_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6754 (all A all B (m1_ordinal4(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k1_ordinal1(B) = k6_ordinal4(A,B))) # label(redefinition_k6_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6755 (all A all B all C (v1_classes2(A) & m1_ordinal4(C,A) & m1_ordinal4(B,A) & -v1_xboole_0(A) -> k8_ordinal4(A,B,C) = k15_ordinal2(B,C))) # label(redefinition_k8_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6756 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k16_ordinal2(k16_ordinal2(A,B),C) = k16_ordinal2(A,k15_ordinal2(C,B)))))))) # label(t31_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6757 (all A (-v1_xboole_0(A) & v1_classes2(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]. 83.32/80.82 6758 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(B,k1_relat_1(A)) & v2_ordinal2(A) -> r1_ordinal1(B,k1_funct_1(A,B))))))) # label(t10_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6759 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(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]. 83.32/80.82 6760 (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]. 83.32/80.82 6761 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> (v2_ordinal2(A) -> v1_funct_1(k5_relat_1(A,B)) & v1_ordinal2(k5_relat_1(A,B)) & v5_ordinal1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B))))))) # label(t12_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6762 (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]. 83.32/80.82 6763 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m2_ordinal4(B,A) -> -(v2_ordinal2(B) & v3_ordinal2(B) & (all C (v3_ordinal1(C) -> -(r2_hidden(C,k1_relat_1(B)) & C = k1_funct_1(B,C)))) & r2_hidden(k5_ordinal2,A)))))) # label(t38_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6764 (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_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(B) -> k1_xboole_0 = B | (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> (k1_relat_1(A) = B & (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 (v3_ordinal1(A) & f1_s1_ordinal4(A) = A)) # label(s1_ordinal4) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6765 (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_1(F) & v1_funct_2(F,k2_zfmisc_1(A,C),B) & m2_relset_1(F,k2_zfmisc_1(A,C),B) -> (all G (m2_finseq_1(G,C) -> k3_finseqop(A,C,B,F,D,k8_finseq_1(C,G,k12_finseq_1(C,E))) = 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))))))))))))))))) # label(t13_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6766 (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_setwiseo(C,A) & v1_finseqop(C,A) -> k2_binop_1(A,A,A,k8_finseqop(A,C,k6_partfun1(A),k6_finseqop(A,C)),B,B) = k3_binop_1(A,C)))))))) # label(t91_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6767 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & m2_relset_1(D,k2_zfmisc_1(B,B),B) -> (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]. 83.32/80.82 6768 (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) -> k4_finseqop(C,F,k2_binop_1(A,B,C,G,D,E)) = k3_finseqop(A,B,C,G,D,k4_finseqop(B,F,E)))))))))))))))) # label(t19_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6769 (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 (m2_relset_1(F,k2_zfmisc_1(A,C),B) & v1_funct_2(F,k2_zfmisc_1(A,C),B) & v1_funct_1(F) -> (all G (m2_finseq_2(G,C,k4_finseq_2(E,C)) -> k3_finseqop(A,C,B,F,D,G) = k1_finseqop(A,C,B,F,k4_finseqop(A,E,D),G))))))))))))))) # label(t21_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6770 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,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]. 83.32/80.82 6771 (all A all B all C all D all E all F (-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(E,A) & m1_subset_1(F,B) & v1_funct_1(D) & -v1_xboole_0(B) & -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]. 83.32/80.82 6772 (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_1(F) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_2(F,k2_zfmisc_1(B,B),B) -> (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,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]. 83.32/80.82 6773 (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_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (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]. 83.32/80.82 6774 (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) -> (all E (m2_relset_1(E,A,A) & v1_funct_2(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]. 83.32/80.82 6775 (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) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> k5_finseqop(A,B,k8_finseq_1(A,C,D),E) = k8_finseq_1(B,k5_finseqop(A,B,C,E),k5_finseqop(A,B,D,E)))))))))))) # label(t10_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6776 (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) -> k1_finseqop(A,A,A,D,k4_finseqop(A,B,k3_binop_1(A,D)),C) = C & k1_finseqop(A,A,A,D,C,k4_finseqop(A,B,k3_binop_1(A,D))) = C))))))))) # label(t57_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6777 (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 (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) -> 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]. 83.32/80.82 6778 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & 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]. 83.32/80.82 6779 (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 (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 (m2_relset_1(G,k2_zfmisc_1(B,B),B) & v1_funct_2(G,k2_zfmisc_1(B,B),B) & v1_funct_1(G) -> (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]. 83.32/80.82 6780 (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 (m2_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> (all F (v1_funct_2(F,C,B) & m2_relset_1(F,C,B) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,k2_zfmisc_1(C,C),C) & v1_funct_2(G,k2_zfmisc_1(C,C),C) -> (all H (m2_relset_1(H,k2_zfmisc_1(B,B),B) & v1_funct_2(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]. 83.32/80.82 6781 (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 (v1_funct_2(C,A,A) & r1_finseqop(A,C,B) & m2_relset_1(C,A,A) & v1_funct_1(C))) <-> v1_finseqop(B,A)))))) # label(d2_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6782 (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)) -> k3_funcop_1(A,k2_funcop_1(B,C),k2_funcop_1(B,D)) = k2_funcop_1(B,k1_funct_1(A,k4_tarski(C,D))))))) # label(t8_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6783 (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) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> (v1_setwiseo(B,A) & v2_binop_1(B,A) & v1_finseqop(B,A) & r6_binop_1(A,C,B) & v1_setwiseo(C,A) & k6_finseqop(A,B) = D -> 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]. 83.32/80.82 6784 (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_2(E,k2_zfmisc_1(A,A),A) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_1(E) -> (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]. 83.32/80.82 6785 (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]. 83.32/80.82 6786 (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) -> 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]. 83.32/80.82 6787 (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_relat_1(E) & v1_funct_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]. 83.32/80.82 6788 (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) & 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)) & 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)))))))))))) # label(t77_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6789 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(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 (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 (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,D,I),k8_funct_2(B,A,D,J)) = k8_funct_2(B,A,D,k2_binop_1(B,B,B,G,I,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]. 83.32/80.82 6790 (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) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,A) & v1_funct_2(E,A,A) -> (E = k7_funcop_1(A,A,C,k6_partfun1(A),B) & r6_binop_1(A,C,D) -> r7_binop_1(A,E,D)))))))))))) # label(t56_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6791 (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 (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> k5_finseqop(A,B,k8_finseq_1(A,D,k12_finseq_1(A,C)),E) = k8_finseq_1(B,k5_finseqop(A,B,D,E),k12_finseq_1(B,k8_funct_2(A,B,E,C))))))))))))) # label(t9_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6792 (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,k2_zfmisc_1(A,A),A) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_1(E) -> (all F (m2_relset_1(F,A,A) & v1_funct_2(F,A,A) & v1_funct_1(F) -> (v1_setwiseo(D,A) & v2_binop_1(D,A) & k6_finseqop(A,D) = F & r6_binop_1(A,E,D) & v1_finseqop(D,A) -> 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)) & 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))))))))))))))) # label(t71_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6793 (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) -> k3_finseqop(A,A,A,D,k3_binop_1(A,D),C) = C))))))))) # label(t58_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6794 $T # label(t60_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6795 $T # label(t81_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6796 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k1_xboole_0 = k5_funcop_1(B,A,k1_xboole_0))) # label(t6_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6797 (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]. 83.32/80.82 6798 (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) -> (v2_binop_1(B,A) & v1_finseqop(B,A) & k8_finseqop(A,B,k6_partfun1(A),k6_finseqop(A,B)) = C & v1_setwiseo(B,A) & v1_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]. 83.32/80.82 6799 $T # label(t3_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6800 (all A (v1_relat_1(A) & v1_funct_1(A) -> k13_funct_3(k1_xboole_0,A) = k1_xboole_0 & k13_funct_3(A,k1_xboole_0) = k1_xboole_0)) # label(t1_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6801 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,A),A) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_1(E) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,A),A) & v1_funct_2(F,k2_zfmisc_1(A,A),A) & v1_funct_1(F) -> (v2_binop_1(E,A) & v1_finseqop(E,A) & r6_binop_1(A,F,E) & C = k3_binop_1(A,E) & v1_setwiseo(E,A) -> k2_funcop_1(B,C) = k8_funcop_1(A,B,F,C,D)))))))))))))) # label(t79_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6802 (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) & 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 (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]. 83.32/80.82 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_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]. 83.32/80.82 6804 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(D) & m1_subset_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) -> m2_finseq_1(k3_finseqop(A,B,C,D,E,F),C))) # label(dt_k3_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6805 (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_finseq_1(E,A) & m1_finseq_1(F,B) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -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]. 83.32/80.82 6806 (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) & v1_funct_2(F,k2_zfmisc_1(A,A),A) & m2_relset_1(F,k2_zfmisc_1(A,A),A) -> (v2_binop_1(F,A) -> k1_finseqop(A,A,A,F,C,k1_finseqop(A,A,A,F,D,E)) = k1_finseqop(A,A,A,F,k1_finseqop(A,A,A,F,C,D),E)))))))))))))) # label(t29_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6807 (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) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) -> (all F (v1_funct_2(F,B,B) & m2_relset_1(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]. 83.32/80.82 6808 (all A all B all C k2_funcop_1(A,k4_tarski(B,C)) = k13_funct_3(k2_funcop_1(A,B),k2_funcop_1(A,C))) # label(t7_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6809 (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 (v1_funct_1(F) & m2_relset_1(F,B,B) & v1_funct_2(F,B,B) -> (r7_binop_1(B,F,E) -> k7_funcop_1(B,A,E,k7_funct_2(A,B,B,D,F),k8_funct_2(B,B,F,C)) = k7_funct_2(A,B,B,k7_funcop_1(B,A,E,D,C),F)))))))))))))) # label(t43_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6810 (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) -> (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)) & k2_binop_1(A,A,A,C,k8_funct_2(A,A,k6_finseqop(A,C),B),B) = k3_binop_1(A,C)))))))) # label(t63_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6811 (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) -> B = k8_funct_2(A,A,k6_finseqop(A,C),k8_funct_2(A,A,k6_finseqop(A,C),B))))))))) # label(t66_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6812 (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 (v1_funct_2(F,k2_zfmisc_1(C,A),B) & m2_relset_1(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]. 83.32/80.82 6813 (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) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (k6_finseqop(A,B) = C <-> r1_finseqop(A,C,B))))))))) # label(d3_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6814 (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) -> C = k2_finseqop(A,A,A,D,C,k3_binop_1(A,D))))))))))) # label(t59_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6815 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) -> (all F (m2_relset_1(F,B,B) & v1_funct_2(F,B,B) & v1_funct_1(F) -> (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]. 83.32/80.82 6816 (all A all B (-v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> 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]. 83.32/80.82 6817 (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,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) -> (v1_setwiseo(E,A) & k6_funcop_1(A,B,E,C,D) = k2_funcop_1(B,k3_binop_1(A,E)) & v1_finseqop(E,A) & v2_binop_1(E,A) -> k7_funct_2(B,A,A,D,k6_finseqop(A,E)) = C & k7_funct_2(B,A,A,C,k6_finseqop(A,E)) = D))))))))))) # label(t76_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6818 (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) -> k8_funct_2(A,A,k6_finseqop(A,B),k3_binop_1(A,B)) = k3_binop_1(A,B)))))) # label(t65_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6819 (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_1(D) & m2_relset_1(D,A,A) & v1_funct_2(D,A,A) -> (v2_binop_1(C,A) & k6_finseqop(A,C) = D & v1_finseqop(C,A) & v1_setwiseo(C,A) -> k8_funct_2(A,A,D,B) = k2_binop_1(A,A,A,k8_finseqop(A,C,k6_partfun1(A),D),k3_binop_1(A,C),B)))))))))) # label(t93_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6820 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k3_funcop_1(A,B,k1_xboole_0) = k1_xboole_0 & k3_funcop_1(A,k1_xboole_0,B) = k1_xboole_0)))) # label(t4_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6821 (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) -> (all E (m2_relset_1(E,A,A) & v1_funct_2(E,A,A) & v1_funct_1(E) -> (v2_binop_1(D,A) & v1_setwiseo(D,A) & v1_finseqop(D,A) & k6_finseqop(A,D) = E & v1_binop_1(D,A) -> 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)) & 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)))))))))))) # label(t90_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6822 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_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]. 83.32/80.82 6823 (all A (v1_relat_1(A) & v1_funct_1(A) -> k15_funct_3(A,k1_xboole_0) = k1_xboole_0 & k1_xboole_0 = k15_funct_3(k1_xboole_0,A))) # label(t2_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6824 (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) -> k2_finseqop(C,A,B,E,k8_finseq_1(C,F,G),D) = k8_finseq_1(B,k2_finseqop(C,A,B,E,F,D),k2_finseqop(C,A,B,E,G,D)))))))))))))))) # label(t16_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6825 (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) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (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)))))) -> k2_finseqop(A,A,A,H,k5_finseqop(B,A,F,E),k8_funct_2(B,A,E,C)) = k5_finseqop(B,A,k2_finseqop(B,B,B,G,F,C),E)))))))))))))))))) # label(t51_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6826 (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) & v1_binop_1(B,A) & v1_finseqop(B,A) & v2_binop_1(B,A) -> r7_binop_1(A,k6_finseqop(A,B),B)))))) # label(t67_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6827 (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) -> (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]. 83.32/80.82 6828 (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) -> (all G (v1_funct_2(G,k2_zfmisc_1(A,A),A) & m2_relset_1(G,k2_zfmisc_1(A,A),A) & v1_funct_1(G) -> (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]. 83.32/80.82 6829 $T # label(t62_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6830 (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) -> k4_finseqop(B,D,k8_funct_2(A,B,E,C)) = k5_finseqop(A,B,k4_finseqop(A,D,C),E))))))))))) # label(t17_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6831 (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_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m2_finseq_2(F,B,k4_finseq_2(D,B)) -> (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) -> (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,E,k2_binop_1(B,B,B,G,I,J)) = k2_binop_1(A,A,A,H,k8_funct_2(B,A,E,I),k8_funct_2(B,A,E,J)))))) -> k5_finseqop(B,A,k3_finseqop(B,B,B,G,C,F),E) = k3_finseqop(A,A,A,H,k8_funct_2(B,A,E,C),k5_finseqop(B,A,F,E))))))))))))))))))) # label(t50_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6832 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(D) & 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_finseq_1(E,A) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k1_finseqop(A,B,C,D,E,F) = k3_funcop_1(D,E,F))) # label(redefinition_k1_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6833 (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 (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 (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) -> k2_binop_1(A,B,C,H,k8_funct_2(D,A,I,F),k8_funct_2(E,B,J,G)) = k1_binop_1(k7_finseqop(H,I,J),F,G))))))))))))))))))))) # label(t86_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6834 (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,k2_zfmisc_1(A,A),A) & v1_funct_2(F,k2_zfmisc_1(A,A),A) & v1_funct_1(F) -> (v1_finseqop(E,A) & r6_binop_1(A,F,E) & k3_binop_1(A,E) = B & v1_setwiseo(E,A) & v2_binop_1(E,A) -> k3_finseqop(A,A,A,F,B,D) = k4_finseqop(A,C,B)))))))))))))) # label(t80_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6835 (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) -> (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]. 83.32/80.82 6836 (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 (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,A) & v1_funct_2(E,A,A) -> (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]. 83.32/80.82 6837 (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) & v1_funct_2(F,k2_zfmisc_1(A,A),A) & m2_relset_1(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]. 83.32/80.82 6838 (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) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) -> (all F (v1_funct_1(F) & v1_funct_2(F,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]. 83.32/80.82 6839 (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,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]. 83.32/80.82 6840 (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) & v1_funct_2(F,C,B) & m2_relset_1(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) & m2_relset_1(H,k2_zfmisc_1(B,B),B) & v1_funct_2(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)))))) -> k8_funcop_1(B,A,H,k8_funct_2(C,B,F,D),k7_funct_2(A,C,B,E,F)) = k7_funct_2(A,C,B,k8_funcop_1(C,A,G,D,E),F)))))))))))))))))) # label(t39_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6841 (all A (-v1_xboole_0(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) & 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) -> k3_binop_1(A,C) = k2_binop_1(A,A,A,C,D,k8_funct_2(A,A,B,D)) & k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),D) = k3_binop_1(A,C))) <-> r1_finseqop(A,B,C)))))))) # label(d1_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6842 (all A all B all C all D all E all F (-v1_xboole_0(A) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(E,A) & m1_finseq_1(F,B) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(C) & -v1_xboole_0(B) -> k5_funcop_1(D,E,F) = k3_finseqop(A,B,C,D,E,F))) # label(redefinition_k3_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6843 (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) & r6_binop_1(A,D,C) & v1_finseqop(C,A) & v1_setwiseo(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]. 83.32/80.82 6844 (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) & v1_finseqop(D,A) & v2_binop_1(D,A) -> k2_funcop_1(B,k3_binop_1(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)) = k6_funcop_1(A,B,D,C,k7_funct_2(B,A,A,C,k6_finseqop(A,D)))))))))))) # label(t75_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6845 (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,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]. 83.32/80.82 6846 (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) -> k2_finseqop(A,A,A,E,D,B) = k3_finseqop(A,A,A,E,B,D)))))))))))) # label(t35_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6847 (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,C),B) & v1_funct_2(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]. 83.32/80.82 6848 (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) -> (v2_binop_1(F,A) -> k2_finseqop(A,A,A,F,k3_finseqop(A,A,A,F,B,E),C) = k3_finseqop(A,A,A,F,B,k2_finseqop(A,A,A,F,E,C))))))))))))))) # label(t30_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6849 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_finseq_1(E,A) & v1_funct_1(D) & -v1_xboole_0(C) -> m2_finseq_1(k2_finseqop(A,B,C,D,E,F),C))) # label(dt_k2_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6850 (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)) -> 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))) = 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))))))))))))))))))))) # label(t11_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6851 (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) -> 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]. 83.32/80.82 6852 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v1_finseqop(D,A) & v2_binop_1(D,A) & v1_setwiseo(D,A) -> C != k2_binop_1(A,A,A,D,B,C) & k2_binop_1(A,A,A,D,C,B) != C | k3_binop_1(A,D) = B))))))))) # label(t69_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6853 (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_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> (all F (m2_relset_1(F,C,B) & v1_funct_2(F,C,B) & v1_funct_1(F) -> (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,k7_funcop_1(C,A,G,E,D),F) = k7_funcop_1(B,A,H,k7_funct_2(A,C,B,E,F),k8_funct_2(C,B,F,D))))))))))))))))))) # label(t40_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6854 (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 (m2_relset_1(F,k2_zfmisc_1(A,C),B) & v1_funct_2(F,k2_zfmisc_1(A,C),B) & v1_funct_1(F) -> (all G (m2_finseq_2(G,C,k4_finseq_2(E,C)) -> k5_relat_1(G,k5_funcop_1(F,D,k6_partfun1(C))) = k3_finseqop(A,C,B,F,D,G))))))))))))))) # label(t23_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6855 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(D,A,A) & m1_relset_1(D,A,A) & v1_funct_1(D) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(B) -> v1_funct_2(k8_finseqop(A,B,C,D),k2_zfmisc_1(A,A),A) & m2_relset_1(k8_finseqop(A,B,C,D),k2_zfmisc_1(A,A),A) & v1_funct_1(k8_finseqop(A,B,C,D)))) # label(dt_k8_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6856 (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) -> k1_finseqop(A,A,A,k8_finseqop(A,E,k6_partfun1(A),F),C,D) = k1_finseqop(A,A,A,E,C,k5_finseqop(A,A,D,F)))))))))))))) # label(t89_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6857 (all A all B all C all D (-v1_xboole_0(A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(D,A,A) & m1_relset_1(D,A,A) & v1_funct_1(D) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> k7_finseqop(B,C,D) = k8_finseqop(A,B,C,D))) # label(redefinition_k8_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6858 (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) -> k4_finseqop(C,F,k2_binop_1(A,B,C,G,D,E)) = k1_finseqop(A,B,C,G,k4_finseqop(A,F,D),k4_finseqop(B,F,E)))))))))))))))) # label(t18_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6859 (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 (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 = k3_funcop_1(D,k2_funcop_1(B,k3_binop_1(A,D)),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]. 83.32/80.82 6860 (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) -> (v2_binop_1(D,A) & v1_finseqop(D,A) & k3_binop_1(A,D) = k2_binop_1(A,A,A,D,B,C) & v1_setwiseo(D,A) -> C = k8_funct_2(A,A,k6_finseqop(A,D),B) & k8_funct_2(A,A,k6_finseqop(A,D),C) = B))))))))) # label(t64_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6861 (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_2(E,k2_zfmisc_1(A,A),A) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,A) & v1_funct_2(F,A,A) -> (r7_binop_1(A,F,E) -> k3_finseqop(A,A,A,E,k8_funct_2(A,A,F,B),k5_finseqop(A,A,D,F)) = k5_finseqop(A,A,k3_finseqop(A,A,A,E,B,D),F)))))))))))))) # label(t53_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6862 $T # label(t61_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6863 (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) -> (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) -> k1_finseqop(A,A,A,G,k3_finseqop(A,A,A,F,B,E),k3_finseqop(A,A,A,F,C,E)) = k3_finseqop(A,A,A,F,k2_binop_1(A,A,A,G,B,C),E)))))))))))))))) # label(t47_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6864 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,k5_numbers) -> k2_finseq_2(B,C) = k4_finseqop(A,B,C))) # label(redefinition_k4_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.32/80.82 6865 (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 (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,A) & m2_relset_1(D,A,A) -> v1_funct_1(k7_finseqop(B,C,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))))))))) # label(t85_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6866 (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) -> (v1_finseqop(E,A) & v2_binop_1(E,A) & v1_setwiseo(E,A) -> k2_binop_1(A,A,A,E,C,B) != k2_binop_1(A,A,A,E,D,B) & k2_binop_1(A,A,A,E,B,D) != k2_binop_1(A,A,A,E,B,C) | D = C))))))))))) # label(t68_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6867 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k4_funcop_1(B,k1_xboole_0,A) = k1_xboole_0)) # label(t5_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6868 (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)) -> k3_funcop_1(F,G,k4_finseqop(C,E,D)) = k4_funcop_1(F,G,D))))))))))))))) # label(t22_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6869 (all A all B all C all D (m1_finseq_1(C,A) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(D) -> k5_finseqop(A,B,C,D) = k5_relat_1(C,D))) # label(redefinition_k5_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6870 (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)) -> k5_relat_1(G,k4_funcop_1(F,k6_partfun1(C),D)) = k4_funcop_1(F,G,D))))))))))))))) # label(t24_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6871 (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) -> k2_finseqop(A,A,A,F,E,k2_binop_1(A,A,A,F,B,C)) = k2_finseqop(A,A,A,F,k2_finseqop(A,A,A,F,E,B),C)))))))))))))) # label(t33_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6872 (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) -> (r6_binop_1(A,D,C) & v1_finseqop(C,A) & v1_setwiseo(C,A) & v2_binop_1(C,A) -> k8_funct_2(A,A,k8_funcop_1(A,A,D,B,k6_partfun1(A)),k3_binop_1(A,C)) = k3_binop_1(A,C)))))))))) # label(t73_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6873 (all A all B all C all D (m1_finseq_1(C,A) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> m2_finseq_1(k5_finseqop(A,B,C,D),B))) # label(dt_k5_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 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 (m2_finseq_2(D,A,k4_finseq_2(B,A)) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,A),A) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_1(E) -> (v1_finseqop(E,A) & v1_setwiseo(E,A) & k1_finseqop(A,A,A,E,C,D) = k4_finseqop(A,B,k3_binop_1(A,E)) & v2_binop_1(E,A) -> C = k5_finseqop(A,A,D,k6_finseqop(A,E)) & D = k5_finseqop(A,A,C,k6_finseqop(A,E))))))))))))) # label(t78_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6875 (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) & v1_finseqop(C,A) & k3_binop_1(A,C) = B & r6_binop_1(A,D,C) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,D,B,E) = B & B = k2_binop_1(A,A,A,D,E,B)))))))))))) # label(t70_finseqop) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6876 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(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 (m2_relset_1(H,E,B) & v1_funct_2(H,E,B) & v1_funct_1(H) -> 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]. 83.37/80.83 6877 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_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]. 83.37/80.83 6878 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (-r2_hidden(B,k2_relat_1(A)) <-> k1_finseq_3(A,k1_tarski(B)) = A)))) # label(t77_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6879 (all A (v1_funct_1(A) & v1_finseq_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]. 83.37/80.83 6880 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v4_ordinal2(A) -> v1_funct_1(k2_finseq_3(A,B)) & v1_finseq_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]. 83.37/80.83 6881 (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]. 83.37/80.83 6882 (all A all B all C (r2_hidden(A,C) & r2_hidden(B,C) <-> k1_finseq_3(k10_finseq_1(A,B),C) = k1_xboole_0)) # label(t84_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6883 (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]. 83.37/80.83 6884 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_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]. 83.37/80.83 6885 $T # label(t37_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6886 (all A k1_finseq_3(k1_xboole_0,A) = k1_xboole_0) # label(t81_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6887 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(B,k3_finseq_1(A)) & r1_xreal_0(np__1,B) <-> r2_hidden(B,k4_finseq_1(A))))))) # label(t27_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6888 (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 (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (B = k7_relat_1(A,k2_finseq_1(C)) & k3_finseq_1(A) = k2_xcmplx_0(C,D) -> C = k3_finseq_1(B)))))))))) # label(t59_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6889 (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) -> (k2_xcmplx_0(C,np__1) = k3_finseq_1(A) & 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]. 83.37/80.83 6890 (all A all B (v2_funct_1(k10_finseq_1(A,B)) <-> B != A)) # label(t103_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6891 (all A (v4_ordinal2(A) -> (k1_xboole_0 = k2_finseq_1(A) <-> -r2_hidden(A,k2_finseq_1(A))))) # label(t7_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6892 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_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]. 83.37/80.83 6893 (all A all B all C (B != A & C != A & C != B <-> v2_funct_1(k11_finseq_1(A,B,C)))) # label(t104_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6894 (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]. 83.37/80.83 6895 (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_xboole_0(k2_relat_1(A),k2_relat_1(B)) & v2_funct_1(B) & v2_funct_1(A) <-> v2_funct_1(k7_finseq_1(A,B))))))) # label(t98_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6896 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B all C (v4_ordinal2(C) -> (k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B))) = C -> k4_finseq_1(k1_finseq_3(A,B)) = k2_finseq_1(C)))))) # label(t69_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6897 (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]. 83.37/80.83 6898 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(k2_xcmplx_0(A,B),k2_finseq_1(A)) -> B = np__0))))) # label(t11_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6899 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(v2_funct_1(A) & k2_tarski(B,C) = k2_relat_1(A) & C != B & A != k10_finseq_1(C,B) & k10_finseq_1(B,C) != A)))) # label(t108_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6900 $T # label(t8_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6901 (all A all B (v4_ordinal2(B) -> (k1_tarski(A) = k2_finseq_1(B) -> A = np__1 & B = np__1))) # label(t22_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6902 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(B),k1_tarski(A))),B) = k2_finseq_3(A,B))))) # label(d2_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6903 (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) -> -(C = k1_funct_1(B,np__1) & B = k8_finseq_1(A,k12_finseq_1(A,C),D))))))))))) # label(t111_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6904 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_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(C)) -> k1_funct_1(A,k1_nat_1(k3_finseq_1(B),D)) = k1_funct_1(C,D)))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(A,D) = k1_funct_1(B,D)))) & k1_nat_1(k3_finseq_1(B),k3_finseq_1(C)) = k3_finseq_1(A) -> A = k7_finseq_1(B,C)))))))) # label(t43_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6905 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(B,k4_finseq_1(A)) & k3_finseq_1(A) = k2_xcmplx_0(C,np__1) -> C = k3_finseq_1(k2_finseq_3(B,A))))))))) # label(t118_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6906 (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]. 83.37/80.83 6907 (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]. 83.37/80.83 6908 $T # label(t101_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6909 (all A all B all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (r1_tarski(B,k2_finseq_1(D)) & r1_tarski(A,k2_finseq_1(C)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> -(r1_xreal_0(F,E) & r2_hidden(F,B) & r2_hidden(E,A)))))) <-> k8_finseq_1(k5_numbers,k14_finseq_1(A),k14_finseq_1(B)) = k14_finseq_1(k2_xboole_0(A,B)))))))) # label(t48_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6910 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (k2_relat_1(A) = k2_relat_1(k1_finseq_3(A,B)) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t74_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6911 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> k7_relat_1(k1_finseq_2(k2_xcmplx_0(A,B)),k2_finseq_1(A)) = k1_finseq_2(A))))) # label(t56_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6912 (all A (v4_ordinal2(A) -> k3_finseq_1(k14_finseq_1(k2_finseq_1(A))) = A)) # label(t52_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6913 (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]. 83.37/80.83 6914 (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_xreal_0(k3_finseq_1(A),k3_finseq_1(B)) <-> r1_tarski(k4_finseq_1(A),k4_finseq_1(B))))))) # label(t32_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6915 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(-r1_xreal_0(B,A) & k10_finseq_1(A,B) != k14_finseq_1(k2_tarski(A,B)) & -r1_xreal_0(A,np__0)))))) # label(t51_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6916 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(k7_relat_1(A,B)) & v1_finseq_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)) <-> (exists C (k2_finseq_1(C) = k3_xboole_0(B,k4_finseq_1(A)) & m2_subset_1(C,k1_numbers,k5_numbers))))))) # label(t62_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6917 (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 (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]. 83.37/80.83 6918 (all A (v4_ordinal2(A) -> v2_funct_1(k1_finseq_2(A)))) # label(t100_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6919 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B -(r2_hidden(B,k4_finseq_1(A)) & np__0 = B)))) # label(t26_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6920 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B))) = k3_finseq_1(k1_finseq_3(A,B))))) # label(t66_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6921 (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 all D (v4_ordinal2(D) -> (k3_finseq_1(A) = k2_xcmplx_0(D,np__1) & B = k7_relat_1(A,k2_finseq_1(D)) -> (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]. 83.37/80.83 6922 (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]. 83.37/80.83 6923 (all A v2_funct_1(k9_finseq_1(A))) # label(t102_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6924 (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]. 83.37/80.83 6925 (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 all D (v4_ordinal2(D) -> (k7_relat_1(A,k2_finseq_1(D)) = B & k2_xcmplx_0(D,np__1) = k3_finseq_1(A) -> (-r2_hidden(k1_funct_1(A,k2_xcmplx_0(D,np__1)),C) <-> k7_finseq_1(k1_finseq_3(B,C),k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(D,np__1)))) = k1_finseq_3(A,C))))))))) # label(t91_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6926 (all A all B all C (k9_finseq_1(B) = k1_finseq_3(k10_finseq_1(A,B),C) -> -r2_hidden(B,C) & r2_hidden(A,C) | A = B)) # label(t86_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6927 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(C,k2_finseq_1(A)) & k2_xcmplx_0(B,np__1) = A -> k3_finseq_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(A),k1_tarski(C)))) = B))))))) # label(t116_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6928 (all A all B k10_finseq_1(A,B) != k1_xboole_0) # label(t38_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6929 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> k1_xboole_0 = k1_finseq_3(A,k2_relat_1(A)))) # label(t79_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6930 (all A (v4_ordinal2(A) -> k6_subset_1(k5_numbers,k2_finseq_1(k2_xcmplx_0(A,np__1)),k2_finseq_1(A)) = k1_tarski(k2_xcmplx_0(A,np__1)))) # label(t16_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6931 (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]. 83.37/80.83 6932 (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 (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) -> k4_finseq_1(B) = k2_finseq_1(C)))))))))) # label(t60_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6933 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_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]. 83.37/80.83 6934 (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]. 83.37/80.83 6935 (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) -> (r2_hidden(A,k2_finseq_1(C)) & r2_hidden(B,k2_finseq_1(D)) & k1_nat_1(C,np__1) = D -> (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]. 83.37/80.83 6936 (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]. 83.37/80.83 6937 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_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]. 83.37/80.83 6938 (all A (v1_finseq_1(A) & v1_funct_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]. 83.37/80.83 6939 $T # label(t47_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6940 (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]. 83.37/80.83 6941 (all A all B all C (k9_finseq_1(A) = k1_finseq_3(k10_finseq_1(A,B),C) -> r2_hidden(B,C) & -r2_hidden(A,C) | B = A)) # label(t88_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6942 (all A all B all C all D (v1_relat_1(B) & v4_ordinal2(D) & v1_finseq_1(B) & v1_funct_1(B) -> ((exists E (m2_subset_1(E,k1_numbers,k5_numbers) & A = E & r2_hidden(E,k4_finseq_1(B)) & r1_xreal_0(E,D) & r2_hidden(k1_funct_1(B,E),C))) <-> r2_hidden(A,a_3_0_finseq_3(B,C,D))))) # label(fraenkel_a_3_0_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6943 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_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]. 83.37/80.83 6944 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v4_ordinal2(B) -> (k7_relat_1(A,k2_finseq_1(B)) = A <-> r1_xreal_0(k3_finseq_1(A),B)))))) # label(t55_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6945 (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]. 83.37/80.83 6946 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_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]. 83.37/80.83 6947 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) & v2_funct_1(A) -> A = k9_finseq_1(B))))) # label(t106_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6948 (all A all B all C all D k11_finseq_1(B,C,D) != k9_finseq_1(A)) # label(t41_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6949 (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]. 83.37/80.83 6950 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(A,k2_finseq_1(B)) -> r2_hidden(k6_xcmplx_0(A,C),k2_finseq_1(B)) | r1_xreal_0(A,C)))))))) # label(t13_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6951 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_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]. 83.37/80.83 6952 (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]. 83.37/80.83 6953 (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_tarski(A,k2_finseq_1(B)) & -r1_xreal_0(D,C) & r1_xreal_0(F,k3_finseq_1(k14_finseq_1(A))) & k1_funct_1(k14_finseq_1(A),F) = C & r1_xreal_0(E,F) & k1_funct_1(k14_finseq_1(A),E) = D & r1_xreal_0(np__1,E)))))))))))) # label(t46_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6954 $T # label(t35_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6955 (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]. 83.37/80.83 6956 (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]. 83.37/80.83 6957 $T # label(t21_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6958 (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]. 83.37/80.83 6959 (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]. 83.37/80.83 6960 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B all C all D (k2_relat_1(A) = k1_enumset1(B,C,D) & v2_funct_1(A) -> C = B | D = C | k3_finseq_1(A) = np__3 | D = B)))) # label(t110_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6961 (all A (v1_funct_1(A) & v1_finseq_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) -> -(k1_funct_1(A,C) != k1_funct_1(k1_finseq_3(A,B),k6_xcmplx_0(C,k4_card_1(D))) & -r2_hidden(k1_funct_1(A,C),B) & a_3_0_finseq_3(A,B,C) = D)))))))) # label(t92_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6962 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k4_finseq_1(A) = k4_finseq_1(k1_finseq_3(A,B)) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t71_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6963 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k4_finseq_1(A) = k4_finseq_1(B) <-> k3_finseq_1(B) = k3_finseq_1(A)))))) # label(t31_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6964 (all A all B all C (v4_ordinal2(C) -> (k2_tarski(A,B) = k2_finseq_1(C) -> B = A | k2_tarski(np__1,np__2) = k2_tarski(A,B) & C = np__2))) # label(t23_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6965 (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 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]. 83.37/80.83 6966 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> -(r2_hidden(A,k4_finseq_1(B)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(k3_finseq_1(B) = k1_nat_1(C,np__1) & k3_finseq_1(k2_finseq_3(A,B)) = C)))) & (-r2_hidden(A,k4_finseq_1(B)) -> B = k2_finseq_3(A,B)))))) # label(t113_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6967 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_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]. 83.37/80.83 6968 $T # label(t36_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6969 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_relat_1(A)) & v2_funct_1(A) -> k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(B))))))) # label(t96_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6970 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C (k2_tarski(B,C) = k2_relat_1(A) & v2_funct_1(A) -> k3_finseq_1(A) = np__2 | B = C)))) # label(t107_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6971 (all A all B all C k9_finseq_1(A) != k10_finseq_1(B,C)) # label(t40_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6972 (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]. 83.37/80.83 6973 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_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]. 83.37/80.83 6974 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_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(D,C) & r1_xreal_0(B,D) & r2_hidden(B,k4_finseq_1(A)) -> k1_funct_1(k2_finseq_3(B,A),D) = k1_funct_1(A,k1_nat_1(D,np__1))))))))))) # label(t120_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6975 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(k6_xcmplx_0(A,B),k2_finseq_1(A)) <-> -r1_xreal_0(A,B)))))) # label(t14_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6976 (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]. 83.37/80.83 6977 (all A (v4_ordinal2(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_finseq_1(A)) -> k4_finseq_1(k14_finseq_1(B)) = k2_finseq_1(k4_card_1(B))))))) # label(t45_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6978 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(B,k4_finseq_1(A)) <-> m2_subset_1(k6_xcmplx_0(k3_finseq_1(A),B),k1_numbers,k5_numbers) & m2_subset_1(k6_xcmplx_0(B,np__1),k1_numbers,k5_numbers)))))) # label(t28_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6979 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (r1_tarski(k2_relat_1(A),B) <-> k1_xboole_0 = k1_finseq_3(A,B))))) # label(t75_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6980 (all A all B (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> v1_relat_1(k1_finseq_3(A,B)) & v1_finseq_1(k1_finseq_3(A,B)) & v1_funct_1(k1_finseq_3(A,B)))) # label(dt_k1_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6981 (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]. 83.37/80.83 6982 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D (k2_relat_1(A) = k1_enumset1(B,C,D) & v2_funct_1(k11_finseq_1(B,C,D)) & v2_funct_1(A) -> k3_finseq_1(A) = np__3)))) # label(t109_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6983 $T # label(t65_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6984 (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 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]. 83.37/80.83 6985 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (k3_finseq_1(k1_finseq_3(A,B)) = k3_finseq_1(A) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t68_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6986 (all A all B all C (k10_finseq_1(A,B) = k1_finseq_3(k10_finseq_1(A,B),C) <-> -r2_hidden(B,C) & -r2_hidden(A,C))) # label(t89_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6987 (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]. 83.37/80.83 6988 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k1_finseq_2(A) = k7_relat_1(k1_finseq_2(A),k2_finseq_1(B)) <-> r1_xreal_0(A,B)))))) # label(t58_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6989 (all A all B all C all D all E k10_finseq_1(A,B) != k11_finseq_1(C,D,E)) # label(t42_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6990 (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]. 83.37/80.83 6991 (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]. 83.37/80.83 6992 (all A all B all C (r2_hidden(C,B) -> r2_hidden(A,B) | k9_finseq_1(A) = k1_finseq_3(k10_finseq_1(A,C),B))) # label(t87_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6993 (all A (v4_ordinal2(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_finseq_1(A)) -> k3_finseq_1(k14_finseq_1(B)) = k4_card_1(B)))))) # label(t44_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6994 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (k2_relat_1(A) != k1_xboole_0 -> r2_hidden(np__1,k4_finseq_1(A))))) # label(t34_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6995 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v2_funct_1(A) & k2_relat_1(A) = k1_tarski(B) -> np__1 = k3_finseq_1(A))))) # label(t105_finseq_3) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6996 (all A all B all C (-v1_xboole_0(B) & m1_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) & v1_funct_1(C) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_funct_1(k1_zfmodel1(A,B,C)) & v1_funct_2(k1_zfmodel1(A,B,C),B,B) & m2_relset_1(k1_zfmodel1(A,B,C),B,B))) # label(dt_k1_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6997 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> ((all B (m1_subset_1(B,A) -> r2_hidden(k3_tarski(B),A))) <-> r2_zf_model(A,k8_zf_model))))) # label(t4_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.37/80.83 6998 (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_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,B) -> r1_zf_model(C,D,k8_zf_lang(A,B)) | r2_hidden(A,k2_zf_model(B))))))))))) # label(t10_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 6999 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> (r2_zf_model(A,k7_zf_model) <-> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k2_tarski(B,C),A))))))))) # label(t2_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7000 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (r1_tarski(k2_zf_model(A),k2_tarski(k2_zf_lang(np__3),k2_zf_lang(np__4))) & 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))))))) -> (all C (v1_funct_1(C) & v1_funct_2(C,B,B) & m2_relset_1(C,B,B) -> (k2_zfmodel1(A,B) = C <-> (all D (v1_funct_1(D) & m2_relset_1(D,k1_zf_lang,B) & v1_funct_2(D,k1_zf_lang,B) -> (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)) <-> r1_zf_model(B,D,A)))))))))))) # label(d2_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7001 (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) -> (all E (-v1_xboole_0(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k1_zf_lang,E) & m2_relset_1(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]. 83.38/80.84 7002 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (-v1_xboole_0(B) -> ((exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & (exists D (m2_relset_1(D,k1_zf_lang,B) & k1_zfmodel1(C,B,D) = A & 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))))))) & r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(C)) & v1_funct_2(D,k1_zf_lang,B) & v1_funct_1(D))))) <-> r2_zfmodel1(A,B)))))) # label(d4_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7003 $T # label(t17_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7004 $T # label(t16_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7005 (all A (-v1_xboole_0(A) -> (v1_zf_model(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,C) <-> r2_hidden(D,B)))) -> C = B))))) & (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k2_tarski(B,C),A))))) & (exists B ((all C (m1_subset_1(C,A) -> -((all D (m1_subset_1(D,A) -> -(r2_hidden(D,B) & r2_xboole_0(C,D)))) & r2_hidden(C,B)))) & k1_xboole_0 != B & m1_subset_1(B,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)))) # label(t21_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7006 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A))) & (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (m2_relset_1(C,k1_zf_lang,A) & v1_funct_2(C,k1_zf_lang,A) & v1_funct_1(C) -> (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_tarski(B),A))) & (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k2_tarski(B,C),A))))) & v1_ordinal1(A) -> v1_zf_model(A) | (all B (m1_subset_1(B,A) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -((all D (m1_subset_1(D,A) -> -(r2_xboole_0(C,D) & r2_hidden(D,B)))) & r2_hidden(C,B)))))))))) # label(t22_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7007 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> ((exists B ((all C -(r2_hidden(C,B) & (all D -(r2_xboole_0(C,D) & r2_hidden(D,B))))) & B != k1_xboole_0 & r2_hidden(B,A))) <-> r2_zf_model(A,k9_zf_model))))) # label(t7_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7008 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> ((all B (r2_hidden(B,A) -> r2_hidden(k3_tarski(B),A))) <-> r2_zf_model(A,k8_zf_model))))) # label(t5_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7009 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> (r2_zf_model(A,k9_zf_model) <-> (exists B (B != k1_xboole_0 & (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))))))) & m1_subset_1(B,A))))))) # label(t6_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7010 (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_2(C,k1_zf_lang,A) & m2_relset_1(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)))))))))))) # label(t19_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7011 (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]. 83.38/80.84 7012 (all A all B (m1_finseq_1(A,k5_numbers) & -v1_xboole_0(B) & v1_zf_lang(A) -> m2_relset_1(k2_zfmodel1(A,B),B,B) & v1_funct_2(k2_zfmodel1(A,B),B,B) & v1_funct_1(k2_zfmodel1(A,B)))) # label(dt_k2_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7013 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k1_zf_lang,A) & v1_funct_2(C,k1_zf_lang,A) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,A) & m2_relset_1(D,k1_zf_lang,A) -> ((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,C,E) != k8_funct_2(k1_zf_lang,A,D,E)))) & r1_zf_model(A,C,B) -> r1_zf_model(A,D,B)))))))))) # label(t14_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7014 (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_relat_1(B) & v1_funct_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]. 83.38/80.84 7015 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> ((all B (r2_hidden(B,A) -> r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A))) <-> r2_zf_model(A,k10_zf_model))))) # label(t9_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.84 7016 (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) -> (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))))))) -> r2_hidden(k2_zf_lang(np__0),k2_zf_model(A)) | (all D (m2_relset_1(D,B,B) & v1_funct_2(D,B,B) & v1_funct_1(D) -> (D = k1_zfmodel1(A,B,C) <-> (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) -> -(k8_funct_2(k1_zf_lang,B,C,F) != k8_funct_2(k1_zf_lang,B,E,F) & F != k2_zf_lang(np__0) & F != k2_zf_lang(np__4) & k2_zf_lang(np__3) != F))) -> (r1_zf_model(B,E,A) <-> k8_funct_2(B,B,D,k8_funct_2(k1_zf_lang,B,E,k2_zf_lang(np__3))) = k8_funct_2(k1_zf_lang,B,E,k2_zf_lang(np__4)))))))))))))))) # label(d1_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7017 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> (r2_zf_model(A,k7_zf_model) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k2_tarski(B,C),A))))))) # label(t3_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7018 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) -> ((all B (m1_subset_1(B,A) -> r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A))) <-> r2_zf_model(A,k10_zf_model))))) # label(t8_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7019 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_zfmodel1(B,A) -> r2_zfmodel1(B,A)))))) # label(t18_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7020 $T # label(t15_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7021 $T # label(t13_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7022 (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) -> (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_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]. 83.38/80.85 7023 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (-v1_xboole_0(B) -> (r1_zfmodel1(A,B) <-> (exists C (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))) & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C)))))))) # label(d3_zfmodel1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7024 (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) -> k4_xboole_0(k2_zf_model(A),k2_tarski(B,C)) = k2_zf_model(k15_zf_lang(B,C,A)))))))) # label(t74_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7025 (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) -> (v10_zf_lang(A) -> v10_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t190_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7026 (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]. 83.38/80.85 7027 (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]. 83.38/80.85 7028 (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 (k5_zf_lang1(k4_zf_lang(A,B),C,D) = k4_zf_lang(E,F) & m2_subset_1(F,k5_numbers,k1_zf_lang))))))))))))) # label(t167_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7029 (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]. 83.38/80.85 7030 (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) -> 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]. 83.38/80.85 7031 (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) -> (k15_zf_lang(F,G,B) = k17_zf_lang(C,D,E,A) -> F = C & G = D & k13_zf_lang(E,A) = B))))))))))))))) # label(t24_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7032 (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) -> (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) -> 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]. 83.38/80.85 7033 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v10_zf_lang(A) -> k25_zf_lang(k21_zf_lang(A)) = k27_zf_lang(A) & k26_zf_lang(k22_zf_lang(A)) = k27_zf_lang(A)))) # label(t31_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7034 (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(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]. 83.38/80.85 7035 (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) -> 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]. 83.38/80.85 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) -> (v6_zf_lang(k6_zf_lang1(A,B,C)) <-> v6_zf_lang(A)))))))) # label(t184_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 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) -> k28_zf_lang(k12_zf_lang(A,B)) = B & A = k27_zf_lang(k12_zf_lang(A,B)))))) # label(t7_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7038 (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_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) -> 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)))) & 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)))))))))))) # label(t136_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7039 (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]. 83.38/80.85 7040 (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) -> (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]. 83.38/80.85 7041 (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(k7_zf_lang(A,B)))))) # label(t154_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7042 (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]. 83.38/80.85 7043 (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 (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(A,k11_zf_lang(B,A))) & r1_zf_model(C,D,k11_zf_lang(A,k11_zf_lang(B,A))))))))))) # label(t116_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7044 (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]. 83.38/80.85 7045 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v9_zf_lang(A) -> v4_zf_lang(A) & v4_zf_lang(k22_zf_lang(k20_zf_lang(A))) & v5_zf_lang(k20_zf_lang(A))))) # label(t39_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7046 (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) -> r2_zf_model(C,k11_zf_lang(A,k13_zf_lang(B,A))))))))) # label(t139_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7047 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k2_zf_model(k8_zf_lang(B,A)) = k4_xboole_0(k2_zf_model(A),k1_tarski(B)))))) # label(t67_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7048 (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 (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),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]. 83.38/80.85 7049 (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) -> (k5_zf_lang1(B,C,D) = A <-> k5_zf_lang1(k6_zf_lang(B),C,D) = k6_zf_lang(A)))))))))) # label(t170_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7050 (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]. 83.38/80.85 7051 (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]. 83.38/80.85 7052 (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]. 83.38/80.85 7053 (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(A,B)),k11_zf_lang(A,k8_zf_lang(C,B))))))))))))) # label(t140_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7054 (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,k8_zf_lang(C,B))) -> r2_zf_model(D,k11_zf_lang(A,B))))))))))) # label(t144_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7055 $T # label(t147_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 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 (-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(A,B))) & r2_zf_model(C,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(A,B))))))))))) # label(t110_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7057 (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_xboole_0(k3_zf_lang1(A),k2_tarski(B,C)) = k3_zf_lang1(k14_zf_lang(B,C,A)))))))) # label(t160_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7058 (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,k16_zf_lang(B,C,D,A))))))))))))) # label(t108_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7059 (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_1(D) & m2_relset_1(D,k1_zf_lang,C) & v1_funct_2(D,k1_zf_lang,C) -> (r1_zf_model(C,D,k8_zf_lang(B,A)) <-> (all E (m1_subset_1(E,C) -> r1_zf_model(C,k1_zf_lang1(C,D,B,E),A)))))))))))) # label(t80_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7060 (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]. 83.38/80.85 7061 (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(B,A)),k11_zf_lang(k13_zf_lang(C,B),A)))))))))))) # label(t142_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7062 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 83.38/80.85 7063 (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(k12_zf_lang(A,B)) = 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))))))) # label(t62_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7064 (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) -> (v6_zf_lang(A) -> k24_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k24_zf_lang(A),B,C) & (k23_zf_lang(A) = B -> k23_zf_lang(k6_zf_lang1(A,B,C)) = C) & (k23_zf_lang(A) != B -> k23_zf_lang(A) = k23_zf_lang(k6_zf_lang1(A,B,C)))))))))) # label(t187_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7065 (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]. 83.38/80.85 7066 (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) -> k24_zf_lang(k16_zf_lang(B,C,D,A)) = k14_zf_lang(C,D,A) & B = k23_zf_lang(k16_zf_lang(B,C,D,A)) & v6_zf_lang(k16_zf_lang(B,C,D,A)))))))))) # label(t25_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7067 (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]. 83.38/80.85 7068 (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) -> k13_zf_lang(B,k13_zf_lang(C,k13_zf_lang(D,A))) = k17_zf_lang(B,C,D,A) & k15_zf_lang(B,C,k13_zf_lang(D,A)) = k17_zf_lang(B,C,D,A))))))))) # label(t21_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7069 (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) -> F = C & B = k14_zf_lang(D,E,A)))))))))))))) # label(t18_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 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 (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]. 83.38/80.85 7071 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> k20_zf_lang(k6_zf_lang(A)) = A)) # label(t3_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7072 (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(k7_zf_lang(A,B),C) -> r3_zf_lang(B,C) & r3_zf_lang(A,C)))))))) # label(t52_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7073 (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_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(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]. 83.38/80.85 7074 (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) -> (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]. 83.38/80.85 7075 (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_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]. 83.38/80.85 7076 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v8_zf_lang(A) -> k22_zf_lang(A) = k20_zf_lang(k22_zf_lang(k20_zf_lang(A)))))) # label(t28_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7077 (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 (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,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]. 83.38/80.85 7078 (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) -> (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]. 83.38/80.85 7079 (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]. 83.38/80.85 7080 $T # label(t76_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7081 (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 (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(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]. 83.38/80.85 7082 (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]. 83.38/80.85 7083 (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]. 83.38/80.85 7084 (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) -> (k13_zf_lang(F,B) = k17_zf_lang(C,D,E,A) -> C = F & B = k15_zf_lang(D,E,A)))))))))))))) # label(t23_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7085 (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]. 83.38/80.85 7086 (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) -> (-(-(r3_zf_lang(A,B) & r2_zf_lang(B,C)) & -(r2_zf_lang(A,B) & r1_zf_lang(B,C)) & -(r3_zf_lang(B,C) & r1_zf_lang(A,B)) & -(r3_zf_lang(A,B) & r1_zf_lang(B,C)) & -(r2_zf_lang(B,C) & r1_zf_lang(A,B)) & -(r3_zf_lang(B,C) & r2_zf_lang(A,B))) -> r3_zf_lang(A,C)))))))) # label(t44_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7087 (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]. 83.38/80.85 7088 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k24_zf_lang(k8_zf_lang(B,A)) = A & k23_zf_lang(k8_zf_lang(B,A)) = B)))) # label(t8_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7089 (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) -> (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]. 83.38/80.85 7090 (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) -> (v11_zf_lang(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)))) <-> r1_zf_model(B,C,A))))))))) # label(t103_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7091 (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) -> (k15_zf_lang(C,D,A) = k13_zf_lang(E,B) -> E = C & B = k13_zf_lang(D,A)))))))))))) # label(t12_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7092 (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(k11_zf_lang(A,B),k11_zf_lang(A,k6_zf_lang(B))),k6_zf_lang(A))) & 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))))))))))) # label(t131_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7093 (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(k6_zf_lang(A),B) -> r3_zf_lang(A,B)))))) # label(t51_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7094 (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) -> -(B != C & r2_hidden(B,k4_zf_lang1(k6_zf_lang1(A,B,C)))))))))) # label(t198_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7095 (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(k21_zf_lang(A),B,C) = k21_zf_lang(k6_zf_lang1(A,B,C)) & k22_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k22_zf_lang(A),B,C)))))))) # label(t192_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7096 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 83.38/80.85 7097 (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(C,D,A) = k14_zf_lang(E,F,B) -> E = C & D = F & A = B))))))))))))) # label(t16_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7098 (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) -> (C != D -> (k6_zf_lang1(k8_zf_lang(C,B),D,E) = k8_zf_lang(C,A) <-> k6_zf_lang1(B,D,E) = A)))))))))))) # label(t173_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7099 $T # label(t88_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7100 (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 C != k1_tarski(D)) & A != B) <-> r2_zf_model(C,k4_zf_lang(A,B))))))))) # label(t93_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7101 (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_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]. 83.38/80.85 7102 (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) -> v6_zf_lang(k14_zf_lang(B,C,A)) & k8_zf_lang(C,A) = k24_zf_lang(k14_zf_lang(B,C,A)) & B = k23_zf_lang(k14_zf_lang(B,C,A)))))))) # label(t13_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7103 (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) <-> -(-(E = A & F = B & B != C & C != A) & -(C = A & E = D & F = D & B = C) & -(A = E & D = F & C = B & A != C) & -(A = C & C != B & F = B & E = D))))))))))))))) # label(t166_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7104 (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,k14_zf_lang(B,C,A)) <-> r2_zf_model(D,A)))))))))) # label(t106_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7105 (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) -> (v11_zf_lang(A) -> (k23_zf_lang(A) != B -> k23_zf_lang(k6_zf_lang1(A,B,C)) = k23_zf_lang(A)) & (k23_zf_lang(A) = B -> C = k23_zf_lang(k6_zf_lang1(A,B,C))) & k24_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k24_zf_lang(A),B,C)))))))) # label(t195_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7106 (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) -> (v9_zf_lang(A) -> k25_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k25_zf_lang(A),B,C) & k6_zf_lang1(k26_zf_lang(A),B,C) = k26_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t193_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7107 (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) -> (k5_zf_lang1(k5_zf_lang(A,B),C,D) = k5_zf_lang(E,F) <-> -(-(C != A & F = B & A = E & B != C) & -(A = C & E = D & D = F & B = C) & -(A != C & D = F & A = E & B = C) & -(A = C & F = B & D = E & B != C))))))))))))))) # label(t168_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7108 (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]. 83.38/80.85 7109 (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) -> (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (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(C,E,F) = A & B = k6_zf_lang1(D,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]. 83.38/80.85 7110 (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_1(F) & v1_funct_2(F,k1_zf_lang,C) & m2_relset_1(F,k1_zf_lang,C) -> (B != A -> 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]. 83.38/80.85 7111 (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) -> (v5_zf_lang(A) -> (r1_zf_model(B,C,k21_zf_lang(A)) & r1_zf_model(B,C,k22_zf_lang(A)) <-> r1_zf_model(B,C,A))))))))) # label(t98_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7112 (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]. 83.38/80.85 7113 (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]. 83.38/80.85 7114 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 83.38/80.85 7115 (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]. 83.38/80.85 7116 $T # label(t77_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7117 (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)) & A = k21_zf_lang(k7_zf_lang(A,B)))))) # label(t4_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7118 (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_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(A,B),k10_zf_lang(B,A))) & r1_zf_model(C,D,k11_zf_lang(k10_zf_lang(A,B),k10_zf_lang(B,A))))))))))) # label(t125_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7119 (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]. 83.38/80.85 7120 (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]. 83.38/80.85 7121 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> k2_zf_model(k4_zf_lang(A,B)) = k2_tarski(A,B))))) # label(t63_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7122 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v10_zf_lang(A) -> v5_zf_lang(A) & v9_zf_lang(k21_zf_lang(A)) & v9_zf_lang(k22_zf_lang(A))))) # label(t40_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7123 (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) -> 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)))) & 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)))))))))))) # label(t135_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7124 (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]. 83.38/80.85 7125 (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) -> r2_zf_model(B,k11_zf_lang(A,k10_zf_lang(A,A))) & r1_zf_model(B,C,k11_zf_lang(A,k10_zf_lang(A,A))))))))) # label(t126_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7126 (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 (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) -> (k1_zf_lang1(A,B,C,D) = 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) -> F = C))) & k8_funct_2(k1_zf_lang,A,E,C) = D))))))))))) # label(d1_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7127 (all A all B all C (v1_zf_lang(A) & m1_subset_1(B,k1_zf_lang) & m1_subset_1(C,k1_zf_lang) & m1_finseq_1(A,k5_numbers) -> k5_zf_lang1(A,B,C) = k6_zf_lang1(A,B,C))) # label(redefinition_k6_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7128 (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) -> (D != C -> (k6_zf_lang1(k13_zf_lang(C,B),D,E) = k13_zf_lang(C,A) <-> A = k6_zf_lang1(B,D,E))))))))))))) # label(t178_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7129 (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]. 83.38/80.85 7130 (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,k5_zf_lang(A,A)))))))) # label(t91_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7131 (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) & r1_zf_lang(B,A)))))) # label(t50_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7132 (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) -> (k8_zf_lang(E,B) = k14_zf_lang(C,D,A) -> k8_zf_lang(D,A) = B & E = C))))))))))) # label(t11_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7133 (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_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]. 83.38/80.85 7134 $T # label(t45_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7135 (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(A) <-> v2_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t180_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7136 (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(B,k11_zf_lang(A,B)) & r3_zf_lang(k6_zf_lang(B),k11_zf_lang(A,B)) & r3_zf_lang(A,k11_zf_lang(A,B)) & r3_zf_lang(k7_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(A,B)))))) # label(t54_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7137 (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,k13_zf_lang(B,A)) <-> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,C) & m2_relset_1(D,k1_zf_lang,C) -> (exists E (m1_subset_1(E,C) & r1_zf_model(C,k1_zf_lang1(C,D,B,E),A)))))))))))) # label(t104_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7138 (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(k5_zf_lang(A,B)) & B = k19_zf_lang(k5_zf_lang(A,B)))))) # label(t2_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7139 $T # label(t132_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7140 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> np__1 != A & A != np__2 & np__3 != A & A != np__4 & A != np__0)) # label(t148_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7141 (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(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]. 83.38/80.85 7142 (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)),k1_enumset1(k6_zf_lang(B),k7_zf_lang(A,k6_zf_lang(B)),k11_zf_lang(A,B))) = k29_zf_lang(k11_zf_lang(A,B)))))) # label(t60_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7143 (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) -> r2_hidden(k5_zf_lang1(A,B,C),k9_zf_lang))))))) # label(t171_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7144 (all A all B all C (m1_subset_1(C,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_relat_1(k5_zf_lang1(A,B,C)) & v1_funct_1(k5_zf_lang1(A,B,C)))) # label(dt_k5_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7145 (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) = k14_zf_lang(B,C,k8_zf_lang(D,A)) & k8_zf_lang(B,k8_zf_lang(C,k8_zf_lang(D,A))) = k16_zf_lang(B,C,D,A))))))))) # label(t15_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7146 (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(k11_zf_lang(A,B)))))) # label(t69_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7147 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> -(v4_zf_lang(A) & (v6_zf_lang(A) | v5_zf_lang(A))) & -(v6_zf_lang(A) & v5_zf_lang(A)) & -(v3_zf_lang(A) & -(-v5_zf_lang(A) & -v6_zf_lang(A) & -v4_zf_lang(A))) & -(v2_zf_lang(A) & -(-v3_zf_lang(A) & -v4_zf_lang(A) & -v5_zf_lang(A) & -v6_zf_lang(A))))) # label(t42_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7148 (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(k11_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)))))) # label(t157_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7149 $T # label(t165_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7150 (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) -> (all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (all G (m2_subset_1(G,k5_numbers,k1_zf_lang) -> (k16_zf_lang(C,D,E,A) = k14_zf_lang(F,G,B) -> G = D & k8_zf_lang(E,A) = B & F = C))))))))))))))) # label(t19_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7151 (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(k6_zf_lang1(A,B,C)) <-> v5_zf_lang(A)))))))) # label(t183_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.85 7152 (all A all B all C (v1_zf_lang(A) & m1_subset_1(B,k1_zf_lang) & m1_subset_1(C,k1_zf_lang) & m1_finseq_1(A,k5_numbers) -> 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]. 83.38/80.86 7153 (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) -> (k13_zf_lang(C,A) = k6_zf_lang1(k13_zf_lang(D,B),D,C) <-> A = k6_zf_lang1(B,D,C)))))))))) # label(t179_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7154 (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) -> (k15_zf_lang(C,D,A) = k15_zf_lang(E,F,B) -> B = A & D = F & C = E))))))))))))) # label(t20_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7155 (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]. 83.38/80.86 7156 (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) -> B = k23_zf_lang(k17_zf_lang(B,C,D,A)) & k24_zf_lang(k17_zf_lang(B,C,D,A)) = k15_zf_lang(C,D,A) & v11_zf_lang(k17_zf_lang(B,C,D,A)))))))))) # label(t26_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 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 (-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(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]. 83.38/80.86 7158 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k2_zf_lang(B) = A)))) # label(t87_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7159 (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(k4_zf_lang(A,B)) = B & k18_zf_lang(k4_zf_lang(A,B)) = A)))) # label(t1_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7160 (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]. 83.38/80.86 7161 (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(k10_zf_lang(A,B)) = 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))))))) # label(t61_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7162 (all A all B all C all D (-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_xboole_0(A) -> v1_funct_1(k2_zf_lang1(A,B,C,D)) & v1_funct_2(k2_zf_lang1(A,B,C,D),A,C) & m2_relset_1(k2_zf_lang1(A,B,C,D),A,C))) # label(dt_k2_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7163 (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) & r3_zf_lang(A,B)))))) # label(t48_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7164 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k25_zf_lang(k11_zf_lang(A,B)) = A & k26_zf_lang(k11_zf_lang(A,B)) = B)))) # label(t6_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7165 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> k3_zf_lang1(A) = k3_zf_lang1(k6_zf_lang(A)))) # label(t153_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7166 (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) -> (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]. 83.38/80.86 7167 (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_funct_1(D) & v1_relat_1(D) -> (k5_zf_lang1(A,B,C) = D <-> k1_relat_1(D) = k4_finseq_1(A) & (all E (r2_hidden(E,k4_finseq_1(A)) -> (k1_funct_1(A,E) = B -> C = k1_funct_1(D,E)) & (B != k1_funct_1(A,E) -> k1_funct_1(D,E) = k1_funct_1(A,E))))))))))))) # label(d4_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7168 (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) -> (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(C,D,E,A) = k17_zf_lang(F,G,H,B) -> C = F & D = G & E = H & A = B))))))))))))))))) # label(t22_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7169 (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]. 83.38/80.86 7170 (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,B)) -> r2_hidden(C,k2_zf_model(A)) | r2_zf_model(D,k11_zf_lang(A,k8_zf_lang(C,B)))))))))))) # label(t141_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7171 (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) -> (v8_zf_lang(A) -> (r1_zf_model(B,C,A) <-> r1_zf_model(B,C,k22_zf_lang(A)) | r1_zf_model(B,C,k21_zf_lang(A)))))))))) # label(t100_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7172 (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 (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,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]. 83.38/80.86 7173 (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) -> 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(t186_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7174 (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) -> (v4_zf_lang(A) -> (r1_zf_model(B,C,A) <-> -r1_zf_model(B,C,k20_zf_lang(A)))))))))) # label(t97_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7175 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v11_zf_lang(A) -> v6_zf_lang(k20_zf_lang(A)) & v4_zf_lang(k24_zf_lang(k20_zf_lang(A))) & v4_zf_lang(A)))) # label(t41_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7176 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)) = k20_zf_lang(k10_zf_lang(A,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]. 83.38/80.86 7177 (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) -> k28_zf_lang(k6_zf_lang1(A,B,C)) = k6_zf_lang1(k28_zf_lang(A),B,C) & k6_zf_lang1(k27_zf_lang(A),B,C) = k27_zf_lang(k6_zf_lang1(A,B,C))))))))) # label(t194_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7178 (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) -> D = G & H = E & A = B & F = C))))))))))))))))) # label(t17_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7179 (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 (m1_subset_1(E,C) & r1_zf_model(C,k1_zf_lang1(C,D,B,E),A))) <-> r1_zf_model(C,D,k13_zf_lang(B,A))))))))))) # label(t82_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7180 (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_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]. 83.38/80.86 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) -> (v8_zf_lang(k6_zf_lang1(A,B,C)) <-> v8_zf_lang(A)))))))) # label(t188_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7182 (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) -> 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]. 83.38/80.86 7183 (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) -> 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]. 83.38/80.86 7184 (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),k7_zf_lang(B,A))) & r2_zf_model(C,k11_zf_lang(k7_zf_lang(A,B),k7_zf_lang(B,A))))))))))) # label(t120_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 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) -> k22_zf_lang(k10_zf_lang(A,B)) = B & k21_zf_lang(k10_zf_lang(A,B)) = A)))) # label(t5_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7186 (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]. 83.38/80.86 7187 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k22_zf_lang(k12_zf_lang(A,B)) = k11_zf_lang(B,A) & k21_zf_lang(k12_zf_lang(A,B)) = k11_zf_lang(A,B))))) # label(t36_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7188 (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(k20_zf_lang(A)) = k23_zf_lang(A)))) # label(t33_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7189 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 83.38/80.86 7190 (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(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(A),k10_zf_lang(A,B)) & r3_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B)),k10_zf_lang(A,B)))))) # label(t55_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7191 (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) -> r2_zf_model(C,k11_zf_lang(k8_zf_lang(B,A),A)))))))) # label(t138_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7192 (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) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_zf_lang,B) & v1_funct_2(D,k1_zf_lang,B) -> (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,D,E) = k8_funct_2(k1_zf_lang,B,C,E)))) -> r1_zf_model(B,D,A)))))))))) # label(t84_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7193 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 83.38/80.86 7194 (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(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]. 83.38/80.86 7195 (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]. 83.38/80.86 7196 (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(k6_zf_lang1(A,B,C)) <-> v11_zf_lang(A)))))))) # label(t191_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7197 $T # label(dt_k3_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7198 (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]. 83.38/80.86 7199 (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(B,A) & r2_zf_lang(A,B)))))) # label(t49_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7200 (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) -> (k6_zf_lang1(k8_zf_lang(D,B),D,C) = k8_zf_lang(C,A) <-> A = k6_zf_lang1(B,D,C)))))))))) # label(t174_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7201 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> r3_zf_lang(k8_zf_lang(B,k6_zf_lang(A)),k13_zf_lang(B,A)) & r3_zf_lang(k6_zf_lang(A),k13_zf_lang(B,A)))))) # label(t56_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7202 (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]. 83.38/80.86 7203 (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]. 83.38/80.86 7204 (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) -> (B != C -> 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]. 83.38/80.86 7205 (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_zf_model(k12_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)))))) # label(t70_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7206 (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) -> B = k23_zf_lang(k15_zf_lang(B,C,A)) & k13_zf_lang(C,A) = k24_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]. 83.38/80.86 7207 (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) -> 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]. 83.38/80.86 7208 (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) -> 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]. 83.38/80.86 7209 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> 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]. 83.38/80.86 7210 (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_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(C,E,F) = A & B = k6_zf_lang1(D,E,F) <-> k6_zf_lang1(k11_zf_lang(C,D),E,F) = k11_zf_lang(A,B)))))))))))))) # label(t176_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7211 (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]. 83.38/80.86 7212 (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]. 83.38/80.86 7213 (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) -> 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]. 83.38/80.86 7214 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> k2_zf_model(A) = k2_zf_model(k6_zf_lang(A)))) # label(t65_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7215 (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]. 83.38/80.86 7216 (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 (r2_hidden(D,C) -> r1_xboole_0(D,C))) | A = B <-> r2_zf_model(C,k6_zf_lang(k5_zf_lang(A,B)))))))))) # label(t94_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7217 (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,A) -> r2_zf_model(E,k17_zf_lang(B,C,D,A))))))))))))) # label(t109_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7218 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> -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]. 83.38/80.86 7219 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> B = k23_zf_lang(k13_zf_lang(B,A)) & A = k24_zf_lang(k13_zf_lang(B,A)))))) # label(t9_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7220 (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) -> (r2_zf_model(C,A) & r2_zf_model(C,k11_zf_lang(A,B)) -> r2_zf_model(C,B)))))))) # label(t133_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7221 (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]. 83.38/80.86 7222 (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 (v1_funct_2(E,k1_zf_lang,D) & m2_relset_1(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]. 83.38/80.86 7223 (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_1(E) & m2_relset_1(E,k1_zf_lang,B) & v1_funct_2(E,k1_zf_lang,B) -> k1_zf_lang1(B,k1_zf_lang1(B,E,A,C),A,D) = k1_zf_lang1(B,E,A,D) & k1_zf_lang1(B,E,A,k8_funct_2(k1_zf_lang,B,E,A)) = E)))))))))) # label(t78_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7224 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (r2_hidden(B,k3_zf_lang1(A)) -> B != np__1 & np__2 != B & np__3 != B & np__4 != B & np__0 != B)))) # label(t150_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7225 (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]. 83.38/80.86 7226 (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 (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (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) & k6_zf_lang1(D,E,F) = B <-> k7_zf_lang(A,B) = k6_zf_lang1(k7_zf_lang(C,D),E,F)))))))))))))) # label(t172_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.86 7227 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v8_zf_lang(A) -> v9_zf_lang(A) & v4_zf_lang(k22_zf_lang(k20_zf_lang(A))) & v4_zf_lang(k21_zf_lang(k20_zf_lang(A))) & v5_zf_lang(k20_zf_lang(A)) & v4_zf_lang(A)))) # label(t38_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 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) -> k10_zf_lang(A,B) = k11_zf_lang(k6_zf_lang(A),B))))) # label(t10_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7229 (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(t57_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7230 (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) -> (v10_zf_lang(A) -> (r1_zf_model(B,C,A) <-> (r1_zf_model(B,C,k27_zf_lang(A)) <-> r1_zf_model(B,C,k28_zf_lang(A))))))))))) # label(t102_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7231 (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 (m1_subset_1(D,C) -> (all E (m2_relset_1(E,k1_zf_lang,C) & v1_funct_2(E,k1_zf_lang,C) & v1_funct_1(E) -> (r1_zf_model(C,E,k8_zf_lang(B,A)) <-> r1_zf_model(C,k1_zf_lang1(C,E,B,D),k8_zf_lang(B,A))))))))))))) # label(t81_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7232 (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_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]. 83.38/80.88 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) -> (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 (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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]. 83.38/80.88 7234 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> r2_hidden(A,k29_zf_lang(A)))) # label(t59_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7235 (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) -> k2_zf_lang1(A,B,C,D) = D))))))))) # label(d2_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7236 (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) -> (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (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) <-> k6_zf_lang1(C,E,F) = A & B = k6_zf_lang1(D,E,F)))))))))))))) # label(t177_zf_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7237 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(B) & 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(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]. 83.38/80.88 7238 $T # label(d4_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7239 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> (all C (v2_relat_1(C) & m1_ordinal1(C,A) & v1_zf_refle(C,A) -> r2_hidden(B,k1_relat_1(C)))))))) # label(t23_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7240 (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]. 83.38/80.88 7241 $T # label(t26_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7242 $T # label(t16_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7243 (all A (v1_funct_1(A) & v1_relat_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]. 83.38/80.88 7244 $T # label(t20_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7245 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_ordinal1(B,A) & m1_ordinal4(C,A) & v1_zf_refle(B,A) & v2_relat_1(B) -> k5_zf_refle(A,B,C) = k1_funct_1(B,C))) # label(redefinition_k5_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7246 $T # label(t1_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7247 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v2_relat_1(B) & v1_zf_refle(B,A) & m1_ordinal1(B,A) -> (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) -> k1_xboole_0 = C | k5_zf_refle(A,B,C) = k3_card_3(k2_ordinal1(B,C))))) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (exists D ((all E (m1_ordinal4(E,A) -> (E = k4_ordinal4(A,D,E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k1_zf_lang,k5_zf_refle(A,B,E)) & m2_relset_1(F,k1_zf_lang,k5_zf_refle(A,B,E)) -> (r1_zf_model(k5_zf_refle(A,B,E),F,C) <-> 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)))) | k1_xboole_0 = E))) & v3_ordinal2(D) & v2_ordinal2(D) & m2_ordinal4(D,A)))))))))) # label(t29_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7248 $T # label(t18_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7249 (all A all B (v2_relat_1(B) & m1_ordinal1(B,A) & v1_zf_refle(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k4_zf_refle(A,B) = k3_card_3(B))) # label(redefinition_k4_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7250 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(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_relat_1(k7_relat_1(A,k4_classes1(B))))))) # label(t10_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7251 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal1(B,A) -> (v1_zf_refle(B,A) <-> k2_ordinal2(A) = k1_relat_1(B)))))) # label(d5_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7252 (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) -> (v4_ordinal1(A) & (all B (m1_ordinal4(B,f1_s5_zf_refle) -> (r2_hidden(B,A) -> p1_s5_zf_refle(B)))) -> p1_s5_zf_refle(A) | A = k2_ordinal4(f1_s5_zf_refle)))) & p1_s5_zf_refle(k2_ordinal4(f1_s5_zf_refle)) -> (all A (m1_ordinal4(A,f1_s5_zf_refle) -> p1_s5_zf_refle(A))) # label(s5_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7253 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & -v1_xboole_0(B) & v1_classes2(B) & m1_ordinal4(C,B) & v1_ordinal2(A) -> k2_zf_refle(A,B,C) = k1_zf_refle(A,B,C))) # label(redefinition_k2_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7254 $T # label(t22_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7255 $T # label(d3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7256 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> v1_relat_1(k7_relat_1(A,k4_classes1(B))) & v1_ordinal2(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(t11_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7257 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> k2_zf_refle(C,A,B) = k3_card_3(k2_ordinal1(C,B)) & k3_card_3(k2_ordinal1(C,B)) = k2_zf_refle(k2_ordinal1(C,B),A,B))))))) # label(t17_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7258 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> (all C (m1_ordinal1(C,A) & v1_zf_refle(C,A) & v2_relat_1(C) -> r1_tarski(k5_zf_refle(A,C,B),k4_zf_refle(A,C)))))))) # label(t24_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7259 (all A (v1_classes2(A) & -v1_xboole_0(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))))))) # label(t6_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7260 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) -> v3_ordinal1(k3_card_3(k8_relat_1(A,B))))) # label(t13_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7261 $T # label(dt_k1_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7262 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> k7_relat_1(B,k4_classes1(A)) = k2_ordinal1(B,A))))) # label(t15_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7263 (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) -> k2_ordinal4(f1_s4_zf_refle) = B | 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]. 83.38/80.88 7264 $T # label(t21_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7265 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_zf_model(A,k8_zf_model))) # label(t3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7266 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (r2_hidden(B,k2_ordinal2(A)) <-> m1_ordinal4(B,A))))) # label(t8_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7267 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (exists B (v2_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_zf_refle(B,A) & v1_relat_1(B) & m1_ordinal1(B,A))))) # label(rc2_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7268 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_ordinal4(C,A) & m1_ordinal4(B,A) -> m1_ordinal4(k3_zf_refle(A,B,C),A))) # label(dt_k3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7269 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & v2_relat_1(B) & m1_ordinal1(B,A) & v1_zf_refle(B,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]. 83.38/80.88 7270 (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]. 83.38/80.88 7271 $T # label(t9_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7272 (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]. 83.38/80.88 7273 (all A all B all C (-v1_xboole_0(A) & m1_ordinal4(C,A) & m1_ordinal4(B,A) & v1_classes2(A) -> k2_xboole_0(B,C) = k3_zf_refle(A,B,C))) # label(redefinition_k3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7274 (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]. 83.38/80.88 7275 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k3_card_3(A)))) # label(t12_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7276 (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,B,C) = k3_zf_refle(A,C,B))) # label(commutativity_k3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7277 (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 (v1_relat_1(A) & (all B (m1_subset_1(B,f2_s2_zf_refle) -> (exists C (m1_ordinal4(C,f1_s2_zf_refle) & k1_funct_1(A,B) = C & p1_s2_zf_refle(B,C) & (all D (m1_ordinal4(D,f1_s2_zf_refle) -> (p1_s2_zf_refle(B,D) -> r1_tarski(C,D)))))))) & f2_s2_zf_refle = k1_relat_1(A) & v1_funct_1(A))) # label(s2_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7278 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,A))))) # label(rc1_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7279 (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]. 83.38/80.88 7280 (all A all B all C (v1_classes2(A) & m1_ordinal4(C,A) & m1_ordinal4(B,A) & -v1_xboole_0(A) -> k3_zf_refle(A,B,B) = B)) # label(idempotence_k3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7281 (all A r1_tarski(k7_ordinal2(A),k1_ordinal1(k3_tarski(k2_ordinal2(A))))) # label(t27_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7282 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & v1_zf_refle(B,A) & m1_ordinal1(B,A) & m1_ordinal4(C,A) & v2_relat_1(B) -> -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]. 83.38/80.88 7283 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (r2_hidden(k5_ordinal2,A) -> v1_zf_model(A)))) # label(t7_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7284 (all A (m1_subset_1(A,f1_s1_zf_refle) -> (exists B (v3_ordinal1(B) & p1_s1_zf_refle(A,B))))) -> (exists A (f1_s1_zf_refle = k1_relat_1(A) & (all B (m1_subset_1(B,f1_s1_zf_refle) -> (exists C (v3_ordinal1(C) & k1_funct_1(A,B) = C & (all D (v3_ordinal1(D) -> (p1_s1_zf_refle(B,D) -> r1_tarski(C,D)))) & p1_s1_zf_refle(B,C))))) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7285 $T # label(t19_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7286 (all A (m1_ordinal4(A,f1_s3_zf_refle) -> (exists B (p1_s3_zf_refle(A,B) & m1_ordinal4(B,f1_s3_zf_refle))))) & (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) -> C = B))))))) -> (exists A ((all B (m1_ordinal4(B,f1_s3_zf_refle) -> p1_s3_zf_refle(B,k4_ordinal4(f1_s3_zf_refle,A,B)))) & m2_ordinal4(A,f1_s3_zf_refle))) # label(s3_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7287 (all A (v3_ordinal1(A) -> k2_ordinal2(k4_classes1(A)) = A)) # label(t14_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7288 (all A all B all C (v5_ordinal1(A) & v1_ordinal2(A) & v1_classes2(B) & m1_ordinal4(C,B) & -v1_xboole_0(B) & v1_funct_1(A) & v1_relat_1(A) -> m1_ordinal4(k2_zf_refle(A,B,C),B))) # label(dt_k2_zf_refle) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7289 (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]. 83.38/80.88 7290 (all A (v3_ordinal1(A) -> (r4_zfrefle1(A,k1_xboole_0) -> A = k1_xboole_0))) # label(t28_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7291 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -(r2_hidden(k5_ordinal2,A) & (all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(r4_zfrefle1(B,k5_ordinal2) & v1_zf_model(C) & C = k4_classes1(B))))))))) # label(t42_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7292 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (exists B (v1_zf_lang(B) & (all C (-v1_xboole_0(C) -> (r2_zf_model(C,A) <-> r2_zf_model(C,B)))) & k2_zf_model(B) = k1_xboole_0 & m2_finseq_1(B,k5_numbers))))) # label(t6_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7293 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> -((all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> -(r2_hidden(B,C) & r3_zfrefle1(D,A) & k4_classes1(C) = D))))) & r2_hidden(k5_ordinal2,A)))))) # label(t36_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7294 (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) -> -(r2_hidden(B,C) & D = k4_classes1(C) & r2_zfrefle1(D,A))))))))))) # label(t40_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7295 (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]. 83.38/80.88 7296 (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]. 83.38/80.88 7297 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> ((all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (k1_xboole_0 = k2_zf_model(C) -> (r2_zf_model(A,C) <-> r2_zf_model(B,C))))) <-> r2_zfrefle1(A,B)))))) # label(d2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7298 (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]. 83.38/80.88 7299 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(r3_zfrefle1(C,A) & C = k4_classes1(B) & r4_zfrefle1(B,k5_ordinal2)))))) & r2_hidden(k5_ordinal2,A)))) # label(t37_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7300 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) -> (v4_ordinal1(k1_relat_1(B)) & v2_ordinal2(B) & r1_ordinal2(A,B) -> k1_xboole_0 = k1_relat_1(B) | r4_zfrefle1(A,k1_relat_1(B))))))) # label(t24_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7301 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> ((all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (r2_zf_model(A,C) <-> r2_zf_model(B,C)))) <-> r2_zfrefle1(A,B)))))) # label(t7_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7302 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> -((all D (m1_ordinal4(D,A) -> -(r2_hidden(B,D) & D = k4_ordinal4(A,C,D)))) & v3_ordinal2(C) & v2_ordinal2(C) & r2_hidden(k5_ordinal2,A)))))))) # label(t30_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 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]. 83.38/80.88 7304 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m2_ordinal4(B,A) -> -(v2_ordinal2(B) & v3_ordinal2(B) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> (C = k4_ordinal4(A,B,C) & D = k4_classes1(C) -> k1_xboole_0 = C | r3_zfrefle1(D,A))))))))) & r2_hidden(k5_ordinal2,A)))) # label(t35_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7305 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> -(r2_hidden(k5_ordinal2,A) & (all D (m1_ordinal4(D,A) -> -(D = k4_ordinal4(A,C,D) & r4_zfrefle1(D,k5_ordinal2) & r2_hidden(B,D)))) & v3_ordinal2(C) & v2_ordinal2(C)))))))) # label(t31_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7306 (all A all B (v1_classes2(B) & -v1_xboole_0(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]. 83.38/80.88 7307 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r3_zfrefle1(A,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)))))) # label(d3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7308 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_zfrefle1(A,B) <-> (all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(B,C) <-> r1_zfrefle1(A,C))))))))) # label(t8_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7309 (all A (-v1_xboole_0(A) -> r1_zfrefle1(A,k1_subset_1(k9_zf_lang)))) # label(t1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7310 (all A (-v1_xboole_0(A) -> (v1_zf_model(A) -> r1_zfrefle1(A,k2_zfrefle1)))) # label(t4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7311 (all A all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) -> v3_ordinal1(A)))) # label(t19_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7312 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) & r4_zfrefle1(B,A) -> A = B))))) # label(t23_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7313 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) & m2_relset_1(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) & v1_funct_1(C) -> -(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) -> k2_ordinal4(A) = E | k4_ordinal4(A,D,E) = k8_ordinal2(k2_ordinal1(D,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)))))))) & k2_ordinal4(A) = k4_ordinal4(A,D,k2_ordinal4(A)) & v3_ordinal2(D))))))))))) # label(t14_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7314 (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]. 83.38/80.88 7315 (all A (v1_ordinal2(A) & v5_ordinal1(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]. 83.38/80.88 7316 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m2_ordinal4(B,A) -> -((all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> (k4_classes1(C) = D & k4_ordinal4(A,B,C) = C -> r2_zfrefle1(D,A) | k1_xboole_0 = C))))) & v3_ordinal2(B) & v2_ordinal2(B)))) & r2_hidden(k5_ordinal2,A)))) # label(t39_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7317 (all A (v1_funct_1(A) & v1_relat_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]. 83.38/80.88 7318 $T # label(dt_k1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7319 (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]. 83.38/80.88 7320 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (v1_ordinal1(B) & r2_zfrefle1(A,B) & v1_zf_model(A) -> v1_zf_model(B)))))) # label(t10_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7321 (all A (-v1_xboole_0(A) -> (r1_zfrefle1(A,k2_zfrefle1) & v1_ordinal1(A) -> v1_zf_model(A)))) # label(t5_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7322 (all A all B (k1_card_1(A) = k1_card_1(B) | r2_wellord2(A,B) -> k1_card_1(k1_zfmisc_1(A)) = k1_card_1(k1_zfmisc_1(B)) & r2_wellord2(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t13_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.88 7323 (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]. 83.38/80.89 7324 $T # label(t11_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7325 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> k1_ordinal3(A,k2_ordinal1(C,B)) = k2_ordinal1(k1_ordinal3(A,C),B))))))) # label(t16_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7326 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> r2_zfrefle1(A,A))) # label(reflexivity_r2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7327 (all A (k1_zfrefle1 = A <-> (all B (r2_hidden(B,A) <-> -(B != k8_zf_model & B != k9_zf_model & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> -(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 != k7_zf_model & k6_zf_model != B) & r2_hidden(B,k9_zf_lang))))) # label(d4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7328 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v1_zf_refle(B,A) & m1_ordinal1(B,A) & v2_relat_1(B) -> -((all C (m1_ordinal4(C,A) -> (v4_ordinal1(C) -> k3_card_3(k2_ordinal1(B,C)) = k5_zf_refle(A,B,C) | C = k1_xboole_0))) & (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) -> (all D (m1_ordinal4(D,A) -> (r2_hidden(C,D) -> r1_tarski(k5_zf_refle(A,B,C),k5_zf_refle(A,B,D))))))) & r2_hidden(k5_ordinal2,A)))))) # label(t38_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7329 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> (v2_ordinal2(B) & v3_ordinal2(B) -> v3_ordinal2(k1_ordinal3(A,B))))))) # label(t17_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7330 (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_tarski(B,C) & r1_zfrefle1(A,C) -> r1_zfrefle1(A,B)))))))) # label(t2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7331 (all A (v1_classes2(A) & -v1_xboole_0(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]. 83.38/80.89 7332 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> (v2_ordinal2(B) -> v2_ordinal2(k1_ordinal3(A,B))))))) # label(t15_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7333 (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]. 83.38/80.89 7334 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r4_zfrefle1(A,A))) # label(reflexivity_r4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7335 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v2_relat_1(B) & v1_zf_refle(B,A) & m1_ordinal1(B,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) -> -(v2_ordinal2(C) & 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)))))) & r2_hidden(k5_ordinal2,A)))))) # label(t32_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7336 (all A (v3_ordinal1(A) -> r4_zfrefle1(k1_ordinal1(A),k4_ordinal2))) # label(t25_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7337 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -((all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(r4_zfrefle1(B,k5_ordinal2) & k4_classes1(B) = C & r2_zfrefle1(C,A)))))) & r2_hidden(k5_ordinal2,A)))) # label(t41_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7338 (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_zfrefle1(A,B) -> r1_zfrefle1(A,k4_subset_1(k9_zf_lang,B,C))))))))) # label(t3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7339 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> A != k1_ordinal1(C))) & r4_zfrefle1(A,k1_ordinal1(B))))))) # label(t26_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7340 $T # label(t18_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7341 (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]. 83.38/80.89 7342 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) <-> (exists C (v1_relat_1(C) & v1_ordinal2(C) & r1_tarski(k2_relat_1(C),A) & v2_ordinal2(C) & A = k8_ordinal2(C) & k1_relat_1(C) = B & v5_ordinal1(C) & v1_funct_1(C)))))))) # label(d5_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7343 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> np__1 != k1_mcart_1(B) & np__2 != k1_mcart_1(B) & np__3 != k1_mcart_1(B) & k1_mcart_1(B) != np__0)))) # label(t48_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7344 (all A (m1_subset_1(A,k8_qc_lang1) -> A = k10_qc_lang1(A))) # label(d12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7345 (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]. 83.38/80.89 7346 $T # label(t26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7347 (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]. 83.38/80.89 7348 (all A (-v1_xboole_0(A) -> ((all B (-v1_xboole_0(B) -> (v1_qc_lang1(B) -> r1_tarski(A,B)))) & v1_qc_lang1(A) <-> k8_qc_lang1 = A))) # label(d10_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7349 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__0 -> A = k11_qc_lang1) & ((exists B (m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) -> v2_qc_lang1(A)) & (np__3 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> v5_qc_lang1(A)) & (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__2 -> v4_qc_lang1(A)) & (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__1 -> v3_qc_lang1(A)))) # label(t36_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7350 (all A all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (k1_funct_1(k16_qc_lang1(B),C) = A & r1_xreal_0(np__1,C) & r2_hidden(k1_funct_1(k16_qc_lang1(B),C),k2_qc_lang1) & r1_xreal_0(C,k3_finseq_1(k16_qc_lang1(B))) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_2_qc_lang1(B))))) # label(fraenkel_a_1_2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7351 (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]. 83.38/80.89 7352 $T # label(t43_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7353 (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]. 83.38/80.89 7354 $T # label(t42_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7355 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (A = k12_qc_lang1(B) <-> k17_qc_lang1(A) = B)))))) # label(d23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7356 (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]. 83.38/80.89 7357 $T # label(t39_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7358 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (A = k13_qc_lang1(B,C) & m1_subset_1(C,k8_qc_lang1))))) <-> v4_qc_lang1(A)))) # label(d19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7359 (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]. 83.38/80.89 7360 $T # label(dt_k5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7361 (all A (m1_subset_1(A,k8_qc_lang1) -> -(v3_qc_lang1(A) & v2_qc_lang1(A)) & -(v5_qc_lang1(A) & v2_qc_lang1(A)) & -(v3_qc_lang1(A) & v5_qc_lang1(A)) & -(v4_qc_lang1(A) & v5_qc_lang1(A)) & -(v4_qc_lang1(A) & v3_qc_lang1(A)) & -(v2_qc_lang1(A) & v4_qc_lang1(A)))) # label(t51_qc_lang1_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7362 (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 (k14_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1)))))))) # label(d20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7363 (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]. 83.38/80.89 7364 $T # label(t27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7365 (all A all B (m2_finseq_1(B,k1_qc_lang1) -> (r2_hidden(A,a_1_1_qc_lang1(B)) <-> (exists C (r2_hidden(k1_funct_1(B,C),k2_qc_lang1) & r1_xreal_0(C,k3_finseq_1(B)) & r1_xreal_0(np__1,C) & A = k1_funct_1(B,C) & m2_subset_1(C,k1_numbers,k5_numbers)))))) # label(fraenkel_a_1_1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7366 (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]. 83.38/80.89 7367 (exists A (v1_funct_2(A,k8_qc_lang1,f1_s3_qc_lang1) & m2_relset_1(A,k8_qc_lang1,f1_s3_qc_lang1) & (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,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)))) & (v5_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B) = f6_s3_qc_lang1(B,k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k21_qc_lang1(B)))) & (v3_qc_lang1(B) -> f4_s3_qc_lang1(k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k17_qc_lang1(B))) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B)) & (v2_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B) = f3_s3_qc_lang1(B)))) & k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k11_qc_lang1) = f2_s3_qc_lang1 & v1_funct_1(A))) # label(s3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7368 (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]. 83.38/80.89 7369 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> p1_s2_qc_lang1(A)) & (p1_s2_qc_lang1(k21_qc_lang1(A)) & v5_qc_lang1(A) -> p1_s2_qc_lang1(A)) & (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)) & (p1_s2_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(A) -> p1_s2_qc_lang1(A)) & p1_s2_qc_lang1(k11_qc_lang1))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s2_qc_lang1(A))) # label(s2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7370 $T # label(t28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7371 $T # label(t32_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7372 (all A all B (m1_finseq_1(B,k1_qc_lang1) & m1_subset_1(A,k5_qc_lang1) -> m1_subset_1(k9_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7373 $T # label(t44_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7374 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k18_qc_lang1(A) = B <-> (exists C (k13_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1))))))))) # label(d24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7375 $T # label(t13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7376 $T # label(t14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7377 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) & (exists D (k9_qc_lang1(C,D) = A & m1_qc_lang1(D,B))))) & m2_subset_1(B,k1_numbers,k5_numbers))) <-> v2_qc_lang1(A)))) # label(d17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7378 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k7_qc_lang1(A) = a_1_0_qc_lang1(A))) # label(d7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7379 $T # label(dt_k1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7380 $T # label(t18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7381 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (A = k14_qc_lang1(C,B) & m2_subset_1(C,k1_qc_lang1,k2_qc_lang1))) <-> B = k21_qc_lang1(A))))))) # label(d27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7382 (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]. 83.38/80.89 7383 (all A (m1_subset_1(A,k8_qc_lang1) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(k11_qc_lang1),np__1)) = np__0 & (v3_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__1) & (v4_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__2) & (v5_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__3) & -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)))) & v2_qc_lang1(A)))) # label(t49_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7384 (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]. 83.38/80.89 7385 $T # label(t11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7386 $T # label(t22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7387 (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_finseq_1(C) & v1_funct_1(C) -> (k7_finseq_1(k10_qc_lang1(B),C) = k10_qc_lang1(A) -> k10_qc_lang1(A) = k10_qc_lang1(B)))))))) # label(t37_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7388 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists C (C = A & k6_qc_lang1(C) = B & m1_subset_1(C,k5_qc_lang1))) <-> r2_hidden(A,a_1_0_qc_lang1(B))))) # label(fraenkel_a_1_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7389 (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]. 83.38/80.89 7390 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k14_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7391 (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]. 83.38/80.89 7392 $T # label(t7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7393 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k2_qc_lang1)) -> ((exists C (m2_relset_1(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & (all D (m1_subset_1(D,k8_qc_lang1) -> (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)) & (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)))) & (v3_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k17_qc_lang1(D)) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)) & (v2_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D) = a_1_2_qc_lang1(D)) & k1_xboole_0 = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k11_qc_lang1))) & B = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,A) & v1_funct_2(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & v1_funct_1(C))) <-> B = k24_qc_lang1(A)))))) # label(d29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7394 $T # label(t24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7395 (all A (m1_subset_1(A,k8_qc_lang1) -> k7_finseq_1(k9_finseq_1(k4_tarski(np__1,np__0)),k10_qc_lang1(A)) = k12_qc_lang1(A))) # label(d14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7396 $T # label(t20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7397 $T # label(t29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7398 $T # label(t30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7399 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (A = k3_finseq_1(B) <-> m1_qc_lang1(B,A)))))) # label(d8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7400 (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]. 83.38/80.89 7401 $T # label(t8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7402 $T # label(t9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7403 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> A = k6_qc_lang1(B))))) # label(t35_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7404 $T # label(t19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7405 $T # label(t25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7406 $T # label(t12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7407 (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]. 83.38/80.89 7408 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m1_subset_1(B,k5_qc_lang1) -> (k15_qc_lang1(A) = B <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D ((exists E (E = B & k9_qc_lang1(E,D) = A & m2_subset_1(E,k5_qc_lang1,k7_qc_lang1(C)))) & m1_qc_lang1(D,C))))))))))) # label(d21_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7409 (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]. 83.38/80.89 7410 $T # label(t6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7411 $T # label(t15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7412 $T # label(t5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7413 (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]. 83.38/80.89 7414 (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]. 83.38/80.89 7415 (all A (m1_subset_1(A,k2_qc_lang1) -> k23_qc_lang1(A) = k1_tarski(A))) # label(redefinition_k23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.89 7416 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> np__1 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) & k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__2 & k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__3 & np__0 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))))) # label(t50_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.90 7417 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_mcart_1(A) = k1_nat_1(np__7,B) <-> B = k6_qc_lang1(A)))))) # label(d6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.90 7418 (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]. 83.38/80.90 7419 (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]. 83.38/80.90 7420 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (B = k19_qc_lang1(A) <-> (exists C (k13_qc_lang1(C,B) = A & m1_subset_1(C,k8_qc_lang1))))))))) # label(d25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.90 7421 (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]. 83.38/80.90 7422 $T # label(t38_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.90 7423 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> ((exists C (A = k14_qc_lang1(B,C) & m1_subset_1(C,k8_qc_lang1))) <-> k20_qc_lang1(A) = B)))))) # label(d26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.90 7424 (all 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))))))) & (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)) -> (all C (m2_finseq_1(C,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__2,np__0)),B),C),A)))))) & (all B (m2_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) & 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]. 83.38/80.90 7425 (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]. 83.38/80.90 7426 $T # label(t40_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.90 7427 (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]. 83.38/80.90 7428 (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]. 83.38/80.90 7429 (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]. 83.38/80.90 7430 $T # label(t31_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.90 7431 p1_s1_qc_lang1(k11_qc_lang1) & (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))))))) & (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]. 83.38/80.91 7432 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> ((exists C ((exists D ((exists E (m1_qc_lang1(E,C) & B = E & k9_qc_lang1(D,E) = A)) & m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(C)))) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> k16_qc_lang1(A) = B)))))) # label(d22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7433 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (k3_finseq_1(B) = k6_qc_lang1(A) -> k7_finseq_1(k12_finseq_1(k5_qc_lang1,A),B) = k9_qc_lang1(A,B)))))) # label(d11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7434 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (A = k12_qc_lang1(B) & m1_subset_1(B,k8_qc_lang1))) <-> v3_qc_lang1(A)))) # label(d18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7435 (all A (m1_subset_1(A,k8_qc_lang1) -> -(v5_qc_lang1(A) & r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k21_qc_lang1(A))))))) # label(t47_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7436 $T # label(t16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7437 $T # label(t3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7438 (all A (m1_subset_1(A,k8_qc_lang1) -> (k24_qc_lang1(A) = k1_xboole_0 <-> v6_qc_lang1(A)))) # label(d30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 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]. 83.38/80.91 7440 $T # label(t41_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7441 (all A (m1_subset_1(A,k8_qc_lang1) -> -(-v4_qc_lang1(A) & -v5_qc_lang1(A) & -v3_qc_lang1(A) & -v2_qc_lang1(A) & k11_qc_lang1 != A))) # label(t33_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7442 (all A (r2_hidden(A,a_0_0_qc_lang1) <-> (exists B exists C (m2_subset_1(B,k1_numbers,k5_numbers) & r1_xreal_0(np__7,B) & k4_tarski(B,C) = A & m2_subset_1(C,k1_numbers,k5_numbers))))) # label(fraenkel_a_0_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7443 $T # label(t17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7444 (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]. 83.38/80.91 7445 (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) -> B = A & F = E & C = D))))))))))))) # label(t21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7446 (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]. 83.38/80.91 7447 (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]. 83.38/80.91 7448 (all A (m1_subset_1(A,k8_qc_lang1) -> k17_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) = k11_qc_lang2(A))) # label(d15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7449 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r3_qc_lang2(B,C) & r3_qc_lang2(A,B) -> r3_qc_lang2(A,C)))))))) # label(t76_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7450 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (B = k15_qc_lang2(A) <-> (all C ((exists D (m1_subset_1(D,k8_qc_lang1) & C = D & r2_qc_lang2(D,A))) <-> r2_hidden(C,B))))))) # label(d23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7451 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> v4_qc_lang2(k7_qc_lang2(A,B,D)) & v4_qc_lang2(k9_qc_lang2(A,B,C,D)))))))))) # label(t38_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7452 (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]. 83.38/80.91 7453 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> k13_qc_lang1(k18_qc_lang1(A),k19_qc_lang1(A)) = A))) # label(t4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 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 (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 & A = F))))))))))))) # label(t28_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7455 (all A all B all C (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(C,k8_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k6_qc_lang2(A,B,C),k8_qc_lang1))) # label(dt_k6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7456 (all A (m1_subset_1(A,k8_qc_lang1) -> (r2_qc_lang2(A,k11_qc_lang1) <-> A = k11_qc_lang1))) # label(t99_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7457 (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(C,D) = k2_qc_lang2(A,B) -> C = A & B = D))))))))) # label(t17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7458 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> k5_qc_lang2(k20_qc_lang1(k17_qc_lang1(A)),k17_qc_lang1(k21_qc_lang1(k17_qc_lang1(A)))) = A))) # label(t56_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7459 (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(D,F,H,B) = k8_qc_lang2(C,E,G,A) -> D = C & F = E & H = G & B = A))))))))))))))))) # label(t27_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7460 (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]. 83.38/80.91 7461 (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) -> C = D & B = A & F = E))))))))))))) # label(t23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7462 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r2_qc_lang2(A,B) & r1_qc_lang2(B,A)))))) # label(t81_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7463 (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]. 83.38/80.91 7464 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> v4_qc_lang1(A) & v2_qc_lang2(k18_qc_lang1(A)) & v2_qc_lang2(k19_qc_lang1(A))))) # label(t51_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7465 (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]. 83.38/80.91 7466 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> k15_qc_lang2(A) = k2_xboole_0(k15_qc_lang2(k17_qc_lang1(A)),k1_tarski(A))))) # label(t117_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7467 (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)) | -r2_qc_lang2(A,B) & -r3_qc_lang2(A,B) & -r1_qc_lang2(A,B)))))))) # label(t120_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7468 $T # label(t34_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7469 (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]. 83.38/80.91 7470 (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]. 83.38/80.91 7471 (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]. 83.38/80.91 7472 (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]. 83.38/80.91 7473 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k13_qc_lang1(A,B) = k13_qc_lang1(C,D) -> A = C & B = D))))))))) # label(t3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7474 (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]. 83.38/80.91 7475 (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]. 83.38/80.91 7476 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(A,k3_qc_lang2(A,B)) & r3_qc_lang2(B,k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(A),k3_qc_lang2(A,B)) & r3_qc_lang2(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B)))))) # label(t94_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7477 (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]. 83.38/80.91 7478 $T # label(t37_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7479 (all A (m1_subset_1(A,k8_qc_lang1) -> k18_qc_lang1(k17_qc_lang1(A)) = k12_qc_lang2(A))) # label(d16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7480 $T # label(t39_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7481 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r3_qc_lang2(A,k13_qc_lang1(B,C)) <-> r2_qc_lang2(A,C) | r2_qc_lang2(A,B)))))))) # label(t89_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7482 $T # label(t36_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7483 $T # label(t41_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7484 (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]. 83.38/80.91 7485 (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]. 83.38/80.91 7486 $T # label(t70_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7487 $T # label(t57_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7488 (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 & k21_qc_lang1(k14_qc_lang1(A,B)) = B)))) # label(t8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7489 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k4_qc_lang2(C,D) = k4_qc_lang2(A,B) -> C = A & D = B))))))))) # label(t18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7490 (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]. 83.38/80.91 7491 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) & r2_qc_lang2(B,A) -> B = A))))) # label(t78_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 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 (m1_subset_1(C,k8_qc_lang1) -> k5_qc_lang2(A,k5_qc_lang2(B,C)) = k7_qc_lang2(A,B,C) & k6_qc_lang2(A,B,C) = k14_qc_lang1(A,k14_qc_lang1(B,C)))))))) # label(t20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7493 (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]. 83.38/80.91 7494 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k18_qc_lang1(k13_qc_lang1(A,B)) = A & k19_qc_lang1(k13_qc_lang1(A,B)) = B)))) # label(t5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7495 (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]. 83.38/80.91 7496 (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]. 83.38/80.91 7497 (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]. 83.38/80.91 7498 (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]. 83.38/80.91 7499 (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]. 83.38/80.91 7500 (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]. 83.38/80.91 7501 (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(A,C) = k14_qc_lang1(B,D) -> C = D & B = A))))))))) # label(t6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7502 $T # label(t15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7503 (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]. 83.38/80.91 7504 (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]. 83.38/80.91 7505 (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(C,E,G,A) = k9_qc_lang2(D,F,H,B) -> C = D & G = H & B = A & E = F))))))))))))))))) # label(t30_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7506 (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]. 83.38/80.91 7507 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(A) -> (k21_qc_lang1(A) = B <-> r1_qc_lang2(B,A))))))) # label(t67_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7508 $T # label(t43_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7509 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(A,B) & r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A)))))))) # label(t71_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7510 (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) -> (r2_qc_lang2(A,k9_qc_lang1(C,D)) <-> k9_qc_lang1(C,D) = A))))))))) # label(t100_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7511 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (A = k2_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1))) & m1_subset_1(B,k8_qc_lang1))) <-> v2_qc_lang2(A)))) # label(d11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7512 (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]. 83.38/80.91 7513 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k2_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7514 (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]. 83.38/80.91 7515 (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]. 83.38/80.91 7516 (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]. 83.38/80.91 7517 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> r2_qc_lang2(A,A))) # label(reflexivity_r2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7518 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) -> A = k2_qc_lang2(k12_qc_lang2(A),k11_qc_lang2(A))))) # label(t54_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7519 (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]. 83.38/80.91 7520 (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]. 83.38/80.91 7521 $T # label(t12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7522 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)))))))))) # label(d9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7523 (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) & 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]. 83.38/80.91 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) -> (k7_qc_lang2(A,B,D) = k5_qc_lang2(C,E) -> E = k5_qc_lang2(B,D) & A = C))))))))))) # label(t24_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7525 (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]. 83.38/80.91 7526 $T # label(t106_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7527 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k5_qc_lang2(A,C) = k5_qc_lang2(B,D) -> A = B & C = D))))))))) # label(t19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7528 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> v5_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(k21_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(A)))) # label(t52_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7529 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (A = B | C = A <-> r1_qc_lang2(A,k13_qc_lang1(B,C))))))))) # label(t62_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7530 (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) -> k7_qc_lang2(B,C,D) = E & A = F))))))))))))) # label(t31_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7531 (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) & r1_qc_lang2(B,C)) & -(r1_qc_lang2(A,B) & r3_qc_lang2(B,C)) & -(r3_qc_lang2(A,B) & r1_qc_lang2(B,C)) & -(r1_qc_lang2(A,B) & r2_qc_lang2(B,C)) & -(r3_qc_lang2(B,C) & r2_qc_lang2(A,B))) -> r3_qc_lang2(A,C)))))))) # label(t83_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7532 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(B,A) & v2_qc_lang1(A)))))) # label(t95_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7533 (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]. 83.38/80.91 7534 (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]. 83.38/80.91 7535 $T # label(t11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7536 (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]. 83.38/80.91 7537 (all A all B all C all D (m1_subset_1(D,k8_qc_lang1) & m1_subset_1(C,k2_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k8_qc_lang2(A,B,C,D),k8_qc_lang1))) # label(dt_k8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7538 (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 & k11_qc_lang2(k2_qc_lang2(A,B)) = B & k13_qc_lang1(A,k12_qc_lang1(B)) = k17_qc_lang1(k2_qc_lang2(A,B)))))) # label(t46_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7539 (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]. 83.38/80.91 7540 (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]. 83.38/80.91 7541 (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]. 83.38/80.91 7542 $T # label(t40_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7543 (all A all B all C (m1_subset_1(C,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k7_qc_lang2(A,B,C),k8_qc_lang1))) # label(dt_k7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7544 $T # label(t35_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7545 (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]. 83.38/80.91 7546 (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]. 83.38/80.91 7547 (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]. 83.38/80.91 7548 (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)))))))) # label(d6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7549 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (A = k3_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1))) & m1_subset_1(B,k8_qc_lang1))) <-> v1_qc_lang2(A)))) # label(d10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7550 (all A (m1_subset_1(A,k8_qc_lang1) -> (r2_qc_lang2(A,k1_qc_lang2) <-> k11_qc_lang1 = A | A = k1_qc_lang2))) # label(t101_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7551 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (B != A & r2_qc_lang2(A,B) <-> r3_qc_lang2(A,B)))))) # label(d22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7552 (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) -> B != k13_qc_lang1(C,A) & k13_qc_lang1(A,C) != B)) & (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> k14_qc_lang1(C,A) != B)) & k12_qc_lang1(A) != B) <-> r1_qc_lang2(A,B)))))) # label(d20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7553 (all A all B all C all D (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(D,k8_qc_lang1) & m1_subset_1(C,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]. 83.38/80.91 7554 (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]. 83.38/80.91 7555 (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]. 83.38/80.91 7556 (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]. 83.38/80.91 7557 $T # label(dt_k15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7558 $T # label(t68_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7559 (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]. 83.38/80.91 7560 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k10_qc_lang2(k3_qc_lang2(A,B)) & k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)) = k17_qc_lang1(k3_qc_lang2(A,B)) & B = k11_qc_lang2(k3_qc_lang2(A,B)))))) # label(t45_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7561 (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]. 83.38/80.91 7562 (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]. 83.38/80.91 7563 (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) -> A = B))))) # label(t1_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7564 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) <-> (exists B ((exists C (m1_subset_1(C,k8_qc_lang1) & k4_qc_lang2(B,C) = A)) & m1_subset_1(B,k8_qc_lang1)))))) # label(d12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7565 (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) & k19_qc_lang1(k4_qc_lang2(A,B)) = k2_qc_lang2(B,A) & B = k14_qc_lang2(k4_qc_lang2(A,B)))))) # label(t47_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7566 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> k4_qc_lang2(k13_qc_lang2(A),k14_qc_lang2(A)) = A))) # label(t55_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7567 (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]. 83.38/80.91 7568 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (B = A <-> r1_qc_lang2(A,k14_qc_lang1(C,B))))))))) # label(t63_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7569 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) & (exists C (A = k5_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1))))) <-> v4_qc_lang2(A)))) # label(d13_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7570 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_tarski(A) = k15_qc_lang2(A) <-> A = k11_qc_lang1 | v2_qc_lang1(A)))) # label(t116_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7571 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> v2_qc_lang2(A) & v3_qc_lang1(A) & v3_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v4_qc_lang1(k17_qc_lang1(A))))) # label(t49_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7572 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_qc_lang2(A,B) & r2_qc_lang2(B,C) -> r2_qc_lang2(A,C)))))))) # label(t77_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7573 (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]. 83.38/80.91 7574 (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]. 83.38/80.91 7575 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(A) -> (k18_qc_lang1(A) = B | k19_qc_lang1(A) = B <-> r1_qc_lang2(B,A))))))) # label(t66_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7576 (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) -> v5_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)) & k20_qc_lang1(k8_qc_lang2(A,B,C,D)) = A)))))))) # label(t33_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7577 (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) & C = k3_finseq_1(D) & A = k1_funct_1(D,np__1) & (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) -> -(r1_qc_lang2(F,G) & k1_funct_1(D,k1_nat_1(E,np__1)) = G & F = k1_funct_1(D,E)))))) & r1_xreal_0(np__1,E)))) & B = k1_funct_1(D,C) & r1_xreal_0(np__1,C) & v1_finseq_1(D))) & m2_subset_1(C,k1_numbers,k5_numbers)))))))) # label(d21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7578 (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) -> k21_qc_lang1(k6_qc_lang2(A,B,C)) = k14_qc_lang1(B,C) & k20_qc_lang1(k6_qc_lang2(A,B,C)) = A & v5_qc_lang1(k6_qc_lang2(A,B,C)))))))) # label(t25_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7579 (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 & A = C))))))))) # label(t16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7580 (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]. 83.38/80.91 7581 (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) -> A = F & B = G & E = k5_qc_lang2(C,D)))))))))))))))) # label(t32_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7582 $T # label(t102_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7583 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k5_qc_lang2(A,B) = k12_qc_lang1(k14_qc_lang1(A,k12_qc_lang1(B))))))) # label(d5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7584 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k13_qc_lang1(A,k12_qc_lang1(B))) = k2_qc_lang2(A,B))))) # label(d2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7585 (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]. 83.38/80.91 7586 (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]. 83.38/80.91 7587 $T # label(t9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.38/80.91 7588 (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) -> (k8_qc_lang2(A,B,C,D) = k6_qc_lang2(F,G,E) -> A = F & B = G & E = k14_qc_lang1(C,D)))))))))))))))) # label(t29_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 7589 $T # label(t44_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 7590 (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]. 83.48/80.94 7591 $T # label(t10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 7592 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(B,A) & v2_qc_lang1(A)))))) # label(t64_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 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) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (k14_qc_lang1(C,E) = k6_qc_lang2(A,B,D) -> A = C & E = k14_qc_lang1(B,D)))))))))))) # label(t22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 7594 (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]. 83.48/80.94 7595 $T # label(d17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 7596 $T # label(t42_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 7597 $T # label(t69_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 7598 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & r1_qc_lang2(B,A)))))) # label(t82_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 7599 (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]. 83.48/80.94 7600 (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(k3_qc_lang2(A,B)))))) # label(t82_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 7601 (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,k2_qc_lang2(A,B)))))))) # label(t59_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 7602 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,f1_s3_qc_lang3) -> ((exists C (m2_relset_1(C,k8_qc_lang1,f1_s3_qc_lang3) & B = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,A) & (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) -> (k11_qc_lang1 = D -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f3_s3_qc_lang3) & (E = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k21_qc_lang1(D)) & v5_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f7_s3_qc_lang3(D,E)) & (v4_qc_lang1(D) & k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k19_qc_lang1(D)) = F & k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k18_qc_lang1(D)) = E -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f6_s3_qc_lang3(E,F)) & (E = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,k17_qc_lang1(D)) & v3_qc_lang1(D) -> f5_s3_qc_lang3(E) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D)) & (v2_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang3,C,D) = f4_s3_qc_lang3(D)))))))) & v1_funct_2(C,k8_qc_lang1,f1_s3_qc_lang3) & v1_funct_1(C))) <-> f2_s3_qc_lang3(A) = B))))) -> f2_s3_qc_lang3(k11_qc_lang1) = f3_s3_qc_lang3 # label(s3_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.94 7603 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,f1_s7_qc_lang3) -> ((exists C (v1_funct_1(C) & v1_funct_2(C,k8_qc_lang1,f1_s7_qc_lang3) & m2_relset_1(C,k8_qc_lang1,f1_s7_qc_lang3) & B = k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,A) & (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,f1_s7_qc_lang3) -> (all F (m1_subset_1(F,f1_s7_qc_lang3) -> (D = k11_qc_lang1 -> f2_s7_qc_lang3 = k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,D)) & (v3_qc_lang1(D) & E = k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,k17_qc_lang1(D)) -> k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,D) = f5_s7_qc_lang3(E)) & (k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,k21_qc_lang1(D)) = E & v5_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,D) = f7_s7_qc_lang3(D,E)) & (v4_qc_lang1(D) & E = k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,k18_qc_lang1(D)) & k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,k19_qc_lang1(D)) = F -> f6_s7_qc_lang3(E,F) = k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,D)) & (v2_qc_lang1(D) -> f4_s7_qc_lang3(D) = k8_funct_2(k8_qc_lang1,f1_s7_qc_lang3,C,D)))))))))) <-> B = f8_s7_qc_lang3(A)))))) & v5_qc_lang1(f3_s7_qc_lang3) -> f8_s7_qc_lang3(f3_s7_qc_lang3) = f7_s7_qc_lang3(f3_s7_qc_lang3,f8_s7_qc_lang3(k21_qc_lang1(f3_s7_qc_lang3))) # label(s7_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7604 $T # label(t4_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7605 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v6_qc_lang1(k5_qc_lang2(A,B)) <-> r1_tarski(k24_qc_lang1(B),k23_qc_lang1(A))))))) # label(t32_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7606 v4_qc_lang1(f8_s6_qc_lang3) & (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,f1_s6_qc_lang3) -> (B = f7_s6_qc_lang3(A) <-> (exists C (v1_funct_1(C) & m2_relset_1(C,k8_qc_lang1,f1_s6_qc_lang3) & B = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,A) & (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,f1_s6_qc_lang3) -> (all F (m1_subset_1(F,f1_s6_qc_lang3) -> (v2_qc_lang1(D) -> f3_s6_qc_lang3(D) = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,D)) & (E = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,k17_qc_lang1(D)) & v3_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,D) = f4_s6_qc_lang3(E)) & (v5_qc_lang1(D) & k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,k21_qc_lang1(D)) = E -> f6_s6_qc_lang3(D,E) = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,D)) & (v4_qc_lang1(D) & F = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,k19_qc_lang1(D)) & E = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,k18_qc_lang1(D)) -> k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,D) = f5_s6_qc_lang3(E,F)) & (D = k11_qc_lang1 -> f2_s6_qc_lang3 = k8_funct_2(k8_qc_lang1,f1_s6_qc_lang3,C,D)))))))) & v1_funct_2(C,k8_qc_lang1,f1_s6_qc_lang3)))))))) -> (all A (m1_subset_1(A,f1_s6_qc_lang3) -> (all B (m1_subset_1(B,f1_s6_qc_lang3) -> (f7_s6_qc_lang3(k19_qc_lang1(f8_s6_qc_lang3)) = B & A = f7_s6_qc_lang3(k18_qc_lang1(f8_s6_qc_lang3)) -> f5_s6_qc_lang3(A,B) = f7_s6_qc_lang3(f8_s6_qc_lang3)))))) # label(s6_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7607 (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]. 83.48/80.97 7608 $T # label(t43_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7609 (all A (m2_subset_1(A,k1_qc_lang1,k3_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> A != B)))) # label(t41_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7610 (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_subset_1(B,k4_qc_lang3(B,k13_qc_lang2(A)),k4_qc_lang3(B,k14_qc_lang2(A))) = k4_qc_lang3(B,A)))))) # label(t60_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7611 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k1_zfmisc_1(k1_qc_lang1)) -> m1_subset_1(k4_qc_lang3(A,B),k1_zfmisc_1(A)))) # label(dt_k4_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7612 (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)) -> (v2_qc_lang1(A) -> a_2_1_qc_lang3(A,B) = k4_qc_lang3(B,A) & k4_qc_lang3(B,A) = k1_qc_lang3(k16_qc_lang1(A),B)))))) # label(t47_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7613 (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]. 83.48/80.97 7614 (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]. 83.48/80.97 7615 (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]. 83.48/80.97 7616 (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)) -> (v2_qc_lang2(A) -> k4_qc_lang3(B,A) = k4_subset_1(B,k4_qc_lang3(B,k12_qc_lang2(A)),k4_qc_lang3(B,k11_qc_lang2(A)))))))) # label(t58_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7617 (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]. 83.48/80.97 7618 (all A (m2_subset_1(A,k1_qc_lang1,k4_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> A != B)))) # label(t42_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7619 (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]. 83.48/80.97 7620 (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_qc_lang3(C,k4_qc_lang2(A,B)) = k4_subset_1(C,k4_qc_lang3(C,A),k4_qc_lang3(C,B)))))))) # label(t61_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7621 (all A all B all C (m2_subset_1(B,k1_numbers,k5_numbers) & m1_qc_lang1(C,B) -> ((exists D (r1_xreal_0(D,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,D),k3_qc_lang1) & r1_xreal_0(np__1,D) & A = k1_funct_1(C,D) & 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]. 83.48/80.97 7622 (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]. 83.48/80.97 7623 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> k4_subset_1(k2_qc_lang1,k24_qc_lang1(k18_qc_lang1(A)),k24_qc_lang1(k19_qc_lang1(A))) = k24_qc_lang1(A)))) # label(t13_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7624 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k24_qc_lang1(k5_qc_lang2(A,B)) = k6_subset_1(k2_qc_lang1,k24_qc_lang1(B),k23_qc_lang1(A)))))) # label(t23_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7625 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k5_qc_lang3(k2_qc_lang2(A,B)) = k4_subset_1(k4_qc_lang1,k5_qc_lang3(A),k5_qc_lang3(B)))))) # label(t72_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7626 $T # label(d1_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7627 (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,k14_qc_lang1(A,B)) = k4_qc_lang3(C,B))))))) # label(t55_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.97 7628 (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]. 83.48/80.98 7629 (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]. 83.48/80.98 7630 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k6_qc_lang3(B) = k6_qc_lang3(k14_qc_lang1(A,B)))))) # label(t81_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.98 7631 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k4_tarski(np__6,A) = k3_qc_lang3(A))) # label(d4_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.98 7632 (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)) = k1_qc_lang3(D,B) & k4_qc_lang3(B,k9_qc_lang1(C,D)) = a_3_0_qc_lang3(A,B,D))))))))) # label(t48_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.98 7633 $T # label(t37_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.98 7634 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> k22_qc_lang1(k16_qc_lang1(A)) = k24_qc_lang1(A)))) # label(t8_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.98 7635 (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,k17_qc_lang1(A)) = k4_qc_lang3(B,A)))))) # label(t49_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.98 7636 (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) -> k24_qc_lang1(k9_qc_lang1(B,C)) = k22_qc_lang1(C))))))) # label(t9_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.98 7637 (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]. 83.48/80.98 7638 (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]. 83.48/80.98 7639 (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]. 83.48/80.98 7640 $T # label(t5_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.98 7641 (all A (m1_subset_1(A,k5_numbers) -> m2_subset_1(k3_qc_lang3(A),k1_qc_lang1,k4_qc_lang1))) # label(dt_k3_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.48/80.98 7642 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,f1_s4_qc_lang3) -> ((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) -> (v5_qc_lang1(D) & E = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k21_qc_lang1(D)) -> k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D) = f8_s4_qc_lang3(D,E)) & (k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k18_qc_lang1(D)) = E & F = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k19_qc_lang1(D)) & v4_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D) = f7_s4_qc_lang3(E,F)) & (E = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,k17_qc_lang1(D)) & v3_qc_lang1(D) -> f6_s4_qc_lang3(E) = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D)) & (v2_qc_lang1(D) -> f5_s4_qc_lang3(D) = k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D)) & (k11_qc_lang1 = D -> k8_funct_2(k8_qc_lang1,f1_s4_qc_lang3,C,D) = f2_s4_qc_lang3))))))) & 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))) <-> B = f3_s4_qc_lang3(A)))))) & v2_qc_lang1(f4_s4_qc_lang3) -> f3_s4_qc_lang3(f4_s4_qc_lang3) = f5_s4_qc_lang3(f4_s4_qc_lang3) # label(s4_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.54/81.00 7643 (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]. 83.54/81.00 7644 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> k24_qc_lang1(k17_qc_lang1(A)) = k24_qc_lang1(A)))) # label(t10_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.54/81.00 7645 (all A (m1_subset_1(A,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(A) -> k4_qc_lang3(A,k1_qc_lang2) = k1_xboole_0)) # label(t51_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.54/81.00 7646 (all A all B (m1_finseq_1(A,k1_qc_lang1) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(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]. 83.54/81.00 7647 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,f1_s5_qc_lang3) -> ((exists C (v1_funct_1(C) & v1_funct_2(C,k8_qc_lang1,f1_s5_qc_lang3) & B = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,A) & (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,f1_s5_qc_lang3) -> (all F (m1_subset_1(F,f1_s5_qc_lang3) -> (D = k11_qc_lang1 -> f2_s5_qc_lang3 = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,D)) & (E = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,k18_qc_lang1(D)) & F = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,k19_qc_lang1(D)) & v4_qc_lang1(D) -> f6_s5_qc_lang3(E,F) = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,D)) & (E = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,k21_qc_lang1(D)) & v5_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,D) = f7_s5_qc_lang3(D,E)) & (k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,k17_qc_lang1(D)) = E & v3_qc_lang1(D) -> f5_s5_qc_lang3(E) = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,D)) & (v2_qc_lang1(D) -> f4_s5_qc_lang3(D) = k8_funct_2(k8_qc_lang1,f1_s5_qc_lang3,C,D)))))))) & m2_relset_1(C,k8_qc_lang1,f1_s5_qc_lang3))) <-> B = f8_s5_qc_lang3(A)))))) & v3_qc_lang1(f3_s5_qc_lang3) -> f5_s5_qc_lang3(f8_s5_qc_lang3(k17_qc_lang1(f3_s5_qc_lang3))) = f8_s5_qc_lang3(f3_s5_qc_lang3) # label(s5_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.54/81.00 7648 (all A (m1_subset_1(A,k8_qc_lang1) -> (v6_qc_lang1(k12_qc_lang1(A)) <-> v6_qc_lang1(A)))) # label(t25_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.54/81.00 7649 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> k24_qc_lang1(A) = k6_subset_1(k2_qc_lang1,k24_qc_lang1(k21_qc_lang1(A)),k23_qc_lang1(k20_qc_lang1(A)))))) # label(t15_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.54/81.00 7650 (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]. 83.54/81.00 7651 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k5_qc_lang3(A),k1_zfmisc_1(k4_qc_lang1)))) # label(dt_k5_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.54/81.00 7652 (all A all B all C (m2_subset_1(B,k1_numbers,k5_numbers) & m1_qc_lang1(C,B) -> ((exists D (m2_subset_1(D,k1_numbers,k5_numbers) & A = k1_funct_1(C,D) & r1_xreal_0(np__1,D) & r1_xreal_0(D,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,D),k4_qc_lang1))) <-> r2_hidden(A,a_2_2_qc_lang3(B,C))))) # label(fraenkel_a_2_2_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.54/81.00 7653 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k6_qc_lang3(A),k1_zfmisc_1(k3_qc_lang1)))) # label(dt_k6_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.54/81.00 7654 (all A all B all C (m2_finseq_1(B,k1_qc_lang1) & m1_subset_1(C,k1_zfmisc_1(k1_qc_lang1)) & -v1_xboole_0(C) -> (r2_hidden(A,a_2_0_qc_lang3(B,C)) <-> (exists D (A = k1_funct_1(B,D) & r2_hidden(k1_funct_1(B,D),C) & r1_xreal_0(D,k3_finseq_1(B)) & r1_xreal_0(np__1,D) & m2_subset_1(D,k1_numbers,k5_numbers)))))) # label(fraenkel_a_2_0_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.54/81.00 7655 $T # label(t45_qc_lang3) # label(axiom) # label(non_clause). [assumption]. 83.54/81.00 7656 (all A (m2_subset_1(A,k1Alarm clock 122.39/120.02 Prover9 interrupted 122.39/120.03 EOF