0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.30 % Computer : n021.cluster.edu 0.10/0.30 % Model : x86_64 x86_64 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.30 % Memory : 8042.1875MB 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.30 % CPULimit : 1200 0.10/0.30 % DateTime : Tue Jul 13 16:22:15 EDT 2021 0.10/0.30 % CPUTime : 87.07/85.14 ============================== Prover9 =============================== 87.07/85.14 Prover9 (32) version 2009-11A, November 2009. 87.07/85.14 Process 17118 was started by sandbox on n021.cluster.edu, 87.07/85.14 Tue Jul 13 16:23:31 2021 87.07/85.14 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_16733_n021.cluster.edu". 87.07/85.14 ============================== end of head =========================== 87.07/85.14 87.07/85.14 ============================== INPUT ================================= 87.07/85.14 87.07/85.14 % Reading from file /tmp/Prover9_16733_n021.cluster.edu 87.07/85.14 87.07/85.14 set(prolog_style_variables). 87.07/85.14 set(auto2). 87.07/85.14 % set(auto2) -> set(auto). 87.07/85.14 % set(auto) -> set(auto_inference). 87.07/85.14 % set(auto) -> set(auto_setup). 87.07/85.14 % set(auto_setup) -> set(predicate_elim). 87.07/85.14 % set(auto_setup) -> assign(eq_defs, unfold). 87.07/85.14 % set(auto) -> set(auto_limits). 87.07/85.14 % set(auto_limits) -> assign(max_weight, "100.000"). 87.07/85.14 % set(auto_limits) -> assign(sos_limit, 20000). 87.07/85.14 % set(auto) -> set(auto_denials). 87.07/85.14 % set(auto) -> set(auto_process). 87.07/85.14 % set(auto2) -> assign(new_constants, 1). 87.07/85.14 % set(auto2) -> assign(fold_denial_max, 3). 87.07/85.14 % set(auto2) -> assign(max_weight, "200.000"). 87.07/85.14 % set(auto2) -> assign(max_hours, 1). 87.07/85.14 % assign(max_hours, 1) -> assign(max_seconds, 3600). 87.07/85.14 % set(auto2) -> assign(max_seconds, 0). 87.07/85.14 % set(auto2) -> assign(max_minutes, 5). 87.07/85.14 % assign(max_minutes, 5) -> assign(max_seconds, 300). 87.07/85.14 % set(auto2) -> set(sort_initial_sos). 87.07/85.14 % set(auto2) -> assign(sos_limit, -1). 87.07/85.14 % set(auto2) -> assign(lrs_ticks, 3000). 87.07/85.14 % set(auto2) -> assign(max_megs, 400). 87.07/85.14 % set(auto2) -> assign(stats, some). 87.07/85.14 % set(auto2) -> clear(echo_input). 87.07/85.14 % set(auto2) -> set(quiet). 87.07/85.14 % set(auto2) -> clear(print_initial_clauses). 87.07/85.14 % set(auto2) -> clear(print_given). 87.07/85.14 assign(lrs_ticks,-1). 87.07/85.14 assign(sos_limit,10000). 87.07/85.14 assign(order,kbo). 87.07/85.14 set(lex_order_vars). 87.07/85.14 clear(print_given). 87.07/85.14 87.07/85.14 % formulas(sos). % not echoed (35644 formulas) 87.07/85.14 87.07/85.14 ============================== end of input ========================== 87.07/85.14 87.07/85.14 % From the command line: assign(max_seconds, 1200). 87.07/85.14 87.07/85.14 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 87.07/85.14 87.07/85.14 % Formulas that are not ordinary clauses: 87.07/85.14 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 2 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 3 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 4 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 5 (all A all B ((all C (A = C <-> r2_hidden(C,B))) <-> B = k1_tarski(A))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 6 (all A all B k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 7 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 8 (all A all B -((all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,C) & r2_hidden(D,B))))) & r2_hidden(A,B))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 9 (all A all B ((all C (r2_hidden(C,B) <-> (exists D (r2_hidden(C,D) & r2_hidden(D,A))))) <-> B = k3_tarski(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 10 (all A exists B ((all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & (all E (r1_tarski(E,C) -> r2_hidden(E,D))))))) & (all C -(-r2_tarski(C,B) & -r2_hidden(C,B) & r1_tarski(C,B))) & (all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & r2_hidden(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 11 (all A all B (r2_tarski(A,B) <-> (exists C ((all D -((all E -(r2_hidden(k4_tarski(E,D),C) & r2_hidden(E,A))) & r2_hidden(D,B))) & (all D all E all F all G (r2_hidden(k4_tarski(F,G),C) & r2_hidden(k4_tarski(D,E),C) -> (D = F <-> E = G))) & (all D -((all E -(r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),C))) & r2_hidden(D,A))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 12 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 13 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 14 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 15 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 16 (all A all B all C (p1_s1_tarski(A,C) & p1_s1_tarski(A,B) -> B = C)) -> (exists A all B ((exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))) <-> r2_hidden(B,A))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 17 (all A all B ((all C (r2_hidden(C,A) -> r2_hidden(C,B))) <-> r1_tarski(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 18 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 19 (all A all B all C ((all D (r2_hidden(D,C) <-> D = B | D = A)) <-> k2_tarski(A,B) = C)) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 20 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 21 (all A all B k2_tarski(B,A) = k2_tarski(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 22 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 23 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 24 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 25 (all A all B k5_xboole_0(B,A) = k5_xboole_0(A,B)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 26 (all A all B ((all C (p1_s3_xboole_0(C) <-> r2_hidden(C,A))) & (all C (p1_s3_xboole_0(C) <-> r2_hidden(C,B))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 27 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 28 (all A ((all B -r2_hidden(B,A)) <-> A = k1_xboole_0)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 29 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f2_s2_xboole_0))) & (all A (r2_hidden(A,f1_s2_xboole_0) <-> p1_s2_xboole_0(A))) -> f1_s2_xboole_0 = f2_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 30 (all A all B all C -(r1_xboole_0(A,B) & r2_hidden(C,k2_xboole_0(A,B)) & -(-r2_hidden(C,A) & r2_hidden(C,B)) & -(r2_hidden(C,A) & -r2_hidden(C,B)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 31 (all A all B (r1_tarski(B,A) | r1_tarski(A,B) <-> r3_xboole_0(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 32 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 33 (all A all B (r1_xboole_0(A,B) <-> k1_xboole_0 = k3_xboole_0(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 34 (all A all B (r1_xboole_0(A,B) -> r1_xboole_0(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 35 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 36 (all A all B (r1_tarski(B,A) & r1_tarski(A,B) <-> A = B)) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 37 (all A all B (r2_xboole_0(A,B) -> -r2_xboole_0(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 38 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 39 (exists A all B (r2_hidden(B,A) <-> r2_hidden(B,f1_s1_xboole_0) & p1_s1_xboole_0(B))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 40 (all A all B all C ((all D ((r2_hidden(D,C) <-> r2_hidden(D,B)) <-> -r2_hidden(D,A))) -> k5_xboole_0(B,C) = A)) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 41 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 42 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 43 (all A (A = k1_xboole_0 <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 44 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 45 (all A all B (r2_xboole_0(A,B) <-> r1_tarski(A,B) & B != A)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 46 (all A all B (-((exists C (r2_hidden(C,B) & r2_hidden(C,A))) & r1_xboole_0(A,B)) & -((all C -(r2_hidden(C,A) & r2_hidden(C,B))) & -r1_xboole_0(A,B)))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 47 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 48 (all A all B k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 49 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 50 (all A all B (-(r1_xboole_0(A,B) & (exists C r2_hidden(C,k3_xboole_0(A,B)))) & -((all C -r2_hidden(C,k3_xboole_0(A,B))) & -r1_xboole_0(A,B)))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 51 (all A all B k3_xboole_0(A,B) = k3_xboole_0(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 52 (all A all B all C (k4_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> -r2_hidden(D,B) & r2_hidden(D,A))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 53 (all A all B (r3_xboole_0(A,B) -> r3_xboole_0(B,A))) # label(symmetry_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 54 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 55 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 56 (all A all B all C ((all D (r2_hidden(D,C) <-> r2_hidden(D,A) | r2_hidden(D,B))) <-> k2_xboole_0(A,B) = C)) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 57 (all A all B all C (k3_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,B) & r2_hidden(D,A))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 58 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 59 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 60 (all A all B all C (-(r2_hidden(A,C) <-> r2_hidden(A,B)) <-> r2_hidden(A,k5_xboole_0(B,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 61 (all A all B -(v1_xboole_0(B) & A != B & v1_xboole_0(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 62 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 63 (all A A = k4_xboole_0(A,k1_xboole_0)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 64 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 65 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 66 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 67 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 68 (all A all B -(v1_xboole_0(B) & r2_hidden(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 69 (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]. 87.07/85.14 70 (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]. 87.07/85.14 71 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 72 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 73 (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]. 87.07/85.14 74 (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]. 87.07/85.14 75 (all A all B (r1_tarski(A,k4_xboole_0(B,A)) -> k1_xboole_0 = A)) # label(t38_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 76 (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]. 87.07/85.14 77 (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]. 87.07/85.14 78 (all A all B all C all D (r1_xboole_0(C,D) & r1_xboole_0(B,D) & r1_xboole_0(A,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 79 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 80 (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]. 87.07/85.14 81 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,C) = k3_xboole_0(A,k2_xboole_0(B,C)))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 82 (all A all B (k1_xboole_0 = k4_xboole_0(A,B) <-> r1_tarski(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 83 (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]. 87.07/85.14 84 (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]. 87.07/85.14 85 (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]. 87.07/85.14 86 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(B,C) & r1_tarski(A,C) -> k1_xboole_0 = A)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 87 (all A all B all C (r1_tarski(A,k5_xboole_0(B,C)) <-> r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 88 (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]. 87.07/85.14 89 (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]. 87.07/85.14 90 (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]. 87.07/85.14 91 (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]. 87.07/85.14 92 (all A (-(-r1_xboole_0(A,A) & A = k1_xboole_0) & -(A != k1_xboole_0 & r1_xboole_0(A,A)))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 93 (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]. 87.07/85.14 94 (all A all B all C k3_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k3_xboole_0(A,B),C)) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 95 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 96 (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]. 87.07/85.14 97 (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]. 87.07/85.14 98 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)))) # label(t9_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 99 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k3_xboole_0(B,C))) # label(t54_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 100 (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]. 87.07/85.14 101 (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]. 87.07/85.14 102 (all A all B (k4_xboole_0(B,A) = k4_xboole_0(A,B) -> A = B)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 103 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),C)) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 104 (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,B) & r1_xboole_0(A,C)))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 105 (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]. 87.07/85.14 106 (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]. 87.07/85.14 107 (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]. 87.07/85.14 108 (all A all B all C k4_xboole_0(A,k2_xboole_0(B,C)) = k4_xboole_0(k4_xboole_0(A,B),C)) # label(t41_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 109 (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]. 87.07/85.14 110 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 111 (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]. 87.07/85.14 112 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,k4_xboole_0(B,A)))) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 113 (all A all B -(r2_xboole_0(A,B) & k4_xboole_0(B,A) = k1_xboole_0)) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 114 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t55_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 115 (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]. 87.07/85.14 116 (all A all B all C k3_xboole_0(k5_xboole_0(A,C),B) = k5_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B))) # label(t112_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 117 (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]. 87.07/85.14 118 (all A all B k2_xboole_0(A,B) = k2_xboole_0(A,k2_xboole_0(A,B))) # label(t6_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 119 (all A all B k4_xboole_0(A,k4_xboole_0(A,B)) = k3_xboole_0(A,B)) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 120 (all A all B -(r2_xboole_0(B,A) & r1_tarski(A,B))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 121 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,B))) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 122 (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]. 87.07/85.14 123 (all A all B all C (k2_xboole_0(A,B) = k2_xboole_0(C,B) & r1_xboole_0(C,B) & r1_xboole_0(A,B) -> A = C)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 124 (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]. 87.07/85.14 125 (all A all B all C all D (r1_xboole_0(C,A) & r1_xboole_0(D,B) & k2_xboole_0(C,D) = k2_xboole_0(A,B) -> C = B)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 126 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t50_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 127 (all A all B all C k4_xboole_0(A,k5_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C))) # label(t102_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 128 (all A all B all C (r1_tarski(A,B) -> k3_xboole_0(k2_xboole_0(A,C),B) = k2_xboole_0(A,k3_xboole_0(C,B)))) # label(t30_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 129 (all A all B all C (r1_xboole_0(A,B) -> k2_xboole_0(k4_xboole_0(C,A),B) = k4_xboole_0(k2_xboole_0(C,B),A))) # label(t87_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 130 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 131 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 132 (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]. 87.07/85.14 133 (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]. 87.07/85.14 134 (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]. 87.07/85.14 135 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 136 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,C) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 137 (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]. 87.07/85.14 138 (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]. 87.07/85.14 139 (all A all B k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 140 (all A all B (r1_xboole_0(A,B) <-> A = k4_xboole_0(A,B))) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 141 (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]. 87.07/85.14 142 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 143 (all A all B all C all D k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D)) # label(t113_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 144 (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]. 87.07/85.14 145 (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]. 87.07/85.14 146 (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]. 87.07/85.14 147 (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]. 87.07/85.14 148 (all A all B all C (-v1_xboole_0(C) -> -(r1_tarski(C,A) & r1_xboole_0(A,B) & r1_tarski(C,B)))) # label(t68_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 149 (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]. 87.07/85.14 150 (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]. 87.07/85.14 151 (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]. 87.07/85.14 152 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 153 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,C))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 154 (all A all B A = k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t51_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 155 (all A all B k2_xboole_0(A,k3_xboole_0(A,B)) = A) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 156 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 157 (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]. 87.07/85.14 158 (all A all B all C -(r1_xboole_0(A,B) & -r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t74_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 159 (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]. 87.07/85.14 160 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) & (all D (r1_tarski(C,D) & r1_tarski(A,D) -> r1_tarski(B,D))) -> B = k2_xboole_0(A,C))) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 161 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 162 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 163 (all A all B (k1_xboole_0 = k2_xboole_0(A,B) -> k1_xboole_0 = A)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 164 (all A all B A = k3_xboole_0(A,k2_xboole_0(A,B))) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 165 (all A all B (-(-r2_xboole_0(A,B) & -r2_xboole_0(B,A) & A != B) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 166 (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]. 87.07/85.14 167 (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]. 87.07/85.14 168 (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]. 87.07/85.14 169 (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]. 87.07/85.14 170 (all A all B all C (r1_tarski(B,C) & r1_tarski(A,B) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 171 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 172 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 173 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B)) = k3_xboole_0(k4_xboole_0(A,C),B)) # label(t111_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 174 (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]. 87.07/85.14 175 (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]. 87.07/85.14 176 (all A (A != k1_xboole_0 -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 177 (all A all B all C k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C))) = k4_xboole_0(k5_xboole_0(A,B),C)) # label(t99_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 178 (all A all B k1_xboole_0 = k4_xboole_0(A,k2_xboole_0(A,B))) # label(t46_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 179 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 180 (all A all B all C ((all D (r1_tarski(D,B) & r1_tarski(D,C) -> r1_tarski(D,A))) & r1_tarski(A,C) & r1_tarski(A,B) -> k3_xboole_0(B,C) = A)) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 181 (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]. 87.07/85.14 182 (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]. 87.07/85.14 183 (all A all B all C all D all E all F all G all H (k5_enumset1(A,B,C,D,E,F,G) = H <-> (all I (r2_hidden(I,H) <-> -(D != I & I != F & I != G & I != E & C != I & I != B & I != A))))) # label(d5_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 184 (all A all B all C all D all E (k2_enumset1(A,B,C,D) = E <-> (all F (-(C != F & F != D & B != F & A != F) <-> r2_hidden(F,E))))) # label(d2_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 185 (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]. 87.07/85.14 186 $T # label(dt_k3_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 187 $T # label(t115_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 188 (all A all B all C all D all E all F all G all H k2_xboole_0(k2_tarski(A,B),k4_enumset1(C,D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t63_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 189 $T # label(t28_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 190 (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]. 87.07/85.14 191 $T # label(t39_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 192 (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]. 87.07/85.14 193 (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]. 87.07/85.14 194 $T # label(t18_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 195 (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]. 87.07/85.14 196 $T # label(t24_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 197 (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]. 87.07/85.14 198 (all A all B all C all D all E all F all G all H all I (k6_enumset1(A,B,C,D,E,F,G,H) = I <-> (all J (-(B != J & J != H & J != G & J != F & E != J & J != D & J != C & J != A) <-> r2_hidden(J,I))))) # label(d6_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 199 (all A all B all C all D all E k2_xboole_0(k2_tarski(A,B),k1_enumset1(C,D,E)) = k3_enumset1(A,B,C,D,E)) # label(t48_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 200 (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]. 87.07/85.14 201 $T # label(dt_k2_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 202 (all A all B all C k1_enumset1(A,B,C) = k2_enumset1(A,A,B,C)) # label(t71_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 203 $T # label(t27_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 204 $T # label(t22_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 205 (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]. 87.07/85.14 206 $T # label(t36_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 207 (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]. 87.07/85.14 208 (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]. 87.07/85.14 209 $T # label(t7_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 210 $T # label(t3_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 211 $T # label(t121_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 212 (all A all B all C all D all E all F all G (G = k4_enumset1(A,B,C,D,E,F) <-> (all H (r2_hidden(H,G) <-> -(A != H & H != D & F != H & E != H & C != H & H != B))))) # label(d4_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 213 $T # label(t10_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 214 (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]. 87.07/85.14 215 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k1_tarski(A),k1_enumset1(B,C,D))) # label(t44_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 216 (all A all B all C all D k2_enumset1(D,B,C,A) = k2_enumset1(A,B,C,D)) # label(t123_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 217 (all A all B all C all D k2_enumset1(B,C,A,D) = k2_enumset1(A,B,C,D)) # label(t110_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 218 $T # label(t37_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 219 (all A all B all C all D k2_enumset1(B,D,C,A) = k2_enumset1(A,B,C,D)) # label(t113_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 220 (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]. 87.07/85.14 221 $T # label(t20_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 222 $T # label(t38_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 223 $T # label(t14_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 224 (all A k1_tarski(A) = k3_enumset1(A,A,A,A,A)) # label(t87_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 225 $T # label(t5_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 226 (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]. 87.07/85.14 227 $T # label(t17_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 228 $T # label(t26_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 229 (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]. 87.07/85.14 230 $T # label(t35_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 231 (all A all B all C all D k3_enumset1(A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t72_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 232 (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]. 87.07/85.14 233 (all A all B all C all D all E all F all G all H k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_enumset1(F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t66_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 234 $T # label(t16_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 235 (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]. 87.07/85.14 236 $T # label(t21_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 237 (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]. 87.07/85.14 238 $T # label(dt_k5_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 239 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_tarski(A),k3_enumset1(B,C,D,E,F))) # label(t51_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 240 (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]. 87.07/85.14 241 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 242 (all A k1_tarski(A) = k2_enumset1(A,A,A,A)) # label(t82_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 243 $T # label(t101_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 244 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k5_enumset1(A,B,C,D,E,F,G),k1_tarski(H))) # label(t68_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 245 $T # label(t33_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 246 (all A all B all C k4_enumset1(A,A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t84_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 247 (all A all B k2_tarski(A,B) = k4_enumset1(A,A,A,A,A,B)) # label(t88_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 248 $T # label(t6_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 249 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G))) # label(t61_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 250 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_enumset1(A,B,C,D),k2_tarski(E,F))) # label(t54_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 251 $T # label(t29_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 252 (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]. 87.07/85.14 253 $T # label(t11_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 254 (all A k1_tarski(A) = k1_enumset1(A,A,A)) # label(t76_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 255 $T # label(t32_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 256 (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]. 87.07/85.14 257 (all A k6_enumset1(A,A,A,A,A,A,A,A) = k1_tarski(A)) # label(t96_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 258 $T # label(t19_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 259 $T # label(t97_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 260 (all A k2_tarski(A,A) = k1_tarski(A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 261 (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]. 87.07/85.14 262 (all A all B all C k1_enumset1(C,B,A) = k1_enumset1(A,B,C)) # label(t102_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 263 (all A k1_tarski(A) = k5_enumset1(A,A,A,A,A,A,A)) # label(t94_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 264 (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]. 87.07/85.14 265 (all A all B all C all D k2_enumset1(A,C,B,D) = k2_enumset1(A,B,C,D)) # label(t104_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 266 (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]. 87.07/85.14 267 $T # label(t120_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.14 268 (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]. 87.07/85.15 269 $T # label(t9_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 270 $T # label(t13_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 271 (all A all B all C all D k2_enumset1(A,D,C,B) = k2_enumset1(A,B,C,D)) # label(t107_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 272 (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]. 87.07/85.15 273 (all A all B k2_tarski(A,B) = k3_enumset1(A,A,A,A,B)) # label(t83_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 274 (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]. 87.07/85.15 275 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k5_enumset1(A,A,A,B,C,D,E)) # label(t80_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 276 $T # label(t30_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 277 $T # label(t1_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 278 (all A all B all C k2_xboole_0(k2_tarski(A,B),k1_tarski(C)) = k1_enumset1(A,B,C)) # label(t43_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 279 (all A all B k2_enumset1(A,A,A,B) = k2_tarski(A,B)) # label(t77_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 280 (all A all B all C all D all E all F all G all H k2_xboole_0(k1_tarski(A),k5_enumset1(B,C,D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t62_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 281 (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]. 87.07/85.15 282 $T # label(t124_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 283 (all A all B all C all D all E all F ((all G (-(G != A & B != G & G != C & D != G & G != E) <-> r2_hidden(G,F))) <-> k3_enumset1(A,B,C,D,E) = F)) # label(d3_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 284 (all A all B k2_tarski(A,B) = k1_enumset1(A,A,B)) # label(t70_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 285 $T # label(dt_k4_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 286 (all A all B all C all D (k1_enumset1(A,B,C) = D <-> (all E (r2_hidden(E,D) <-> -(E != C & E != B & E != A))))) # label(d1_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 287 (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]. 87.07/85.15 288 (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]. 87.07/85.15 289 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k4_enumset1(A,A,B,C,D,E)) # label(t73_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 290 $T # label(t2_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 291 $T # label(t15_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 292 (all A all B all C all D k2_enumset1(A,B,C,D) = k4_enumset1(A,A,A,B,C,D)) # label(t79_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 293 $T # label(dt_k6_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 294 $T # label(t34_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 295 $T # label(t8_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 296 (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]. 87.07/85.15 297 $T # label(t25_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 298 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E))) # label(t49_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 299 (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]. 87.07/85.15 300 $T # label(t23_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 301 (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]. 87.07/85.15 302 (all A k1_tarski(A) = k4_enumset1(A,A,A,A,A,A)) # label(t91_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 303 (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]. 87.07/85.15 304 $T # label(t4_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 305 (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]. 87.07/85.15 306 (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]. 87.07/85.15 307 $T # label(t12_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 308 $T # label(t122_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 309 $T # label(t31_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 310 (all A all B all C all D all E all F all G k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_tarski(F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t60_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 311 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(C,B,D,A)) # label(t117_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 312 (all A all B all C all D all E k2_xboole_0(k1_tarski(A),k2_enumset1(B,C,D,E)) = k3_enumset1(A,B,C,D,E)) # label(t47_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 313 (all A all B all C all D k2_enumset1(B,D,A,C) = k2_enumset1(A,B,C,D)) # label(t112_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 314 (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]. 87.07/85.15 315 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_tarski(A,B),k3_enumset1(C,D,E,F,G))) # label(t57_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 316 $T # label(t40_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 317 $T # label(t114_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 318 $T # label(t106_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 319 (all A all B all C all D k2_xboole_0(k1_enumset1(A,B,C),k1_tarski(D)) = k2_enumset1(A,B,C,D)) # label(t46_enumset1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 320 (all A all B all C all D (k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B) -> A = k1_xboole_0 | k1_xboole_0 = B | B = D & C = A)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 321 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k3_zfmisc_1(A,B,C),D)) # label(d4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 322 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 | k1_tarski(A) = k4_xboole_0(k1_tarski(A),B))) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 323 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 324 (all A all B k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 325 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 326 (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]. 87.07/85.15 327 (all A all B -((all C -(B != C & r2_hidden(C,A))) & k1_xboole_0 != A & A != k1_tarski(B))) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 328 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 329 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 330 (all A all B (A = k1_tarski(B) | k1_xboole_0 = A <-> r1_tarski(A,k1_tarski(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 331 (all A all B (A = k1_xboole_0 | k1_xboole_0 = B <-> k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 332 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 333 (all A all B all C -((all D all E k4_tarski(D,E) != A) & r2_hidden(A,k2_zfmisc_1(B,C)))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 334 (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]. 87.07/85.15 335 (all A all B k3_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_tarski(A)) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 336 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 337 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 338 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 339 (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]. 87.07/85.15 340 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 341 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 342 (all A all B all C -(k2_tarski(A,B) != k4_xboole_0(k2_tarski(A,B),C) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C) & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k1_xboole_0 != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 343 (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]. 87.07/85.15 344 (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]. 87.07/85.15 345 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 346 (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]. 87.07/85.15 347 (all A all B all C -(-r2_hidden(A,B) & -r2_hidden(C,B) & -r1_xboole_0(k2_tarski(A,C),B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 348 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 349 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> k2_tarski(A,C) = k3_xboole_0(k2_tarski(A,C),B))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 350 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 351 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 352 (all A all B (r1_xboole_0(k1_tarski(A),B) | k1_tarski(A) = k3_xboole_0(k1_tarski(A),B))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 353 (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]. 87.07/85.15 354 (all A all B ((all C all D (r2_hidden(D,k2_xboole_0(A,B)) & r2_hidden(C,k2_xboole_0(A,B)) -> D = C | r1_xboole_0(C,D))) -> k3_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k3_xboole_0(A,B)))) # label(t101_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 355 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 356 (all A all B all C -(r1_tarski(k1_tarski(A),k2_tarski(B,C)) & C != A & A != B)) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 357 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <-> r2_hidden(A,C) & r2_hidden(B,D))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 358 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> A = B)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 359 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)))) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 360 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(A != k1_xboole_0 & A != k2_tarski(B,C) & A != k1_tarski(C) & A != k1_tarski(B)))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 361 (all A all B k4_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_xboole_0) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 362 (all A all B all C (k2_zfmisc_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 363 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 364 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 365 (all A all B all C -(B != C & B != k1_xboole_0 & k1_xboole_0 != C & k1_tarski(A) = k2_xboole_0(B,C))) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 366 (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]. 87.07/85.15 367 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(B,C)) & r2_hidden(A,k2_zfmisc_1(D,E)) -> r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))))) # label(t137_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 368 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 369 (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]. 87.07/85.15 370 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A))) & (all C -(r2_hidden(C,B) & (all D all E k4_tarski(D,E) != C))) & (all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,A))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 371 (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]. 87.07/85.15 372 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 373 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 374 (all A all B all C -(-r1_tarski(B,C) & (r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C))) & k1_xboole_0 != A)) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 375 (all A all B all C (r2_hidden(A,C) & r2_hidden(B,C) <-> r1_tarski(k2_tarski(A,B),C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 376 (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]. 87.07/85.15 377 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))) <-> r2_hidden(A,C) & B = D)) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 378 (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]. 87.07/85.15 379 (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]. 87.07/85.15 380 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 <-> r2_hidden(A,B))) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 381 (all A A = k3_tarski(k1_tarski(A))) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 382 (all A all B all C all D all E -((all F all G -(k4_tarski(F,G) = A & r2_hidden(G,k3_xboole_0(C,E)) & r2_hidden(F,k3_xboole_0(B,D)))) & r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 383 (all A all B all C all D -(C != A & A != D & k2_tarski(C,D) = k2_tarski(A,B))) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 384 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 385 (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]. 87.07/85.15 386 (all A all B all C -(-(k1_xboole_0 = C & k1_tarski(A) = B) & -(k1_tarski(A) = C & k1_xboole_0 = B) & -(k1_tarski(A) = B & C = k1_tarski(A)) & k2_xboole_0(B,C) = k1_tarski(A))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 387 (all A all B k2_xboole_0(A,B) = k3_tarski(k2_tarski(A,B))) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 388 (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]. 87.07/85.15 389 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 390 (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]. 87.07/85.15 391 (all A all B all C (k2_zfmisc_1(C,k2_tarski(A,B)) = k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) & k2_zfmisc_1(k2_tarski(A,B),C) = k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 392 (all A all B all C k1_xboole_0 != k2_xboole_0(k2_tarski(A,B),C)) # label(t50_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 393 (all A all B (r2_hidden(A,B) -> k1_tarski(A) = k3_xboole_0(B,k1_tarski(A)))) # label(t52_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 394 (all A all B k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t14_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 395 (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]. 87.07/85.15 396 (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]. 87.07/85.15 397 (all A all B all C (k2_zfmisc_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) = k2_zfmisc_1(k4_xboole_0(A,B),C))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 398 (all A all B (k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> A = B)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 399 (all A all B (B != A -> k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 400 (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]. 87.07/85.15 401 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 402 (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]. 87.07/85.15 403 (all A all B all C (k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0 <-> -(k2_tarski(B,C) != A & A != k1_tarski(C) & A != k1_tarski(B) & k1_xboole_0 != A))) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 404 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 405 (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]. 87.07/85.15 406 (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]. 87.07/85.15 407 (all A all B (k2_zfmisc_1(A,B) = k2_zfmisc_1(B,A) -> k1_xboole_0 = B | A = B | k1_xboole_0 = A)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 408 (all A all B all C all D (D = B & C = A <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))))) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 409 (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]. 87.07/85.15 410 (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]. 87.07/85.15 411 (all A all B (r1_tarski(A,k2_zfmisc_1(B,A)) | r1_tarski(A,k2_zfmisc_1(A,B)) -> k1_xboole_0 = A)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 412 (all A all B all C (-r2_hidden(B,C) & -r2_hidden(A,C) <-> k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 413 (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]. 87.07/85.15 414 (all A all B (k1_tarski(B) = k3_xboole_0(A,k1_tarski(B)) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 415 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 416 (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]. 87.07/85.15 417 (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]. 87.07/85.15 418 (all A all B all C all D (r1_xboole_0(A,B) | r1_xboole_0(C,D) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 419 (all A all B all C all D -(A != C & A != D & r1_tarski(k2_tarski(A,B),k2_tarski(C,D)))) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 420 (all A all B (k1_zfmisc_1(A) = B <-> (all C (r1_tarski(C,A) <-> r2_hidden(C,B))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 421 (all A all B all C all D all E all F (r1_tarski(A,k2_zfmisc_1(B,C)) & (all G all H (r2_hidden(k4_tarski(G,H),A) <-> r2_hidden(k4_tarski(G,H),D))) & r1_tarski(D,k2_zfmisc_1(E,F)) -> D = A)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 422 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> A = k1_xboole_0)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 423 (all A all B all C (k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0 <-> r2_hidden(A,C) & r2_hidden(B,C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 424 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 425 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 426 (all A all B all C k2_zfmisc_1(k2_zfmisc_1(A,B),C) = k3_zfmisc_1(A,B,C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 427 (all A all B all C -(r2_hidden(B,C) & B != A & k1_tarski(A) = k3_xboole_0(k2_tarski(A,B),C))) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 428 (all A all B all C (r2_hidden(A,B) -> r2_hidden(C,B) & A != C | k1_tarski(A) = k3_xboole_0(k2_tarski(A,C),B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 429 (all A all B all C all D k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 430 (all A all B all C (r2_hidden(A,B) & A != C <-> r2_hidden(A,k4_xboole_0(B,k1_tarski(C))))) # label(t64_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 431 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 432 (all A all B -(k1_xboole_0 = k4_xboole_0(A,k1_tarski(B)) & A != k1_xboole_0 & A != k1_tarski(B))) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 433 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 434 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> B = k2_xboole_0(k2_tarski(A,C),B))) # label(t48_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 435 (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]. 87.07/85.15 436 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 437 (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]. 87.07/85.15 438 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 439 (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]. 87.07/85.15 440 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 441 (all A all B all C all D -(r2_hidden(D,A) & (all E all F -(r2_hidden(E,B) & D = k4_tarski(E,F) & r2_hidden(F,C))) & r1_tarski(A,k2_zfmisc_1(B,C)))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 442 (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]. 87.07/85.15 443 (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]. 87.07/85.15 444 (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]. 87.07/85.15 445 (all A exists B ((all C -(-r2_tarski(C,B) & -r2_hidden(C,B) & r1_tarski(C,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & (all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & r2_hidden(A,B))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 446 (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]. 87.07/85.15 447 (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]. 87.07/85.15 448 (all A all B all C ((B = A | r2_hidden(B,C)) & -r2_hidden(A,C) <-> k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),C))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 449 (all A all B all C (k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 450 (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]. 87.07/85.15 451 (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]. 87.07/85.15 452 (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]. 87.07/85.15 453 (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]. 87.07/85.15 454 (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]. 87.07/85.15 455 (all A all B (A != k1_xboole_0 -> k1_xboole_0 != k2_zfmisc_1(k1_tarski(B),A) & k1_xboole_0 != k2_zfmisc_1(A,k1_tarski(B)))) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 456 (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]. 87.07/85.15 457 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 458 (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]. 87.07/85.15 459 (all A all B -(A = B & r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 460 (all A all B all C all D (k4_tarski(C,D) = k4_tarski(A,B) -> A = C & D = B)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 461 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 462 (all A all B all C (k2_zfmisc_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & k4_tarski(E,F) = D & r2_hidden(F,B))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 463 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 464 (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]. 87.07/85.15 465 (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]. 87.07/85.15 466 (all A all B (k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k2_xboole_0(A,B)) -> r3_xboole_0(A,B))) # label(t82_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 467 (all A all B (k1_tarski(A) = k3_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 468 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 469 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 470 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k5_subset_1(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 471 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 472 (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]. 87.07/85.15 473 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m1_subset_1(C,B) <-> m2_subset_1(C,A,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 474 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 475 (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]. 87.07/85.15 476 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 477 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_xboole_0(D,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 478 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 479 (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]. 87.07/85.15 480 (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]. 87.07/85.15 481 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 482 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 483 (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]. 87.07/85.15 484 (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]. 87.07/85.15 485 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) | r2_hidden(E,D) <-> r2_hidden(E,B)))) -> B = k4_subset_1(A,C,D)))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 486 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,k3_subset_1(A,C)) <-> r1_tarski(B,C)))))) # label(t44_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 487 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 488 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 489 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f3_s4_subset_1) <-> p1_s4_subset_1(A)))) & (all A (m1_subset_1(A,f1_s4_subset_1) -> (p1_s4_subset_1(A) <-> r2_hidden(A,f2_s4_subset_1)))) -> f2_s4_subset_1 = f3_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 490 (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]. 87.07/85.15 491 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 492 (all A all B (m1_subset_1(B,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 493 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 494 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,D) & r2_hidden(E,C)))) -> B = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 495 (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]. 87.07/85.15 496 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),C) = k3_subset_1(A,k6_subset_1(A,B,C)))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 497 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_xboole_0(B,C) = k6_subset_1(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 498 (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]. 87.07/85.15 499 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) & -r2_hidden(E,D) <-> r2_hidden(E,B)))) -> k6_subset_1(A,C,D) = B))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 500 (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]. 87.07/85.15 501 (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]. 87.07/85.15 502 (all A k1_xboole_0 = k1_subset_1(A)) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 503 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,k3_subset_1(A,B)) = k2_subset_1(A))) # label(t25_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 504 (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]. 87.07/85.15 505 (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]. 87.07/85.15 506 (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]. 87.07/85.15 507 (all A all B ((v1_xboole_0(A) -> (m1_subset_1(B,A) <-> v1_xboole_0(B))) & (-v1_xboole_0(A) -> (m1_subset_1(B,A) <-> r2_hidden(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 508 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k4_subset_1(A,B,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 509 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),B) <-> k2_subset_1(A) = B))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 510 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (k1_xboole_0 != A -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 511 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k5_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 512 (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]. 87.07/85.15 513 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -(r2_hidden(E,D) <-> r2_hidden(E,C))))) -> B = k7_subset_1(A,C,D)))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 514 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 515 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 516 (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]. 87.07/85.15 517 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 518 (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]. 87.07/85.15 519 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 520 (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]. 87.07/85.15 521 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 522 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 523 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 524 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 525 (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]. 87.07/85.15 526 (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]. 87.07/85.15 527 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 528 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 529 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 530 (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]. 87.07/85.15 531 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 532 (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]. 87.07/85.15 533 (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]. 87.07/85.15 534 (all A k3_subset_1(A,k2_subset_1(A)) = k1_subset_1(A)) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 535 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 536 (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]. 87.07/85.15 537 (all A (v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 538 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (A != k1_xboole_0 -> m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A))))))) # label(t56_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 539 (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]. 87.07/85.15 540 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k7_subset_1(A,C,B))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 541 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 542 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 543 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 544 (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]. 87.07/85.15 545 (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]. 87.07/85.15 546 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 547 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,B) -> r2_hidden(D,C))) -> r1_tarski(B,C)))))) # label(t48_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 548 (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]. 87.07/85.15 549 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 550 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 551 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) & r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) -> k3_subset_1(A,C) = B))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 552 (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]. 87.07/85.15 553 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) -> r2_hidden(D,C)))) -> r1_tarski(B,C)))))) # label(t7_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 554 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,k3_subset_1(A,C)) = k6_subset_1(A,B,C))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 555 (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]. 87.07/85.15 556 (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]. 87.07/85.15 557 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 558 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 559 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 560 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,k3_subset_1(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 561 (all A (-$T -> (all B (m1_subset_1(B,A) -> k8_subset_1(A) = B)))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 562 (all A (m1_subset_1(A,k1_zfmisc_1(f1_s2_subset_1)) -> (all B (m1_subset_1(B,k1_zfmisc_1(f1_s2_subset_1)) -> ((all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,B)))) & (all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,A)))) -> B = A))))) # label(s2_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 563 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 564 (all A exists B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 565 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 566 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 567 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k1_xboole_0 != A -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 568 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) <-> r1_xboole_0(B,C)))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 569 (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]. 87.07/85.15 570 (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]. 87.07/85.15 571 (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]. 87.07/85.15 572 (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,A) -> (r2_hidden(D,C) <-> -r2_hidden(D,B)))) -> k3_subset_1(A,C) = B))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 573 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 574 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (k1_subset_1(A) = B <-> r1_tarski(B,k3_subset_1(A,B))))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 575 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 576 (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]. 87.07/85.15 577 (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]. 87.07/85.15 578 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(B,C))) -> r1_tarski(B,k1_setfam_1(A)) | A = k1_xboole_0)) # label(t6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 579 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,A) -> (r2_hidden(B,k8_setfam_1(A,C)) <-> (all D (r2_hidden(D,C) -> r2_hidden(B,D))))))) # label(t58_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 580 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 581 (all A (-v1_xboole_0(A) & v1_setfam_1(A) -> (all B (m1_subset_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.15 582 (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]. 87.07/85.15 583 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = C))))) # label(t44_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 584 (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]. 87.07/85.16 585 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 586 (all A all B all C (C = k2_setfam_1(A,B) <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & r2_hidden(F,B) & D = k2_xboole_0(E,F))))))) # label(d4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 587 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(k7_setfam_1(A,B),C) <-> r1_tarski(B,k7_setfam_1(A,C))))))) # label(t52_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 588 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 589 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 590 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 591 (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]. 87.07/85.16 592 (all A all B all C (r1_setfam_1(C,k2_tarski(A,B)) -> (all D -(r2_hidden(D,C) & -r1_tarski(D,A) & -r1_tarski(D,B))))) # label(t25_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 593 (all A all B all C ((all D (r2_hidden(D,B) -> r1_xboole_0(D,C))) & r1_tarski(C,k3_tarski(k2_xboole_0(A,B))) -> r1_tarski(C,k3_tarski(A)))) # label(t57_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 594 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(k1_xboole_0 != B & k7_setfam_1(A,B) = k1_xboole_0))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 595 (all A all B all C (k3_setfam_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & D = k3_xboole_0(E,F) & r2_hidden(E,A))))))) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 596 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_xboole_0 -> A = k8_setfam_1(A,B)) & (k1_xboole_0 != B -> k8_setfam_1(A,B) = k6_setfam_1(A,B)))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 597 (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]. 87.07/85.16 598 (all A (-r2_hidden(k1_xboole_0,A) <-> v1_setfam_1(A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 599 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 600 (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]. 87.07/85.16 601 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 602 (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]. 87.07/85.16 603 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 604 (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]. 87.07/85.16 605 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 606 (all A all B -(k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 607 (all A all B (r2_setfam_1(B,A) -> k1_xboole_0 = A | r1_tarski(k1_setfam_1(B),k1_setfam_1(A)))) # label(t19_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 608 (all A all B ((A = k1_xboole_0 -> (B = k1_xboole_0 <-> k1_setfam_1(A) = B)) & (A != k1_xboole_0 -> ((all C ((all D (r2_hidden(D,A) -> r2_hidden(C,D))) <-> r2_hidden(C,B))) <-> B = k1_setfam_1(A))))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 609 (all A all B (B != k1_xboole_0 -> k2_xboole_0(A,k1_setfam_1(B)) = k1_setfam_1(k2_setfam_1(k1_tarski(A),B)))) # label(t35_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 610 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,B) = C <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> r2_hidden(k3_subset_1(A,D),B))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 611 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)))) # label(fc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 612 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 613 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 614 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 615 (all A all B (B != k1_xboole_0 -> k1_setfam_1(k4_setfam_1(k1_tarski(A),B)) = k4_xboole_0(A,k3_tarski(B)))) # label(t37_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 616 (all A all B (v1_setfam_1(B) & v1_setfam_1(A) -> v1_setfam_1(k2_xboole_0(A,B)))) # label(fc4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 617 (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]. 87.07/85.16 618 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & D = k4_xboole_0(E,F) & r2_hidden(E,A))))) <-> C = k4_setfam_1(A,B))) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 619 (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]. 87.07/85.16 620 (all A all B (k1_xboole_0 != B -> k4_xboole_0(A,k1_setfam_1(B)) = k3_tarski(k4_setfam_1(k1_tarski(A),B)))) # label(t38_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 621 (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]. 87.07/85.16 622 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 623 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 624 (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]. 87.07/85.16 625 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 626 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 627 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 628 (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]. 87.07/85.16 629 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 630 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 631 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,C) = k7_setfam_1(A,B) -> B = C))))) # label(t53_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 632 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 633 (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]. 87.07/85.16 634 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k6_subset_1(A,k2_subset_1(A),k5_setfam_1(A,B)) = k6_setfam_1(A,k7_setfam_1(A,B))))) # label(t47_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 635 (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]. 87.07/85.16 636 (all A all B ((all C -(r2_hidden(C,A) & (all D -(r2_hidden(D,B) & r1_tarski(C,D))))) <-> r1_setfam_1(A,B))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 637 (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]. 87.07/85.16 638 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 639 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 640 (all A all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> v1_xboole_0(k7_setfam_1(A,B)))) # label(fc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 641 (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]. 87.07/85.16 642 (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]. 87.07/85.16 643 (all A (r1_setfam_1(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 644 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 645 (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]. 87.07/85.16 646 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 647 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 648 (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]. 87.07/85.16 649 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 650 (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]. 87.07/85.16 651 (all A all B k1_setfam_1(k2_tarski(A,B)) = k3_xboole_0(A,B)) # label(t12_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 652 (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]. 87.07/85.16 653 (all A all B ((all C -((all D -(r2_hidden(D,A) & r1_tarski(D,C))) & r2_hidden(C,B))) <-> r2_setfam_1(A,B))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 654 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 655 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (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]. 87.07/85.16 656 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 657 (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]. 87.07/85.16 658 (all A all B k2_setfam_1(A,B) = k2_setfam_1(B,A)) # label(commutativity_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 659 (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]. 87.07/85.16 660 (all A k1_setfam_1(k1_tarski(A)) = A) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 661 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 662 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 663 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k6_setfam_1(A,B) = k1_setfam_1(B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 664 (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]. 87.07/85.16 665 (exists A (-v1_xboole_0(A) & v1_setfam_1(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 666 (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]. 87.07/85.16 667 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | A = k1_xboole_0)) # label(t7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 668 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_tarski(A) -> k1_tarski(k1_xboole_0) = k7_setfam_1(A,B)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 669 (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]. 87.07/85.16 670 (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]. 87.07/85.16 671 (all A all B (r1_tarski(A,B) <-> m1_subset_1(A,k1_zfmisc_1(B)))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 672 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 673 (all A all B (m1_subset_1(A,B) -> r2_hidden(A,B) | v1_xboole_0(B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 674 (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]. 87.07/85.16 675 (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]. 87.07/85.16 676 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 677 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B))))))) # label(t106_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 678 (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]. 87.07/85.16 679 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 680 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k2_relat_1(A)) -> B = k1_xboole_0))))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 681 (all A k1_xboole_0 = k8_relat_1(A,k1_xboole_0)) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 682 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 683 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 684 (all A all B (v1_relat_1(B) -> k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))) = k7_relat_1(B,A))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 685 (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]. 87.07/85.16 686 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 687 (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]. 87.07/85.16 688 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 689 (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]. 87.07/85.16 690 (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]. 87.07/85.16 691 (all A all B (v1_relat_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k7_relat_1(B,A)))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 692 (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]. 87.07/85.16 693 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k8_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(B,k8_relat_1(A,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 694 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 695 (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]. 87.07/85.16 696 (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]. 87.07/85.16 697 (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]. 87.07/85.16 698 (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]. 87.07/85.16 699 (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]. 87.07/85.16 700 (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]. 87.07/85.16 701 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 702 (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]. 87.07/85.16 703 (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]. 87.07/85.16 704 (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]. 87.07/85.16 705 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 706 (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]. 87.07/85.16 707 (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]. 87.07/85.16 708 (all A all B (v1_relat_1(B) -> k3_xboole_0(k2_relat_1(B),A) = k2_relat_1(k8_relat_1(A,B)))) # label(t119_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 709 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k1_relat_1(C) = k1_tarski(A) & k2_relat_1(C) = k1_tarski(B)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 710 (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]. 87.07/85.16 711 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k2_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 712 (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]. 87.07/85.16 713 (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]. 87.07/85.16 714 (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]. 87.07/85.16 715 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 716 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 717 (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]. 87.07/85.16 718 (all A k7_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 719 (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]. 87.07/85.16 720 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 721 (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]. 87.07/85.16 722 (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]. 87.07/85.16 723 (all A all B (v3_relat_1(A) & v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 724 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k7_relat_1(C,B))) <-> r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B)))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 725 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 726 (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]. 87.07/85.16 727 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k5_relat_1(B,k6_relat_1(A)) = B))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 728 (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]. 87.07/85.16 729 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 730 (all A all B (v1_relat_1(B) -> k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)) = k9_relat_1(B,A))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 731 (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]. 87.07/85.16 732 (all A (v1_relat_1(A) -> (all B (r1_xboole_0(B,k1_relat_1(A)) -> k7_relat_1(A,B) = k1_xboole_0)))) # label(t187_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 733 (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]. 87.07/85.16 734 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0))))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 735 (all A (v1_relat_1(A) -> k2_relat_1(A) = k9_relat_1(A,k1_relat_1(A)))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 736 (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]. 87.07/85.16 737 (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]. 87.07/85.16 738 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) <-> k1_relat_1(A) = k1_xboole_0))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 739 (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]. 87.07/85.16 740 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 741 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 742 (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]. 87.07/85.16 743 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t40_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 744 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 745 (exists A (v1_relat_1(A) & v3_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 746 (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]. 87.07/85.16 747 (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]. 87.07/85.16 748 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 749 (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]. 87.07/85.16 750 (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]. 87.07/85.16 751 (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]. 87.07/85.16 752 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 753 (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]. 87.07/85.16 754 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k5_relat_1(A,B)) = k9_relat_1(B,k2_relat_1(A)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 755 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C))))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 756 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (C = k5_relat_1(A,B) <-> (all D all E ((exists F (r2_hidden(k4_tarski(F,E),B) & r2_hidden(k4_tarski(D,F),A))) <-> r2_hidden(k4_tarski(D,E),C)))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 757 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k8_relat_1(B,C))) <-> r2_hidden(A,k2_relat_1(C)) & r2_hidden(A,B)))) # label(t115_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 758 (all A (v1_relat_1(A) -> k5_relat_1(A,k1_xboole_0) = k1_xboole_0 & k1_xboole_0 = k5_relat_1(k1_xboole_0,A))) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 759 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 760 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 761 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k7_relat_1(k5_relat_1(B,C),A) = k5_relat_1(k7_relat_1(B,A),C))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 762 (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]. 87.07/85.16 763 (all A all B (v1_relat_1(B) -> -(-v3_relat_1(k7_relat_1(B,A)) & v3_relat_1(B)))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 764 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 765 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 766 (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]. 87.07/85.16 767 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 768 (all A (v1_relat_1(A) -> (all B all C (k10_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),A))))))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 769 (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]. 87.07/85.16 770 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & r1_tarski(C,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 771 (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]. 87.07/85.16 772 (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]. 87.07/85.16 773 (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]. 87.07/85.16 774 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 775 (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]. 87.07/85.16 776 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,C) = k7_relat_1(A,C) & k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 777 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k4_xboole_0(A,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 778 (all A all B (v1_relat_1(B) -> -((all C -r2_hidden(C,k2_relat_1(B))) & r2_hidden(A,k1_relat_1(B))))) # label(t18_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 779 (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]. 87.07/85.16 780 (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]. 87.07/85.16 781 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 782 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (k8_relat_1(A,B) = C <-> (all D all E (r2_hidden(k4_tarski(D,E),B) & r2_hidden(E,A) <-> r2_hidden(k4_tarski(D,E),C)))))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 783 (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]. 87.07/85.16 784 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k3_relat_1(C) = k2_tarski(A,B)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 785 (all A (v1_relat_1(A) -> k10_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t171_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 786 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 787 (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]. 87.07/85.16 788 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 789 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(D,C),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> k4_relat_1(A) = B))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 790 (all A (v1_relat_1(A) -> k2_relat_1(k4_relat_1(A)) = k1_relat_1(A) & k1_relat_1(k4_relat_1(A)) = k2_relat_1(A))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 791 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k1_relat_1(B) = A & r1_tarski(k2_relat_1(C),A) & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D)) & k5_relat_1(B,D) = k6_relat_1(A) -> C = D))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 792 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 793 (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]. 87.07/85.16 794 (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]. 87.07/85.16 795 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 796 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(B),A) <-> k1_xboole_0 = k9_relat_1(B,A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 797 (all A (v1_relat_1(A) -> A = k8_relat_1(k2_relat_1(A),A))) # label(t126_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 798 (all A (v1_relat_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 799 (all A (v1_relat_1(A) -> A = k4_relat_1(k4_relat_1(A)))) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 800 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k3_xboole_0(A,B),C) = k8_relat_1(A,k8_relat_1(B,C)))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 801 (all A all B all C all D all E (v1_relat_1(E) -> (E = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) -> k2_relat_1(E) = k2_tarski(B,D) & k1_relat_1(E) = k2_tarski(A,C)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 802 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 803 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 804 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 805 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C))))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 806 (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]. 87.07/85.16 807 (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]. 87.07/85.16 808 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 809 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_relat_1(A)) = A)) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 810 (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]. 87.07/85.16 811 (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]. 87.07/85.16 812 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 813 (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]. 87.07/85.16 814 (all A (v1_relat_1(A) <-> (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 815 (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]. 87.07/85.16 816 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)))) # label(t100_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 817 (all A k9_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 818 (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]. 87.07/85.16 819 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 820 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_relat_1(A),k2_relat_1(B)) & r1_tarski(k1_relat_1(A),k1_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 821 (all A all B all C (v1_relat_1(C) -> k8_relat_1(A,k7_relat_1(C,B)) = k7_relat_1(k8_relat_1(A,C),B))) # label(t140_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 822 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 823 (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]. 87.07/85.16 824 (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]. 87.07/85.16 825 (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]. 87.07/85.16 826 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(C,A) & C = D <-> r2_hidden(k4_tarski(C,D),B))) <-> k6_relat_1(A) = B))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 827 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k10_relat_1(A,k1_relat_1(B)) = k1_relat_1(k5_relat_1(A,B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 828 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 829 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 830 (all A all B (v1_relat_1(B) -> k5_relat_1(k6_relat_1(A),B) = k7_relat_1(B,A))) # label(t94_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 831 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> B = k2_relat_1(A))))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 832 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C))) <-> r2_hidden(k4_tarski(A,B),D) & r2_hidden(B,C)))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 833 (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]. 87.07/85.16 834 (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]. 87.07/85.16 835 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k10_relat_1(C,B)) <-> (exists D (r2_hidden(D,k2_relat_1(C)) & r2_hidden(k4_tarski(A,D),C) & r2_hidden(D,B)))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 836 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> A = B))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 837 (all A (v1_xboole_0(A) -> v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 838 (exists A (v1_relat_1(A) & (all B all C (p1_s1_relat_1(B,C) & r2_hidden(C,f2_s1_relat_1) & r2_hidden(B,f1_s1_relat_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 839 (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]. 87.07/85.16 840 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k2_relat_1(k8_relat_1(A,B))))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 841 (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]. 87.07/85.16 842 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t135_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 843 (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]. 87.07/85.16 844 (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]. 87.07/85.16 845 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 846 (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]. 87.07/85.16 847 (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]. 87.07/85.16 848 (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]. 87.07/85.16 849 (all A (v1_relat_1(A) -> A = k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))))) # label(t22_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 850 (all A all B (v1_relat_1(B) -> -(A != k1_xboole_0 & r1_tarski(A,k2_relat_1(B)) & k10_relat_1(B,A) = k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 851 (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]. 87.07/85.16 852 (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]. 87.07/85.16 853 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 854 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 855 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 856 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> r2_hidden(k4_tarski(D,E),A) & r2_hidden(D,B))) <-> k7_relat_1(A,B) = C))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 857 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k3_xboole_0(B,k2_zfmisc_1(k1_relat_1(B),A)))) # label(t124_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 858 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.16 859 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k4_xboole_0(A,B),C))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 860 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) | k1_relat_1(A) = k1_xboole_0 -> A = k1_xboole_0))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 861 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k1_xboole_0 = k5_relat_1(A,B)))))) # label(t67_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 862 (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]. 87.07/85.17 863 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 864 (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]. 87.07/85.17 865 (all A (v1_relat_1(A) -> k8_relat_1(k1_xboole_0,A) = k1_xboole_0)) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 866 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 867 (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]. 87.07/85.17 868 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 869 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 870 (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]. 87.07/85.17 871 (all A (v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D ((exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(E,D),A))) <-> r2_hidden(D,C))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 872 (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]. 87.07/85.17 873 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(A),k1_relat_1(B)) -> k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A)))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 874 (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]. 87.07/85.17 875 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(B),A) <-> k7_relat_1(B,A) = k1_xboole_0))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 876 (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]. 87.07/85.17 877 (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]. 87.07/85.17 878 (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]. 87.07/85.17 879 (all A (v1_xboole_0(A) -> v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 880 (all A all B (v1_relat_1(B) -> k10_relat_1(B,A) = k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 881 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 882 (all A all B (v1_relat_1(B) -> k5_relat_1(B,k6_relat_1(A)) = k8_relat_1(A,B))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 883 (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]. 87.07/85.17 884 (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]. 87.07/85.17 885 (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]. 87.07/85.17 886 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 887 (all A (v1_xboole_0(A) -> v1_xboole_0(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 888 (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]. 87.07/85.17 889 (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]. 87.07/85.17 890 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 891 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 892 (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]. 87.07/85.17 893 (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]. 87.07/85.17 894 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 895 (all A (v1_relat_1(A) -> (all B (k1_relat_1(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 896 (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]. 87.07/85.17 897 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k2_relat_1(k7_relat_1(B,A)))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 898 (all A k10_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 899 (all A all B (v1_relat_1(B) -> -(k9_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & k1_xboole_0 != A))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 900 (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]. 87.07/85.17 901 (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]. 87.07/85.17 902 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(C,k9_relat_1(B,A)) = k9_relat_1(k5_relat_1(B,C),A))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 903 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 904 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k3_xboole_0(A,B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 905 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B) & v2_funct_1(A)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 906 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 907 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)))) -> k5_relat_1(A,B) = C))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 908 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 909 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 910 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 911 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k5_relat_1(C,A) = k5_relat_1(B,A) & k1_relat_1(C) = k1_relat_1(B) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> B = C)))))))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 912 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,k1_relat_1(A)) & r2_hidden(E,B) & k1_funct_1(A,E) = D)))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 913 (all A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 914 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 915 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 916 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 917 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> (D = k1_funct_1(A,C) <-> k1_funct_1(B,D) = C))) & k1_relat_1(B) = k2_relat_1(A) & k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 918 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> A = k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) & A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A)))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 919 (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]. 87.07/85.17 920 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((-r2_hidden(B,k1_relat_1(A)) -> (C = k1_xboole_0 <-> k1_funct_1(A,B) = C)) & (r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> r2_hidden(k4_tarski(B,C),A))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 921 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(A) = B <-> A = k1_relat_1(B) & (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C)))))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 922 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B)))) <-> v3_relat_1(A)))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 923 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 924 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 925 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_funct_1(A)) & v1_relat_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 926 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 927 (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]. 87.07/85.17 928 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 929 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 930 (exists A (v1_relat_1(A) & f1_s4_funct_1 = k1_relat_1(A) & (all B (m1_subset_1(B,f1_s4_funct_1) -> k1_funct_1(A,B) = f2_s4_funct_1(B))) & v1_funct_1(A))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 931 (all A ((all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> D = C)) <-> v1_funct_1(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 932 (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]. 87.07/85.17 933 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A) & k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 934 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k9_relat_1(A,k3_xboole_0(B,C)) = k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 935 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -((all C k1_tarski(C) != k10_relat_1(A,k1_tarski(B))) & r2_hidden(B,k2_relat_1(A)))) <-> v2_funct_1(A)))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 936 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 937 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 938 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 939 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(B,k1_funct_1(C,A)) = k1_funct_1(k5_relat_1(C,B),A)))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 940 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 941 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 942 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k9_relat_1(A,k4_xboole_0(B,C)) = k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 943 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 944 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))) = k3_xboole_0(k9_relat_1(C,A),B))) # label(t150_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 945 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 946 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & k2_relat_1(A) = k1_relat_1(B) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 947 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 948 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 949 (all A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A) -> v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 950 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 951 (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> C = B)) & (all A -((all B -p1_s2_funct_1(A,B)) & r2_hidden(A,f1_s2_funct_1))) -> (exists A (k1_relat_1(A) = f1_s2_funct_1 & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 952 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 953 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & k1_relat_1(A) = k1_relat_1(B) -> B = A))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 954 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k7_relat_1(C,A) = B <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A)))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 955 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & k1_funct_1(C,A) = B <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 956 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 957 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k5_relat_1(k6_relat_1(A),C),B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 958 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(B) & r1_tarski(k2_relat_1(C),A) & B = k5_relat_1(C,B) & v2_funct_1(B) & k1_relat_1(C) = A -> k6_relat_1(A) = C))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 959 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 960 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 961 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 962 (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]. 87.07/85.17 963 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k5_relat_1(k6_relat_1(A),B)))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 964 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 965 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 966 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> k5_relat_1(k2_funct_1(B),k2_funct_1(A)) = k2_funct_1(k5_relat_1(A,B))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 967 (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]. 87.07/85.17 968 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 969 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 970 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k1_relat_1(A) = k2_relat_1(B) & k5_relat_1(B,A) = k6_relat_1(k2_relat_1(A)) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 971 (all A all B -(-(A = k1_xboole_0 & B != k1_xboole_0) & (all C (v1_funct_1(C) & v1_relat_1(C) -> -(k1_relat_1(C) = B & r1_tarski(k2_relat_1(C),A)))))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 972 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A))))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 973 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C (r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,C) = k1_funct_1(A,B) & r2_hidden(C,k1_relat_1(A)) -> B = C)) <-> v2_funct_1(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 974 (all A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A) -> v1_funct_1(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 975 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 976 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(A) = k2_relat_1(k5_relat_1(A,k2_funct_1(A))) & k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A)))))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 977 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 978 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 979 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 980 (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]. 87.07/85.17 981 (all A ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(B) = A & k1_relat_1(C) = A -> C = B))))) -> k1_xboole_0 = A)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 982 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 983 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_relat_1(C) = k1_tarski(A) & k1_tarski(A) = k2_relat_1(B) & k1_relat_1(B) = k1_relat_1(C) -> B = C))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 984 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(A) = k1_relat_1(k2_funct_1(A)) & k2_relat_1(k2_funct_1(A)) = k1_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 985 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) <-> k10_relat_1(B,k1_tarski(A)) != k1_xboole_0))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 986 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k5_relat_1(B,C) = k5_relat_1(B,D) & k1_relat_1(D) = A & k1_relat_1(C) = A -> D = C))))) -> A = k2_relat_1(B)))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 987 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 988 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C all D ((r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C -> r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D) & (r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D -> r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C))) & k2_relat_1(A) = k1_relat_1(B) <-> B = k2_funct_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 989 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 990 (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]. 87.07/85.17 991 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 992 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 993 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))) = k9_relat_1(B,k10_relat_1(B,A)))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 994 (all A (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 995 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k5_relat_1(B,D) = k5_relat_1(B,C) & k1_relat_1(D) = A & k1_relat_1(C) = A & k2_relat_1(B) = A -> C = D))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 996 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k10_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 997 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 998 (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]. 87.07/85.17 999 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1000 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1001 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1002 (all A (A != k1_xboole_0 -> (all B exists C (v1_funct_1(C) & k1_tarski(B) = k2_relat_1(C) & k1_relat_1(C) = A & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1003 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k10_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1004 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1005 (exists A (v1_relat_1(A) & v1_funct_1(A) & v3_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1006 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k3_xboole_0(A,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1007 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1008 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1009 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1010 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A) <-> r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A))))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1011 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_relat_1(A) <-> (all B -(v1_xboole_0(k1_funct_1(A,B)) & r2_hidden(B,k1_relat_1(A))))))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1012 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(C,B) = k1_funct_1(k8_relat_1(A,C),B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1013 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,A),k2_relat_1(B))))) # label(t12_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1014 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & (all D (r2_hidden(D,k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,D),A))) <-> k8_relat_1(A,C) = B))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1015 (all A (v1_funct_1(A) & v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A & k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A)) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1016 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1017 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1018 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1019 (all A all B k5_relat_1(k6_relat_1(B),k6_relat_1(A)) = k6_relat_1(k3_xboole_0(A,B))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1020 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k4_relat_1(A) = k2_funct_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1021 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k2_relat_1(A) & A = k5_relat_1(A,B) -> B = k6_relat_1(k1_relat_1(B))))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1022 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1023 (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]. 87.07/85.17 1024 (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]. 87.07/85.17 1025 (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]. 87.07/85.17 1026 (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]. 87.07/85.17 1027 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) & v2_funct_1(B) -> A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A)))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1028 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) & (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))) -> v1_funct_1(A) & v1_relat_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1029 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1030 (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]. 87.07/85.17 1031 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1032 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1033 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C)) & k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1034 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1035 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(B,k2_relat_1(C)) & r1_tarski(A,k2_relat_1(C)) & k10_relat_1(C,A) = k10_relat_1(C,B) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1036 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1037 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1038 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1039 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1040 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1041 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1042 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,A) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1043 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1044 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_tarski(A) -> k1_tarski(k1_funct_1(B,A)) = k2_relat_1(B)))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1045 (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]. 87.07/85.17 1046 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k10_relat_1(k2_funct_1(B),A) = k9_relat_1(B,A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1047 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1048 (exists A (v1_relat_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> f2_s3_funct_1(B) = k1_funct_1(A,B))) & k1_relat_1(A) = f1_s3_funct_1 & v1_funct_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1049 (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]. 87.07/85.17 1050 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1051 (exists A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1052 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1053 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1054 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k9_relat_1(k2_funct_1(B),A) = k10_relat_1(B,A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1055 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k9_relat_1(B,k10_relat_1(B,A)) = A))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1056 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1057 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1058 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1059 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1060 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (v1_funct_1(B) & k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1061 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1062 (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]. 87.07/85.17 1063 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1064 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),B) <-> r2_hidden(D,C))) <-> C = k10_relat_1(A,B))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1065 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k1_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1066 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1067 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1068 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & r1_tarski(A,k1_relat_1(C)) & v2_funct_1(C) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1069 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (B = k2_relat_1(A) <-> (all C ((exists D (r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D))) <-> r2_hidden(C,B))))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1070 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(k8_relat_1(A,C),B),k9_relat_1(C,B)))) # label(t120_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1071 (all A all B all C (p1_s1_funct_1(A,C) & p1_s1_funct_1(A,B) -> B = C)) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s1_funct_1) & p1_s1_funct_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))) & v1_relat_1(A))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1072 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1073 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1074 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k9_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1075 (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]. 87.07/85.17 1076 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(k5_relat_1(B,A)) = k1_relat_1(B) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1077 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(B,A) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1078 (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]. 87.07/85.17 1079 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,k2_funct_1(A)) & k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1080 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1081 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(C)) -> k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B)) = k9_relat_1(C,k2_tarski(A,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1082 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1083 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1084 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1085 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1086 (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]. 87.07/85.17 1087 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1088 (all A all B (v1_relat_1(B) -> ((all C -(k10_relat_1(B,k1_tarski(C)) = k1_xboole_0 & r2_hidden(C,A))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1089 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) <-> r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A)))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1090 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(C = k1_funct_1(B,D) & r2_hidden(D,k1_relat_1(B)))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1091 (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]. 87.07/85.17 1092 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1093 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1094 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k9_relat_1(k6_relat_1(A),B) = B)) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1095 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) & r1_xboole_0(A,B) -> r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t125_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.17 1096 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1097 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1098 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1099 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1100 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1101 $T # label(t39_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1102 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r1_tarski(B,A) -> v1_funct_1(B) & v1_relat_1(B))))) # label(t6_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1103 $T # label(t63_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1104 $T # label(t21_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1105 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_relat_1(A) & r1_tarski(A,B) -> B = A))))) # label(t9_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1106 $T # label(t60_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1107 (all A (v1_relat_1(A) & v1_funct_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]. 87.07/85.18 1108 (all A all B (v1_funct_1(k1_tarski(k4_tarski(A,B))) & v1_relat_1(k1_tarski(k4_tarski(A,B))))) # label(t15_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1109 $T # label(t7_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1110 (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),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]. 87.07/85.18 1111 $T # label(t72_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1112 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,A),B) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(k4_tarski(A,k1_funct_1(C,A)),k8_relat_1(B,C))))) # label(t67_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1113 $T # label(t78_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1114 (all A all B all C all D ((A = C -> B = D) <-> v1_funct_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) & v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))))) # label(t19_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1115 $T # label(t81_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1116 $T # label(t62_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1117 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(B)) & r1_tarski(B,C) -> k7_relat_1(B,A) = k7_relat_1(C,A)))))) # label(t88_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1118 $T # label(t20_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1119 (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(C,k8_relat_1(A,B)),k5_relat_1(C,B)) & r1_tarski(k5_relat_1(k8_relat_1(A,B),D),k5_relat_1(B,D)))))))) # label(t69_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1120 $T # label(t59_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1121 $T # label(t42_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1122 $T # label(t48_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1123 $T # label(t51_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1124 $T # label(t44_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1125 $T # label(t82_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1126 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_tarski(A) = k1_relat_1(B) -> B = k1_tarski(k4_tarski(A,k1_funct_1(B,A)))))) # label(t18_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1127 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B) <-> r2_hidden(k4_tarski(A,k1_funct_1(C,A)),k7_relat_1(C,B))))) # label(t52_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1128 $T # label(t41_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1129 $T # label(t1_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1130 $T # label(t85_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1131 $T # label(t80_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1132 $T # label(t77_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1133 (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]. 87.07/85.18 1134 $T # label(t61_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1135 $T # label(t70_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1136 $T # label(t73_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1137 (all A (v1_funct_1(A) & v1_relat_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]. 87.07/85.18 1138 $T # label(t40_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1139 $T # label(t58_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1140 $T # label(t86_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1141 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k1_funct_1(C,A),B) & r2_hidden(k4_tarski(A,k1_funct_1(C,A)),C) <-> r2_hidden(A,k10_relat_1(C,B))))) # label(t87_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1142 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) <-> r1_tarski(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)))))))) # label(t8_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1143 (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) -> 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]. 87.07/85.18 1144 $T # label(t50_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1145 $T # label(t75_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1146 $T # label(t74_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1147 $T # label(t83_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1148 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> v1_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]. 87.07/85.18 1149 $T # label(t23_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1150 $T # label(t55_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1151 (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) -> (v2_funct_1(B) & C = k2_xboole_0(A,B) & r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) & v2_funct_1(A) -> v2_funct_1(C)))))))) # label(t37_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1152 $T # label(t14_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1153 $T # label(t84_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1154 $T # label(t17_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1155 $T # label(t65_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1156 $T # label(t66_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1157 $T # label(t57_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1158 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(B)) & k2_xboole_0(D,B) = C -> k1_funct_1(B,A) = k1_funct_1(C,A)))))))) # label(t35_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1159 $T # label(t4_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1160 (all A (v1_funct_1(A) & v1_relat_1(A) -> (k1_xboole_0 = A -> v2_funct_1(A)))) # label(t46_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1161 (all A (v1_funct_1(A) & v1_relat_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]. 87.07/85.18 1162 $T # label(t11_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1163 $T # label(t71_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1164 (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]. 87.07/85.18 1165 $T # label(t24_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1166 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(C,D),A) -> C = B))))) # label(t25_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1167 (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) -> v2_funct_1(A)))))) # label(t26_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1168 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k1_funct_1(C,A) = B))) # label(t16_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1169 $T # label(t76_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1170 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) & r1_tarski(C,B) -> v1_funct_1(k2_xboole_0(A,C)) & v1_relat_1(k2_xboole_0(A,C))))))))) # label(t32_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1171 (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(k2_relat_1(A),k3_xboole_0(k2_relat_1(B),k2_relat_1(C))) & r1_tarski(k1_relat_1(A),k3_xboole_0(k1_relat_1(B),k1_relat_1(C)))))))))) # label(t28_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1172 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> -(k1_funct_1(B,A) != k1_funct_1(D,A) & k1_funct_1(C,A) != k1_funct_1(B,A) & B = k2_xboole_0(C,D) & r2_hidden(A,k1_relat_1(B))))))))) # label(t36_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1173 (all A (v1_relat_1(A) & v1_funct_1(A) -> (k1_xboole_0 = A -> k2_funct_1(A) = k1_xboole_0))) # label(t49_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1174 $T # label(t45_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1175 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C)) & r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B))))))))) # label(t13_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1176 $T # label(t43_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1177 $T # label(t53_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1178 (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) -> (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]. 87.07/85.18 1179 $T # label(t22_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1180 $T # label(t10_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1181 $T # label(t2_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1182 $T # label(t5_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1183 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k7_relat_1(A,k1_tarski(B)) = k1_tarski(k4_tarski(B,k1_funct_1(A,B))))))) # label(t89_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1184 (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) -> (B = k3_xboole_0(C,D) & r2_hidden(A,k1_relat_1(B)) -> 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]. 87.07/85.18 1185 $T # label(t3_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1186 $T # label(t68_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1187 (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) -> (k2_xboole_0(B,C) = A -> k1_relat_1(A) = k2_xboole_0(k1_relat_1(B),k1_relat_1(C)) & 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]. 87.07/85.18 1188 (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) -> (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]. 87.07/85.18 1189 $T # label(t56_grfunc_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1190 (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]. 87.07/85.18 1191 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1192 (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]. 87.07/85.18 1193 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1194 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v3_relat_2(A) & v3_relat_2(B) -> v3_relat_2(k2_xboole_0(A,B)) & v3_relat_2(k3_xboole_0(A,B)) & v3_relat_2(k4_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1195 (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]. 87.07/85.18 1196 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1197 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) <-> (all C all D all E (r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B) -> r2_hidden(k4_tarski(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1198 (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]. 87.07/85.18 1199 (all A (v1_relat_1(A) -> (r2_relat_2(A,k3_relat_1(A)) <-> v2_relat_2(A)))) # label(d10_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1200 (all A (v1_relat_1(A) -> (r1_relat_2(A,k3_relat_1(A)) <-> v1_relat_2(A)))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1201 (all A (v1_relat_1(A) -> (r4_relat_2(A,k3_relat_1(A)) <-> v4_relat_2(A)))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1202 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k2_relat_1(A) = k2_relat_1(k4_relat_1(A)) & k1_relat_1(k4_relat_1(A)) = k1_relat_1(A)))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1203 (all A (v1_relat_1(A) -> (v8_relat_2(A) <-> r8_relat_2(A,k3_relat_1(A))))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1204 (all A (v1_relat_1(A) -> (v7_relat_2(A) -> v6_relat_2(A) & v1_relat_2(A)))) # label(t46_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1205 (all A (v1_relat_1(A) -> (r1_xboole_0(k6_relat_1(k3_relat_1(A)),A) <-> v2_relat_2(A)))) # label(t18_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1206 (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]. 87.07/85.18 1207 (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]. 87.07/85.18 1208 (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]. 87.07/85.18 1209 (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]. 87.07/85.18 1210 (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]. 87.07/85.18 1211 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1212 (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]. 87.07/85.18 1213 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1214 (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]. 87.07/85.18 1215 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1216 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1217 (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]. 87.07/85.18 1218 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1219 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1220 (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]. 87.07/85.18 1221 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1222 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1223 (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]. 87.07/85.18 1224 (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]. 87.07/85.18 1225 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A))) <-> r5_relat_2(A,B))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1226 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1227 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1228 (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]. 87.07/85.18 1229 (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]. 87.07/85.18 1230 (all A (v1_relat_1(A) -> (r3_relat_2(A,k3_relat_1(A)) <-> v3_relat_2(A)))) # label(d11_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1231 (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]. 87.07/85.18 1232 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1233 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1234 (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]. 87.07/85.18 1235 (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]. 87.07/85.18 1236 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(D,B) & C != D & -r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B))) <-> r6_relat_2(A,B))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1237 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v8_relat_2(A) & v8_relat_2(B) -> v8_relat_2(k3_xboole_0(A,B))))))) # label(t43_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1238 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1239 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) <-> (all C all D (r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) -> C = D)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1240 (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]. 87.07/85.18 1241 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) -> r2_hidden(k4_tarski(D,C),A))) <-> r3_relat_2(A,B))))) # label(d3_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1242 (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]. 87.07/85.18 1243 (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]. 87.07/85.18 1244 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1245 (all A (v1_relat_1(A) -> (all B (r7_relat_2(A,B) <-> (all C all D -(-r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B) & r2_hidden(C,B))))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1246 (all A (v1_relat_1(A) -> (r1_tarski(k3_xboole_0(A,k4_relat_1(A)),k6_relat_1(k1_relat_1(A))) <-> v4_relat_2(A)))) # label(t39_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1247 (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]. 87.07/85.18 1248 (all A (v1_relat_1(A) -> (r1_tarski(k6_relat_1(k3_relat_1(A)),A) <-> v1_relat_2(A)))) # label(t17_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1249 (all A (v1_relat_1(A) -> (v7_relat_2(A) <-> r7_relat_2(A,k3_relat_1(A))))) # label(d15_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1250 (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]. 87.07/85.18 1251 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(A) & v5_relat_2(B) -> v5_relat_2(k3_xboole_0(A,B))))))) # label(t37_relat_2) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1252 (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]. 87.07/85.18 1253 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_ordinal1(A,B) <-> r1_tarski(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1254 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1255 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1256 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1257 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1258 (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]. 87.07/85.18 1259 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_ordinal1(k1_relat_1(A)) <-> v5_ordinal1(A)))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1260 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1261 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1262 (all A all B (r2_hidden(A,k1_ordinal1(B)) <-> A = B | r2_hidden(A,B))) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1263 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1264 (all A all B (k1_ordinal1(A) = k1_ordinal1(B) -> B = A)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1265 (all A all B (v3_ordinal1(B) -> -(r1_tarski(A,B) & (all C (v3_ordinal1(C) -> -(r2_hidden(C,A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D))))))) & k1_xboole_0 != A))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1266 (all A -(all B (v3_ordinal1(B) <-> r2_hidden(B,A)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1267 (all A exists B ((all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))) & -r2_hidden(B,A) & v3_ordinal1(B))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1268 (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]. 87.07/85.18 1269 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r1_ordinal1(k1_ordinal1(A),B)))))) # label(t33_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1270 (all A all B all C all D -(r2_hidden(D,A) & r2_hidden(C,D) & r2_hidden(B,C) & r2_hidden(A,B))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1271 (all A all B all C all D all E -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,D) & r2_hidden(E,A) & r2_hidden(D,E))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1272 (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]. 87.07/85.18 1273 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1274 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1275 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1276 (exists A (p1_s1_ordinal1(A) & v3_ordinal1(A))) -> (exists A (v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & p1_s1_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1277 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1278 (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]. 87.07/85.18 1279 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,k1_ordinal1(B)) <-> r1_ordinal1(A,B)))))) # label(t34_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1280 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1281 (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]. 87.07/85.18 1282 (all A (v3_ordinal1(A) <-> v1_ordinal1(A) & v2_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1283 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1284 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1285 (all A ((all B (r2_hidden(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) & v6_ordinal1(A) -> v1_relat_1(k3_tarski(A)) & v5_ordinal1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1286 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1287 (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]. 87.07/85.18 1288 (all A all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (m1_ordinal1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1289 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_tarski(A,B) & r2_hidden(B,C) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1290 (exists A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1291 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r3_xboole_0(B,C))) <-> v6_ordinal1(A))) # label(d9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1292 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1293 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1294 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal1(C) -> (r2_hidden(C,A) & r2_hidden(A,B) -> r2_hidden(C,B)))))))) # label(t19_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1295 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1296 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1297 (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]. 87.07/85.18 1298 (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]. 87.07/85.18 1299 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1300 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(A,B) & B != A & -r2_xboole_0(B,A)))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1301 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1302 (all A (v3_ordinal1(A) -> v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1303 (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]. 87.07/85.18 1304 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1305 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1306 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1307 (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]. 87.07/85.18 1308 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1309 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1310 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1311 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(A,B) | r2_hidden(B,A))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1312 (all A (v2_ordinal1(A) <-> (all B all C -(r2_hidden(B,A) & -r2_hidden(B,C) & C != B & -r2_hidden(C,B) & r2_hidden(C,A))))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1313 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1314 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1315 (all A (v1_xboole_0(A) -> v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1316 (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]. 87.07/85.18 1317 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_hidden(A,B) & A != B & -r2_hidden(B,A)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1318 (all A all B all C all D all E all F -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(F,A) & r2_hidden(C,D))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1319 (all A (v3_ordinal1(A) -> -((all B (v3_ordinal1(B) -> k1_ordinal1(B) != A)) & -v4_ordinal1(A)) & -((exists B (v3_ordinal1(B) & k1_ordinal1(B) = A)) & v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1320 (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]. 87.07/85.18 1321 (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]. 87.07/85.18 1322 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1323 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (all C (v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,f1_s4_ordinal1) & C = k2_ordinal1(A,B) -> f2_s4_ordinal1(C) = k1_funct_1(A,B)))))) & k1_relat_1(A) = f1_s4_ordinal1 & v1_funct_1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1324 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1325 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1326 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1327 (all A (v1_ordinal1(A) <-> (all B (r2_hidden(B,A) -> r1_tarski(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1328 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v2_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v1_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1329 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1330 (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]. 87.07/85.18 1331 k1_relat_1(f3_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & B = k2_ordinal1(f3_s3_ordinal1,A) -> f2_s3_ordinal1(B) = k1_funct_1(f3_s3_ordinal1,A)))))) & k1_relat_1(f4_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f4_s3_ordinal1,A) = B -> f2_s3_ordinal1(B) = k1_funct_1(f4_s3_ordinal1,A)))))) -> f4_s3_ordinal1 = f3_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1332 (all A (A = k3_tarski(A) <-> v4_ordinal1(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1333 (all A all B -(r2_hidden(A,B) & r1_tarski(B,A))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1334 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & A = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> f3_s5_ordinal1(k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & B = f3_s5_ordinal1(C))) <-> f2_s5_ordinal1(A) = B)))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f2_s5_ordinal1(A) = k1_funct_1(f1_s5_ordinal1,A)))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A)) = k1_funct_1(f1_s5_ordinal1,A)))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1335 (all A (v1_relat_1(A) -> r4_wellord1(A,A))) # label(t48_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1336 $T # label(t6_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1337 $T # label(t14_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1338 (all A all B all C all D (v1_relat_1(D) -> (all E (v1_relat_1(E) -> (v2_wellord1(E) & r2_hidden(A,k3_relat_1(D)) & r2_hidden(C,k3_relat_1(E)) & r4_wellord1(D,k2_wellord1(E,k1_wellord1(E,B))) & r4_wellord1(k2_wellord1(D,k1_wellord1(D,A)),k2_wellord1(E,k1_wellord1(E,C))) & r2_hidden(B,k3_relat_1(E)) & v2_wellord1(D) -> 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]. 87.07/85.18 1339 (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]. 87.07/85.18 1340 (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]. 87.07/85.18 1341 (all A all B all C (v1_relat_1(C) -> -(r4_wellord1(k2_wellord1(C,k1_wellord1(C,A)),k2_wellord1(C,k1_wellord1(C,B))) & A != B & r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C)))) # label(t58_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1342 (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]. 87.07/85.18 1343 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & r3_wellord1(A,B,C))) <-> r4_wellord1(A,B)))))) # label(d8_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 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]. 87.07/85.18 1345 (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]. 87.07/85.18 1346 $T # label(t3_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1347 (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]. 87.07/85.18 1348 (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]. 87.07/85.18 1349 $T # label(t56_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1350 (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]. 87.07/85.18 1351 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r4_wellord1(A,k2_wellord1(A,k1_wellord1(A,B))) & r2_hidden(B,k3_relat_1(A))))))) # label(t57_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1352 $T # label(t34_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1353 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) -> (all D all E (r2_hidden(k4_tarski(D,E),A) -> E = D | r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & k1_funct_1(C,E) != k1_funct_1(C,D)))))))))) # label(t45_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1354 (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]. 87.07/85.18 1355 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> k3_relat_1(k2_wellord1(B,k1_wellord1(B,A))) = k1_wellord1(B,A)))) # label(t40_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1356 (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]. 87.07/85.18 1357 $T # label(t4_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1358 (all A (v1_relat_1(A) -> (all B (r1_wellord1(A,B) <-> (all C -(r1_tarski(C,B) & (all D -(r2_hidden(D,C) & r1_xboole_0(k1_wellord1(A,D),C))) & C != k1_xboole_0)))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1359 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(B,k3_relat_1(C)) & (all D (r2_hidden(D,k1_wellord1(C,A)) -> r2_hidden(k4_tarski(D,B),C) & D != B)) & r2_hidden(A,k3_relat_1(C)) -> r2_hidden(k4_tarski(A,B),C)))) # label(t42_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1360 (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]. 87.07/85.18 1361 (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]. 87.07/85.18 1362 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> (all C -(r1_tarski(C,A) & k1_xboole_0 != C & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),B))) & r2_hidden(D,C)))))))) # label(t9_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1363 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1364 (all A (v1_relat_1(A) -> (v2_wellord1(A) <-> v1_relat_2(A) & v6_relat_2(A) & v1_wellord1(A) & v4_relat_2(A) & v8_relat_2(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1365 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k2_wellord1(C,A) = k2_wellord1(k2_wellord1(C,B),A)))) # label(t29_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1366 (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]. 87.07/85.18 1367 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k3_relat_1(B)) & v2_wellord1(B) -> A = k3_relat_1(k2_wellord1(B,A))))) # label(t39_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1368 (all A all B (v1_relat_1(B) -> r2_hidden(A,k3_relat_1(B)) | k1_wellord1(B,A) = k1_xboole_0)) # label(t2_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1369 $T # label(t44_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1370 (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))) & k1_xboole_0 != B))))) # label(t10_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1371 (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]. 87.07/85.18 1372 $T # label(t1_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1373 (all A all B all C (v1_relat_1(C) -> k2_wellord1(k2_wellord1(C,A),B) = k2_wellord1(C,k3_xboole_0(A,B)))) # label(t26_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1374 (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]. 87.07/85.18 1375 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k3_relat_1(A) = k1_relat_1(C) & (all D all E (r2_hidden(D,k3_relat_1(A)) & r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & r2_hidden(E,k3_relat_1(A)) <-> r2_hidden(k4_tarski(D,E),A))) & v2_funct_1(C) & k3_relat_1(B) = k2_relat_1(C) <-> r3_wellord1(A,B,C)))))))) # label(d7_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.18 1376 (all A all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k2_wellord1(B,A)),A) & r1_tarski(k3_relat_1(k2_wellord1(B,A)),k3_relat_1(B)))) # label(t20_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1377 $T # label(t46_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1378 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) -> (-(k3_relat_1(B) != A & (all C -(k1_wellord1(B,C) = A & r2_hidden(C,k3_relat_1(B))))) <-> (all C (r2_hidden(C,A) -> (all D (r2_hidden(k4_tarski(D,C),B) -> r2_hidden(D,A))))))))) # label(t36_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1379 (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) -> D = C)))))))))) # label(t55_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1380 (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(C,B) = k1_wellord1(k2_wellord1(C,k1_wellord1(C,A)),B)))) # label(t35_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1381 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r2_hidden(B,k3_relat_1(A)) & (exists C (r2_hidden(C,k3_relat_1(A)) & -r2_hidden(k4_tarski(C,B),A))) & (all C -((all D -(r2_hidden(D,k3_relat_1(A)) & r2_hidden(k4_tarski(B,D),A) & B != D & -r2_hidden(k4_tarski(C,D),A))) & r2_hidden(k4_tarski(B,C),A) & r2_hidden(C,k3_relat_1(A)))))) | k3_relat_1(A) = k1_xboole_0))) # label(t12_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1382 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_wellord1(A) & r3_wellord1(A,B,C) -> (all D -((all E -(r2_hidden(E,k3_relat_1(B)) & k9_relat_1(C,k1_wellord1(A,D)) = k1_wellord1(B,E))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t60_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1383 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_wellord1(C,B)) <-> r2_hidden(A,C) & r2_hidden(A,k2_zfmisc_1(B,B))))) # label(t16_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1384 (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]. 87.07/85.19 1385 (all A (v1_relat_1(A) -> k2_wellord1(A,k3_relat_1(A)) = A)) # label(t30_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1386 (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) -> D = C | k1_funct_1(B,D) != k1_funct_1(B,C) & r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,D)),A))) & 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]. 87.07/85.19 1387 (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]. 87.07/85.19 1388 (all A (v1_relat_1(A) -> ((all B -(r1_tarski(B,k3_relat_1(A)) & k1_xboole_0 != B & (all C -(r2_hidden(C,B) & r1_xboole_0(k1_wellord1(A,C),B))))) <-> v1_wellord1(A)))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1389 (all A all B (v1_relat_1(B) -> -(r1_tarski(A,k3_relat_1(B)) & v2_wellord1(B) & (all C -(r4_wellord1(k2_wellord1(B,k1_wellord1(B,C)),k2_wellord1(B,A)) & r2_hidden(C,k3_relat_1(B)))) & -r4_wellord1(B,k2_wellord1(B,A))))) # label(t64_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1390 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,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]. 87.07/85.19 1391 (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]. 87.07/85.19 1392 $T # label(t7_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1393 (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]. 87.07/85.19 1394 (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]. 87.07/85.19 1395 (all A (v1_relat_1(A) -> (r2_wellord1(A,k3_relat_1(A)) <-> v2_wellord1(A)))) # label(t8_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1396 (all A (v1_relat_1(A) -> -((all B -((all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A))) & r2_hidden(B,k3_relat_1(A)))) & k1_xboole_0 != k3_relat_1(A) & v2_wellord1(A)))) # label(t11_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1397 (all A (v1_relat_1(A) -> (all B all C (k1_wellord1(A,B) = C <-> (all D (r2_hidden(k4_tarski(D,B),A) & B != D <-> r2_hidden(D,C))))))) # label(d1_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1398 (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]. 87.07/85.19 1399 (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]. 87.07/85.19 1400 (all A all B all C (v1_relat_1(C) -> (r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C) -> (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]. 87.07/85.19 1401 (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) -> (v1_wellord1(A) -> v1_wellord1(B)) & (v4_relat_2(A) -> v4_relat_2(B)) & (v6_relat_2(A) -> v6_relat_2(B)) & (v8_relat_2(A) -> v8_relat_2(B)) & (v1_relat_2(A) -> v1_relat_2(B))))))))) # label(t53_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1402 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) <-> r8_relat_2(A,B) & r6_relat_2(A,B) & r1_wellord1(A,B) & r4_relat_2(A,B) & r1_relat_2(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1403 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> r3_wellord1(B,A,k2_funct_1(C))))))))) # label(t49_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1404 (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]. 87.07/85.19 1405 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_wellord1(A) & r3_wellord1(A,B,C) -> (all D -((all E -(r4_wellord1(k2_wellord1(A,k1_wellord1(A,D)),k2_wellord1(B,k1_wellord1(B,E))) & r2_hidden(E,k3_relat_1(B)))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t61_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1406 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) & v2_wellord1(A) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k3_wellord1(A,B) = C <-> r3_wellord1(A,B,C))))))))) # label(d9_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1407 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> -(v2_wellord1(A) & v2_wellord1(B) & -r4_wellord1(A,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)))))))) # label(t63_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1408 (all A (v1_relat_1(A) -> (v1_wellord1(A) <-> r1_wellord1(A,k3_relat_1(A))))) # label(t5_wellord1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1409 (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]. 87.07/85.19 1410 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (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]. 87.07/85.19 1411 (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]. 87.07/85.19 1412 (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]. 87.07/85.19 1413 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1414 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1415 (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]. 87.07/85.19 1416 (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]. 87.07/85.19 1417 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1418 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1419 (all A all B all C (m2_relset_1(C,A,B) -> (k5_relset_1(A,B,C) = B <-> (all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(E,D),C))))))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1420 (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]. 87.07/85.19 1421 (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]. 87.07/85.19 1422 (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]. 87.07/85.19 1423 (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]. 87.07/85.19 1424 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1425 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1426 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k4_xboole_0(C,D) = k3_relset_1(A,B,C,D))) # label(redefinition_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1427 (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]. 87.07/85.19 1428 (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]. 87.07/85.19 1429 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_relset_1(A,B,C,C) = C)) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1430 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> C = k1_xboole_0))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1431 (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]. 87.07/85.19 1432 (all A all B all C (m1_relset_1(C,A,B) -> C = k6_relset_1(A,B,k6_relset_1(A,B,C)))) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1433 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1434 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(C,f2_s1_relset_1) & p1_s1_relset_1(B,C) & r2_hidden(B,f1_s1_relset_1))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1435 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k1_relset_1(A,B,C,C) = C)) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1436 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1437 (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]. 87.07/85.19 1438 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1439 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> ((exists E (r2_hidden(k4_tarski(E,D),C) & m1_subset_1(E,B))) <-> r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1440 (all A all B all C all D (m2_relset_1(D,A,B) -> -((all E all F -(C = k4_tarski(E,F) & r2_hidden(E,A) & r2_hidden(F,B))) & r2_hidden(C,D)))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1441 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1442 (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]. 87.07/85.19 1443 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1444 (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]. 87.07/85.19 1445 (all A all B all C (m1_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k1_relat_1(C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1446 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1447 (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]. 87.07/85.19 1448 (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]. 87.07/85.19 1449 (all A all B all C all D (m2_relset_1(D,B,A) -> (r1_tarski(B,C) -> k8_relset_1(B,A,D,C) = D))) # label(t34_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1450 (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]. 87.07/85.19 1451 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1452 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k3_xboole_0(C,D) = k2_relset_1(A,B,C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1453 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> k5_relset_1(A,B,C) = B & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1454 (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]. 87.07/85.19 1455 (all A all B (m2_relset_1(B,A,A) -> B = k5_relat_1(k6_relat_1(A),B) & B = k5_relat_1(B,k6_relat_1(A)))) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1456 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) -> (all E (m1_subset_1(E,A) -> ((exists F (m1_subset_1(F,C) & r2_hidden(F,B) & r2_hidden(k4_tarski(E,F),D))) <-> r2_hidden(E,k11_relset_1(A,C,D,B))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1457 (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]. 87.07/85.19 1458 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(D,E),C)))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1459 (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]. 87.07/85.19 1460 (all A all B all C (m1_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k2_relat_1(C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1461 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1462 (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]. 87.07/85.19 1463 (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]. 87.07/85.19 1464 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,C) -> ((exists H (m1_subset_1(H,B) & r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E))) <-> r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1465 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -((all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C)))) & r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1466 (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]. 87.07/85.19 1467 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1468 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1469 (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]. 87.07/85.19 1470 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1471 (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]. 87.07/85.19 1472 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1473 (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]. 87.07/85.19 1474 (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]. 87.07/85.19 1475 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,D) = k1_relset_1(A,B,D,C))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1476 (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]. 87.07/85.19 1477 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1478 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,D) = k2_relset_1(A,B,D,C))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1479 (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]. 87.07/85.19 1480 (all A all B all C all D (m1_relset_1(D,A,B) -> k8_relat_1(C,D) = k9_relset_1(A,B,C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1481 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1482 (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]. 87.07/85.19 1483 (exists A (m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1) & (all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (p1_s2_relset_1(B,C) <-> r2_hidden(k4_tarski(B,C),A)))))))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1484 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1485 (all A all B all C (m2_relset_1(C,B,A) -> (r1_tarski(k6_relat_1(B),C) -> r1_tarski(B,k5_relset_1(B,A,C)) & B = k4_relset_1(B,A,C)))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1486 (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]. 87.07/85.19 1487 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1488 (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]. 87.07/85.19 1489 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1490 (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]. 87.07/85.19 1491 (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]. 87.07/85.19 1492 (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]. 87.07/85.19 1493 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k4_relset_1(B,A,k6_relset_1(A,B,C)) & k4_relset_1(A,B,C) = k5_relset_1(B,A,k6_relset_1(A,B,C)))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1494 (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]. 87.07/85.19 1495 (all A all B all C all D (m1_relset_1(C,A,B) -> k7_relat_1(C,D) = k8_relset_1(A,B,C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1496 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,A) -> (all E (m1_subset_1(E,A) -> ((exists F (m1_subset_1(F,C) & r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D))) <-> r2_hidden(E,k10_relset_1(C,A,D,B))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1497 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1498 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1499 (all A all B all C (m2_relset_1(C,B,A) -> k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) = k4_relset_1(B,A,C) & k5_relset_1(B,A,C) = k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1500 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1501 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1502 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1503 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1504 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1505 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1506 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1507 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1508 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & r1_tarski(B,C) & r1_tarski(A,C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1509 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1510 (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]. 87.07/85.19 1511 (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]. 87.07/85.19 1512 (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]. 87.07/85.19 1513 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1514 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r2_hidden(C,k2_relat_1(D)) & (all E (m1_subset_1(E,A) -> -(C = k1_funct_1(D,E) & r2_hidden(E,k4_relset_1(A,B,D)))))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1515 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1516 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1517 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E)))) & k4_relset_1(A,B,D) = k4_relset_1(A,B,C) -> D = C))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1518 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C))) # label(t142_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1519 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1520 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1521 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k4_relset_1(k1_xboole_0,A,B) = k1_xboole_0 & k2_relat_1(B) = k1_xboole_0)) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1522 (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]. 87.07/85.19 1523 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k3_partfun1(C,A,B),k3_partfun1(D,A,B))))))) # label(t81_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1524 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_partfun1(k2_funct_1(C),B,A) = k2_funct_1(k3_partfun1(C,A,B))))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1525 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_xboole_0(A,B) = C -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,D) = k1_funct_1(A,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1526 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)))) # label(t128_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.07/85.19 1527 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),C,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1528 (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]. 87.14/85.19 1529 (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]. 87.14/85.19 1530 (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]. 87.14/85.19 1531 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A) -> k3_partfun1(k5_relat_1(D,E),C,B) = k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B))))))) # label(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1532 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (k4_relset_1(A,k1_tarski(B),D) = k4_relset_1(A,k1_tarski(B),C) -> C = D))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1533 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1534 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1535 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k9_relat_1(C,A) = k2_relat_1(C))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1536 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1537 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,A,C),k3_partfun1(D,B,C))))) # label(t82_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1538 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1539 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A) & v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1540 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1541 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1542 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1543 (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]. 87.14/85.19 1544 (all A all B all C (v1_funct_1(A) & v1_relat_1(A) -> m2_relset_1(k3_partfun1(A,B,C),B,C) & v1_funct_1(k3_partfun1(A,B,C)))) # label(dt_k3_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1545 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1546 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1547 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1548 (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]. 87.14/85.19 1549 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1550 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1551 (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s1_partfun1 & (all B (r2_hidden(B,f1_s1_partfun1) -> (p1_s1_partfun1(B) -> f2_s1_partfun1(B) = k1_funct_1(A,B)) & (-p1_s1_partfun1(B) -> f3_s1_partfun1(B) = k1_funct_1(A,B)))) & v1_relat_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1552 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1553 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1554 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1555 (all A (v1_funct_1(A) & v1_relat_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1556 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1557 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k2_relat_1(D),C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1558 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> (r1_tarski(B,D) & r1_tarski(A,C) -> m2_relset_1(E,C,D) & v1_funct_1(E)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1559 (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]. 87.14/85.19 1560 (all A all B (v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1561 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1562 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1563 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1564 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k4_relset_1(A,B,D),C) -> m2_relset_1(D,C,B) & v1_funct_1(D)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1565 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k2_partfun1(A,B,k3_partfun1(D,A,B),C) = k3_partfun1(D,k3_xboole_0(A,C),B))) # label(t96_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1566 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k3_partfun1(A,B,C) = k7_relat_1(k8_relat_1(C,A),B)))) # label(d3_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1567 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1568 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1569 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A ((all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> k1_funct_1(A,B) = f3_s3_partfun1(B))) & (all B (p1_s3_partfun1(B) & r2_hidden(B,f1_s3_partfun1) <-> r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)))) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & v1_funct_1(A))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1570 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1571 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k9_relset_1(A,B,C,D)) & m2_relset_1(k9_relset_1(A,B,C,D),A,C))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1572 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1573 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1574 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1575 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> k2_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k4_relset_1(A,k1_xboole_0,B))) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1576 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1577 (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]. 87.14/85.19 1578 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(k1_xboole_0))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1579 (all A k6_partfun1(A) = k6_relat_1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1580 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) -> k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1581 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1582 (all A exists B (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v3_relat_2(B) & v1_relat_2(B) & v1_relat_1(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1583 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1584 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & v1_funct_1(F) & m1_relset_1(E,A,B) & v1_funct_1(E) -> m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) & v1_funct_1(k1_partfun1(A,B,C,D,E,F)))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1585 (all A (v8_relat_2(A) & v3_relat_2(A) & v1_relat_1(A) -> v1_relat_2(A) & v1_relat_1(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1586 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1587 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1588 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (v1_funct_1(C) & C = k2_xboole_0(A,B) & v1_relat_1(C))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1589 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,C,A),k3_partfun1(D,C,B))))) # label(t83_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1590 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (k1_xboole_0 != A -> k1_xboole_0 = k5_partfun1(A,k1_xboole_0,B)))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1591 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((k1_xboole_0 = B -> k1_xboole_0 = A) & r1_partfun1(C,D) & (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(C,E) & r1_partfun1(D,E) & v1_partfun1(E,A,B))))))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1592 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1593 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1594 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_partfun1(E,A,C),k3_partfun1(E,B,D))))) # label(t84_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1595 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C))) <-> r1_partfun1(A,B))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1596 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)) & r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1597 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1598 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1599 (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]. 87.14/85.19 1600 (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]. 87.14/85.19 1601 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1602 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(D,C) & r1_partfun1(C,E) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1603 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1604 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1605 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1606 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C))) <-> r1_partfun1(A,B)))))) # label(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1607 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1608 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1609 (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]. 87.14/85.19 1610 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1611 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1612 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> m2_relset_1(C,A,B) & v1_funct_1(C))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1613 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1614 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B))) # label(dt_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1615 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1616 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1617 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) & k1_xboole_0 = B -> A = k1_xboole_0))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1618 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> C = k3_partfun1(C,A,B)))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1619 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> f4_s5_partfun1(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & (all B all C (r2_hidden(B,f1_s5_partfun1) & p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1620 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(k8_relat_1(A,B),B))) # label(t145_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.19 1621 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_1(B) & m2_relset_1(B,k1_relat_1(B),A)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1622 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),A,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1623 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1624 (all A (m2_relset_1(k6_partfun1(A),A,A) & v1_partfun1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1625 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k7_relat_1(C,D) = k2_partfun1(A,B,C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1626 (all A all B all C (C = k4_partfun1(A,B) <-> (all D ((exists E (v1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & r1_tarski(k1_relat_1(E),A) & E = D & v1_funct_1(E))) <-> r2_hidden(D,C))))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1627 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,k1_xboole_0) -> C = D)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1628 (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]. 87.14/85.20 1629 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1630 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k1_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1631 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1632 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1633 (all A (v1_relat_1(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1634 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (k4_relset_1(k2_zfmisc_1(A,B),C,D) = k4_relset_1(k2_zfmisc_1(A,B),C,E) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1635 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1636 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1637 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> k3_partfun1(D,B,k3_xboole_0(A,C)) = k9_relset_1(B,C,A,k3_partfun1(D,B,C)))) # label(t97_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1638 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(C,D) = k1_funct_1(C,E) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1639 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t92_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1640 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (v1_relat_1(C) & v1_funct_1(C) -> C != k2_xboole_0(A,B))) & (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1641 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & k1_funct_1(D,E) = C))) & r2_hidden(C,k9_relat_1(D,A))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1642 (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]. 87.14/85.20 1643 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1644 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1645 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1646 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> v2_funct_1(B))) # label(t66_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1647 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1648 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(k6_relat_1(A),C))) # label(t36_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1649 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1650 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (v1_partfun1(E,A,B) & r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1651 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1652 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1653 (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]. 87.14/85.20 1654 (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]. 87.14/85.20 1655 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1656 (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]. 87.14/85.20 1657 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1658 (all A all B all C (r2_hidden(A,f1_s4_partfun1) & p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) -> r2_hidden(C,f3_s4_partfun1))) & (all A all B all C all D (p1_s4_partfun1(A,B,C) & p1_s4_partfun1(A,B,D) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> C = D)) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1) & (all B all C (r2_hidden(C,f2_s4_partfun1) & (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(B,f1_s4_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & v1_funct_1(A))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1659 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1660 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1661 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) <-> k1_tarski(C) = k5_partfun1(A,B,C)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1662 (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]. 87.14/85.20 1663 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1664 (all A all B all C all D (m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1665 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) & k1_relat_1(D) = k1_tarski(A) -> m2_relset_1(D,B,C) & v1_funct_1(D)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1666 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k10_relat_1(C,B) = k4_relset_1(A,B,C))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1667 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1668 (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]. 87.14/85.20 1669 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1670 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1671 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) <-> r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,k1_relat_1(D))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1672 (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]. 87.14/85.20 1673 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1674 (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]. 87.14/85.20 1675 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1676 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(B,C) & r1_tarski(A,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1677 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1678 (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]. 87.14/85.20 1679 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1680 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1681 (all A all B exists C (v1_funct_1(C) & v1_relat_1(C) & m1_relset_1(C,A,B))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1682 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1683 (all A all B (m2_relset_1(k1_xboole_0,A,B) & v1_funct_1(k1_xboole_0))) # label(t56_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1684 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1685 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1686 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1687 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (v1_partfun1(C,A,B) & r1_partfun1(C,D) & v1_partfun1(D,A,B) -> C = D))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1688 (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]. 87.14/85.20 1689 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1690 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1691 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & r1_partfun1(C,D) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1692 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1693 (all A all B all C (m2_relset_1(C,A,B) -> k5_relat_1(C,k6_relat_1(B)) = C)) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1694 (all A all B all C (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,C) & p1_s2_partfun1(A,B) -> B = C)) & (all A all B (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) -> r2_hidden(B,f2_s2_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B ((exists C p1_s2_partfun1(B,C)) & r2_hidden(B,f1_s2_partfun1) <-> r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)))))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1695 (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]. 87.14/85.20 1696 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1697 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (D = k5_partfun1(A,B,C) <-> (all E ((exists F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_partfun1(F,A,B) & r1_partfun1(C,F) & E = F)) <-> r2_hidden(E,D))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1698 (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]. 87.14/85.20 1699 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1700 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1701 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1702 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1703 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1704 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1705 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,D) -> m2_relset_1(C,A,B) & v1_funct_1(C)))))) # label(t33_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1706 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & r1_partfun1(A,B) -> B = A))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1707 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1708 (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]. 87.14/85.20 1709 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1710 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1711 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1712 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_tarski(B) = k5_partfun1(k1_xboole_0,A,B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1713 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k9_relat_1(C,A),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1714 (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]. 87.14/85.20 1715 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k4_tarski(k4_tarski(A,B),C),D)) # label(t31_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1716 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D),k3_mcart_1(A,B,E),k3_mcart_1(A,C,E)) = k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k2_tarski(D,E))) # label(t45_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1717 (all A all B all C all D k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k1_tarski(D)) = k2_tarski(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D))) # label(t41_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1718 (all A all B all C all D k3_mcart_1(k4_tarski(A,B),C,D) = k4_mcart_1(A,B,C,D)) # label(t32_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1719 (all A all B (k1_xboole_0 != k2_zfmisc_1(A,B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) != C & C != k2_mcart_1(C))))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1720 (all A all B all C -(B != k1_xboole_0 & (exists D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) & (exists E exists F exists G (D = k3_mcart_1(E,F,G) & -(k5_mcart_1(A,B,C,D) = E & k6_mcart_1(A,B,C,D) = F & G = k7_mcart_1(A,B,C,D)))))) & C != k1_xboole_0 & k1_xboole_0 != A)) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1721 (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]. 87.14/85.20 1722 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D -((r2_hidden(D,A) | r2_hidden(C,A)) & k4_tarski(C,D) = B)))))) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1723 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A != k1_mcart_1(A) & k2_mcart_1(A) != A)) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1724 (all A all B all C all D all E all F all G all H (r1_tarski(C,D) & r1_tarski(G,H) & r1_tarski(E,F) & r1_tarski(A,B) -> r1_tarski(k4_zfmisc_1(A,C,E,G),k4_zfmisc_1(B,D,F,H)))) # label(t88_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1725 (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]. 87.14/85.20 1726 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1727 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1728 (all A all B all C all D all E all F all G all H (-r1_xboole_0(k4_zfmisc_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) -> -r1_xboole_0(B,F) & -r1_xboole_0(D,H) & -r1_xboole_0(C,G) & -r1_xboole_0(A,E))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1729 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1730 (all A all B all C all D all E all F all G all H -(A != k1_xboole_0 & k1_xboole_0 != B & k1_xboole_0 != D & F != k1_xboole_0 & k1_xboole_0 != G & H != k1_xboole_0 & (exists I ((exists J (J = I & -(k10_mcart_1(A,B,C,D,I) = k10_mcart_1(E,F,G,H,J) & k11_mcart_1(E,F,G,H,J) = k11_mcart_1(A,B,C,D,I) & k9_mcart_1(E,F,G,H,J) = k9_mcart_1(A,B,C,D,I) & k8_mcart_1(E,F,G,H,J) = k8_mcart_1(A,B,C,D,I)) & m1_subset_1(J,k4_zfmisc_1(E,F,G,H)))) & m1_subset_1(I,k4_zfmisc_1(A,B,C,D)))) & k1_xboole_0 != E & k1_xboole_0 != C)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1731 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B (B = k2_mcart_1(A) <-> (all C all D (k4_tarski(C,D) = A -> B = D)))))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1732 (all A all B all C -(B != k1_xboole_0 & k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)) = D)) & k1_xboole_0 != A)) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1733 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k1_tarski(D))) -> (C = k1_mcart_1(A) | k1_mcart_1(A) = B) & k2_mcart_1(A) = D)) # label(t17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1734 (all A all B all C all D -(k1_xboole_0 != A & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k9_mcart_1(A,B,C,D,E) != E & k11_mcart_1(A,B,C,D,E) != E & k10_mcart_1(A,B,C,D,E) != E & k8_mcart_1(A,B,C,D,E) != E)) & k1_xboole_0 != D & C != k1_xboole_0 & k1_xboole_0 != B)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1735 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) -> k13_mcart_1(A,B,C,D,E,F) = k3_zfmisc_1(D,E,F))) # label(redefinition_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1736 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != C & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k4_mcart_1(k8_mcart_1(A,B,C,D,E),k9_mcart_1(A,B,C,D,E),k10_mcart_1(A,B,C,D,E),k11_mcart_1(A,B,C,D,E)) = E)) & D != k1_xboole_0 & B != k1_xboole_0)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1737 (all A all B all C (r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C) -> r2_hidden(A,k2_zfmisc_1(B,C)) | (all D all E k4_tarski(D,E) != A))) # label(t11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1738 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1739 (all A all B all C -(A != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> D != k6_mcart_1(A,B,C,D) & D != k7_mcart_1(A,B,C,D) & D != k5_mcart_1(A,B,C,D))) & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1740 (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]. 87.14/85.20 1741 (all A all B all C all D all E all F all G all H (r2_hidden(k4_mcart_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) <-> r2_hidden(C,G) & r2_hidden(D,H) & r2_hidden(B,F) & r2_hidden(A,E))) # label(t84_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1742 (all A -((all B -(r2_hidden(B,A) & (all C all D all E (r2_hidden(E,B) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1743 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1744 (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]. 87.14/85.20 1745 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k15_mcart_1(A)) & v1_relat_1(k15_mcart_1(A)))) # label(dt_k15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1746 (all A all B all C all D all E all F (k3_mcart_1(A,B,C) = k3_mcart_1(D,E,F) -> C = F & B = E & A = D)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1747 (all A all B all C all D all E all F -(A != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != F & (exists G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) & (exists H (H = G & -(k5_mcart_1(A,B,C,G) = k5_mcart_1(D,E,F,H) & k6_mcart_1(D,E,F,H) = k6_mcart_1(A,B,C,G) & k7_mcart_1(A,B,C,G) = k7_mcart_1(D,E,F,H)) & m1_subset_1(H,k3_zfmisc_1(D,E,F)))))) & E != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1748 (all A all B all C all D k4_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D)) = k1_tarski(k4_mcart_1(A,B,C,D))) # label(t65_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1749 (all A all B all C all D k3_zfmisc_1(k2_zfmisc_1(A,B),C,D) = k4_zfmisc_1(A,B,C,D)) # label(t54_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1750 (all A all B all C (k3_zfmisc_1(A,B,C) != k1_xboole_0 <-> A != k1_xboole_0 & B != k1_xboole_0 & C != k1_xboole_0)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1751 (all A all B all C -(C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,C) -> (E = k7_mcart_1(A,B,C,D) <-> (all F all G all H (k3_mcart_1(F,G,H) = D -> H = E))))))) & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1752 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(A,B,C,D) = k4_zfmisc_1(E,F,G,H) -> C = k1_xboole_0 | D = k1_xboole_0 | G = C & H = D & B = F & E = A | k1_xboole_0 = B | k1_xboole_0 = A)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1753 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> D = F))))))) -> k1_xboole_0 = B | k1_xboole_0 = C | k5_mcart_1(A,B,C,E) = D | A = k1_xboole_0))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1754 (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]. 87.14/85.20 1755 (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]. 87.14/85.20 1756 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,k1_tarski(C))) -> C = k2_mcart_1(A) & r2_hidden(k1_mcart_1(A),B))) # label(t13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1757 (all A all B all C all D all E all F all G all H (m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(A)) -> m1_subset_1(k14_mcart_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))) # label(dt_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1758 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & r1_xboole_0(B,A))))) # label(t1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1759 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(A,B,C,D) = k4_zfmisc_1(E,F,G,H) -> D = H & G = C & B = F & E = A | k1_xboole_0 = k4_zfmisc_1(A,B,C,D))) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1760 (all A all B all C all D all E all F (A = k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) & B = k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) & k20_mcart_1(k4_tarski(F,k4_tarski(D,E))) = E & k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) = D)) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1761 (all A all B all C all D all E all F (r2_hidden(k3_mcart_1(A,B,C),k3_zfmisc_1(D,E,F)) <-> r2_hidden(A,D) & r2_hidden(B,E) & r2_hidden(C,F))) # label(t73_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1762 (all A all B -(-(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C = k4_tarski(k1_mcart_1(C),k2_mcart_1(C)))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1763 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(A != k1_xboole_0 & k1_xboole_0 != C & (exists E exists F exists G (-(k5_mcart_1(A,B,C,D) = E & G = k7_mcart_1(A,B,C,D) & F = k6_mcart_1(A,B,C,D)) & D = k3_mcart_1(E,F,G))) & B != k1_xboole_0))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1764 (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]. 87.14/85.20 1765 (all A ((exists B exists C k4_tarski(B,C) = A) -> k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A)) # label(t8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1766 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1767 (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]. 87.14/85.20 1768 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k3_mcart_1(A,B,C),D)) # label(d4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1769 (all A -(A != k1_xboole_0 & (all B -((all C all D all E all F -((r2_hidden(C,A) | r2_hidden(D,A)) & B = k4_mcart_1(C,D,E,F))) & r2_hidden(B,A))))) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1770 (all A all B all C all D all E all F all G all H (m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(A)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = k4_zfmisc_1(E,F,G,H))) # label(redefinition_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1771 (all A all B all C all D k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D) = k4_zfmisc_1(A,B,C,D)) # label(t53_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1772 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1773 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> G = E))))))))) -> k1_xboole_0 = B | D = k1_xboole_0 | E = k8_mcart_1(A,B,C,D,F) | C = k1_xboole_0 | k1_xboole_0 = A))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1774 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> H = D))))))) -> C = k1_xboole_0 | D = k7_mcart_1(A,B,C,E) | B = k1_xboole_0 | A = k1_xboole_0))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1775 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> k3_zfmisc_1(A,B,C) = k1_xboole_0 | D = A & E = B & C = F)) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1776 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> D = G))))))) -> A = k1_xboole_0 | k6_mcart_1(A,B,C,E) = D | C = k1_xboole_0 | k1_xboole_0 = B))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1777 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> k1_mcart_1(A) = B & k2_mcart_1(A) = C)) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1778 (all A all B all C all D all E all F k6_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(A,D,E),k3_mcart_1(A,C,F),k3_mcart_1(A,D,F),k3_mcart_1(B,C,E),k3_mcart_1(B,D,E),k3_mcart_1(B,C,F),k3_mcart_1(B,D,F)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k2_tarski(E,F))) # label(t46_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1779 (all A all B all C all D (-(-r1_tarski(A,k4_zfmisc_1(A,B,C,D)) & -r1_tarski(A,k4_zfmisc_1(B,C,D,A)) & -r1_tarski(A,k4_zfmisc_1(D,A,B,C)) & -r1_tarski(A,k4_zfmisc_1(C,D,A,B))) -> k1_xboole_0 = A)) # label(t63_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1780 (all A all B all C all D k2_tarski(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D)) = k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k1_tarski(D))) # label(t40_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1781 (all A -((all B -(r2_hidden(B,A) & (all C all D (r2_hidden(D,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))))) & k1_xboole_0 != A)) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.20 1782 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -(k1_xboole_0 != C & (exists F exists G exists H exists I (-(k10_mcart_1(A,B,C,D,E) = H & I = k11_mcart_1(A,B,C,D,E) & G = k9_mcart_1(A,B,C,D,E) & F = k8_mcart_1(A,B,C,D,E)) & E = k4_mcart_1(F,G,H,I))) & k1_xboole_0 != D & B != k1_xboole_0 & A != k1_xboole_0))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1783 (all A all B all C all D -(C != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,B) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = H)) <-> F = k9_mcart_1(A,B,C,D,E)))))) & k1_xboole_0 != D & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1784 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1785 (all A all B -(B != k1_xboole_0 & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k2_mcart_1(C) != C & C != k1_mcart_1(C))) & k1_xboole_0 != A)) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1786 (all A all B all C all D all E ((all F (r2_hidden(F,A) <-> (exists G exists H exists I exists J (r2_hidden(G,B) & r2_hidden(I,D) & k4_mcart_1(G,H,I,J) = F & r2_hidden(J,E) & r2_hidden(H,C))))) -> A = k4_zfmisc_1(B,C,D,E))) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1787 (all A -(k1_xboole_0 != A & (all B -((all C all D all E -((r2_hidden(D,A) | r2_hidden(C,A)) & B = k3_mcart_1(C,D,E))) & r2_hidden(B,A))))) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1788 (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]. 87.14/85.21 1789 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_mcart_1(k1_funct_1(A,C)))) & k1_relat_1(B) = k1_relat_1(A) <-> k15_mcart_1(A) = B))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1790 (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]. 87.14/85.21 1791 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> E = H))))))))) -> D = k1_xboole_0 | E = k9_mcart_1(A,B,C,D,F) | C = k1_xboole_0 | B = k1_xboole_0 | A = k1_xboole_0))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1792 (all A all B all C all D all E all F (-r1_xboole_0(k3_zfmisc_1(A,B,C),k3_zfmisc_1(D,E,F)) -> -r1_xboole_0(C,F) & -r1_xboole_0(B,E) & -r1_xboole_0(A,D))) # label(t52_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1793 (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]. 87.14/85.21 1794 (all A k20_mcart_1(A) = k2_mcart_1(k2_mcart_1(A))) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1795 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,C) -> (k10_mcart_1(A,B,C,D,E) = F <-> (all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> F = I))))))) & k1_xboole_0 != D & k1_xboole_0 != C & B != k1_xboole_0 & A != k1_xboole_0)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1796 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1797 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1798 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1799 (all A ((exists B exists C k4_tarski(B,C) = A) -> k2_mcart_1(A) != A & k1_mcart_1(A) != A)) # label(t20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1800 (all A all B all C all D ((all E ((exists F exists G exists H (r2_hidden(F,B) & r2_hidden(H,D) & k3_mcart_1(F,G,H) = E & r2_hidden(G,C))) <-> r2_hidden(E,A))) -> A = k3_zfmisc_1(B,C,D))) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1801 (all A all B (k2_mcart_1(k4_tarski(A,B)) = B & k1_mcart_1(k4_tarski(A,B)) = A)) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1802 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1803 (all A all B all C all D k2_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(k4_tarski(A,C),k4_tarski(A,D),k4_tarski(B,C),k4_tarski(B,D))) # label(t25_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1804 (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]. 87.14/85.21 1805 (all A all B all C all D -(C != k1_xboole_0 & k1_xboole_0 != D & (exists E ((exists F exists G exists H exists I (E = k4_mcart_1(F,G,H,I) & -(G = k9_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = I & k10_mcart_1(A,B,C,D,E) = H & F = k8_mcart_1(A,B,C,D,E)))) & m1_subset_1(E,k4_zfmisc_1(A,B,C,D)))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1806 (all A all B all C all D -(k1_xboole_0 != B & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,D) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = J)) <-> k11_mcart_1(A,B,C,D,E) = F))))) & C != k1_xboole_0 & A != k1_xboole_0)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1807 (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]. 87.14/85.21 1808 (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]. 87.14/85.21 1809 (all A k1_mcart_1(k2_mcart_1(A)) = k19_mcart_1(A)) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1810 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k16_mcart_1(A)) & v1_funct_1(k16_mcart_1(A)))) # label(dt_k16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1811 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k2_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B) <-> B = k16_mcart_1(A)))))) # label(d13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1812 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> k1_xboole_0 = A | C = k1_xboole_0 | D = A & E = B & F = C | k1_xboole_0 = B)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1813 (all A all B all C -(k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,A) -> (k5_mcart_1(A,B,C,D) = E <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> F = E))))))) & k1_xboole_0 != C & k1_xboole_0 != A)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1814 (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]. 87.14/85.21 1815 (all A all B all C all D all E -((all F all G all H all I -(r2_hidden(H,D) & r2_hidden(I,E) & k4_mcart_1(F,G,H,I) = A & r2_hidden(G,C) & r2_hidden(F,B))) & r2_hidden(A,k4_zfmisc_1(B,C,D,E)))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1816 (all A all B all C -(k1_xboole_0 != A & k1_xboole_0 != B & k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k2_mcart_1(k1_mcart_1(D)) = k6_mcart_1(A,B,C,D) & k2_mcart_1(D) = k7_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = k1_mcart_1(k1_mcart_1(D)))))) # label(t50_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1817 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1818 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> I = E))))))))) -> B = k1_xboole_0 | C = k1_xboole_0 | k10_mcart_1(A,B,C,D,F) = E | D = k1_xboole_0 | k1_xboole_0 = A))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1819 (all A all B (k4_zfmisc_1(A,A,A,A) = k4_zfmisc_1(B,B,B,B) -> A = B)) # label(t58_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1820 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,B) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1821 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k2_tarski(C,D))) -> (D = k2_mcart_1(A) | C = k2_mcart_1(A)) & k1_mcart_1(A) = B)) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1822 (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]. 87.14/85.21 1823 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> k2_zfmisc_1(C,D) = k12_mcart_1(A,B,C,D))) # label(redefinition_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1824 (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]. 87.14/85.21 1825 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),D)) -> (k1_mcart_1(A) = C | B = k1_mcart_1(A)) & r2_hidden(k2_mcart_1(A),D))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1826 (all A ((exists B exists C k4_tarski(B,C) = A) -> (all B ((all C all D (k4_tarski(C,D) = A -> B = C)) <-> B = k1_mcart_1(A))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1827 (all A all B all C -(k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,B) -> (E = k6_mcart_1(A,B,C,D) <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> E = G))))))) & C != k1_xboole_0 & A != k1_xboole_0)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1828 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != B & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k1_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k8_mcart_1(A,B,C,D,E) & k9_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(k1_mcart_1(E))) & k11_mcart_1(A,B,C,D,E) = k2_mcart_1(E) & k2_mcart_1(k1_mcart_1(E)) = k10_mcart_1(A,B,C,D,E))) & k1_xboole_0 != C)) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1829 (all A -((all B -(r2_hidden(B,A) & (all C all D all E all F all G (r2_hidden(C,D) & r2_hidden(F,G) & r2_hidden(G,B) & r2_hidden(E,F) & r2_hidden(D,E) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 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) -> (k4_mcart_1(G,H,I,J) = F -> E = J))))))))) -> k1_xboole_0 = A | k11_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = D | k1_xboole_0 = C | k1_xboole_0 = B))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1831 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)))) # label(t23_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1832 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(B,k2_tarski(C,D))) -> r2_hidden(k1_mcart_1(A),B) & (k2_mcart_1(A) = C | k2_mcart_1(A) = D))) # label(t16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1833 (all A k1_mcart_1(k1_mcart_1(A)) = k17_mcart_1(A)) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1834 (all A all B all C all D -(r2_hidden(A,k3_zfmisc_1(B,C,D)) & (all E all F all G -(r2_hidden(F,C) & k3_mcart_1(E,F,G) = A & r2_hidden(G,D) & r2_hidden(E,B))))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1835 (all A all B all C all D all E all F all G all H (k4_mcart_1(E,F,G,H) = k4_mcart_1(A,B,C,D) -> E = A & H = D & G = C & F = B)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1836 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1837 (all A all B all C all D -(k1_xboole_0 != A & C != k1_xboole_0 & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,A) -> (F = k8_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> G = F))))))) & k1_xboole_0 != B)) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1838 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k2_tarski(D,E))) -> (k2_mcart_1(A) = E | k2_mcart_1(A) = D) & (k1_mcart_1(A) = C | B = k1_mcart_1(A)))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1839 (all A all B all C all D (k4_zfmisc_1(A,B,C,D) != k1_xboole_0 <-> B != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != C & A != k1_xboole_0)) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1840 (all A -((all B -((all C all D all E all F (r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(F,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1841 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> (all I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) -> (r2_hidden(I,k4_zfmisc_1(E,F,G,H)) -> r2_hidden(k8_mcart_1(A,B,C,D,I),E) & r2_hidden(k9_mcart_1(A,B,C,D,I),F) & r2_hidden(k11_mcart_1(A,B,C,D,I),H) & r2_hidden(k10_mcart_1(A,B,C,D,I),G)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1842 (all A all B all C k1_tarski(k3_mcart_1(A,B,C)) = k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C))) # label(t39_mcart_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1843 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1844 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1845 (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]. 87.14/85.21 1846 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1847 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1848 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1849 (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]. 87.14/85.21 1850 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1851 (all A (-v1_xboole_0(A) -> -((all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))) & k1_relat_1(B) = A))) & (all B -(k1_xboole_0 = B & r2_hidden(B,A)))))) # label(t28_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1852 (all A all B (v1_relat_1(B) -> (B = k1_wellord2(A) <-> A = k3_relat_1(B) & (all C all D (r2_hidden(D,A) & r2_hidden(C,A) -> (r1_tarski(C,D) <-> r2_hidden(k4_tarski(C,D),B))))))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1853 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1854 (all A -((all B -(p1_s1_wellord2(A,B) & r2_hidden(B,f2_s1_wellord2))) & r2_hidden(A,f1_s1_wellord2))) -> (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s1_wellord2 & (all B (r2_hidden(B,f1_s1_wellord2) -> p1_s1_wellord2(B,k1_funct_1(A,B)))) & r1_tarski(k2_relat_1(A),f2_s1_wellord2) & v1_relat_1(A))) # label(s1_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1855 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1856 (all A all B ((exists C (v1_funct_1(C) & k1_relat_1(C) = A & B = k2_relat_1(C) & v2_funct_1(C) & v1_relat_1(C))) <-> r2_wellord2(A,B))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1857 (all A (v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_wellord1(A,k1_wellord2(C)) & r4_wellord1(A,k1_wellord2(B)) -> C = B))))))) # label(t12_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1858 (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]. 87.14/85.21 1859 (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]. 87.14/85.21 1860 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1861 (all A all B all C (r2_wellord2(B,C) & r2_wellord2(A,B) -> r2_wellord2(A,C))) # label(t22_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1862 (all A (v1_relat_1(A) -> -((all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & v2_wellord1(A)))) # label(t14_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1863 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1864 (all A -((all B all C -(r2_hidden(B,f2_s2_wellord2) & r2_hidden(C,f3_s2_wellord2) & p1_s2_wellord2(A,B,C))) & r2_hidden(A,f1_s2_wellord2))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (exists B (k1_relat_1(B) = f1_s2_wellord2 & (all C (r2_hidden(C,f1_s2_wellord2) -> p1_s2_wellord2(C,k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = f1_s2_wellord2 & v1_funct_1(B) & v1_relat_1(B))))) # label(s2_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1865 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> k1_wellord1(k1_wellord2(B),A) = A))))) # label(t10_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1866 (all A all B (r2_wellord2(A,B) <-> r2_tarski(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1867 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1868 (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]. 87.14/85.21 1869 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1870 (all A exists B (r2_wellord1(B,A) & v1_relat_1(B))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1871 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> v2_wellord1(k2_wellord1(B,A)) & A = k3_relat_1(k2_wellord1(B,A))))) # label(t25_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1872 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1873 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1874 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1875 (all A (-v1_xboole_0(A) -> -((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r1_xboole_0(B,C) | C = B)) & (all B exists C (r2_hidden(C,A) & (all D k1_tarski(D) != k3_xboole_0(B,C)))) & (all B -(r2_hidden(B,A) & B = k1_xboole_0))))) # label(t27_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1876 (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]. 87.14/85.21 1877 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1878 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1879 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1880 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1881 (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]. 87.14/85.21 1882 (all A all B all C (v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1883 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (A = k2_relat_1(C) & k2_relat_1(B) = A -> A = k2_relat_1(k4_funct_2(A,B,C))))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1884 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,k1_tarski(B)) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> C = D)))) # label(t66_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1885 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1886 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1887 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1888 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (exists E (r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(D,E) != k1_funct_1(C,E))))) & (k1_xboole_0 = B -> A = k1_xboole_0)))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1889 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1890 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (exists C (v1_funct_2(C,A,A) & r1_partfun1(B,C) & m2_relset_1(C,A,A) & v1_funct_1(C))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1891 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1892 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (v2_funct_1(B) -> (all C all D (r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(C,A) -> C = D))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1893 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1894 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1895 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1896 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(A != k1_xboole_0 & B != k1_xboole_0 & -((all D all E (v1_funct_1(E) & m2_relset_1(E,D,A) & v1_funct_2(E,D,A) -> (all F (v1_funct_1(F) & v1_funct_2(F,D,A) & m2_relset_1(F,D,A) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> E = F))))) <-> v2_funct_1(C))))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1897 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1898 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1899 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))) -> D = E))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1900 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k6_partfun1(A) = k5_funct_2(A,B,k6_funct_2(A,B)) & k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1901 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t166_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1902 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> (r1_partfun1(C,D) <-> (all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E))))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1903 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1904 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1905 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) & k2_relat_1(B) = A -> v1_funct_1(B) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1906 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1907 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k3_funct_2(A,B,C,B) = A))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1908 (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & (all B (m1_subset_1(B,f1_s4_funct_2) -> k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B))) & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 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) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) | B = k1_xboole_0))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1910 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1911 (exists A (f4_s10_funct_2 = k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) & (all B (m1_subset_1(B,f1_s10_funct_2) -> (f3_s10_funct_2 != B -> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B)))) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1912 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) -> (r1_tarski(B,A) -> B = k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) & k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1913 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (m1_subset_1(C,f3_s7_funct_2) & p1_s7_funct_2(A,B,C))))))) -> (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & (all B (m1_subset_1(B,f1_s7_funct_2) -> (all C (m1_subset_1(C,f2_s7_funct_2) -> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))))) & v1_funct_1(A))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1914 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> B = k1_xboole_0 | v2_funct_1(C) & k2_relat_1(D) = A))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1915 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1916 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> A = k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)))) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1917 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1918 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1919 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1920 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_1(B) & v1_funct_2(B,A,A) & v1_relat_2(B) & v1_partfun1(B,A,A) -> v1_funct_1(B) & v2_funct_1(B) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1921 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1922 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> k2_funct_2(A,B,C,A) = k2_relat_1(C)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1923 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1924 (all A all B all C (m2_relset_1(C,A,B) -> C = k7_relset_1(A,B,B,B,C,k6_partfun1(B)) & k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C)) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1925 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,C) & v1_funct_2(E,B,C) -> (v2_funct_1(E) & k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C -> k2_relat_1(D) = B | C = k1_xboole_0))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1926 (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]. 87.14/85.21 1927 (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]. 87.14/85.21 1928 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1929 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & (all E k1_tarski(E) != B) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1930 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1931 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B) -> k2_relat_1(C) = B))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1932 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1933 (all A (r2_hidden(A,f1_s9_funct_2) -> (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)) & (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & (all B (r2_hidden(B,f1_s9_funct_2) -> (-p1_s9_funct_2(B) -> k1_funct_1(A,B) = f4_s9_funct_2(B)) & (p1_s9_funct_2(B) -> f3_s9_funct_2(B) = k1_funct_1(A,B)))) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2) & v1_funct_1(A))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1934 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1935 (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]. 87.14/85.21 1936 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1937 (all A -((all B -(r2_hidden(B,f2_s1_funct_2) & p1_s1_funct_2(A,B))) & r2_hidden(A,f1_s1_funct_2))) -> (exists A ((all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2) & v1_funct_1(A))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 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) -> (B != k1_xboole_0 -> (all E ((exists F (r2_hidden(F,A) & E = k1_funct_1(D,F) & r2_hidden(F,C))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1939 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> D = k2_partfun1(A,B,D,C)))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1940 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1941 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,A,B) & v1_funct_1(E) & m1_relset_1(E,B,C) & v1_funct_2(E,B,C) & m1_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_1(k7_funct_2(A,B,C,D,E)))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1942 (all A all B k1_funct_2(A,B) = k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B))) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1943 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(C) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_relat_1(B,C) = k5_funct_2(A,B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1944 (all A all B all C ((all D ((exists E (E = D & A = k1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & v1_funct_1(E) & v1_relat_1(E))) <-> r2_hidden(D,C))) <-> C = k1_funct_2(A,B))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1945 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1946 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1947 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1948 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> k1_xboole_0 != A & B = k1_xboole_0 | r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C)))))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1949 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1950 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1951 (all A all B all C (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v3_funct_2(k5_funct_2(A,B,C),A,A) & m2_relset_1(k5_funct_2(A,B,C),A,A) & v1_funct_2(k5_funct_2(A,B,C),A,A) & v1_funct_1(k5_funct_2(A,B,C)))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1952 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> v2_funct_1(D) | B = k1_xboole_0 & k1_xboole_0 != A | k1_xboole_0 != B & C = k1_xboole_0))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1953 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1954 (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]. 87.14/85.21 1955 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1956 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(B) -> m2_relset_1(B,k1_xboole_0,A) & v1_funct_2(B,k1_xboole_0,A) & v1_funct_1(B)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1957 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (B = k4_funct_2(A,B,C) & k2_relat_1(B) = A -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1958 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1959 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(C,A) -> k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) | B = k1_xboole_0))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1960 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> B = C))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1961 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_partfun1(C,D) -> k1_xboole_0 = B & A != k1_xboole_0 | r2_hidden(D,k5_partfun1(A,B,C))))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1962 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 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) -> (r1_tarski(C,A) -> m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_2(k2_partfun1(A,B,D,C),C,B) & v1_funct_1(k2_partfun1(A,B,D,C)) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1964 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1965 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1966 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1967 (all A all B all C (m1_relset_1(C,A,B) -> (v1_partfun1(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_funct_2(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1968 (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]. 87.14/85.21 1969 (all A all B (r2_hidden(A,f1_s6_funct_2) & r2_hidden(B,f2_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s6_funct_2) & r2_hidden(C,f2_s6_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C))) & m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1970 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_2(C,A,B) <-> B = k2_relat_1(C)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1971 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_tarski(k2_relat_1(D),C) -> A != k1_xboole_0 & k1_xboole_0 = B | v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C)))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1972 (all A all B (m2_relset_1(B,A,A) -> k7_relset_1(A,A,A,A,k6_partfun1(A),B) = B & B = k7_relset_1(A,A,A,A,B,k6_partfun1(A)))) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1973 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> k1_relat_1(C) = A & r1_tarski(k2_relat_1(C),B)))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1974 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1975 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1976 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1977 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1978 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1979 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(C) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k4_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1980 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) -> k9_funct_2(A,B,C) = D)) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1981 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_2(C,A,B) & m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_1(C) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1982 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1983 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1984 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v2_funct_1(C) & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) & B = k2_relat_1(C) -> k1_xboole_0 = B | D = k2_funct_1(C) | A = k1_xboole_0))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1985 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1986 (all A exists B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v2_funct_1(B) & m1_relset_1(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1987 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) -> (B != k1_xboole_0 -> k1_tarski(k1_funct_1(C,A)) = k2_relat_1(C)))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1988 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> ((all C all D (r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(C,A) -> D = C)) <-> v2_funct_1(B)))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1989 f4_s11_funct_2 != f3_s11_funct_2 -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & f4_s11_funct_2 != B & f3_s11_funct_2 != B))) & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) = f6_s11_funct_2 & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) = f5_s11_funct_2)) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1990 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_partfun1(C,D) -> k1_xboole_0 != A & B = k1_xboole_0 | D = C))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1991 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1992 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.21 1993 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) & v1_funct_2(D,k1_tarski(A),B) -> (k1_xboole_0 != B -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 1994 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 1995 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C)))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 1996 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 1997 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 1998 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 1999 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2000 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2001 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) -> (all D (m2_relset_1(D,A,A) & v1_funct_2(D,A,A) & v1_funct_1(D) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2002 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v3_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_2(C,A,B) & v2_funct_2(C,A,B) & v2_funct_1(C) & v1_funct_1(C)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2003 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (k2_relat_1(C) = B <-> (all D -(r2_hidden(D,B) & k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D))))))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2004 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2005 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2006 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E -((all F -(k1_funct_1(D,F) = E & r2_hidden(F,C) & r2_hidden(F,A))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2007 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B = k2_relat_1(C) & v2_funct_1(C) -> k1_xboole_0 = B | k5_relat_1(C,k2_funct_1(C)) = k6_partfun1(A) & k6_partfun1(B) = k5_relat_1(k2_funct_1(C),C)))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2008 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2009 (all A all B all C (m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> (v1_funct_2(C,A,B) <-> A = k4_relset_1(A,B,C))) & (B = k1_xboole_0 -> A = k1_xboole_0 | (v1_funct_2(C,A,B) <-> C = k1_xboole_0)))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2010 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E -(r2_hidden(E,A) & k1_funct_1(D,E) = C)) & B = k2_relat_1(D) & r2_hidden(C,B)))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2011 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2012 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(k1_funct_1(D,F) = E & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2013 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2014 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> ((all D all E (r2_hidden(D,A) & r2_hidden(E,A) & k1_funct_1(C,D) = k1_funct_1(C,E) -> D = E)) <-> v2_funct_1(C))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2015 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2016 (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & (all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C))))) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2017 (all A all B all C all D all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> -((k1_xboole_0 = C -> B = k1_xboole_0) & -r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D))) & (k1_xboole_0 = B -> k1_xboole_0 = A)))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2018 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2019 (all A all B all C all D (-v1_xboole_0(A) & m1_relset_1(C,A,B) & m1_subset_1(D,A) & v1_funct_2(C,A,B) & v1_funct_1(C) -> k1_funct_1(C,D) = k8_funct_2(A,B,C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2020 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) & k2_relat_1(D) = B -> k1_xboole_0 != B & C = k1_xboole_0 | v2_funct_1(E) & v2_funct_1(D)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2021 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2022 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2023 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (r2_hidden(C,A) & r2_hidden(k1_funct_1(E,C),D) -> k1_funct_1(k9_relset_1(A,B,D,E),C) = k1_funct_1(E,C) | k1_xboole_0 = B))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2024 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_2(B,k1_relat_1(B),A) & m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2025 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k5_relat_1(D,E) = k7_funct_2(A,B,C,D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2026 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2027 (all A all B -(r2_hidden(A,f1_s5_funct_2) & r2_hidden(B,f2_s5_funct_2) & (all C -(p1_s5_funct_2(A,B,C) & r2_hidden(C,f3_s5_funct_2))))) -> (exists A ((all B all C (r2_hidden(C,f2_s5_funct_2) & r2_hidden(B,f1_s5_funct_2) -> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_1(A))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2028 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2029 (all A all B (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v1_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & v1_funct_1(k6_funct_2(A,B)))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2030 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))))) -> E = D))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2031 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (k2_relat_1(E) = C & B = k2_relat_1(D) -> k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C | C = k1_xboole_0 | B = k1_xboole_0))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2032 (all A all B all C all D all E all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (r2_hidden(D,A) & r2_hidden(E,B) -> r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) | C = k1_xboole_0))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2033 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2034 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2035 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (-(A != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 = B) -> v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2036 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2037 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B != k1_xboole_0 -> (B = k2_relat_1(C) <-> (all D (k1_xboole_0 != D -> (all E (v1_funct_1(E) & m2_relset_1(E,B,D) & v1_funct_2(E,B,D) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,F) = k1_partfun1(A,B,B,D,C,E) -> E = F))))))))))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2038 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2) & (all B (m1_subset_1(B,f1_s13_funct_2) -> f3_s13_funct_2(B) = k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2039 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (B = k4_funct_2(A,C,B) & v2_funct_1(B) -> C = k6_partfun1(A)))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2040 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2041 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_partfun1(A,A,k3_partfun1(B,A,A)) = k1_tarski(B))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2042 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) -> k2_funct_2(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2043 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r2_hidden(C,A) & v2_funct_1(D) -> C = k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) | B = k1_xboole_0))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2044 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (m1_subset_1(B,f2_s3_funct_2) & p1_s3_funct_2(A,B))))) -> (exists A (m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2) & (all B (m1_subset_1(B,f1_s3_funct_2) -> p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)))) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_1(A))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2045 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2046 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2047 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (k5_funct_2(A,B,C) = C -> k6_partfun1(A) = B))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2048 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2049 (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]. 87.14/85.22 2050 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E B != k1_tarski(E)) & k5_partfun1(A,B,D) = k5_partfun1(A,B,C) -> C = D))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2051 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((all D -(r2_hidden(D,B) & (all E -(D = k1_funct_1(C,E) & r2_hidden(E,A))))) -> k2_relat_1(C) = B | k1_xboole_0 = B))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2052 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2053 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2054 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2055 (all A all B (v1_funct_1(B) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> k2_funct_1(B) = k6_funct_2(A,B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2056 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (B != k1_xboole_0 -> (all E (r2_hidden(E,A) & r2_hidden(k1_funct_1(D,E),C) <-> r2_hidden(E,k10_relat_1(D,C))))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2057 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & (all B (m1_subset_1(B,f1_s12_funct_2) -> k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B))) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2058 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_2(C,A,B) & v1_partfun1(C,A,B) & -v1_xboole_0(C) & v1_funct_1(C)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2059 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2060 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(-v2_funct_1(C) & (exists D (m2_relset_1(D,B,A) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & v1_funct_2(D,B,A) & v1_funct_1(D))) & B != k1_xboole_0))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2061 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_2(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k2_funct_2(k1_xboole_0,A,C,B))) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2062 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(B,A) -> k1_funct_1(D,k1_funct_1(C,B)) = k1_funct_1(k5_relat_1(C,D),B)))))) # label(t70_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2063 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2064 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> k2_funct_2(A,A,B,A) = k2_relat_1(B))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2065 (all A all B (v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_1(C) -> (k5_funct_2(A,B,C) = k6_partfun1(A) -> C = k6_funct_2(A,B)))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2066 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (v2_funct_1(C) & v2_funct_2(C,A,B) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2067 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A (m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2) & (all B (r2_hidden(B,f1_s2_funct_2) -> k1_funct_1(A,B) = f3_s2_funct_2(B))) & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2) & v1_funct_1(A))) # label(s2_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2068 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2069 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2070 (all A (k1_xboole_0 != A -> k1_xboole_0 = k1_funct_2(A,k1_xboole_0))) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2071 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D) | B = k1_xboole_0 & k1_xboole_0 != A))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2072 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> A = k3_funct_2(A,B,C,k2_funct_2(A,B,C,A))))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2073 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> -((all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> -r1_partfun1(C,D))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2074 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2075 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2076 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2077 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2078 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> v1_partfun1(C,A,B) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2079 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),B) | k1_xboole_0 = B))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2080 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> -(r1_partfun1(C,E) & r1_partfun1(D,E)))) & r1_partfun1(C,D)))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2081 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = B -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2082 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2083 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) -> v1_funct_1(k4_funct_2(A,B,C)) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_2(k4_funct_2(A,B,C),A,A))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2084 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2085 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2086 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> r1_tarski(k2_relat_1(B),A) & A = k4_relset_1(A,A,B))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2087 (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]. 87.14/85.22 2088 (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]. 87.14/85.22 2089 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2090 (all A all B exists C (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & v1_relat_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2091 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (m1_subset_1(B,f2_s14_funct_2) & p1_s14_funct_2(A,B))))) -> (exists A (v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2) & (all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2092 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2093 (all A all B all C all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,A) -> B = k1_funct_1(D,C)))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2094 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (B = k2_relat_1(C) & (all E all F ((E = k1_funct_1(C,F) & r2_hidden(F,A) -> r2_hidden(E,B) & F = k1_funct_1(D,E)) & (r2_hidden(E,B) & k1_funct_1(D,E) = F -> r2_hidden(F,A) & k1_funct_1(C,F) = E))) & v2_funct_1(C) -> k1_xboole_0 = A | k2_funct_1(C) = D | k1_xboole_0 = B))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2095 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2096 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2097 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2098 (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(C) = A & A = k1_relat_1(B) -> 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]. 87.14/85.22 2099 (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(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(C)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D))) <-> k13_funct_3(A,B) = C))))))) # label(d8_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2100 (all A all B (v1_relat_1(B) & v1_funct_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]. 87.14/85.22 2101 (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]. 87.14/85.22 2102 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> 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]. 87.14/85.22 2103 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2104 (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,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> (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]. 87.14/85.22 2105 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(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]. 87.14/85.22 2106 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k5_relat_1(k1_funct_3(A),k1_funct_3(B)) = k1_funct_3(k5_relat_1(A,B)))))) # label(t20_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2107 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2108 (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]. 87.14/85.22 2109 (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) -> (k1_relat_1(C) = k1_relat_1(D) & k13_funct_3(D,C) = k13_funct_3(A,B) & k1_relat_1(B) = k1_relat_1(A) -> D = A & B = C))))))))) # label(t74_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2110 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t12_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2111 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (B = k1_relat_1(C) & r2_hidden(A,B) & B = k1_relat_1(D) -> 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]. 87.14/85.22 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]. 87.14/85.22 2113 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k7_funct_3(A,B) <-> k1_relat_1(C) = k2_zfmisc_1(A,B) & (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]. 87.14/85.22 2114 (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]. 87.14/85.22 2115 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_funct_1(k15_funct_3(A,B)) & v1_relat_1(k15_funct_3(A,B)))) # label(dt_k15_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2116 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k10_relat_1(B,k3_tarski(A)) = k3_tarski(k10_relat_1(k1_funct_3(B),A))))) # label(t19_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2117 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(D) = k1_relat_1(C) & r1_tarski(k2_relat_1(D),B) & r1_tarski(k2_relat_1(C),A) -> D = k5_relat_1(k13_funct_3(C,D),k10_funct_3(A,B)) & k5_relat_1(k13_funct_3(C,D),k9_funct_3(A,B)) = C))))) # label(t72_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2118 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funct_3(A)) & v1_relat_1(k1_funct_3(A)))) # label(dt_k1_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2119 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2120 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & A = k1_relat_1(B) -> A = k1_relat_1(k13_funct_3(B,C))))))) # label(t70_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2121 (all A all B (v1_relat_1(B) & v1_funct_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]. 87.14/85.22 2122 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r1_tarski(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k9_relat_1(A,C))) & k1_relat_1(B) = k1_zfmisc_1(k1_relat_1(A)) <-> B = k1_funct_3(A)))))) # label(d1_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2123 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D all E (r2_hidden(D,k1_relat_1(A)) & r2_hidden(E,k1_relat_1(B)) -> k1_funct_1(C,k4_tarski(D,E)) = k4_tarski(k1_funct_1(A,D),k1_funct_1(B,E)))) & k1_relat_1(C) = k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B)) <-> k15_funct_3(A,B) = C))))))) # label(d9_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2124 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2125 (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]. 87.14/85.22 2126 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,C) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) & v1_funct_2(E,A,C) -> 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)) & v1_funct_1(k16_funct_3(A,B,C,D,E,F)))) # label(dt_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2127 (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,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & -(k5_relat_1(k13_funct_3(D,E),k9_funct_3(B,C)) = D & k5_relat_1(k13_funct_3(D,E),k10_funct_3(B,C)) = E) & (C = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t81_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2128 (all A all B all C all D all E all F (v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & v1_funct_1(F) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) -> 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]. 87.14/85.22 2129 (all A all B all C (k4_funct_3(C,B) = k4_funct_3(A,B) & r1_tarski(C,B) & r1_tarski(A,B) -> C = A)) # label(t47_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2130 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> k7_funct_2(A,k2_zfmisc_1(B,C),C,k14_funct_3(A,B,C,D,E),k10_funct_3(B,C)) = E & k7_funct_2(A,k2_zfmisc_1(B,C),B,k14_funct_3(A,B,C,D,E),k9_funct_3(B,C)) = D)))))))) # label(t82_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2131 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2132 (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,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]. 87.14/85.22 2133 (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]. 87.14/85.22 2134 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2135 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k11_funct_3(A) <-> (all C (r2_hidden(C,A) -> k4_tarski(C,C) = k1_funct_1(B,C))) & A = k1_relat_1(B)))) # label(d7_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2136 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k15_funct_3(A,B)))))) # label(t88_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2137 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2138 (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]. 87.14/85.22 2139 (all A all B (A != k1_xboole_0 -> B = k2_relat_1(k7_funct_3(B,A)))) # label(t60_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2140 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_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]. 87.14/85.22 2141 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2142 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2143 (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]. 87.14/85.22 2144 (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]. 87.14/85.22 2145 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 87.14/85.22 2146 (all A all B (v1_funct_1(k4_funct_3(A,B)) & v1_relat_1(k4_funct_3(A,B)))) # label(dt_k4_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2147 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k10_relat_1(B,k3_tarski(A)) = k3_tarski(k9_relat_1(k3_funct_3(B),A))))) # label(t30_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2148 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k3_funct_3(A)) & v1_funct_1(k3_funct_3(A)))) # label(dt_k3_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2149 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) & (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> E = k1_funct_1(C,k4_tarski(D,E)))) <-> C = k8_funct_3(A,B)))) # label(d6_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2150 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2151 (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]. 87.14/85.22 2152 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> m2_relset_1(k6_funct_3(A,B),B,A) & v1_funct_2(k6_funct_3(A,B),B,A) & v1_funct_1(k6_funct_3(A,B)))) # label(dt_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2153 (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]. 87.14/85.22 2154 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_2(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_1(k3_funct_3(A)))) # label(t39_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2155 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s2_funct_3) & r2_hidden(C,f2_s2_funct_3) -> k1_funct_1(A,k4_tarski(B,C)) = f3_s2_funct_3(B,C))) & k1_relat_1(A) = k2_zfmisc_1(f1_s2_funct_3,f2_s2_funct_3))) # label(s2_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2156 (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]. 87.14/85.22 2157 (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]. 87.14/85.22 2158 (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(k13_funct_3(B,D),k15_funct_3(A,C)) = k13_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)))))))))) # label(t91_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2159 (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]. 87.14/85.22 2160 (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]. 87.14/85.22 2161 (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]. 87.14/85.22 2162 (all A all B (m2_relset_1(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)) & v1_funct_2(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)) & v1_funct_1(k5_funct_3(A,B)))) # label(dt_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2163 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(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]. 87.14/85.22 2164 (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) -> 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]. 87.14/85.22 2165 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) & -v1_xboole_0(C) -> k14_funct_3(A,B,C,D,E) = k13_funct_3(D,E))) # label(redefinition_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2166 (all A all B all C all D all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,C,D) & v1_funct_2(F,C,D) -> v1_funct_1(k15_funct_3(E,F)) & v1_funct_2(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) & m2_relset_1(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))) # label(t95_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2167 (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]. 87.14/85.22 2168 (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) & m2_relset_1(F,C,D) & v1_funct_2(F,C,D) -> -(k13_funct_3(k5_relat_1(k9_funct_3(A,C),E),k5_relat_1(k10_funct_3(A,C),F)) != k16_funct_3(A,C,B,D,E,F) & (k1_xboole_0 = D -> C = k1_xboole_0) & (k1_xboole_0 = B -> A = k1_xboole_0)))))) # label(t97_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2169 (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]. 87.14/85.22 2170 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2171 (all A all B (k1_xboole_0 != A -> k2_relat_1(k8_funct_3(A,B)) = B)) # label(t62_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2172 (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]. 87.14/85.22 2173 (all A all B all C (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> k2_funct_3(A,B,C) = k1_funct_3(C))) # label(redefinition_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2174 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k1_funct_3(B))) -> k1_funct_1(k1_funct_3(B),A) = k9_relat_1(B,A)))) # label(t8_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2175 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_3(B))) -> k1_funct_1(k3_funct_3(B),A) = k10_relat_1(B,A)))) # label(t24_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2176 (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]. 87.14/85.22 2177 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(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]. 87.14/85.22 2178 (all 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,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,A,C) & m2_relset_1(F,A,C) -> (all G (v1_funct_2(G,A,C) & m2_relset_1(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 & G = F))))))))))))) # label(t84_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2179 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k2_zfmisc_1(A,B) = k1_relat_1(D) & (all E all F (r2_hidden(F,B) & r2_hidden(E,A) -> k1_funct_1(D,k4_tarski(E,F)) = k1_funct_1(C,k4_tarski(E,F)))) & k2_zfmisc_1(A,B) = k1_relat_1(C) -> D = C))))) # label(t6_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2180 (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]. 87.14/85.22 2181 (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]. 87.14/85.22 2182 (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]. 87.14/85.22 2183 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2184 (all A all B all C all D all E (-v1_xboole_0(C) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & v1_funct_1(D) & -v1_xboole_0(B) -> m2_relset_1(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & v1_funct_2(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & v1_funct_1(k14_funct_3(A,B,C,D,E)))) # label(dt_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2185 (all A (v1_funct_1(k12_funct_3(A)) & v1_funct_2(k12_funct_3(A),A,k2_zfmisc_1(A,A)) & m2_relset_1(k12_funct_3(A),A,k2_zfmisc_1(A,A)))) # label(dt_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2186 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2187 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2188 (all A k11_funct_3(A) = k12_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2189 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2190 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2191 (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) -> 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]. 87.14/85.22 2192 (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_zfmisc_1(k2_relat_1(A)) & (all C (r1_tarski(C,k2_relat_1(A)) -> k10_relat_1(A,C) = k1_funct_1(B,C))) <-> B = k3_funct_3(A)))))) # label(d2_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2193 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t27_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2194 (all A all B all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) & v1_funct_2(D,A,C) & v1_funct_1(D) -> r1_tarski(k10_relat_1(k1_funct_3(D),B),k1_zfmisc_1(A)))))) # label(t14_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2195 (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(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]. 87.14/85.22 2196 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.22 2197 (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]. 87.14/85.23 2198 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k9_relat_1(k3_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t29_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2199 (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(C)) & r1_tarski(k10_relat_1(C,A),k2_relat_1(B)) -> r1_tarski(A,k2_relat_1(k5_relat_1(B,C)))))))) # label(t5_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2200 (all A all B all C (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> 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)) & v1_funct_1(k2_funct_3(A,B,C)))) # label(dt_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2201 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k10_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t28_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2202 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v2_funct_1(A) -> r1_tarski(k9_relat_1(k1_funct_3(A),B),k10_relat_1(k3_funct_3(A),B)))))) # label(t36_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2203 (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]. 87.14/85.23 2204 (all A all B all C (r2_hidden(A,k4_xboole_0(B,C)) -> np__0 = k1_funct_1(k4_funct_3(C,B),A))) # label(t43_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2205 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_2(F,A,C) & m2_relset_1(F,A,C) & v1_funct_1(F) -> (all G (v1_funct_2(G,A,C) & m2_relset_1(G,A,C) & v1_funct_1(G) -> (k13_funct_3(D,F) = k13_funct_3(E,G) -> E = D & G = F | k1_xboole_0 = C & A != k1_xboole_0 | B = k1_xboole_0 & A != k1_xboole_0))))))))) # label(t83_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2206 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> -((B = k1_xboole_0 -> 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))) & (C = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t78_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2207 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k2_funct_2(k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A)),k1_relat_1(A),k9_funct_3(k1_relat_1(A),k2_relat_1(A)),A))) # label(t100_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2208 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> (all F (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]. 87.14/85.23 2209 (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_1(k1_funct_3(C)) & v1_funct_2(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & m2_relset_1(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B))))) # label(t22_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2210 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_funct_1(k13_funct_3(A,B)) & v1_relat_1(k13_funct_3(A,B)))) # label(dt_k13_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2211 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2212 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k2_tarski(np__0,np__1)) & v1_funct_2(B,A,k2_tarski(np__0,np__1)) -> B = k4_funct_3(k3_funct_2(A,k2_tarski(np__0,np__1),B,k1_tarski(np__1)),A))) # label(t49_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2213 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,C,D) & m2_relset_1(F,C,D) -> (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]. 87.14/85.23 2214 (all A all B all C all D (r2_hidden(A,f1_s1_funct_3) & p1_s1_funct_3(A,B,C) & p1_s1_funct_3(A,B,D) & r2_hidden(B,f2_s1_funct_3) -> D = C)) & (all A all B -(r2_hidden(B,f2_s1_funct_3) & (all C -p1_s1_funct_3(A,B,C)) & r2_hidden(A,f1_s1_funct_3))) -> (exists A (k2_zfmisc_1(f1_s1_funct_3,f2_s1_funct_3) = k1_relat_1(A) & (all B all C (r2_hidden(B,f1_s1_funct_3) & r2_hidden(C,f2_s1_funct_3) -> p1_s1_funct_3(B,C,k1_funct_1(A,k4_tarski(B,C))))) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2215 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k4_funct_3(A,B) = C <-> k1_relat_1(C) = B & (all D (r2_hidden(D,B) -> (-r2_hidden(D,A) -> np__0 = k1_funct_1(C,D)) & (r2_hidden(D,A) -> k1_funct_1(C,D) = np__1)))))) # label(d3_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2216 (all A all 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) -> (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]. 87.14/85.23 2217 (all A all B (m2_relset_1(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & v1_funct_2(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & v1_funct_1(k10_funct_3(A,B)))) # label(dt_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2218 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2219 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> 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]. 87.14/85.23 2220 (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))) -> k4_tarski(k1_funct_1(A,C),k1_funct_1(B,D)) = k1_funct_1(k15_funct_3(A,B),k4_tarski(C,D)))))))) # label(t86_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2221 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_xboole_0 = k1_funct_1(k1_funct_3(A),k1_xboole_0))) # label(t9_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2222 (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]. 87.14/85.23 2223 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_2(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & m2_relset_1(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & v1_funct_1(k1_funct_3(A)))) # label(t21_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2224 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2225 (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]. 87.14/85.23 2226 (all A all B (-v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(D,B)) = k10_relat_1(k13_funct_3(C,D),k2_zfmisc_1(A,B)))))))) # label(t77_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2227 (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]. 87.14/85.23 2228 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k1_funct_3(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t10_funct_3) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2229 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,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]. 87.14/85.23 2230 (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]. 87.14/85.23 2231 $T # label(t6_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2232 (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]. 87.14/85.23 2233 (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]. 87.14/85.23 2234 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & m1_subset_1(F,B) & m1_subset_1(G,C) & m1_subset_1(H,D) & m1_subset_1(E,A) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> m1_subset_1(k5_domain_1(A,B,C,D,E,F,G,H),k4_zfmisc_1(A,B,C,D)))) # label(dt_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2235 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(E,A) & m1_subset_1(F,B) & m1_subset_1(H,D) & m1_subset_1(G,C) & -v1_xboole_0(D) -> k5_domain_1(A,B,C,D,E,F,G,H) = k4_mcart_1(E,F,G,H))) # label(redefinition_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2236 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists D (r2_hidden(D,C) & D = A & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_1_domain_1(B,C))))) # label(fraenkel_a_2_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2237 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k14_domain_1(A,B,C,D) = k17_mcart_1(D))) # label(redefinition_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2238 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k6_domain_1(A,B) = k1_tarski(B))) # label(redefinition_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2239 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (r2_hidden(A,k4_zfmisc_1(B,C,D,E)) <-> (exists F ((exists G ((exists H (m1_subset_1(H,D) & (exists I (m1_subset_1(I,E) & k4_mcart_1(F,G,H,I) = A)))) & m1_subset_1(G,C))) & m1_subset_1(F,B)))))))))))) # label(t31_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2240 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(E) & -v1_xboole_0(C) -> (r2_hidden(A,a_4_2_domain_1(B,C,D,E)) <-> (exists F exists G exists H exists I (m1_subset_1(F,B) & m1_subset_1(G,C) & m1_subset_1(I,E) & p1_s4_domain_1(F,G,H,I) & A = k5_domain_1(B,C,D,E,F,G,H,I) & m1_subset_1(H,D)))))) # label(fraenkel_a_4_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2241 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_3_domain_1(A,B,C) = k6_subset_1(A,B,C))))))) # label(t60_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2242 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & C = A)) <-> r2_hidden(A,a_1_0_domain_1(B))))) # label(fraenkel_a_1_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2243 $T # label(t47_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2244 $T # label(t27_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2245 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> (all D (m1_subset_1(D,k2_zfmisc_1(A,B)) -> (k1_mcart_1(C) = k1_mcart_1(D) & k2_mcart_1(C) = k2_mcart_1(D) -> C = D))))))))) # label(t12_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2246 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) -> (r2_hidden(A,a_3_0_domain_1(B,C,D)) <-> (exists E exists F exists G (m1_subset_1(G,D) & A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(F,C) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2247 (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]. 87.14/85.23 2248 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> F = A))))))) <-> k5_mcart_1(B,C,D,E) = A))))))))) # label(t24_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2249 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (m1_subset_1(E,B) & -(r2_hidden(E,C) <-> r2_hidden(E,D)) & E = A)) <-> r2_hidden(A,a_3_7_domain_1(B,C,D))))) # label(fraenkel_a_3_7_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2250 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F ((exists G ((exists H (m1_subset_1(H,C) & (exists I ((exists J (F = k4_mcart_1(G,H,I,J) & m1_subset_1(J,E))) & m1_subset_1(I,D))))) & m1_subset_1(G,B))) <-> r2_hidden(F,A))) <-> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t33_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2251 (all A all B (-v1_xboole_0(B) -> ((exists C (A = C & p2_s5_domain_1(C) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_4_domain_1(B))))) # label(fraenkel_a_1_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2252 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_5_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t62_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2253 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> a_6_0_domain_1(A,B,C,D,E,F) = k13_mcart_1(A,B,C,D,E,F))))))))))))) # label(t54_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2254 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k7_domain_1(A,C,B) = k7_domain_1(A,B,C))) # label(commutativity_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2255 $T # label(t29_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2256 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(B,A) -> k10_domain_1(A,B,C,D,E,F) = k3_enumset1(B,C,D,E,F))) # label(redefinition_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2257 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p1_s5_domain_1(B) -> p2_s5_domain_1(B)))) -> r1_tarski(a_1_3_domain_1(A),a_1_4_domain_1(A))))) # label(s5_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2258 (all A all B (-v1_xboole_0(B) -> ((exists C (C = A & -$T & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_1_domain_1(B))))) # label(fraenkel_a_1_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2259 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E ((exists F ((exists G ((exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))) & m1_subset_1(G,C))) & m1_subset_1(F,B))) <-> r2_hidden(E,A))) -> k3_zfmisc_1(B,C,D) = A))))))))) # label(t16_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2260 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> -(r2_hidden(A,k2_zfmisc_1(B,C)) & (all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,C) -> A != k4_tarski(D,E)))))))))) # label(t9_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2261 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> k2_mcart_1(C) = k3_domain_1(A,B,C))) # label(redefinition_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2262 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k11_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (F = k5_domain_1(B,C,D,E,G,H,I,J) -> J = A)))))))))))))))))))) # label(t43_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2263 $T # label(t20_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2264 (all A ((exists B (m1_subset_1(B,f1_s10_domain_1) & p1_s10_domain_1(B) & B = A)) <-> r2_hidden(A,a_0_4_domain_1))) # label(fraenkel_a_0_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2265 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & p1_s6_domain_1(C) & C = A)) <-> r2_hidden(A,a_1_5_domain_1(B))))) # label(fraenkel_a_1_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2266 $T # label(t13_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2267 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_6_domain_1(B,C,D)) <-> (exists E ((-r2_hidden(E,D) <-> r2_hidden(E,C)) & E = A & m1_subset_1(E,B)))))) # label(fraenkel_a_3_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2268 (all A (r2_hidden(A,a_0_3_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p1_s10_domain_1(B) & p2_s10_domain_1(B) & B = A)))) # label(fraenkel_a_0_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2269 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(A) -> k16_domain_1(A,B,C,D) = k19_mcart_1(D))) # label(redefinition_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2270 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) & -v1_xboole_0(E) -> (r2_hidden(A,a_4_0_domain_1(B,C,D,E)) <-> (exists F exists G exists H exists I (m1_subset_1(I,E) & A = k5_domain_1(B,C,D,E,F,G,H,I) & m1_subset_1(H,D) & m1_subset_1(G,C) & m1_subset_1(F,B)))))) # label(fraenkel_a_4_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2271 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F (r2_hidden(F,A) <-> (exists G ((exists H (m1_subset_1(H,C) & (exists I ((exists J (m1_subset_1(J,E) & k4_mcart_1(G,H,I,J) = F)) & m1_subset_1(I,D))))) & m1_subset_1(G,B))))) -> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t32_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2272 (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]. 87.14/85.23 2273 $T # label(t38_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2274 (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]. 87.14/85.23 2275 (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]. 87.14/85.23 2276 (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]. 87.14/85.23 2277 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> ((exists E exists F exists G (m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(G,D) & k4_domain_1(B,C,D,E,F,G) = A & p1_s3_domain_1(E,F,G))) <-> r2_hidden(A,a_3_8_domain_1(B,C,D))))) # label(fraenkel_a_3_8_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2278 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> G = A))))))) <-> k6_mcart_1(B,C,D,E) = A))))))))) # label(t25_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2279 (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]. 87.14/85.23 2280 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k8_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> G = A)))))))))))))))))))) # label(t40_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2281 (all A all B all C all D all E (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_4_1_domain_1(B,C,D,E)) <-> (exists F exists G (m1_subset_1(F,B) & m1_subset_1(G,C) & r2_hidden(G,E) & r2_hidden(F,D) & k1_domain_1(B,C,F,G) = A))))) # label(fraenkel_a_4_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2282 (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]. 87.14/85.23 2283 $T # label(t36_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2284 $T # label(t46_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2285 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists E (E = A & (r2_hidden(E,C) & -r2_hidden(E,D) | r2_hidden(E,D) & -r2_hidden(E,C)) & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_4_domain_1(B,C,D))))) # label(fraenkel_a_3_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2286 $T # label(t7_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2287 (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]. 87.14/85.23 2288 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & A = C & p1_s1_domain_1(C)))))) # label(fraenkel_a_1_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2289 $T # label(t3_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2290 (all A ((exists B exists C (m1_subset_1(C,f2_s9_domain_1) & p1_s9_domain_1(B,C) & A = f4_s9_domain_1(B,C) & m1_subset_1(B,f1_s9_domain_1))) <-> r2_hidden(A,a_0_2_domain_1))) # label(fraenkel_a_0_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2291 $T # label(t1_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2292 (all A (r2_hidden(A,a_0_1_domain_1) <-> (exists B (m1_subset_1(B,f1_s8_domain_1) & p1_s8_domain_1(B) & f3_s8_domain_1(B) = A)))) # label(fraenkel_a_0_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2293 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(C) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(I,k1_zfmisc_1(E)) & m1_subset_1(F,k1_zfmisc_1(B)) & -v1_xboole_0(E) & -v1_xboole_0(D) & -v1_xboole_0(B) -> ((exists J exists K exists L exists M (m1_subset_1(K,C) & m1_subset_1(M,E) & A = k5_domain_1(B,C,D,E,J,K,L,M) & r2_hidden(J,F) & r2_hidden(M,I) & r2_hidden(L,H) & r2_hidden(K,G) & m1_subset_1(L,D) & m1_subset_1(J,B))) <-> r2_hidden(A,a_8_0_domain_1(B,C,D,E,F,G,H,I))))) # label(fraenkel_a_8_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2294 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) -> ((exists D exists E (k1_domain_1(B,C,D,E) = A & p1_s2_domain_1(D,E) & m1_subset_1(E,C) & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_3_domain_1(B,C))))) # label(fraenkel_a_2_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2295 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (A = E & -r2_hidden(E,D) & r2_hidden(E,C) & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_3_domain_1(B,C,D))))) # label(fraenkel_a_3_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2296 (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]. 87.14/85.23 2297 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k7_domain_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2298 (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]. 87.14/85.23 2299 $T # label(t11_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2300 $T # label(t10_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2301 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_6_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & A = C & p2_s6_domain_1(C)))))) # label(fraenkel_a_1_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2302 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> m1_subset_1(k10_domain_1(A,B,C,D,E,F),k1_zfmisc_1(A)))) # label(dt_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2303 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,B) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)))) # label(dt_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2304 (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]. 87.14/85.23 2305 $T # label(t34_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2306 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(A) -> k17_domain_1(A,B,C,D) = k20_mcart_1(D))) # label(redefinition_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2307 (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]. 87.14/85.23 2308 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((exists E (m1_subset_1(E,B) & (exists F ((exists G (m1_subset_1(G,D) & A = k3_mcart_1(E,F,G))) & m1_subset_1(F,C))))) <-> r2_hidden(A,k3_zfmisc_1(B,C,D))))))))) # label(t15_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2309 (all A (r2_hidden(A,a_0_0_domain_1) <-> (exists B (m1_subset_1(B,f1_s7_domain_1) & p1_s7_domain_1(B) & B = A)))) # label(fraenkel_a_0_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2310 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> a_3_0_domain_1(A,B,C) = k3_zfmisc_1(A,B,C))))))) # label(t50_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2311 (all A all B all C all D (m1_subset_1(C,A) & m1_subset_1(D,B) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k4_tarski(C,D) = k1_domain_1(A,B,C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2312 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> H = A))))))))) <-> k9_mcart_1(B,C,D,E,F) = A))))))))))) # label(t41_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2313 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,A) & m1_subset_1(E,B) & m1_subset_1(F,C) & -v1_xboole_0(C) -> m1_subset_1(k4_domain_1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)))) # label(dt_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2314 (all A all B all C all D all E all F all G (m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(G,k1_zfmisc_1(D)) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_6_0_domain_1(B,C,D,E,F,G)) <-> (exists H exists I exists J (m1_subset_1(H,B) & m1_subset_1(I,C) & r2_hidden(H,E) & r2_hidden(I,F) & r2_hidden(J,G) & k4_domain_1(B,C,D,H,I,J) = A & m1_subset_1(J,D)))))) # label(fraenkel_a_6_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2315 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_5_domain_1(B,C,D)) <-> (exists E (A = E & (-r2_hidden(E,C) <-> r2_hidden(E,D)) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2316 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k2_tarski(B,C) = k7_domain_1(A,B,C))) # label(redefinition_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2317 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> m1_subset_1(k3_domain_1(A,B,C),B))) # label(dt_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2318 $T # label(t35_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2319 $T # label(t2_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2320 $T # label(t18_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2321 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(B,A) -> m1_subset_1(k9_domain_1(A,B,C,D,E),k1_zfmisc_1(A)))) # label(dt_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2322 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(F,A) & m1_subset_1(H,A) & m1_subset_1(G,A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> k12_domain_1(A,B,C,D,E,F,G,H) = k5_enumset1(B,C,D,E,F,G,H))) # label(redefinition_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2323 $T # label(t30_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2324 $T # label(t21_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2325 $T # label(t4_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2326 $T # label(t39_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2327 (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]. 87.14/85.23 2328 $T # label(t5_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2329 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) -> k2_enumset1(B,C,D,E) = k9_domain_1(A,B,C,D,E))) # label(redefinition_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2330 $T # label(t44_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2331 $T # label(t19_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2332 (all A all B all C all D all E all F all G (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & -v1_xboole_0(A) -> k11_domain_1(A,B,C,D,E,F,G) = k4_enumset1(B,C,D,E,F,G))) # label(redefinition_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2333 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) -> m1_subset_1(k14_domain_1(A,B,C,D),A))) # label(dt_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2334 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> k12_mcart_1(A,B,C,D) = a_4_1_domain_1(A,B,C,D))))))))) # label(t53_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2335 (all A all B all C all D all E all F all G all H all I (m1_subset_1(E,A) & m1_subset_1(H,A) & m1_subset_1(I,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k6_enumset1(B,C,D,E,F,G,H,I) = k13_domain_1(A,B,C,D,E,F,G,H,I))) # label(redefinition_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2336 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_4_domain_1(A,B,C))))))) # label(t61_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2337 (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]. 87.14/85.23 2338 $T # label(t23_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2339 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> (A = k7_mcart_1(B,C,D,E) <-> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> H = A)))))))))))))))) # label(t26_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2340 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p2_s6_domain_1(B) <-> p1_s6_domain_1(B)))) -> a_1_6_domain_1(A) = a_1_5_domain_1(A)))) # label(s6_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2341 (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]. 87.14/85.23 2342 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(A) -> m1_subset_1(k2_domain_1(A,B,C),A))) # label(dt_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2343 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k2_zfmisc_1(A,B) = a_2_0_domain_1(A,B))))) # label(t49_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2344 (all A all B all C all D all E all F all G (m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k11_domain_1(A,B,C,D,E,F,G),k1_zfmisc_1(A)))) # label(dt_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2345 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_3_domain_1(B)) <-> (exists C (A = C & p1_s5_domain_1(C) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2346 (all A all B all C all D all E all F all G all H (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> m1_subset_1(k12_domain_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(A)))) # label(dt_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2347 $T # label(t37_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2348 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_0_domain_1(B,C)) <-> (exists D exists E (k1_domain_1(B,C,D,E) = A & m1_subset_1(E,C) & m1_subset_1(D,B)))))) # label(fraenkel_a_2_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2349 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E (r2_hidden(E,A) <-> (exists F (m1_subset_1(F,B) & (exists G (m1_subset_1(G,C) & (exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))))))))) <-> A = k3_zfmisc_1(B,C,D)))))))))) # label(t17_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2350 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> (k8_mcart_1(A,B,C,D,E) = k8_mcart_1(A,B,C,D,F) & k9_mcart_1(A,B,C,D,F) = k9_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = k11_mcart_1(A,B,C,D,F) & k10_mcart_1(A,B,C,D,E) = k10_mcart_1(A,B,C,D,F) -> F = E))))))))))))) # label(t45_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2351 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_2_domain_1(B,C)) <-> (exists D (m1_subset_1(D,B) & -r2_hidden(D,C) & A = D))))) # label(fraenkel_a_2_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2352 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> (k5_mcart_1(A,B,C,D) = k5_mcart_1(A,B,C,E) & k7_mcart_1(A,B,C,E) = k7_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) = k6_mcart_1(A,B,C,E) -> E = D))))))))))) # label(t28_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2353 (all A all B all C all D (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> k8_domain_1(A,B,C,D) = k1_enumset1(B,C,D))) # label(redefinition_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2354 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(B,A) -> m1_subset_1(k8_domain_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2355 $T # label(t22_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2356 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) -> k18_mcart_1(D) = k15_domain_1(A,B,C,D))) # label(redefinition_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2357 $T # label(t14_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2358 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,A) & m1_subset_1(E,B) & m1_subset_1(F,C) -> k4_domain_1(A,B,C,D,E,F) = k3_mcart_1(D,E,F))) # label(redefinition_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2359 $T # label(t8_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2360 (all A (-v1_xboole_0(A) -> a_1_0_domain_1(A) = A)) # label(t48_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2361 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = a_3_2_domain_1(A,B,C))))))) # label(t59_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2362 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (A = k10_mcart_1(B,C,D,E,F) <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> I = A)))))))))))))))))))) # label(t42_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2363 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_1_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & A = E & r2_hidden(E,C) & r2_hidden(E,D)))))) # label(fraenkel_a_3_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.23 2364 (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]. 87.14/85.23 2365 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(I,A) & m1_subset_1(D,A) & m1_subset_1(B,A) -> m1_subset_1(k13_domain_1(A,B,C,D,E,F,G,H,I),k1_zfmisc_1(A)))) # label(dt_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2366 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists E ((r2_hidden(E,C) | r2_hidden(E,D)) & E = A & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_2_domain_1(B,C,D))))) # label(fraenkel_a_3_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2367 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2368 (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_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) -> k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E)) = k8_funct_2(A,A,B,k2_binop_1(A,A,A,C,D,E)))))) <-> r7_binop_1(A,B,C)))))))) # label(d20_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2369 (all A (m1_relset_1(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) -> (v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_funct_1(A) -> v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_binop_1(A,k1_xboole_0) & v2_binop_1(A,k1_xboole_0) & v1_xboole_0(A)))) # label(cc1_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2370 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_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) <-> r5_binop_1(A,C,B))))))))) # label(t27_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2371 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2372 (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) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> k1_binop_1(B,C,C) = C))))) # label(d4_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2373 (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) -> (r3_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(B,D,C) & D = k1_binop_1(B,C,D)))))))) # label(t11_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2374 (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 (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r5_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> 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))))))))))))))) # label(d19_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2375 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2376 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2377 (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) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_binop_1(B,C,k1_binop_1(B,D,E)) = k1_binop_1(B,k1_binop_1(B,C,D),E)))))))))) # label(d3_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2378 (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 (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) -> 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))))))))))))) # label(d9_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2379 (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) -> (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]. 87.14/85.24 2380 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2381 (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_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),F) = 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)))))))))))))))) # label(t25_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2382 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2383 (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,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)))))))) <-> r4_binop_1(A,B,C)))))))) # label(d18_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 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 (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_binop_1(B,C,D) = k1_binop_1(B,D,C))))) <-> v1_binop_1(B,A)))) # label(d2_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2385 (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 (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]. 87.14/85.24 2386 (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_subset_1(F,B) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> 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]. 87.14/85.24 2387 (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) -> (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]. 87.14/85.24 2388 (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) <-> r2_binop_1(A,C,B))))))) # label(t15_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2389 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r1_binop_1(A,C,B) <-> r2_binop_1(A,C,B))))))) # label(t16_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2390 (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 (m1_subset_1(D,A) -> D = k2_binop_1(A,A,A,C,B,D))) <-> r1_binop_1(A,B,C)))))))) # label(d16_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2391 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2392 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2393 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,D,k2_binop_1(A,A,A,B,E,F)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,D,F)))))))))))))))) # label(t24_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2394 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C))))) # label(d1_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2395 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> m1_subset_1(k3_binop_1(A,B),A))) # label(dt_k3_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2396 (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) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> C = k2_binop_1(A,A,A,B,C,C)))))))) # label(d15_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2397 (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) -> (r3_binop_1(A,C,B) <-> r1_binop_1(A,C,B))))))) # label(t14_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2398 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r3_binop_1(A,B,C) <-> r2_binop_1(A,B,C) & r1_binop_1(A,B,C)))))) # label(d7_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2399 (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) -> ((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]. 87.14/85.24 2400 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2401 (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & (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_1(A))) # label(s2_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2402 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_binop_1(A,D,B) & r1_binop_1(A,C,B) -> D = C))))))) # label(t17_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2403 (all A all B (m1_subset_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> k1_binop_1(C,D,B) = D)) <-> r2_binop_1(A,B,C)))))) # label(d6_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2404 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_funct_1(B,k1_binop_1(C,D,E)) = k1_binop_1(C,k1_funct_1(B,D),k1_funct_1(B,E)))))) <-> r7_binop_1(A,B,C)))))) # label(d12_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2405 (all A all B all C all D all E all F (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(B) & -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]. 87.14/85.24 2406 (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) -> (r1_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> k1_binop_1(C,B,D) = D))))))) # label(d5_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2407 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r5_binop_1(A,C,B) <-> r4_binop_1(A,C,B))))))))) # label(t28_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2408 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2409 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k2_binop_1(A,B,C,E,F,G) = k2_binop_1(A,B,C,D,F,G))))) -> E = D))))))))))) # label(t2_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2410 (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) <-> r4_binop_1(A,C,B))))))))) # label(t26_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2411 (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_2(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & m2_relset_1(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & (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)))))) & v1_funct_1(A))) # label(s1_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2412 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2413 (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]. 87.14/85.24 2414 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2415 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2416 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (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]. 87.14/85.24 2417 (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 (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]. 87.14/85.24 2418 (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]. 87.14/85.24 2419 (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 (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]. 87.14/85.24 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 (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r6_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F)) & k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F)) = k1_binop_1(B,k1_binop_1(C,D,E),F)))))))))))) # label(t23_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2421 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2422 (all A all B all C all D (-v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2423 (all A all B all C (v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k3_funcop_1(A,B,C)) & v1_relat_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2424 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F) = k8_funct_2(B,A,D,G))) -> k7_funcop_1(A,B,C,E,F) = D))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2425 (all A (k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2426 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_funct_1(k4_funcop_1(A,B,C)) & v1_relat_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2427 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k4_funcop_1(C,A,D)) = k4_funcop_1(C,k5_relat_1(B,A),D)))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2428 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(D,B,A) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> k3_funcop_1(C,D,E) = k6_funcop_1(A,B,C,D,E))) # label(redefinition_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2429 (all A all B k10_relat_1(k2_funcop_1(A,B),k1_tarski(B)) = A) # label(t21_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2430 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) = k8_funct_2(B,A,D,G))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2431 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2432 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k8_funcop_1(A,B,C,D,E)))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2433 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> (all E (m1_subset_1(E,A) -> k1_funct_1(k1_funcop_1(D),E) = k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))))))))))))) # label(t71_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2434 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> ((all E (r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)) = k1_funct_1(D,E))) & k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) -> k3_funcop_1(C,A,B) = D))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2435 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D)) = k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D)))))))))))))) # label(t77_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2436 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) -> D = k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)))) # label(involutiveness_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2437 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)))))))))))))) # label(t48_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2438 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D)) = k4_funcop_1(C,k7_relat_1(A,B),D)))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2439 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> -((all D all E k4_tarski(D,E) != k1_funct_1(A,C)) & k1_funct_1(A,C) != k1_funct_1(B,C)) & (all D all E (k4_tarski(D,E) = k1_funct_1(A,C) -> k4_tarski(E,D) = k1_funct_1(B,C))))) <-> k1_funcop_1(A) = B))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2440 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E) = k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F))))))))))))) # label(t60_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2441 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funcop_1(A) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2442 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A) = k5_funcop_1(B,C,A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2443 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k5_relat_1(k3_funcop_1(D,B,C),A) = k3_funcop_1(k5_relat_1(D,A),B,C))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2444 (all A k13_funct_3(k6_partfun1(A),k6_partfun1(A)) = k12_funct_3(A)) # label(t2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2445 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C))))))) # label(t70_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2446 (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]. 87.14/85.24 2447 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2448 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k4_funcop_1(C,B,D),A) = k4_funcop_1(k5_relat_1(C,A),B,D)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2449 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k5_relat_1(A,k2_funcop_1(B,C)) = k2_funcop_1(k10_relat_1(A,B),C)))) # label(t25_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2450 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))) = k8_funcop_1(B,A,C,E,D))))))))))) # label(t69_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2451 (all A all B all C (-r2_hidden(B,C) -> k10_relat_1(k2_funcop_1(A,B),C) = k1_xboole_0)) # label(t22_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2452 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v1_binop_1(C,B) -> k7_funcop_1(B,A,C,D,E) = k8_funcop_1(B,A,C,E,D)))))))))))) # label(t79_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2453 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2454 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A)) -> k3_xboole_0(k1_relat_1(B),k1_relat_1(C)) = k1_relat_1(k3_funcop_1(A,B,C))))))))) # label(t84_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2455 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A) = k4_funcop_1(A,B,C)))))) # label(d4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2456 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2457 (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]. 87.14/85.24 2458 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,B,A) & m1_subset_1(E,A) & m1_relset_1(D,B,A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) -> m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k7_funcop_1(A,B,C,D,E)))) # label(dt_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2459 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> v1_funct_1(k4_funcop_1(C,D,E)) & v1_funct_2(k4_funcop_1(C,D,E),A,B) & m2_relset_1(k4_funcop_1(C,D,E),A,B))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2460 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E)) = k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E)))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2461 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> ((all G (m1_subset_1(G,A) -> k8_funct_2(A,B,F,G) = k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)))) -> k6_funcop_1(B,A,C,D,E) = F))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2462 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2463 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) -> k2_funcop_1(k1_relat_1(A),B) = A)))) # label(t15_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2464 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k2_funcop_1(B,k1_funct_1(A,C)) = k5_relat_1(k2_funcop_1(B,C),A))))) # label(t23_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2465 (all A all B (A != k1_xboole_0 -> k1_tarski(B) = k2_relat_1(k2_funcop_1(A,B)))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2466 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(B,D) = k7_relat_1(A,D) -> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D)))))))))) # label(t29_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2467 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D all E (v1_relat_1(E) & v1_funct_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,C,A),D) = k7_relat_1(k3_funcop_1(E,C,B),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2468 (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]. 87.14/85.24 2469 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) -> v1_funct_1(k10_funcop_1(A,B,C,D)) & v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 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 (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F) = k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F))))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2471 (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]. 87.14/85.24 2472 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,A) & v1_funct_2(D,A,A) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C) = k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2473 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k4_funcop_1(B,A,D))) -> k1_funct_1(k4_funcop_1(B,A,D),C) = k1_binop_1(B,k1_funct_1(A,C),D))))))) # label(t35_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2474 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(k7_relat_1(A,C),B)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2475 (all A all B (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) # label(fc7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2476 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2477 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k5_funcop_1(D,E,B),C) = k7_relat_1(k5_funcop_1(D,E,A),C))))))))) # label(t43_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2478 (all A (v1_relat_1(A) -> (all B all C (k2_zfmisc_1(B,C) = A -> B = k1_xboole_0 | B = k1_relat_1(A) & k2_relat_1(A) = C | C = k1_xboole_0)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2479 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k5_relat_1(C,k3_funcop_1(D,A,B)) = k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)))))))))) # label(t31_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2480 (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]. 87.14/85.24 2481 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(A) -> k2_relat_1(D) = k9_funcop_1(A,B,C,D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2482 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2483 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C))))))))) # label(t55_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2484 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,B) & m2_relset_1(E,B,B) -> k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))))))))))))) # label(t52_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2485 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F)) = k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F)))))))))))))) # label(t76_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2486 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & m1_subset_1(D,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k8_funcop_1(A,B,C,D,E) = k5_funcop_1(C,D,E))) # label(redefinition_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2487 (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]. 87.14/85.24 2488 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(B) & k1_relat_1(A) = k1_xboole_0 -> B = A))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2489 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = B)) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2490 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = k1_relat_1(A) -> k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B))))))))) # label(t3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2491 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k5_relat_1(B,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2492 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B))))))) # label(t46_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2493 (all A all B (-v1_xboole_0(B) -> v1_funct_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2494 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> k5_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2495 (exists A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2496 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E) = k8_funct_2(B,A,D,E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2497 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & m1_subset_1(E,A) & v1_funct_1(C) & -v1_xboole_0(B) -> k7_funcop_1(A,B,C,D,E) = k4_funcop_1(C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2498 (all A all B (r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) & A = k1_relat_1(k2_funcop_1(A,B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2499 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_funcop_1(k5_relat_1(C,A),D,B) = k5_relat_1(k5_funcop_1(C,D,B),A)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2500 (all A (v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2501 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2502 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k7_funcop_1(B,A,C,D,E) = k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2503 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C))))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2504 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (v3_binop_1(C,B) -> k6_funcop_1(B,A,C,D,D) = D))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2505 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2506 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k4_funcop_1(D,B,E),C) = k7_relat_1(k4_funcop_1(D,A,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2507 (all A all B all C (r2_hidden(B,C) -> A = k10_relat_1(k2_funcop_1(A,B),C))) # label(t20_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2508 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funcop_1(A)) & v1_relat_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2509 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C))))))) # label(t56_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2510 (all A all B all C (r2_hidden(C,B) -> v1_funct_1(k2_funcop_1(A,C)) & v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(k2_funcop_1(A,C),A,B))) # label(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2511 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A))) -> k1_binop_1(B,D,k1_funct_1(A,C)) = k1_funct_1(k5_funcop_1(B,D,A),C))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2512 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2513 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) = k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F))))))))))))))) # label(t78_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.24 2514 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E)))))))))))) # label(t82_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2515 (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]. 87.14/85.25 2516 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k1_funcop_1(D) = k10_funcop_1(A,B,C,D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2517 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2518 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) <-> v1_funcop_1(A)))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2519 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> m2_relset_1(k5_funcop_1(C,E,D),A,B) & v1_funct_2(k5_funcop_1(C,E,D),A,B) & v1_funct_1(k5_funcop_1(C,E,D)))))))))))) # label(t65_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2520 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)) = k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2521 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> v1_funct_1(k3_funcop_1(C,D,E)) & m2_relset_1(k3_funcop_1(C,D,E),A,B) & v1_funct_2(k3_funcop_1(C,D,E),A,B))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2522 (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]. 87.14/85.25 2523 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2524 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2525 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k4_relat_1(k9_funcop_1(A,B,C,D)) = k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2526 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2527 (all A all B all C all D all E (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k6_funcop_1(A,B,C,D,E)) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2528 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)))))) # label(t6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2529 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2530 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) -> v1_relat_1(k5_funcop_1(A,B,C)) & v1_funct_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2531 (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]. 87.14/85.25 2532 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(B != k1_xboole_0 & r2_hidden(C,k1_relat_1(A)) & k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)) = k1_xboole_0)))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2533 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,D,E) = k6_funcop_1(B,A,C,E,D)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2534 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))) = k6_funcop_1(B,A,C,D,D))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2535 (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]. 87.14/85.25 2536 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k13_funct_3(A,k7_relat_1(B,C)) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2537 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(k3_funcop_1(C,A,B),D))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2538 (all A all B all C k1_funcop_1(k2_funcop_1(A,k4_tarski(B,C))) = k2_funcop_1(A,k4_tarski(C,B))) # label(t26_funcop_1) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2539 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_4(A,B)) & v1_relat_1(k1_funct_4(A,B)))) # label(dt_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2540 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2541 (all A all B all C all D all E (-v1_xboole_0(E) -> (all F (-v1_xboole_0(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),E) & m2_relset_1(G,k2_zfmisc_1(A,B),E) -> (all H (m2_relset_1(H,k2_zfmisc_1(C,D),F) & v1_funct_2(H,k2_zfmisc_1(C,D),F) & v1_funct_1(H) -> m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)) & v1_funct_1(k3_funct_4(G,H)))))))))) # label(t64_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2542 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_funct_4(A,B)) <-> r1_partfun1(A,B)))))) # label(t29_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2543 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> A = k1_funct_4(A,A))) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2544 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> B = k1_funct_4(B,A) & k1_funct_4(A,B) = B))))) # label(t79_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2545 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D)))))) # label(t51_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2546 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r1_partfun1(B,C) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2547 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (C != k1_xboole_0 -> k2_funct_4(k2_funct_4(D)) = D))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2548 (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]. 87.14/85.25 2549 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(C,k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(A,C))))))) # label(t76_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2550 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> k2_zfmisc_1(B,A) = k1_relat_1(k2_funct_4(C))))) # label(t47_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2551 (all A all B all C all D (A != B -> k1_funct_1(k4_funct_4(A,B,C,D),B) = D & k1_funct_1(k4_funct_4(A,B,C,D),A) = C)) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2552 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> k1_funct_4(B,A) = k1_funct_4(A,B)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2553 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),k7_relat_1(k8_relat_1(A,D),B))))))) # label(t10_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2554 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(C),k1_relat_1(A)) & r1_tarski(k2_relat_1(D),k1_relat_1(B)) & r1_partfun1(A,B) -> k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B)) = k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B))))))))))) # label(t73_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2555 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(A),k1_relat_1(k1_funct_4(A,B))) & r1_tarski(k1_relat_1(B),k1_relat_1(k1_funct_4(A,B))))))) # label(t11_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2556 (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]. 87.14/85.25 2557 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (-r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,A) = k1_funct_1(k1_funct_4(C,B),A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2558 (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]. 87.14/85.25 2559 (all A all B all C all D all E all F all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (v1_funct_2(H,k2_zfmisc_1(D,E),F) & m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_1(H) -> -(C != k1_xboole_0 & F != k1_xboole_0 & -(v1_funct_1(k3_funct_4(G,H)) & m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)))))))) # label(t63_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2560 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) -> v1_funct_1(k5_funct_4(A,B,C,D,E)) & v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A))) # label(dt_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2561 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(A,k1_funct_4(B,A)))))) # label(t26_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2562 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2563 (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]. 87.14/85.25 2564 (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]. 87.14/85.25 2565 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(k2_funct_4(C))) -> k1_funct_1(C,k4_tarski(B,A)) = k1_funct_1(k2_funct_4(C),k4_tarski(A,B))))) # label(t44_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2566 (all A all B all C all D k4_funct_4(A,B,C,D) = k1_funct_4(k2_funcop_1(k1_tarski(A),C),k2_funcop_1(k1_tarski(B),D))) # label(d4_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2567 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,k1_funct_4(B,C)))))))) # label(t15_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2568 (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]. 87.14/85.25 2569 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k1_funct_4(B,C))) <-> r2_hidden(A,k1_relat_1(B)) | r2_hidden(A,k1_relat_1(C))))))) # label(t13_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2570 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (v1_partfun1(D,A,B) -> k1_funct_4(C,D) = D))))) # label(t37_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2571 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_xboole_0(A,B) = k1_funct_4(A,B) <-> r1_partfun1(A,B)))))) # label(t31_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2572 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_relat_1(k2_funct_4(C)) = k2_relat_1(C)))) # label(t48_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2573 (all A all B all C all D (A != C -> k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t71_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2574 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(A)) = A))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2575 (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]. 87.14/85.25 2576 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2577 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D all E all F all G (r2_hidden(k4_tarski(D,E),k1_relat_1(A)) & r2_hidden(k4_tarski(F,G),k1_relat_1(B)) -> k4_tarski(k1_funct_1(A,k4_tarski(D,E)),k1_funct_1(B,k4_tarski(F,G))) = k1_funct_1(C,k4_tarski(k4_tarski(D,F),k4_tarski(E,G))))) & (all D (r2_hidden(D,k1_relat_1(C)) <-> (exists E exists F exists G exists H (k4_tarski(k4_tarski(E,G),k4_tarski(F,H)) = D & r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & r2_hidden(k4_tarski(E,F),k1_relat_1(A)))))) <-> C = k3_funct_4(A,B)))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2578 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k2_funct_4(A)),k2_relat_1(A)))) # label(t42_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2579 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2580 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k3_funct_4(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t59_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2581 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (C != k1_xboole_0 -> v1_funct_1(k2_funct_4(D)) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C)))) # label(t50_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2582 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> B = k7_relat_1(k1_funct_4(A,B),k1_relat_1(B)))))) # label(t24_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2583 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> k4_funct_4(B,C,D,E) = k5_funct_4(A,B,C,D,E))) # label(redefinition_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2584 (all A all B all C all D all E all F (k4_funct_4(A,B,E,F) = k4_funct_4(A,B,C,D) -> E = C & F = D | B = A)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2585 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_xboole_0(k1_relat_1(A),C) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(B,C))))))) # label(t77_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2586 (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]. 87.14/85.25 2587 (all A all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> k1_funct_4(C,D) = D)))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2588 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_funct_4(A) = B <-> (all C all D (r2_hidden(k4_tarski(C,D),k1_relat_1(A)) -> k1_funct_1(A,k4_tarski(C,D)) = k1_funct_1(B,k4_tarski(D,C)))) & (all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (r2_hidden(k4_tarski(D,E),k1_relat_1(A)) & k4_tarski(E,D) = C))))))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2589 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(B,A) = k5_relat_1(B,k7_relat_1(A,k2_relat_1(B))))))) # label(t2_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2590 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k1_relat_1(E) = k2_tarski(A,B) & D = k1_funct_1(E,B) & C = k1_funct_1(E,A) -> k4_funct_4(A,B,C,D) = E))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2591 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k1_relat_1(C))),B)))))))) # label(t27_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2592 (all A -((all B all C -r1_tarski(A,k2_zfmisc_1(B,C))) & (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2593 (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]. 87.14/85.25 2594 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(B,A),k1_relat_1(k2_funct_4(C))) <-> r2_hidden(k4_tarski(A,B),k1_relat_1(C))))) # label(t43_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2595 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k1_funct_4(A,B) = k2_xboole_0(A,B)))))) # label(t32_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2596 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_tarski(A,k1_funct_4(A,B))))))) # label(t33_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2597 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_relat_1(B) -> k1_funct_4(A,C) = k1_funct_4(k1_funct_4(A,B),C)))))))) # label(t78_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2598 (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]. 87.14/85.25 2599 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k7_relat_1(k1_funct_4(A,B),k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),A))))) # label(t25_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2600 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> B = k1_funct_4(A,B)))))) # label(t20_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2601 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> k2_funct_4(k2_funct_4(D)) = D)) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2602 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_funct_1(k3_funct_4(A,B)) & v1_relat_1(k3_funct_4(A,B)))) # label(dt_k3_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2603 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> k1_xboole_0 = A | B = D)) # label(t7_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2604 (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]. 87.14/85.25 2605 (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]. 87.14/85.25 2606 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r1_tarski(k1_relat_1(A),C) & r1_xboole_0(C,D) & r1_tarski(k1_relat_1(B),D) -> k7_relat_1(k1_funct_4(A,B),D) = B & A = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t81_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2607 (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]. 87.14/85.25 2608 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funct_4(A,k1_xboole_0) = A)) # label(t22_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2609 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t36_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2610 (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]. 87.14/85.25 2611 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) = k7_relat_1(A,k2_xboole_0(B,C))))) # label(t83_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2612 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_xboole_0(k1_relat_1(B),C) & r1_tarski(k1_relat_1(A),C) -> A = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t82_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2613 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_4(k1_xboole_0,A) = A)) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2614 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_funct_4(k2_funct_4(C)) = C))) # label(t53_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2615 (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]. 87.14/85.25 2616 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t9_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2617 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> k2_funct_4(k2_funct_4(D)) = D)))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2618 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k7_relat_1(k1_funct_4(A,B),C) = k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C))))))) # label(t75_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2619 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)))))) # label(t30_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2620 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k1_funct_4(C,D) = D))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2621 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> k1_funct_4(B,C) = C)))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2622 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(E),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(F),k2_zfmisc_1(C,D)) -> r1_tarski(k1_relat_1(k3_funct_4(E,F)),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))))) # label(t60_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2623 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D)))) # label(t49_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2624 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F))) -> k4_tarski(k1_funct_1(E,k4_tarski(A,C)),k1_funct_1(F,k4_tarski(B,D))) = k1_funct_1(k3_funct_4(E,F),k4_tarski(k4_tarski(A,B),k4_tarski(C,D)))))))) # label(t58_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2625 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (k1_relat_1(F) = k2_zfmisc_1(C,D) & k1_relat_1(E) = k2_zfmisc_1(A,B) -> k1_relat_1(k3_funct_4(E,F)) = k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D))))))) # label(t61_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2626 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k1_funct_4(A,B) <-> k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D (r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D)) & (-r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(A,D) = k1_funct_1(C,D))))))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2627 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t18_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2628 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k1_funct_4(C,D),A,B) & v1_funct_1(k1_funct_4(C,D)))))) # label(t41_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2629 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r1_xboole_0(k1_relat_1(B),k1_relat_1(C)) -> k1_funct_1(B,A) = k1_funct_1(k1_funct_4(B,C),A)))))) # label(t17_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2630 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r1_tarski(k1_relat_1(A),k2_xboole_0(B,C)) -> k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) = A)))) # label(t74_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2631 (all A all B all C all D (B != A -> k2_tarski(C,D) = k2_relat_1(k4_funct_4(A,B,C,D)))) # label(t67_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.14/85.25 2632 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r2_hidden(k4_tarski(A,C),k1_relat_1(E)) & r2_hidden(k4_tarski(B,D),k1_relat_1(F)) <-> r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F)))))))) # label(t57_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2633 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2634 (all A (v3_ordinal1(A) -> (all B all C (r2_hidden(A,B) & r1_tarski(B,C) -> r1_ordinal1(k6_ordinal2(C),k6_ordinal2(B)))))) # label(t24_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2635 (all A (v3_ordinal1(A) -> (p1_s1_ordinal2(A) -> p1_s1_ordinal2(k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s1_ordinal2(B)))) -> A = k1_xboole_0 | p1_s1_ordinal2(A)))) & p1_s1_ordinal2(k1_xboole_0) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2636 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2637 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2638 (all A (v3_ordinal1(A) -> (all B (B = f1_s8_ordinal2(A) <-> (exists C (v1_funct_1(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s8_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f4_s8_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & f2_s8_ordinal2 = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C))))))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2639 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = B & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s6_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D))))) & f4_s6_ordinal2 = k1_funct_1(C,k1_xboole_0))) <-> f2_s6_ordinal2(A) = B)))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A)) = f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,A) = f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) | k1_xboole_0 = A))) & (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_xboole_0) = f4_s6_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> k1_funct_1(f1_s6_ordinal2,A) = f2_s6_ordinal2(A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2640 (all A (v3_ordinal1(A) -> (all B -((all C (v3_ordinal1(C) -> -(r1_ordinal1(A,C) & r2_hidden(C,B)))) & r2_hidden(A,k7_ordinal2(B)))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2641 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,C) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C))))))) <-> v2_ordinal2(A)))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2642 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k10_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & k9_ordinal2(C) = B & k1_relat_1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & v1_ordinal2(C) & v1_relat_1(C)))))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2643 (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]. 87.27/85.34 2644 (exists A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2645 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2646 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2647 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f1_s14_ordinal2(A) = B <-> (exists C (v5_ordinal1(C) & v1_ordinal2(C) & B = k1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s14_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & f2_s14_ordinal2 = k1_funct_1(C,k1_xboole_0) & v1_funct_1(C) & v1_relat_1(C)))))))) -> f1_s14_ordinal2(k1_xboole_0) = f2_s14_ordinal2 # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2648 (exists A (v1_funct_1(A) & v1_ordinal2(A) & k1_relat_1(A) = f1_s3_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> k1_funct_1(A,B) = f2_s3_ordinal2(B)))) & v5_ordinal1(A) & v1_relat_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2649 (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]. 87.27/85.34 2650 (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]. 87.27/85.34 2651 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k14_ordinal2(B,D) = k1_funct_1(C,D)))) & k1_relat_1(C) = A -> k8_ordinal2(C) = k14_ordinal2(B,A)))) | k1_xboole_0 = A))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2652 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2653 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_ordinal2(A) <-> (exists B (r1_tarski(k2_relat_1(A),B) & v3_ordinal1(B)))))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2654 (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]. 87.27/85.34 2655 (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]. 87.27/85.34 2656 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2657 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2658 (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]. 87.27/85.34 2659 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2660 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> k12_ordinal2(k2_ordinal1(B,A)) = k13_ordinal2(A,B))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2661 (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]. 87.27/85.34 2662 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2663 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r1_ordinal1(k1_ordinal1(A),k1_ordinal1(B))))))) # label(t1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2664 (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]. 87.27/85.34 2665 (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]. 87.27/85.34 2666 f2_s10_ordinal2 != k1_xboole_0 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> f3_s10_ordinal2(A) = k1_funct_1(f1_s10_ordinal2,A)))) & k1_relat_1(f1_s10_ordinal2) = f2_s10_ordinal2 & v4_ordinal1(f2_s10_ordinal2) & (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s10_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | f6_s10_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_funct_1(C,k1_xboole_0) = f4_s10_ordinal2 & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C))) <-> B = f3_s10_ordinal2(A))))) -> f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) = f3_s10_ordinal2(f2_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2667 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f3_s16_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & B = k1_ordinal2(C) & k1_funct_1(C,k1_xboole_0) = f4_s16_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s16_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f6_s16_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & k1_ordinal1(A) = k1_relat_1(C) & v1_relat_1(C)))))))) & f2_s16_ordinal2 != k1_xboole_0 & k1_relat_1(f1_s16_ordinal2) = f2_s16_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> k1_funct_1(f1_s16_ordinal2,A) = f3_s16_ordinal2(A)))) & v4_ordinal1(f2_s16_ordinal2) -> f3_s16_ordinal2(f2_s16_ordinal2) = f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2668 (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]. 87.27/85.34 2669 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & k1_ordinal1(B) = k1_relat_1(D) & k4_ordinal2 = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k15_ordinal2(A,k1_funct_1(D,E))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_xboole_0 = E | k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & k1_ordinal2(D) = C & v1_ordinal2(D) & v5_ordinal1(D))) <-> C = k16_ordinal2(A,B)))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2670 (exists A (v1_funct_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s2_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> k1_funct_1(A,B) = f2_s2_ordinal2(B)))) & v1_relat_1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2671 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(k15_ordinal2(A,B),B) = k15_ordinal2(k1_ordinal1(A),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2672 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k4_ordinal2) = A & k16_ordinal2(k4_ordinal2,A) = k4_ordinal2)) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2673 (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]. 87.27/85.34 2674 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2675 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2676 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A) & k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2677 (all A (v3_ordinal1(A) -> (exists B (r2_hidden(A,B) & v4_ordinal1(B) & v3_ordinal1(B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2678 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2679 (all A (A = k5_ordinal2 <-> r2_hidden(k1_xboole_0,A) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v3_ordinal1(A) & v4_ordinal1(A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2680 (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]. 87.27/85.34 2681 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2682 (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]. 87.27/85.34 2683 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k7_ordinal2(k1_tarski(A)))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2684 (all A all B (v5_ordinal1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_ordinal1(k1_funct_1(A,B)) & v2_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2685 (all A all B (v3_ordinal1(A) & v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2686 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v5_ordinal1(C) & v1_ordinal2(C) & k1_relat_1(C) = k1_relat_1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k8_ordinal2(C) = B & v1_funct_1(C) & v1_relat_1(C))) <-> B = k11_ordinal2(A)))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2687 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k1_xboole_0) = k4_ordinal2)) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2688 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2689 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2690 (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]. 87.27/85.34 2691 (all A (v3_ordinal1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2692 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k16_ordinal2(B,D)))) -> k12_ordinal2(C) = k16_ordinal2(B,A)))) | k1_xboole_0 = A))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2693 (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]. 87.27/85.34 2694 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> (k1_ordinal1(A) = k1_relat_1(B) -> k1_funct_1(B,A) = k1_ordinal2(B)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.27/85.34 2695 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2696 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2697 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2698 (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]. 87.46/85.49 2699 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2700 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) -> k3_tarski(k8_ordinal2(C)) = k15_ordinal2(A,B))))))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2701 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2702 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2703 (all A all B (v3_ordinal1(B) -> v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2704 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f4_s15_ordinal2(A) <-> (exists C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & f1_s15_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | f3_s15_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f2_s15_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v1_funct_1(C)))))))) -> (all A (v3_ordinal1(A) -> f2_s15_ordinal2(A,f4_s15_ordinal2(A)) = f4_s15_ordinal2(k1_ordinal1(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2705 (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]. 87.46/85.49 2706 (all A (v3_ordinal1(A) -> (exists B ((exists C (v3_ordinal1(C) & v4_ordinal1(B) & v4_ordinal2(C) & k14_ordinal2(B,C) = A)) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2707 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> f2_s11_ordinal2 = k1_funct_1(A,k1_xboole_0)) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s11_ordinal2) -> k1_xboole_0 = B | k1_funct_1(A,B) = f4_s11_ordinal2(B,k2_ordinal1(A,B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> f3_s11_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & f1_s11_ordinal2 = k1_relat_1(A) & v1_ordinal2(A) & v1_funct_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2708 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k4_ordinal2) = k1_ordinal1(A))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.49 2709 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f2_s12_ordinal2(A) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f6_s12_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_funct_1(C,k1_xboole_0) = f4_s12_ordinal2 & B = k1_ordinal2(C)))))))) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_xboole_0) = f4_s12_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s12_ordinal2) -> A = k1_xboole_0 | f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,A)))) & f3_s12_ordinal2 = k1_relat_1(f1_s12_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> f2_s12_ordinal2(A) = k1_funct_1(f1_s12_ordinal2,A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.51 2710 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.51 2711 (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]. 87.46/85.51 2712 (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]. 87.46/85.51 2713 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.51 2714 (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]. 87.46/85.51 2715 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) & v1_ordinal2(D) & k1_ordinal2(D) = C & A = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_funct_1(D,E) = k8_ordinal2(k2_ordinal1(D,E)) | E = k1_xboole_0))) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k1_ordinal1(k1_funct_1(D,E))))) & k1_ordinal1(B) = k1_relat_1(D))) <-> C = k14_ordinal2(A,B)))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.51 2716 (all A all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) & r1_tarski(k2_ordinal2(A),B) <-> k7_ordinal2(A) = B))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.51 2717 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.51 2718 (exists A (v2_ordinal1(A) & v4_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.51 2719 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.51 2720 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.51 2721 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal1(B) & v1_ordinal2(A) -> v1_ordinal2(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.51 2722 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.51 2723 (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]. 87.46/85.51 2724 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & k1_ordinal2(C) = B & v1_ordinal2(C) & v1_relat_1(C))) & B != A & (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = A & k1_relat_1(C) = k1_ordinal1(f1_s13_ordinal2) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & v1_ordinal2(C)))))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2725 (exists A (v3_ordinal1(A) & (exists B (v1_relat_1(B) & v5_ordinal1(B) & A = k1_ordinal2(B) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(B) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(C) -> k1_funct_1(B,C) = f4_s13_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & v1_ordinal2(B) & v1_funct_1(B))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2726 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2727 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2728 (all A k6_ordinal2(A) = k1_setfam_1(k2_ordinal2(A))) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2729 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2730 (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]. 87.46/85.54 2731 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s9_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f3_s9_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f1_s9_ordinal2 & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C) & v1_relat_1(C))) <-> f4_s9_ordinal2(A) = B)))) -> (all A (v3_ordinal1(A) -> f4_s9_ordinal2(k1_ordinal1(A)) = f2_s9_ordinal2(A,f4_s9_ordinal2(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2732 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v5_ordinal1(D) & v1_ordinal2(D) & k1_funct_1(D,k1_xboole_0) = k1_xboole_0 & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k1_funct_1(D,E) = k3_tarski(k8_ordinal2(k2_ordinal1(D,E))) | E = k1_xboole_0))) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k14_ordinal2(k1_funct_1(D,E),B) = k1_funct_1(D,k1_ordinal1(E))))) & k1_relat_1(D) = k1_ordinal1(A) & C = k1_ordinal2(D) & v1_funct_1(D) & v1_relat_1(D))) <-> C = k15_ordinal2(A,B)))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2733 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k1_funct_1(A,k3_tarski(k1_relat_1(A))) = k1_ordinal2(A))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2734 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2735 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2736 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.54 2737 f1_s4_ordinal2 = k1_relat_1(f5_s4_ordinal2) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A)) | k1_xboole_0 = A))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_xboole_0 = A | f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A))))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f5_s4_ordinal2,k1_xboole_0)) -> f6_s4_ordinal2 = f5_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2738 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2739 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2740 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2741 (all A all B -((exists C (v1_funct_1(C) & k1_ordinal2(C) = A & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> f4_s7_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & v5_ordinal1(C) & v1_relat_1(C))) & A != B & (exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & B = k1_ordinal2(C) & v1_relat_1(C))))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2742 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(B,C) = f4_s7_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & k1_funct_1(B,k1_xboole_0) = f2_s7_ordinal2 & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(B) & k1_ordinal2(B) = A & v5_ordinal1(B))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2743 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k1_funct_1(A,B) = C & v4_ordinal1(B) & r2_hidden(B,k1_relat_1(A)) -> r1_ordinal2(C,k2_ordinal1(A,B)) | k1_xboole_0 = B))))) <-> v3_ordinal2(A)))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2744 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A) & (exists D (D = C & v4_ordinal1(D) & v3_ordinal1(D))))) <-> B = k3_ordinal2(A))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2745 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2746 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (k1_xboole_0 != A -> ((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -((all E (v3_ordinal1(E) -> -((all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,F),D) & r2_hidden(C,k1_funct_1(B,F))))) & r2_hidden(E,k1_relat_1(B))))) & r2_hidden(A,D) & r2_hidden(C,A)))))) <-> r1_ordinal2(A,B))) & (A = k1_xboole_0 -> ((exists C ((all D (v3_ordinal1(D) -> (r1_ordinal1(C,D) & r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_xboole_0))) & r2_hidden(C,k1_relat_1(B)) & v3_ordinal1(C))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2747 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2748 (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]. 87.46/85.55 2749 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2750 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2751 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> ((exists B (v3_ordinal1(B) & r1_ordinal2(B,A))) -> (all B (v3_ordinal1(B) -> (k12_ordinal2(A) = B <-> r1_ordinal2(B,A))))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2752 (exists A (v1_relat_1(A) & v5_ordinal1(A) & f1_s5_ordinal2 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> f3_s5_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s5_ordinal2) & v4_ordinal1(B) -> k1_funct_1(A,B) = f4_s5_ordinal2(B,k2_ordinal1(A,B)) | B = k1_xboole_0))) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s5_ordinal2) & v1_funct_1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2753 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k16_ordinal2(A,k1_ordinal1(B)) = k15_ordinal2(A,k16_ordinal2(A,B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2754 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2755 (all A all B ((all C (r2_hidden(C,A) & v3_ordinal1(C) <-> r2_hidden(C,B))) <-> B = k2_ordinal2(A))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2756 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2757 (all A (v3_ordinal1(A) -> k1_xboole_0 = k6_ordinal3(k1_xboole_0,A) & k7_ordinal3(k1_xboole_0,A) = k1_xboole_0 & k7_ordinal3(A,k1_xboole_0) = A)) # label(t83_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2758 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> -(k1_xboole_0 != C & k14_ordinal2(A,C) = B))) & r2_hidden(A,B)))))) # label(t31_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2759 (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]. 87.46/85.55 2760 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k15_ordinal2(k14_ordinal2(A,B),C) = k14_ordinal2(k15_ordinal2(A,C),k15_ordinal2(B,C)))))))) # label(t54_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2761 $T # label(t43_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2762 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(k15_ordinal2(A,B) = k1_xboole_0 & A != k1_xboole_0 & k1_xboole_0 != B))))) # label(t34_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2763 $T # label(t3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2764 (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]. 87.46/85.55 2765 (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]. 87.46/85.55 2766 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> k1_xboole_0 = C | r2_hidden(A,k15_ordinal2(B,C)) & r2_hidden(A,k15_ordinal2(C,B))))))))) # label(t35_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2767 (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]. 87.46/85.55 2768 (all A (v3_ordinal1(A) -> (A != k1_xboole_0 -> r2_hidden(k1_xboole_0,A)))) # label(t10_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2769 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k14_ordinal2(A,B) = k1_xboole_0 -> A = k1_xboole_0 & B = k1_xboole_0))))) # label(t29_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2770 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(A,k14_ordinal2(C,B)) & r2_hidden(A,k14_ordinal2(B,C))))))))) # label(t28_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2771 $T # label(t14_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2772 (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)) -> B = k1_xboole_0 | r1_ordinal1(A,C)))))))) # label(t38_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2773 (all A (v3_ordinal1(A) -> k1_xboole_0 = k6_ordinal2(A))) # label(t11_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2774 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k15_ordinal2(A,B) = k4_ordinal2 -> B = k4_ordinal2 & k4_ordinal2 = A))))) # label(t41_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2775 (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]. 87.46/85.55 2776 (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(B,A),C) = k14_ordinal2(k15_ordinal2(D,A),E) & r2_hidden(C,A) & r2_hidden(E,A) -> C = E & B = D))))))))))) # label(t56_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2777 (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]. 87.46/85.55 2778 (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) -> (B = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,B) -> k15_ordinal2(D,A) = k1_funct_1(C,D)))) -> k15_ordinal2(B,A) = k8_ordinal2(C)))) | k1_xboole_0 = B))))) # label(t57_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2779 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r2_hidden(D,C) & A = k14_ordinal2(k15_ordinal2(B,C),D) -> k7_ordinal3(A,C) = D & k6_ordinal3(A,C) = B))))))))) # label(t79_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2780 (all A (v3_ordinal1(A) -> k7_ordinal3(A,k4_ordinal2) = k1_xboole_0 & A = k6_ordinal3(A,k4_ordinal2))) # label(t84_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2781 $T # label(t44_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2782 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k3_xboole_0(A,B) = B | k3_xboole_0(A,B) = A)))) # label(t16_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2783 (all A (v3_ordinal1(A) -> (r2_hidden(A,k4_ordinal2) -> k1_xboole_0 = A))) # label(t17_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2784 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k2_xboole_0(A,B) = B | k2_xboole_0(A,B) = A)))) # label(t15_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2785 (all A r1_tarski(A,k1_ordinal1(A))) # label(t1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2786 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v3_ordinal1(C) -> ((all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (E = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A)) -> k14_ordinal2(C,E) = k1_funct_1(B,D)))))) & k1_relat_1(A) = k1_relat_1(B) -> 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]. 87.46/85.55 2787 (all A all B (v3_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> v1_relat_1(k2_ordinal3(A,B)) & v1_ordinal2(k2_ordinal3(A,B)) & v5_ordinal1(k2_ordinal3(A,B)) & v1_funct_1(k2_ordinal3(A,B)))) # label(dt_k2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2788 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k1_xboole_0 != A -> r1_ordinal1(B,k15_ordinal2(B,A)) & r1_ordinal1(B,k15_ordinal2(A,B))))))) # label(t39_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2789 (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]. 87.46/85.55 2790 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k5_ordinal3(A,k14_ordinal2(B,C)) = k5_ordinal3(k5_ordinal3(A,B),C))))))) # label(t70_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2791 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,k15_ordinal2(B,C)) -> r2_hidden(k7_ordinal3(A,C),C) & r2_hidden(k6_ordinal3(A,C),B)))))))) # label(t80_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2792 (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]. 87.46/85.55 2793 $T # label(d1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2794 (all A all B (v3_ordinal1(A) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> v1_funct_1(k1_ordinal3(A,B)) & v5_ordinal1(k1_ordinal3(A,B)) & v1_ordinal2(k1_ordinal3(A,B)) & v1_relat_1(k1_ordinal3(A,B)))) # label(dt_k1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2795 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> k14_ordinal2(A,C) != B)) & r1_ordinal1(A,B)))))) # label(t30_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2796 (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]. 87.46/85.55 2797 $T # label(t40_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2798 (all A all B (v1_relat_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(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]. 87.46/85.55 2799 (all A (v3_ordinal1(A) -> k1_xboole_0 = k5_ordinal3(A,A))) # label(t67_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2800 $T # label(t64_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2801 (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]. 87.46/85.55 2802 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> -(r2_hidden(A,k15_ordinal2(B,C)) & v4_ordinal1(B) & (all D (v3_ordinal1(D) -> -(r2_hidden(A,k15_ordinal2(D,C)) & r2_hidden(D,B))))))))))) # label(t49_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2803 (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]. 87.46/85.55 2804 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> k2_ordinal2(B) = B)))) # label(t8_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2805 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (all C (v3_ordinal1(C) -> (k1_relat_1(A) = k1_relat_1(B) & v4_ordinal1(k8_ordinal2(A)) & (all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (E = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A)) -> k15_ordinal2(E,C) = k1_funct_1(B,D)))))) -> k1_relat_1(A) = k1_xboole_0 | k15_ordinal2(k8_ordinal2(A),C) = k8_ordinal2(B) | k1_xboole_0 = C))))))) # label(t50_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2806 (all A (v3_ordinal1(A) -> k2_ordinal2(k1_tarski(A)) = k1_tarski(A))) # label(t9_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2807 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k5_ordinal3(A,B)))) # label(dt_k5_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2808 (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]. 87.46/85.55 2809 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> B = k5_ordinal3(k14_ordinal2(A,B),A))))) # label(t65_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2810 (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]. 87.46/85.55 2811 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k1_xboole_0 = B -> (C = k6_ordinal3(A,B) <-> C = k1_xboole_0)) & (B != k1_xboole_0 -> (k6_ordinal3(A,B) = C <-> (exists D (r2_hidden(D,B) & A = k14_ordinal2(k15_ordinal2(C,B),D) & v3_ordinal1(D))))))))))) # label(d7_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2812 (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]. 87.46/85.55 2813 (all A all B (v3_ordinal1(A) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k3_ordinal3(A,B)) & v1_funct_1(k3_ordinal3(A,B)) & v5_ordinal1(k3_ordinal3(A,B)) & v1_ordinal2(k3_ordinal3(A,B)))) # label(dt_k3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2814 (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]. 87.46/85.55 2815 (all A all B (r1_tarski(k1_ordinal1(A),B) -> r1_tarski(A,B))) # label(t2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2816 (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]. 87.46/85.55 2817 (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]. 87.46/85.55 2818 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k1_xboole_0 != A -> k6_ordinal3(k15_ordinal2(B,A),A) = B))))) # label(t81_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2819 (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]. 87.46/85.55 2820 (all A (v3_ordinal1(A) -> -(k4_ordinal2 != A & k1_xboole_0 != A & r1_ordinal1(A,k4_ordinal2)))) # label(t19_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2821 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,k14_ordinal2(C,A)) -> A = k1_xboole_0 | r2_hidden(k5_ordinal3(B,C),A)))))))) # label(t73_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2822 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k1_xboole_0 = k7_ordinal3(k15_ordinal2(A,B),B))))) # label(t82_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2823 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k14_ordinal2(A,C) = k14_ordinal2(A,B) -> B = C))))))) # label(t24_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2824 (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]. 87.46/85.55 2825 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> -(-r2_hidden(A,B) & (all D (v3_ordinal1(D) -> -(r2_hidden(D,C) & A = k14_ordinal2(B,D)))) & r2_hidden(A,k14_ordinal2(B,C))))))))) # label(t42_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2826 (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]. 87.46/85.55 2827 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (all C (v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C) -> (k2_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(k1_funct_1(B,D),A))))))))))) # label(d3_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2828 $T # label(t46_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2829 (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]. 87.46/85.55 2830 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) -> (C = k1_ordinal3(A,B) <-> (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k14_ordinal2(A,k1_funct_1(B,D)) = k1_funct_1(C,D)))) & k1_relat_1(C) = k1_relat_1(B)))))))) # label(d2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2831 (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(k15_ordinal2(A,C),k15_ordinal2(B,D)) | -(k1_xboole_0 != D & r1_ordinal1(C,D)) & -r2_hidden(C,D)))))))))) # label(t22_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2832 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(k8_ordinal2(A)) -> k1_relat_1(A) = k1_xboole_0 | B = k1_xboole_0 | k8_ordinal2(k4_ordinal3(B,A)) = k15_ordinal2(k8_ordinal2(A),B)))))) # label(t52_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2833 $T # label(t63_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2834 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(B,k14_ordinal2(A,B)) & r1_ordinal1(A,k14_ordinal2(A,B)))))) # label(t27_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2835 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v2_ordinal1(k2_xboole_0(A,B)) & v3_ordinal1(k2_xboole_0(A,B)) & v1_ordinal1(k2_xboole_0(A,B)))) # label(fc1_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2836 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (r1_ordinal1(C,D) & r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(A,C),k15_ordinal2(B,D))))))))))) # label(t23_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2837 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (-r1_ordinal1(B,A) -> (C = k5_ordinal3(A,B) <-> k1_xboole_0 = C)) & (r1_ordinal1(B,A) -> (k14_ordinal2(B,C) = A <-> C = k5_ordinal3(A,B))))))))) # label(d6_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2838 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> k15_ordinal2(k15_ordinal2(A,B),C) = k15_ordinal2(A,k15_ordinal2(B,C)))))))) # label(t58_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2839 $T # label(t61_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2840 $T # label(t62_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.55 2841 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v1_ordinal1(k3_xboole_0(A,B)) & v2_ordinal1(k3_xboole_0(A,B)) & v3_ordinal1(k3_xboole_0(A,B)))) # label(fc2_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2842 (all A (v3_ordinal1(A) -> k1_xboole_0 = k5_ordinal3(k1_xboole_0,A) & A = k5_ordinal3(A,k1_xboole_0))) # label(t69_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2843 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -(r2_hidden(D,A) & B = k14_ordinal2(k15_ordinal2(C,A),D)))))) & k1_xboole_0 != A))))) # label(t55_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2844 (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]. 87.46/85.56 2845 $T # label(t59_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2846 (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) -> k14_ordinal2(B,k8_ordinal2(A)) = k8_ordinal2(k1_ordinal3(B,A))))))) # label(t51_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2847 (all A (v3_ordinal1(A) -> k6_ordinal2(k1_tarski(A)) = A)) # label(t12_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2848 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) -> (k1_relat_1(C) = k1_relat_1(B) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) -> k15_ordinal2(A,k1_funct_1(B,D)) = k1_funct_1(C,D)))) <-> k3_ordinal3(A,B) = C))))))) # label(d4_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2849 $T # label(t4_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2850 (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]. 87.46/85.56 2851 (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]. 87.46/85.56 2852 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(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)) -> k1_funct_1(C,D) = k15_ordinal2(k1_funct_1(B,D),A)))) & k1_relat_1(C) = k1_relat_1(B) <-> k4_ordinal3(A,B) = C))))))) # label(d5_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2853 (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]. 87.46/85.56 2854 (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]. 87.46/85.56 2855 $T # label(t45_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2856 (all A v3_ordinal1(k3_tarski(k2_ordinal2(A)))) # label(t7_ordinal3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2857 (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]. 87.46/85.56 2858 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> k14_ordinal2(B,A) = k14_ordinal2(A,B))))) # label(t3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2859 $T # label(t12_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2860 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> k4_arytm_3(A,A) = A & A = k3_arytm_3(A,A))) # label(t21_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2861 (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]. 87.46/85.56 2862 (all A (m1_subset_1(A,k6_arytm_3) -> A = k11_arytm_3(A,k13_arytm_3))) # label(t59_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2863 (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) -> -(A = k10_arytm_3(D,E) & r3_arytm_3(D,B) & r3_arytm_3(E,C))))))))))))) # label(t95_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2864 (all A (v3_ordinal1(A) & v4_ordinal2(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]. 87.46/85.56 2865 (all A (v3_ordinal1(A) & v1_xboole_0(A) -> v1_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(cc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2866 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (A != k1_xboole_0 -> k5_arytm_3(A,A) = k4_ordinal2))) # label(t32_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2867 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> k11_arytm_3(A,k11_arytm_3(B,C)) = k11_arytm_3(k11_arytm_3(A,B),C))))))) # label(t58_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2868 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> -(k5_arytm_3(A,B) = k1_xboole_0 & k1_xboole_0 != A))))) # label(t30_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2869 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal2(k14_ordinal2(A,B)) -> r2_hidden(B,k5_ordinal2) & r2_hidden(A,k5_ordinal2)))))) # label(t1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2870 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -(k12_arytm_3 != A & (all C (m1_subset_1(C,k6_arytm_3) -> B != k11_arytm_3(A,C)))))))) # label(t61_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2871 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (r2_hidden(k1_xboole_0,A) -> r2_hidden(k7_ordinal3(B,A),A)))))) # label(t10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2872 (all A (m1_subset_1(A,k6_arytm_3) -> -(k12_arytm_3 != A & (all B (m1_subset_1(B,k6_arytm_3) -> k11_arytm_3(A,B) != k13_arytm_3))))) # label(t60_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2873 (all A (m1_subset_1(A,k6_arytm_3) & v3_ordinal1(A) -> (all B (m1_subset_1(B,k6_arytm_3) & v3_ordinal1(B) -> k2_arytm_3(A,B) = k11_arytm_3(A,B))))) # label(t65_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2874 (all A all B (v4_ordinal2(B) & v3_ordinal1(B) & v4_ordinal2(A) & v3_ordinal1(A) -> v1_ordinal1(k5_ordinal3(A,B)) & v3_ordinal1(k5_ordinal3(A,B)) & v4_ordinal2(k5_ordinal3(A,B)) & v2_ordinal1(k5_ordinal3(A,B)))) # label(fc4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2875 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) -> m1_subset_1(k5_arytm_3(A,B),k5_ordinal2))) # label(dt_k5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 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) -> -(r3_arytm_3(C,A) & (-r3_arytm_3(C,B) & r3_arytm_3(A,B) | -r3_arytm_3(B,A) & r3_arytm_3(B,C))))))))) # label(t76_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2877 (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]. 87.46/85.56 2878 (all A (m1_subset_1(A,k6_arytm_3) -> (r3_arytm_3(A,k12_arytm_3) -> k12_arytm_3 = A))) # label(t72_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2879 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> k9_arytm_3(k1_arytm_3(k2_arytm_3(k7_arytm_3(A),k8_arytm_3(B)),k2_arytm_3(k7_arytm_3(B),k8_arytm_3(A))),k2_arytm_3(k8_arytm_3(A),k8_arytm_3(B))) = k10_arytm_3(A,B))))) # label(d10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2880 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> -(-(k1_xboole_0 = B & k1_xboole_0 = A) & (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (all D (v3_ordinal1(D) & v4_ordinal2(D) -> (all E (v4_ordinal2(E) & v3_ordinal1(E) -> -(k2_arytm_3(C,E) = B & k2_arytm_3(C,D) = A & r1_arytm_3(D,E))))))))))))) # label(t8_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2881 (all A all B -v3_ordinal1(k4_tarski(A,B))) # label(t36_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2882 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k2_arytm_3(A,B)))) # label(dt_k2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2883 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (r1_arytm_3(A,B) -> A = k5_arytm_3(A,B)))))) # label(t28_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2884 (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]. 87.46/85.56 2885 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) -> v4_ordinal2(k6_ordinal3(A,B)) & v3_ordinal1(k6_ordinal3(A,B)) & v2_ordinal1(k6_ordinal3(A,B)) & v1_ordinal1(k6_ordinal3(A,B)))) # label(fc6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2886 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (all D (v3_ordinal1(D) & v4_ordinal2(D) -> -(k1_xboole_0 != B & k1_xboole_0 != A & -(k9_arytm_3(C,B) = k9_arytm_3(D,A) <-> k2_arytm_3(C,A) = k2_arytm_3(B,D))))))))))) # label(t51_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2887 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (all D (v3_ordinal1(D) & v4_ordinal2(D) -> k9_arytm_3(k2_arytm_3(B,D),k2_arytm_3(C,A)) = k11_arytm_3(k9_arytm_3(B,C),k9_arytm_3(D,A)))))))))) # label(t55_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2888 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> k1_xboole_0 = k5_arytm_3(k1_xboole_0,A) & (k1_xboole_0 != A -> k4_ordinal2 = k5_arytm_3(A,k1_xboole_0)))) # label(t31_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2889 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]. 87.46/85.56 2890 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (k10_arytm_3(A,B) = k10_arytm_3(C,B) -> C = A))))))) # label(t69_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2891 (all A (m1_subset_1(A,k6_arytm_3) -> (v3_ordinal1(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(A)))) # label(cc4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2892 (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]. 87.46/85.56 2893 (all A all B (m1_subset_1(B,k6_arytm_3) & m1_subset_1(A,k6_arytm_3) -> k10_arytm_3(B,A) = k10_arytm_3(A,B))) # label(commutativity_k10_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2894 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> r2_arytm_3(A,A))) # label(reflexivity_r2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2895 (exists A (v4_ordinal2(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A))) # label(rc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2896 (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]. 87.46/85.56 2897 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> k2_arytm_3(k5_arytm_3(A,B),k4_arytm_3(A,B)) = A)))) # label(t26_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2898 (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,k10_arytm_3(A,C)) & (all D (m1_subset_1(D,k6_arytm_3) -> -(k10_arytm_3(A,D) = B & r3_arytm_3(D,C))))))))))) # label(t94_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2899 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> k5_arytm_3(A,B) = k6_ordinal3(A,k4_arytm_3(A,B)))))) # label(d5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2900 (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]. 87.46/85.56 2901 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> k4_ordinal2 = k5_arytm_3(k4_ordinal2,A) & A = k5_arytm_3(A,k4_ordinal2))) # label(t29_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2902 (all 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) -> (all D (m1_subset_1(D,k6_arytm_3) -> -(r2_hidden(B,A) & r2_hidden(C,A) & B != D & C != D & C != B & r2_hidden(D,A)))))))) & (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (r3_arytm_3(C,B) & r2_hidden(B,A) -> r2_hidden(C,A)))))) & (exists B (m1_subset_1(B,k6_arytm_3) & r2_hidden(B,A) & B != k12_arytm_3))))) # label(t82_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2903 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> k3_arytm_3(A,B) = k3_arytm_3(B,A))) # label(commutativity_k3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2904 (exists A (m1_subset_1(A,k6_arytm_3) & -v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(rc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2905 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (r3_arytm_3(A,B) & r3_arytm_3(B,A) -> B = A))))) # label(t73_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 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(B,C) & -r3_arytm_3(C,A)))) & -r3_arytm_3(B,A)))))) # label(t101_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2907 (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) -> A = k12_arytm_3))))) # label(t70_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2908 (all A (v4_ordinal2(A) & v3_ordinal1(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]. 87.46/85.56 2909 (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) & B != C & A = C))))))) # label(t97_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2910 (all A (m1_subset_1(A,k5_ordinal2) -> (all B (m1_subset_1(B,k5_ordinal2) -> (r2_hidden(k4_tarski(A,B),k6_arytm_3) <-> r1_arytm_3(A,B) & k1_xboole_0 != B & k4_ordinal2 != B))))) # label(t39_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2911 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (k12_arytm_3 = A <-> B = k10_arytm_3(A,B)))))) # label(t92_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2912 (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)) -> A = k12_arytm_3 | r3_arytm_3(B,C)))))))) # label(t88_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2913 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (m1_subset_1(C,k5_ordinal2) -> (k4_arytm_3(A,B) = C <-> r2_arytm_3(C,A) & r2_arytm_3(C,B) & (all D (v4_ordinal2(D) & v3_ordinal1(D) -> (r2_arytm_3(D,B) & r2_arytm_3(D,A) -> r2_arytm_3(D,C))))))))))) # label(d4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2914 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(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]. 87.46/85.56 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) -> (r3_arytm_3(B,C) & r3_arytm_3(A,B) -> r3_arytm_3(A,C)))))))) # label(t74_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2916 (all A (m1_subset_1(A,k6_arytm_3) -> -((all B (m1_subset_1(B,k6_arytm_3) -> -(-r2_hidden(B,k5_ordinal2) & -r3_arytm_3(A,B)))) & k12_arytm_3 != A))) # label(t80_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2917 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> k2_arytm_3(A,B) = k15_ordinal2(A,B))) # label(redefinition_k2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2918 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> -(-r3_arytm_3(B,D) & -r3_arytm_3(A,C) & k11_arytm_3(C,D) = k11_arytm_3(A,B)))))))))) # label(t91_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2919 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (all C (v3_ordinal1(C) & v4_ordinal2(C) -> (A != k1_xboole_0 -> k9_arytm_3(k2_arytm_3(B,A),k2_arytm_3(C,A)) = k9_arytm_3(B,C)))))))) # label(t50_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2920 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_arytm_3(A,B) <-> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> (all E (v3_ordinal1(E) -> (A = k15_ordinal2(C,D) & B = k15_ordinal2(C,E) -> C = k4_ordinal2)))))))))))) # label(d1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2921 (all A (m1_subset_1(A,k6_arytm_3) -> -(k1_xboole_0 = k7_arytm_3(A) & A != k1_xboole_0) & -(k1_xboole_0 != k7_arytm_3(A) & A = k1_xboole_0))) # label(t43_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2922 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> v4_ordinal2(k14_ordinal2(A,B)) & v3_ordinal1(k14_ordinal2(A,B)) & v2_ordinal1(k14_ordinal2(A,B)) & v1_ordinal1(k14_ordinal2(A,B)))) # label(fc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2923 k13_arytm_3 = f2_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) & f1_s2_arytm_3 = k12_arytm_3 -> (exists A (m1_subset_1(A,k6_arytm_3) & -p1_s2_arytm_3(k10_arytm_3(A,f2_s2_arytm_3)) & p1_s2_arytm_3(A) & r2_hidden(A,k5_ordinal2))) # label(s2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2924 (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(k1_arytm_3(B,C),A) = k10_arytm_3(k9_arytm_3(B,A),k9_arytm_3(C,A))))))))) # label(t53_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 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) -> A != k10_arytm_3(B,C) & B != k10_arytm_3(A,C))))))) # label(t100_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2926 (all A all B (m1_subset_1(A,k6_arytm_3) & m1_subset_1(B,k6_arytm_3) -> r3_arytm_3(A,B) | r3_arytm_3(B,A))) # label(connectedness_r3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2927 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(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]. 87.46/85.56 2928 (all A (m1_subset_1(A,k6_arytm_3) -> (A = k12_arytm_3 <-> r2_hidden(a_1_0_arytm_3(A),k6_arytm_3)))) # label(t81_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2929 (all A (m1_subset_1(A,k6_arytm_3) -> (r2_hidden(A,k5_ordinal2) <-> k4_ordinal2 = k8_arytm_3(A)))) # label(t44_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2930 (all A (m1_subset_1(A,k6_arytm_3) -> k9_arytm_3(k7_arytm_3(A),k8_arytm_3(A)) = A)) # label(t45_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2931 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> (r1_arytm_3(A,B) -> r1_arytm_3(B,A)))) # label(symmetry_r1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2932 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (m1_subset_1(C,k5_ordinal2) -> (r2_arytm_3(A,C) & (all D (v4_ordinal2(D) & v3_ordinal1(D) -> (r2_arytm_3(B,D) & r2_arytm_3(A,D) -> r2_arytm_3(C,D)))) & r2_arytm_3(B,C) <-> C = k3_arytm_3(A,B)))))))) # label(d3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 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) -> (k11_arytm_3(A,B) = k11_arytm_3(A,C) -> B = C | k12_arytm_3 = A))))))) # label(t62_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2934 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> v4_ordinal2(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & v1_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)))) # label(fc2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2935 (all A (m1_subset_1(A,k6_arytm_3) -> (exists B (k10_arytm_3(B,B) = A & m1_subset_1(B,k6_arytm_3))))) # label(t66_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2936 (all A (r2_hidden(A,a_0_0_arytm_3) <-> (exists B exists C (m1_subset_1(B,k5_ordinal2) & r1_arytm_3(B,C) & C != k1_xboole_0 & k4_tarski(B,C) = A & m1_subset_1(C,k5_ordinal2))))) # label(fraenkel_a_0_0_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 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(k10_arytm_3(B,C),A) & C != k12_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) & E != C & r3_arytm_3(E,C) & k10_arytm_3(D,E) = A)))))))))))) # label(t98_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2938 (all A (m1_subset_1(A,k6_arytm_3) -> k1_xboole_0 != k8_arytm_3(A))) # label(t41_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2939 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) -> 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]. 87.46/85.56 2940 (all A (m1_subset_1(A,k6_arytm_3) -> (-r2_hidden(A,k5_ordinal2) -> k4_tarski(k7_arytm_3(A),k8_arytm_3(A)) = A & k4_ordinal2 != k8_arytm_3(A)))) # label(t42_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2941 $T # label(dt_k6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2942 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(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]. 87.46/85.56 2943 (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]. 87.46/85.56 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) -> k10_arytm_3(A,k10_arytm_3(B,C)) = k10_arytm_3(k10_arytm_3(A,B),C))))))) # label(t57_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2945 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (r2_arytm_3(B,A) & r2_arytm_3(A,B) -> A = B))))) # label(t13_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2946 (all A (m1_subset_1(A,k6_arytm_3) & v3_ordinal1(A) -> (all B (m1_subset_1(B,k6_arytm_3) & v3_ordinal1(B) -> k10_arytm_3(A,B) = k1_arytm_3(A,B))))) # label(t64_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2947 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal2(k15_ordinal2(A,B)) -> r2_hidden(B,k5_ordinal2) & r2_hidden(A,k5_ordinal2) | v1_xboole_0(k15_ordinal2(A,B))))))) # label(t2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2948 (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]. 87.46/85.56 2949 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> k15_ordinal2(B,A) = k15_ordinal2(A,B))))) # label(t4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2950 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> m1_subset_1(k4_arytm_3(A,B),k5_ordinal2))) # label(dt_k4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2951 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> ((exists C (k2_arytm_3(A,C) = B & v4_ordinal2(C) & v3_ordinal1(C))) <-> r2_arytm_3(A,B)))))) # label(t9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2952 (all A -r2_hidden(k4_tarski(k12_arytm_3,A),k6_arytm_3)) # label(t68_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2953 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (r2_hidden(A,k5_ordinal2) & r2_hidden(k10_arytm_3(A,B),k5_ordinal2) -> r2_hidden(B,k5_ordinal2)))))) # label(t78_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2954 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> k1_xboole_0 = k3_arytm_3(A,k1_xboole_0) & A = k4_arytm_3(A,k1_xboole_0))) # label(t19_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2955 (exists A (v1_ordinal1(A) & v2_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(A) & v1_xboole_0(A) & m1_subset_1(A,k6_arytm_3))) # label(rc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2956 $T # label(t84_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2957 (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]. 87.46/85.56 2958 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> k4_arytm_3(B,A) = k4_arytm_3(A,B))) # label(commutativity_k4_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2959 (all A all B (m1_subset_1(A,k6_arytm_3) & m1_subset_1(B,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]. 87.46/85.56 2960 (all A (v3_ordinal1(A) -> r1_arytm_3(k4_ordinal2,A))) # label(t6_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2961 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> -(-r3_arytm_3(B,A) & -r3_arytm_3(C,A) & (all D (m1_subset_1(D,k6_arytm_3) -> -(-r3_arytm_3(D,A) & r3_arytm_3(D,C) & r3_arytm_3(D,B))))))))))) # label(t96_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2962 (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]. 87.46/85.56 2963 (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) & -r3_arytm_3(k10_arytm_3(B,k13_arytm_3),A) & r2_hidden(A,k5_ordinal2)))))) # label(t79_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2964 (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]. 87.46/85.56 2965 (all A (v3_ordinal1(A) & v4_ordinal2(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]. 87.46/85.56 2966 (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]. 87.46/85.56 2967 (all A (v4_ordinal2(A) & v3_ordinal1(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]. 87.46/85.56 2968 (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]. 87.46/85.56 2969 (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 (v4_ordinal2(C) & A = k4_tarski(C,B) & v3_ordinal1(C))))) & (r2_hidden(A,k5_ordinal2) -> (B = k8_arytm_3(A) <-> B = k4_ordinal2)))))) # label(d8_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2970 (all A all B (v3_ordinal1(A) & v4_ordinal2(A) & v3_ordinal1(B) & v4_ordinal2(B) -> m1_subset_1(k9_arytm_3(A,B),k6_arytm_3))) # label(dt_k9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2971 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> 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]. 87.46/85.56 2972 (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]. 87.46/85.56 2973 (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 | k7_arytm_3(k9_arytm_3(A,B)) = A & k8_arytm_3(k9_arytm_3(A,B)) = B))))) # label(t49_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2974 (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) & k11_arytm_3(B,D) = A))) & r3_arytm_3(A,k11_arytm_3(B,C))))))))) # label(t87_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2975 (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]. 87.46/85.56 2976 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (r3_arytm_3(A,B) <-> (exists C (m1_subset_1(C,k6_arytm_3) & B = k10_arytm_3(A,C)))))))) # label(d12_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2977 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) & v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k1_arytm_3(A,B)))) # label(dt_k1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2978 (all A all B (v3_ordinal1(B) & v4_ordinal2(B) & v4_ordinal2(A) & v3_ordinal1(A) -> k1_arytm_3(A,B) = k14_ordinal2(A,B))) # label(redefinition_k1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2979 (all A (-v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_arytm_3)) -> -(r2_hidden(A,k6_arytm_3) & (all B (m1_subset_1(B,k6_arytm_3) -> -(r2_hidden(B,A) & (all C (m1_subset_1(C,k6_arytm_3) -> (r2_hidden(C,A) -> r3_arytm_3(C,B)))))))))) # label(t99_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2980 (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]. 87.46/85.56 2981 (all A all B -r2_hidden(k4_tarski(A,B),k5_ordinal2)) # label(t38_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2982 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (all C (v4_ordinal2(C) & v3_ordinal1(C) -> (all D (v4_ordinal2(D) & v3_ordinal1(D) -> -(k9_arytm_3(k1_arytm_3(k2_arytm_3(C,A),k2_arytm_3(B,D)),k2_arytm_3(B,A)) != k10_arytm_3(k9_arytm_3(C,B),k9_arytm_3(D,A)) & A != k1_xboole_0 & k1_xboole_0 != B))))))))) # label(t52_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2983 (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(t75_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2984 (all A all B (v4_ordinal2(B) & v3_ordinal1(B) & v4_ordinal2(A) & v3_ordinal1(A) -> k2_arytm_3(B,A) = k2_arytm_3(A,B))) # label(commutativity_k2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2985 $T # label(t67_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2986 (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]. 87.46/85.56 2987 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> (all C (m1_subset_1(C,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> (k10_arytm_3(A,B) = k10_arytm_3(C,D) & r3_arytm_3(A,C) -> r3_arytm_3(D,B)))))))))) # label(t93_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2988 (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]. 87.46/85.56 2989 (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]. 87.46/85.56 2990 (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]. 87.46/85.56 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) -> -(-r3_arytm_3(C,B) & r3_arytm_3(C,A) & -r3_arytm_3(B,A)))))))) # label(t77_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2992 (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(k2_arytm_3(B,A),k2_arytm_3(C,A)) = k5_arytm_3(B,C)))))))) # label(t33_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2993 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(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]. 87.46/85.56 2994 (all A (v3_ordinal1(A) & v4_ordinal2(A) -> (k1_xboole_0 != A -> k4_ordinal2 = k9_arytm_3(A,A)))) # label(t47_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2995 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> (k5_arytm_3(B,A) = k4_ordinal2 -> k9_arytm_3(A,B) = k5_arytm_3(A,B)) & -(k9_arytm_3(A,B) != k4_tarski(k5_arytm_3(A,B),k5_arytm_3(B,A)) & k4_ordinal2 != k5_arytm_3(B,A) & B != k1_xboole_0) & (k1_xboole_0 = B -> k9_arytm_3(A,B) = k1_xboole_0))))) # label(d9_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2996 (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]. 87.46/85.56 2997 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k5_ordinal2) -> (r2_hidden(A,k5_ordinal2) -> (B = A <-> B = k7_arytm_3(A))) & (-r2_hidden(A,k5_ordinal2) -> ((exists C (v3_ordinal1(C) & v4_ordinal2(C) & A = k4_tarski(B,C))) <-> k7_arytm_3(A) = B)))))) # label(d7_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 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) -> (r2_arytm_3(A,k1_arytm_3(B,C)) & r2_arytm_3(A,B) -> r2_arytm_3(A,C)))))))) # label(t16_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 2999 (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) -> -(C != k4_ordinal2 & k1_xboole_0 != C & 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]. 87.46/85.56 3000 (all A all B (v3_ordinal1(A) & v4_ordinal2(B) & v3_ordinal1(B) & v4_ordinal2(A) -> v1_ordinal1(k15_ordinal2(A,B)) & v4_ordinal2(k15_ordinal2(A,B)) & v3_ordinal1(k15_ordinal2(A,B)) & v2_ordinal1(k15_ordinal2(A,B)))) # label(fc5_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3001 (all A (m1_subset_1(A,k6_arytm_3) -> (all B (m1_subset_1(B,k6_arytm_3) -> -(k12_arytm_3 != B & k12_arytm_3 != A & k12_arytm_3 = k11_arytm_3(A,B)))))) # label(t86_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3002 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> r2_arytm_3(k4_ordinal2,A) & r2_arytm_3(A,k1_xboole_0))) # label(t14_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3003 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v4_ordinal2(B) & v3_ordinal1(B) -> r2_arytm_3(k3_arytm_3(A,B),k2_arytm_3(A,B)))))) # label(t17_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3004 (all A ((exists B (m1_subset_1(B,k5_ordinal2) & k4_tarski(B,k4_ordinal2) = A)) <-> r2_hidden(A,a_0_1_arytm_3))) # label(fraenkel_a_0_1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3005 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_arytm_3(A,B) <-> (exists C (B = k15_ordinal2(A,C) & v3_ordinal1(C)))))))) # label(d2_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3006 (all A (m1_subset_1(A,k5_ordinal2) -> v4_ordinal2(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc3_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3007 (all A (v4_ordinal2(A) & v3_ordinal1(A) -> (all B (v3_ordinal1(B) & v4_ordinal2(B) -> (k4_arytm_3(A,B) = k1_xboole_0 -> A = k1_xboole_0))))) # label(t20_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3008 (all A (v3_ordinal1(A) -> (all B (m1_subset_1(B,A) -> v3_ordinal1(B) & v2_ordinal1(B) & v1_ordinal1(B))))) # label(cc1_arytm_3) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3009 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(all C (m1_subset_1(C,k2_arytm_2) -> k7_arytm_2(A,C) != B & k7_arytm_2(B,C) != A)))))) # label(t11_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3010 (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]. 87.46/85.56 3011 (all A all B (m1_subset_1(A,k1_arytm_2) & m1_subset_1(B,k1_arytm_2) -> k6_arytm_2(A,B) = k6_arytm_2(B,A))) # label(commutativity_k6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3012 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (A = k12_arytm_3 -> k8_arytm_2(A,B) = k12_arytm_3))))) # label(t4_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3013 (all A (m1_subset_1(A,k2_arytm_2) -> -((all B (m1_subset_1(B,k2_arytm_2) -> k8_arytm_2(A,B) != k13_arytm_3)) & A != k12_arytm_3))) # label(t15_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3014 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r2_hidden(A,k6_arytm_3) -> r2_hidden(B,k6_arytm_3) | (r1_arytm_2(A,B) <-> r2_hidden(A,B))) & (r2_hidden(B,k6_arytm_3) -> r2_hidden(A,k6_arytm_3) | (-r2_hidden(B,A) <-> r1_arytm_2(A,B))) & -(-(r2_hidden(B,k6_arytm_3) & -r2_hidden(A,k6_arytm_3)) & -(r1_tarski(A,B) <-> r1_arytm_2(A,B)) & -(-r2_hidden(B,k6_arytm_3) & r2_hidden(A,k6_arytm_3)) & -(r2_hidden(B,k6_arytm_3) & r2_hidden(A,k6_arytm_3))) & (r2_hidden(B,k6_arytm_3) & r2_hidden(A,k6_arytm_3) -> (r1_arytm_2(A,B) <-> (exists C (m1_subset_1(C,k6_arytm_3) & (exists D (m1_subset_1(D,k6_arytm_3) & B = D & r3_arytm_3(C,D) & A = C)))))))))) # label(d5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3015 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (k7_arytm_2(A,B) = k7_arytm_2(A,C) -> B = C))))))) # label(t12_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 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,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]. 87.46/85.56 3017 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k12_arytm_3 = k7_arytm_2(A,B) -> k12_arytm_3 = A))))) # label(t6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3018 (all A all B (m1_subset_1(B,k1_arytm_2) & m1_subset_1(A,k1_arytm_2) -> m2_subset_1(k6_arytm_2(A,B),k1_zfmisc_1(k6_arytm_3),k1_arytm_2))) # label(dt_k6_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3019 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (B = k12_arytm_3 -> k7_arytm_2(A,B) = A) & (k12_arytm_3 = A -> B = k7_arytm_2(A,B)) & -(k4_arytm_2(k5_arytm_2(k3_arytm_2(A),k3_arytm_2(B))) != k7_arytm_2(A,B) & k12_arytm_3 != A & k12_arytm_3 != B))))) # label(d8_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3020 (all A (m1_subset_1(A,k2_arytm_2) -> m2_subset_1(k3_arytm_2(A),k1_zfmisc_1(k6_arytm_3),k1_arytm_2))) # label(dt_k3_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3021 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (-r2_hidden(A,k6_arytm_3) -> (A = B <-> k3_arytm_2(A) = B)) & (r2_hidden(A,k6_arytm_3) -> (B = k3_arytm_2(A) <-> (exists C (m1_subset_1(C,k6_arytm_3) & C = A & B = a_1_0_arytm_2(C))))))))) # label(d3_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3022 (all A ((exists B ((all C (m1_subset_1(C,k6_arytm_3) -> (r2_hidden(C,B) -> (all D (m1_subset_1(D,k6_arytm_3) -> (r3_arytm_3(D,C) -> r2_hidden(D,B)))) & (exists D (m1_subset_1(D,k6_arytm_3) & r2_hidden(D,B) & -r3_arytm_3(D,C)))))) & A = B & m1_subset_1(B,k1_zfmisc_1(k6_arytm_3)))) <-> r2_hidden(A,a_0_0_arytm_2))) # label(fraenkel_a_0_0_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3023 (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]. 87.46/85.56 3024 (all A all B (m1_subset_1(A,k1_arytm_2) & m1_subset_1(B,k1_arytm_2) -> k5_arytm_2(B,A) = k5_arytm_2(A,B))) # label(commutativity_k5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3025 $T # label(t5_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3026 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> k4_arytm_2(k6_arytm_2(k3_arytm_2(A),k3_arytm_2(B))) = k8_arytm_2(A,B))))) # label(d9_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3027 (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]. 87.46/85.56 3028 (all A all B (m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) -> k7_arytm_2(B,A) = k7_arytm_2(A,B))) # label(commutativity_k7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3029 (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]. 87.46/85.56 3030 (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]. 87.46/85.56 3031 (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]. 87.46/85.56 3032 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(r1_arytm_2(A,B) & (all C (m1_subset_1(C,k2_arytm_2) -> k7_arytm_2(A,C) != B))))))) # label(t10_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.56 3033 (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) -> (r2_hidden(A,a_2_1_arytm_2(B,C)) <-> (exists D exists E (m1_subset_1(D,k6_arytm_3) & m1_subset_1(E,k6_arytm_3) & r2_hidden(D,B) & r2_hidden(E,C) & k11_arytm_3(D,E) = A))))) # label(fraenkel_a_2_1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3034 (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]. 87.46/85.57 3035 (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 (m1_subset_1(C,k2_arytm_2) & r2_hidden(C,B))) & (all C (m1_subset_1(C,k2_arytm_2) -> (exists D (m1_subset_1(D,k2_arytm_2) & (exists E (m1_subset_1(E,k2_arytm_2) & -(r1_arytm_2(C,E) & r1_arytm_2(D,C)) & r2_hidden(E,B) & r2_hidden(D,A))))))) & (all C (m1_subset_1(C,k2_arytm_2) -> (all D (m1_subset_1(D,k2_arytm_2) -> (r2_hidden(D,B) & r2_hidden(C,A) -> r1_arytm_2(C,D)))))) & (exists C (m1_subset_1(C,k2_arytm_2) & r2_hidden(C,A)))))))) # label(t9_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3036 $T # label(dt_k2_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3037 (all A all B (m1_subset_1(B,k2_arytm_2) & m1_subset_1(A,k2_arytm_2) -> r1_arytm_2(B,A) | r1_arytm_2(A,B))) # label(connectedness_r1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3038 (all A (m1_subset_1(A,k2_arytm_2) -> (r2_hidden(A,k5_ordinal2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r1_arytm_2(B,A) & A != B & r2_hidden(B,k5_ordinal2) <-> r2_hidden(B,A))))))) # label(t19_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3039 (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]. 87.46/85.57 3040 (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]. 87.46/85.57 3041 (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) -> (k13_arytm_3 = C & r2_hidden(B,A) -> r2_hidden(k7_arytm_2(B,C),A)))))) -> r1_tarski(k5_ordinal2,A)))) # label(t18_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3042 (all A (m2_subset_1(A,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> (all B (m2_subset_1(B,k1_zfmisc_1(k6_arytm_3),k1_arytm_2) -> k6_arytm_2(A,B) = a_2_1_arytm_2(A,B))))) # label(d7_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3043 (all A -r2_hidden(k4_tarski(k12_arytm_3,A),k2_arytm_2)) # label(t3_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 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,k6_arytm_3) -> (all D (m1_subset_1(D,k6_arytm_3) -> -(A = C & D = B & k8_arytm_2(A,B) = k11_arytm_3(C,D)))))) & r2_hidden(B,k6_arytm_3) & r2_hidden(A,k6_arytm_3)))))) # label(t22_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3045 (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]. 87.46/85.57 3046 (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_0_arytm_2(B,C)) <-> (exists D exists E (m1_subset_1(D,k6_arytm_3) & m1_subset_1(E,k6_arytm_3) & r2_hidden(E,C) & r2_hidden(D,B) & A = k10_arytm_3(D,E)))))) # label(fraenkel_a_2_0_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3047 (all A (r2_hidden(A,a_0_1_arytm_2) <-> (exists B (m1_subset_1(B,k6_arytm_3) & a_1_0_arytm_2(B) = A & B != k12_arytm_3)))) # label(fraenkel_a_0_1_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3048 (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) -> (r2_hidden(D,A) <-> -r3_arytm_3(C,D)))) & m1_subset_1(C,k6_arytm_3))) -> (B = k4_arytm_2(A) <-> (exists C (C = B & (all D (m1_subset_1(D,k6_arytm_3) -> (r2_hidden(D,A) <-> -r3_arytm_3(C,D)))) & m1_subset_1(C,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) <-> -r3_arytm_3(C,D)))))) -> (k4_arytm_2(A) = B <-> B = A)))))) # label(d4_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3049 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (k13_arytm_3 = A -> k8_arytm_2(A,B) = B))))) # label(t16_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 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) -> k8_arytm_2(A,k7_arytm_2(B,C)) = k7_arytm_2(k8_arytm_2(A,B),k8_arytm_2(A,C)))))))) # label(t14_arytm_2) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3051 (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]. 87.46/85.57 3052 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) & r1_arytm_2(C,A) -> k7_arytm_2(k1_arytm_1(B,A),C) = k1_arytm_1(B,k1_arytm_1(A,C))))))))) # label(t14_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 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(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]. 87.46/85.57 3054 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(k7_arytm_2(A,C),k7_arytm_2(B,C)) <-> r1_arytm_2(A,B)))))))) # label(t7_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3055 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r1_arytm_2(B,A) & r1_arytm_2(A,B) -> B = A))))) # label(t4_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3056 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (A = k1_xboole_0 -> k4_tarski(k1_xboole_0,B) = k2_arytm_1(A,B) | B = k1_xboole_0))))) # label(t19_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 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) -> r1_arytm_2(k8_arytm_2(A,C),k8_arytm_2(B,C))))))))) # label(t8_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3058 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,B) & r1_arytm_2(A,C) -> k7_arytm_2(k1_arytm_1(C,A),B) = k7_arytm_2(k1_arytm_1(B,A),C)))))))) # label(t15_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3059 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> -(k1_xboole_0 != C & 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))) & -r1_arytm_2(A,B)))))))) # label(t27_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 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(B,A) -> (A = k7_arytm_2(C,B) <-> C = k1_arytm_1(A,B))) & (-r1_arytm_2(B,A) -> (C = k1_xboole_0 <-> k1_arytm_1(A,B) = C)))))))) # label(d1_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3061 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r1_arytm_2(A,B) & B = k1_xboole_0 -> k1_xboole_0 = A))))) # label(t5_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 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) -> k8_arytm_2(C,k1_arytm_1(B,A)) = k2_arytm_1(k8_arytm_2(C,B),k8_arytm_2(C,A))))))))) # label(t26_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 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) -> k2_arytm_1(k7_arytm_2(C,B),A) = k2_arytm_1(C,k1_arytm_1(A,B))))))))) # label(t21_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3064 (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]. 87.46/85.57 3065 (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]. 87.46/85.57 3066 (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) -> k1_arytm_1(A,B) = k2_arytm_1(A,B)))))) # label(d2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3067 (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]. 87.46/85.57 3068 $T # label(dt_k2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3069 (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]. 87.46/85.57 3070 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(B,A) -> k1_xboole_0 = C | 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_arytm_1(A,B) = k1_xboole_0))))))) # label(t28_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3071 (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]. 87.46/85.57 3072 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (r1_arytm_2(A,B) & k1_xboole_0 = k1_arytm_1(B,A) -> B = A))))) # label(t10_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 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,B) -> r1_arytm_2(k1_arytm_1(C,B),k1_arytm_1(C,A))))))))) # label(t16_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3074 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(k1_arytm_1(A,B) = k1_xboole_0 & -r1_arytm_2(A,B)))))) # label(t9_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3075 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (B = k7_arytm_2(A,B) -> k1_xboole_0 = A))))) # label(t1_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 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) -> 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]. 87.46/85.57 3077 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> -(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]. 87.46/85.57 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]. 87.46/85.57 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(C,B) & r1_arytm_2(A,B) -> k2_arytm_1(k1_arytm_1(B,A),C) = k2_arytm_1(k1_arytm_1(B,C),A)))))))) # label(t25_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3080 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> -(A != k1_xboole_0 & k1_xboole_0 != B & k8_arytm_2(A,B) = k1_xboole_0))))) # label(t2_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3081 (all A (m1_subset_1(A,k2_arytm_2) -> (all B (m1_subset_1(B,k2_arytm_2) -> (all C (m1_subset_1(C,k2_arytm_2) -> (r1_arytm_2(A,C) & r1_arytm_2(A,B) -> k7_arytm_2(k1_arytm_1(B,A),C) = k7_arytm_2(B,k1_arytm_1(C,A))))))))) # label(t12_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3082 (all A (m1_subset_1(A,k2_arytm_2) -> k1_xboole_0 = k2_arytm_1(A,A))) # label(t18_arytm_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3083 (all A all B all C (v1_finset_1(A) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3084 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3085 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3086 (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]. 87.46/85.57 3087 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3088 (all A -(v1_finset_1(A) & k1_xboole_0 != A & (all B -((all C (r2_hidden(C,A) -> r1_tarski(B,C))) & r2_hidden(B,A))) & v6_ordinal1(A))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3089 (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]. 87.46/85.57 3090 (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]. 87.46/85.57 3091 (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]. 87.46/85.57 3092 (all A all B all C (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(C) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3093 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_finset_1(k1_relat_1(A)) <-> v1_finset_1(A)))) # label(t29_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3094 (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]. 87.46/85.57 3095 (all A -(v1_finset_1(A) & v6_ordinal1(A) & (all B -((all C (r2_hidden(C,A) -> r1_tarski(C,B))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3096 (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]. 87.46/85.57 3097 (all A (v1_finset_1(k1_zfmisc_1(A)) <-> v1_finset_1(A))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3098 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3099 (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]. 87.46/85.57 3100 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(D) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3101 (all A ((exists B (v1_relat_1(B) & v1_funct_1(B) & k2_relat_1(B) = A & r2_hidden(k1_relat_1(B),k5_ordinal2))) <-> v1_finset_1(A))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3102 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3103 (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]. 87.46/85.57 3104 (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]. 87.46/85.57 3105 (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]. 87.46/85.57 3106 (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]. 87.46/85.57 3107 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3108 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3109 (exists A (-v1_xboole_0(A) & v1_finset_1(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3110 (all A exists B (v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v2_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) & v3_ordinal1(B) & v1_ordinal1(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3111 (all A all B (-v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3112 (all A all B (v1_finset_1(k2_zfmisc_1(B,A)) -> v1_finset_1(B) | A = k1_xboole_0)) # label(t22_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3113 (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]. 87.46/85.57 3114 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_xboole_0(A,B)))) # label(t14_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3115 (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]. 87.46/85.57 3116 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k5_xboole_0(A,B)))) # label(fc17_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3117 (all A all B (v1_funct_1(A) & v1_finset_1(B) & v1_relat_1(A) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3118 (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]. 87.46/85.57 3119 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3120 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3121 (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]. 87.46/85.57 3122 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3123 (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]. 87.46/85.57 3124 (all A all B all C all D (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(D) & v1_finset_1(A) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(t21_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3125 (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]. 87.46/85.57 3126 (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s1_finset_1 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (p1_s1_finset_1(B) -> k1_funct_1(A,B) = f2_s1_finset_1(B)) & (-p1_s1_finset_1(B) -> k1_funct_1(A,B) = f3_s1_finset_1(B))))) & v1_relat_1(A))) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3127 p1_s2_finset_1(k1_xboole_0) & (all A all B (p1_s2_finset_1(B) & r1_tarski(B,f1_s2_finset_1) & r2_hidden(A,f1_s2_finset_1) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) & v1_finset_1(f1_s2_finset_1) -> p1_s2_finset_1(f1_s2_finset_1) # label(s2_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3128 (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]. 87.46/85.57 3129 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3130 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3131 (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]. 87.46/85.57 3132 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & (all C -(r2_hidden(C,B) & (all D (r1_tarski(C,D) & r2_hidden(D,B) -> D = C))))))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3133 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_finset_1(B) & -v1_xboole_0(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3134 (all A (v1_finset_1(k3_tarski(A)) <-> v1_finset_1(A) & (all B (r2_hidden(B,A) -> v1_finset_1(B))))) # label(t25_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3135 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k2_relat_1(A))))) # label(t26_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3136 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3137 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_finset_1(B) & -v1_xboole_0(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3138 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3139 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3140 (all A (-v1_xboole_0(k5_finsub_1(A)) & v4_finsub_1(k5_finsub_1(A)) & v3_finsub_1(k5_finsub_1(A)) & v1_finsub_1(k5_finsub_1(A)))) # label(fc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3141 (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]. 87.46/85.57 3142 (all A ((all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k2_xboole_0(B,C),A))) <-> v1_finsub_1(A))) # label(d1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3143 $T # label(t6_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3144 (all A (v1_finsub_1(A) & v3_finsub_1(A) <-> v4_finsub_1(A))) # label(d4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3145 $T # label(t22_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3146 $T # label(t31_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3147 (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]. 87.46/85.57 3148 (all A (-v1_xboole_0(A) & v4_finsub_1(A) -> r2_hidden(k1_xboole_0,A))) # label(t18_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3149 $T # label(t4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3150 $T # label(t9_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3151 (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]. 87.46/85.57 3152 $T # label(t12_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3153 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_finset_1(A) -> m1_subset_1(B,k5_finsub_1(A))))) # label(t34_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3154 $T # label(t5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3155 (all A all B all C (v4_finsub_1(C) & -v1_xboole_0(C) -> (m1_subset_1(A,C) & m1_subset_1(B,C) -> m1_subset_1(k5_xboole_0(A,B),C)))) # label(t14_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3156 (all A (v2_finsub_1(A) <-> (all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k3_xboole_0(B,C),A))))) # label(d2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3157 (all A (v1_finset_1(A) -> k5_finsub_1(A) = k1_zfmisc_1(A))) # label(t27_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3158 $T # label(t33_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3159 (all A v4_finsub_1(k1_zfmisc_1(A))) # label(t20_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3160 $T # label(t2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3161 (all A ((all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_xboole_0(B,C),A))) <-> v3_finsub_1(A))) # label(d3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3162 $T # label(t1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3163 $T # label(t29_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3164 (all A all B all C (v4_finsub_1(C) & -v1_xboole_0(C) -> (m1_subset_1(B,C) & m1_subset_1(A,C) -> m1_subset_1(k3_xboole_0(A,B),C)))) # label(t13_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3165 (all A all B k3_xboole_0(k5_finsub_1(A),k5_finsub_1(B)) = k5_finsub_1(k3_xboole_0(A,B))) # label(t24_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3166 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k2_xboole_0(B,C) = k1_finsub_1(A,B,C))) # label(redefinition_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3167 $T # label(t8_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3168 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k3_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t16_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3169 $T # label(t7_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3170 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k4_finsub_1(A,C,B) = k4_finsub_1(A,B,C))) # label(commutativity_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3171 $T # label(t3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3172 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> m1_subset_1(k3_finsub_1(A,B,C),A))) # label(dt_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3173 $T # label(t11_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3174 (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]. 87.46/85.57 3175 (all A v4_finsub_1(k5_finsub_1(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3176 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> k5_xboole_0(B,C) = k4_finsub_1(A,B,C))) # label(redefinition_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3177 (all A (-v1_xboole_0(A) & v4_finsub_1(A) -> (all B (v4_finsub_1(B) & -v1_xboole_0(B) -> -v1_xboole_0(k3_xboole_0(A,B)) & v4_finsub_1(k3_xboole_0(A,B)))))) # label(t21_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3178 (all A all B (v4_finsub_1(B) -> (k5_finsub_1(A) = B <-> (all C (r2_hidden(C,B) <-> v1_finset_1(C) & r1_tarski(C,A)))))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3179 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> k3_finsub_1(A,B,B) = B)) # label(idempotence_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3180 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> m1_subset_1(B,k1_zfmisc_1(A)))) # label(t32_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3181 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k3_xboole_0(B,C) = k3_finsub_1(A,B,C))) # label(redefinition_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3182 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k2_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t17_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3183 (all A (v4_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v1_finsub_1(k1_zfmisc_1(A)) & -v1_xboole_0(k1_zfmisc_1(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3184 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) -> k4_xboole_0(B,C) = k2_finsub_1(A,B,C))) # label(redefinition_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3185 (all A (v4_finsub_1(A) -> v1_finsub_1(A) & v3_finsub_1(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3186 (exists A (-v1_xboole_0(A) & v2_finsub_1(A) & v3_finsub_1(A) & v4_finsub_1(A) & v1_finsub_1(A))) # label(rc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3187 (all A r1_tarski(k5_finsub_1(A),k1_zfmisc_1(A))) # label(t26_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3188 (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]. 87.46/85.57 3189 (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]. 87.46/85.57 3190 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k1_finsub_1(A,B,B) = B)) # label(idempotence_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3191 $T # label(t19_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3192 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> m1_subset_1(k2_finsub_1(A,B,C),A))) # label(dt_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3193 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k2_xboole_0(B,C),A) & r2_hidden(k4_xboole_0(B,C),A))) <-> v4_finsub_1(A))) # label(t10_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3194 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k1_finsub_1(A,C,B) = k1_finsub_1(A,B,C))) # label(commutativity_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3195 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k3_finsub_1(A,C,B) = k3_finsub_1(A,B,C))) # label(commutativity_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3196 (all A (v1_finsub_1(A) & v3_finsub_1(A) -> v4_finsub_1(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3197 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> m1_subset_1(k1_finsub_1(A,B,C),A))) # label(dt_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3198 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))))) # label(t18_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3199 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (v1_binop_1(C,A) & v3_binop_1(C,A) & v2_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> (r2_hidden(F,D) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,F),k7_setwiseo(B,A,C,D,E)) = k7_setwiseo(B,A,C,D,E))))))))))))))) # label(t31_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3200 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k3_tarski(k8_setwiseo(A,k5_finsub_1(B),C,D)) = k10_setwiseo(A,B,D,C))))))) # label(t61_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3201 (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]. 87.46/85.57 3202 (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]. 87.46/85.57 3203 $T # label(t2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3204 (all A r3_binop_1(k5_finsub_1(A),k1_setwiseo(A),k9_setwiseo(A))) # label(t52_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3205 (all A k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)) = k1_xboole_0) # label(t55_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3206 (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) -> (v1_binop_1(D,B) & v1_setwiseo(D,B) & v3_binop_1(D,B) & v2_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) -> ((all G (m1_subset_1(G,k5_finsub_1(C)) -> (all H (m1_subset_1(H,k5_finsub_1(C)) -> k8_funct_2(k5_finsub_1(C),B,F,k5_setwiseo(C,G,H)) = k2_binop_1(B,B,B,D,k8_funct_2(k5_finsub_1(C),B,F,G),k8_funct_2(k5_finsub_1(C),B,F,H)))))) & 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(A)) -> k8_funct_2(k5_finsub_1(C),B,F,k10_setwiseo(A,C,G,E)) = k7_setwiseo(A,B,D,G,k7_funct_2(A,k5_finsub_1(C),B,E,F)))))))))))))))) # label(t65_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3207 (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) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> -(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) & k1_xboole_0 != F & E != k1_xboole_0)))))))))))))) # label(t30_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3208 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (r2_hidden(E,k10_setwiseo(A,B,D,C)) <-> (exists F (m1_subset_1(F,A) & r2_hidden(F,D) & r2_hidden(E,k8_funct_2(A,k5_finsub_1(B),C,F)))))))))))) # label(t70_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3209 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (v1_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> k7_setwiseo(B,A,C,k2_setwiseo(B,E),D) = k8_funct_2(B,A,D,E)))))))))))) # label(t26_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3210 (all A (m1_subset_1(k1_setwiseo(A),k5_finsub_1(A)) & v1_xboole_0(k1_setwiseo(A)))) # label(dt_k1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3211 (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) -> (v2_binop_1(C,A) & v1_setwiseo(C,A) & v1_binop_1(C,A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> k7_setwiseo(B,A,C,k1_setwiseo(B),D) = k3_binop_1(A,C)))))))))) # label(t40_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3212 p1_s2_setwiseo(k1_setwiseo(f1_s2_setwiseo)) & (all A (m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo)) -> (all B (m1_subset_1(B,f1_s2_setwiseo) -> (p1_s2_setwiseo(A) -> p1_s2_setwiseo(k5_setwiseo(f1_s2_setwiseo,A,k2_setwiseo(f1_s2_setwiseo,B))) | r2_hidden(B,A)))))) -> (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]. 87.46/85.57 3213 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (v3_binop_1(C,A) & v1_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)) = k7_setwiseo(B,A,C,k3_setwiseo(B,E,F),D)))))))))))))) # label(t27_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3214 (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,B) -> k1_tarski(k8_funct_2(B,A,C,D)) = k2_funct_2(B,A,C,k1_tarski(D)))))))))) # label(t13_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3215 (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) -> (v1_binop_1(C,B) & v3_binop_1(C,B) & v1_setwiseo(C,B) & v2_binop_1(C,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> (k8_setwiseo(A,B,E,G) = k8_setwiseo(A,B,D,F) -> k7_setwiseo(A,B,C,G,E) = k7_setwiseo(A,B,C,F,D))))))))))))))))) # label(t43_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3216 (all A all B all C all D (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> k1_enumset1(B,C,D) = k4_setwiseo(A,B,C,D))) # label(redefinition_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3217 (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]. 87.46/85.57 3218 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,A) -> k8_funct_2(A,k5_finsub_1(B),C,D) = k10_setwiseo(A,B,k2_setwiseo(A,D),C))))))) # label(t56_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3219 (exists 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)) & v1_funct_1(A))) # label(s1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3220 (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]. 87.46/85.57 3221 (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) -> (v2_binop_1(C,B) & v3_binop_1(C,B) & v1_setwiseo(C,B) & v1_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(D,D),D) & v1_funct_2(E,k2_zfmisc_1(D,D),D) & v1_funct_1(E) -> (v2_binop_1(E,D) & v3_binop_1(E,D) & v1_setwiseo(E,D) & v1_binop_1(E,D) -> (all F (v1_funct_1(F) & v1_funct_2(F,A,B) & m2_relset_1(F,A,B) -> (all G (m2_relset_1(G,B,D) & v1_funct_2(G,B,D) & v1_funct_1(G) -> ((all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)) = k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)))))) & k3_binop_1(D,E) = k8_funct_2(B,D,G,k3_binop_1(B,C)) -> (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]. 87.46/85.57 3222 (all A v3_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t49_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3223 (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)) -> (all B (m1_subset_1(B,k5_finsub_1(f1_s3_setwiseo)) -> (p1_s3_setwiseo(B) & p1_s3_setwiseo(A) -> B = k1_xboole_0 | p1_s3_setwiseo(k5_setwiseo(f1_s3_setwiseo,A,B)) | A = k1_xboole_0))))) -> (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]. 87.46/85.57 3224 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> ((exists C (m1_subset_1(C,A) & r3_binop_1(A,C,B))) <-> v1_setwiseo(B,A)))))) # label(d2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3225 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_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) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> (r2_hidden(G,D) -> k8_funct_2(B,A,E,G) = F))) -> k7_setwiseo(B,A,C,D,E) = F))) | k1_xboole_0 = D))))))))))) # label(t33_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3226 (all A all B all C (r2_hidden(A,k2_xboole_0(B,k1_tarski(C))) <-> A = C | r2_hidden(A,B))) # label(t6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3227 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> m1_subset_1(k6_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3228 (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]. 87.46/85.57 3229 p1_s4_setwiseo(k1_setwiseo(f1_s4_setwiseo)) & (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)))))))) -> (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]. 87.46/85.57 3230 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (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) -> k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F))))))))))))))) # label(t29_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3231 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) & m1_subset_1(D,k5_finsub_1(A)) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & -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]. 87.46/85.57 3232 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & m2_relset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) -> ((all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k2_binop_1(k5_finsub_1(A),k5_finsub_1(A),k5_finsub_1(A),B,C,D) = k5_setwiseo(A,C,D))))) <-> k9_setwiseo(A) = B))) # label(d4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3233 $T # label(t17_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3234 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)) = k10_setwiseo(A,B,k3_setwiseo(A,D,E),C))))))))) # label(t57_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3235 $T # label(t10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3236 (all A all B (v1_funct_2(B,A,k5_finsub_1(A)) & m2_relset_1(B,A,k5_finsub_1(A)) & v1_funct_1(B) -> (k11_setwiseo(A) = B <-> (all C (r2_hidden(C,A) -> k1_tarski(C) = k1_funct_1(B,C)))))) # label(d6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3237 $T # label(t9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.57 3238 (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) -> (v1_setwiseo(B,A) -> (all C (m1_subset_1(C,A) -> C = k2_binop_1(A,A,A,B,k3_binop_1(A,B),C) & k2_binop_1(A,A,A,B,C,k3_binop_1(A,B)) = C))))))) # label(t23_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.58 3239 (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)) -> k10_setwiseo(A,B,k1_setwiseo(A),C) = k1_xboole_0)))) # label(t59_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.58 3240 (all A (v1_funct_1(k11_setwiseo(A)) & v1_funct_2(k11_setwiseo(A),A,k5_finsub_1(A)) & m2_relset_1(k11_setwiseo(A),A,k5_finsub_1(A)))) # label(dt_k11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.58 3241 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,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]. 87.46/85.58 3242 $T # label(t24_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.58 3243 (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) & v3_binop_1(C,B) -> -v1_setwiseo(C,B) & D = k1_xboole_0 | (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,A) -> k8_funct_2(A,B,E,H) = k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,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) -> k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))) = k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)))))))) & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> H = k1_funct_1(G,k1_xboole_0)))) & F = k8_funct_2(k5_finsub_1(A),B,G,D))) <-> k7_setwiseo(A,B,C,D,E) = F)))))))))))))) # label(t25_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.58 3244 (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(k4_setwiseo(A,B,C,D),k5_finsub_1(A)))) # label(dt_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.58 3245 (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]. 87.46/85.58 3246 (all A (v1_funct_1(k9_setwiseo(A)) & m2_relset_1(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_2(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]. 87.46/85.58 3247 (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) & v1_setwiseo(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D))))))))))))))) # label(t42_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.58 3248 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k3_setwiseo(A,C,B) = k3_setwiseo(A,B,C))) # label(commutativity_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.46/85.58 3249 (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]. 87.46/85.58 3250 (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) -> (v3_binop_1(D,A) & v2_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 (m2_relset_1(F,B,k5_finsub_1(C)) & v1_funct_2(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)) -> k2_binop_1(A,A,A,D,k8_funct_2(k5_finsub_1(C),A,G,H),k8_funct_2(k5_finsub_1(C),A,G,I)) = k8_funct_2(k5_finsub_1(C),A,G,k5_setwiseo(C,H,I)))))) -> k7_setwiseo(B,A,D,E,k7_funct_2(B,k5_finsub_1(C),A,F,G)) = k8_funct_2(k5_finsub_1(C),A,G,k10_setwiseo(B,C,E,F))))))))))))))))) # label(t64_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3251 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)))) # label(dt_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3252 (all A v1_setwiseo(k9_setwiseo(A),k5_finsub_1(A))) # label(t53_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3253 (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]. 87.57/85.59 3254 (all A all B all C all D (m1_subset_1(C,k5_finsub_1(A)) & v1_funct_2(D,A,k5_finsub_1(B)) & m1_relset_1(D,A,k5_finsub_1(B)) & v1_funct_1(D) & -v1_xboole_0(A) -> m1_subset_1(k10_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3255 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> (r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),C)) <-> B = C))))) # label(t68_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3256 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> m1_subset_1(k3_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3257 (all A all B all C -(-r1_tarski(A,B) & -r2_hidden(C,A) & r1_tarski(A,k2_xboole_0(B,k1_tarski(C))))) # label(t5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3258 $T # label(t48_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3259 (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 (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (v2_binop_1(C,B) & v1_binop_1(C,B) -> -v1_setwiseo(C,B) & k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> (k7_setwiseo(A,B,C,D,E) = F <-> (exists 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,A) -> k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)) = k8_funct_2(A,B,E,H))) & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> k1_xboole_0 = H | (all I (m1_subset_1(I,A) -> (r2_hidden(I,k6_setwiseo(A,D,H)) -> 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,B) -> (r3_binop_1(B,H,C) -> H = k1_funct_1(G,k1_xboole_0)))) & F = k8_funct_2(k5_finsub_1(A),B,G,D) & v1_funct_1(G))))))))))))))))) # label(d3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3260 (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)) -> C = B))))))))) # label(t69_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3261 (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]. 87.57/85.59 3262 (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) -> (r3_binop_1(A,k3_binop_1(A,B),B) <-> v1_setwiseo(B,A)))))) # label(t22_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3263 $T # label(t1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3264 (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]. 87.57/85.59 3265 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,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]. 87.57/85.59 3266 (all A v2_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t51_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3267 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,k5_finsub_1(B)) & m2_relset_1(D,A,k5_finsub_1(B)) -> 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]. 87.57/85.59 3268 (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]. 87.57/85.59 3269 $T # label(t7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3270 (all A v1_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t50_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3271 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k9_relat_1(C,k4_xboole_0(B,k10_relat_1(C,A))) = k4_xboole_0(k9_relat_1(C,B),A))) # label(t11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3272 (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) -> (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) -> (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]. 87.57/85.59 3273 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (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_2(F,B,C) & m2_relset_1(F,B,C) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,C,A) & v1_funct_2(G,C,A) -> 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]. 87.57/85.59 3274 (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) -> (v2_binop_1(D,A) & v1_setwiseo(D,A) & v1_binop_1(D,A) & v3_binop_1(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_1(G) & v1_funct_2(G,C,A) & m2_relset_1(G,C,A) -> 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]. 87.57/85.59 3275 (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) -> (v1_binop_1(C,B) & v2_binop_1(C,B) & v3_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]. 87.57/85.59 3276 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (v2_binop_1(C,B) & v3_binop_1(C,B) & v1_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(D,D),D) & m2_relset_1(E,k2_zfmisc_1(D,D),D) -> (v2_binop_1(E,D) & v3_binop_1(E,D) & v1_binop_1(E,D) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (all G (v1_funct_2(G,B,D) & m2_relset_1(G,B,D) & v1_funct_1(G) -> ((all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)) = k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)))))) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> (H != k1_xboole_0 -> k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)) = k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)))))))))))))))))))))) # label(t39_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3277 (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]. 87.57/85.59 3278 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,C) -> r2_hidden(k8_funct_2(A,B,E,F),D)))) -> r1_tarski(k2_funct_2(A,B,E,C),D)))))))))) # label(t15_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3279 (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) -> (v3_binop_1(C,A) & v1_binop_1(C,A) & v2_binop_1(C,A) & v1_setwiseo(C,A) -> (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E) = k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F))))))))))))))) # label(t41_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3280 (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) -> (v1_binop_1(C,B) & v2_binop_1(C,B) & v3_binop_1(C,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_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)) -> (k2_funct_2(A,B,E,G) = k2_funct_2(A,B,D,F) -> k7_setwiseo(A,B,C,F,D) = k7_setwiseo(A,B,C,G,E) | k1_xboole_0 = F)))))))))))))))) # label(t35_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3281 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(C) & m1_subset_1(D,k5_finsub_1(A)) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & -v1_xboole_0(B) -> k8_setwiseo(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 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) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> (r1_tarski(E,F) -> k1_xboole_0 = E | 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))))))))))))))) # label(t32_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.59 3283 (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]. 87.57/85.59 3284 (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]. 87.57/85.59 3285 (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]. 87.57/85.60 3286 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> B = k5_setwiseo(A,B,B))) # label(idempotence_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3287 $T # label(t47_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3288 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> k4_xboole_0(B,C) = k6_setwiseo(A,B,C))) # label(redefinition_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3289 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(D,k5_finsub_1(A)) & m1_relset_1(C,A,B) & -v1_xboole_0(B) -> m1_subset_1(k8_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3290 $T # label(t20_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3291 (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_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_2(F,B,k5_finsub_1(C)) & m2_relset_1(F,B,k5_finsub_1(C)) & v1_funct_1(F) -> 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]. 87.57/85.60 3292 $T # label(t46_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3293 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k5_setwiseo(A,B,C) = k5_setwiseo(A,C,B))) # label(commutativity_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3294 (all A k1_setwiseo(A) = k1_xboole_0) # label(d1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3295 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & r6_binop_1(A,D,C) & v1_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]. 87.57/85.60 3296 $T # label(t21_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3297 (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]. 87.57/85.60 3298 $T # label(t66_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3299 (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,k2_zfmisc_1(A,A),A) & v1_funct_2(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,G,k7_setwiseo(B,A,C,E,F)) = k7_setwiseo(B,A,C,E,k8_funcop_1(A,B,D,G,F)))))))))))))))))) # label(t36_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3300 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,B,A) & v1_funct_2(C,B,A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (k2_funct_2(B,A,C,D) = k1_xboole_0 -> D = k1_xboole_0))))))))) # label(t19_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3301 (all A (-v1_xboole_0(A) -> (all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,k5_finsub_1(B)) & v1_funct_2(D,A,k5_finsub_1(B)) -> (all 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)) & v1_funct_1(E) -> (k1_setwiseo(C) = k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k1_setwiseo(B)) & (all F (m1_subset_1(F,k5_finsub_1(B)) -> (all G (m1_subset_1(G,k5_finsub_1(B)) -> 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)) = k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k5_setwiseo(B,F,G)))))) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> k10_setwiseo(A,C,F,k7_funct_2(A,k5_finsub_1(B),k5_finsub_1(C),D,E)) = k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k10_setwiseo(A,B,F,D))))))))))) # label(t72_setwiseo) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3302 (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]. 87.57/85.60 3303 (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]. 87.57/85.60 3304 (all A (r2_hidden(A,a_0_22_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s13_fraenkel) & p1_s13_fraenkel(B,C) & A = f4_s13_fraenkel(B,C) & m1_subset_1(B,f1_s13_fraenkel))))) # label(fraenkel_a_0_22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3305 (exists A ((all B (m1_subset_1(B,f1_s24_fraenkel) -> ((exists C (m1_subset_1(C,f2_s24_fraenkel) & p1_s24_fraenkel(B,C) & B = f4_s24_fraenkel(C) & r2_hidden(C,f3_s24_fraenkel))) <-> r2_hidden(B,A)))) & m1_subset_1(A,k5_finsub_1(f1_s24_fraenkel)))) # label(s24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3306 (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]. 87.57/85.60 3307 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (all D (m2_fraenkel(D,A,B,C) <-> m1_subset_1(D,C))))) # label(redefinition_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3308 (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]. 87.57/85.60 3309 (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]. 87.57/85.60 3310 (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]. 87.57/85.60 3311 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_fraenkel(k1_funct_2(A,B)) & v1_finset_1(k1_funct_2(A,B)))) # label(fc2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3312 (all A ((exists B (A = f2_s14_fraenkel(B) & p1_s14_fraenkel(B) & p2_s14_fraenkel(B) & m1_subset_1(B,f1_s14_fraenkel))) <-> r2_hidden(A,a_0_26_fraenkel))) # label(fraenkel_a_0_26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3313 (all A (m1_subset_1(A,f1_s5_fraenkel) -> f3_s5_fraenkel(A) = f2_s5_fraenkel(A))) -> a_0_9_fraenkel = a_0_8_fraenkel # label(s5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3314 (all A (r2_hidden(A,a_0_3_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s2_fraenkel) & p2_s2_fraenkel(B,C) & A = f3_s2_fraenkel(B,C) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3315 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3316 (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]. 87.57/85.60 3317 (all A ((exists B (p2_s3_fraenkel(B) & A = f2_s3_fraenkel(B) & m1_subset_1(B,f1_s3_fraenkel))) <-> r2_hidden(A,a_0_5_fraenkel))) # label(fraenkel_a_0_5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3318 (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]. 87.57/85.60 3319 (all A ((exists B (p2_s1_fraenkel(B) & A = f2_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]. 87.57/85.60 3320 (all A (m1_subset_1(A,f1_s16_fraenkel) -> (all B (m1_subset_1(B,f2_s16_fraenkel) -> -((all C (m1_subset_1(C,f1_s16_fraenkel) -> -(p2_s16_fraenkel(C,B) & f3_s16_fraenkel(C,B) = f3_s16_fraenkel(A,B)))) & p1_s16_fraenkel(A,B)))))) -> r1_tarski(a_0_30_fraenkel,a_0_31_fraenkel) # label(s16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3321 (all A (r2_hidden(A,a_0_2_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s2_fraenkel) & A = f3_s2_fraenkel(B,C) & p1_s2_fraenkel(B,C) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3322 (all A ((exists B exists C (m1_subset_1(C,f2_s4_fraenkel) & A = f3_s4_fraenkel(B,C) & 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]. 87.57/85.60 3323 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(D,A) & r1_tarski(C,B) -> (all E (m1_subset_1(E,k1_funct_2(C,D)) -> m2_relset_1(E,B,A) & v1_funct_1(E))) | k1_funct_2(C,D) = k1_xboole_0)))) # label(t6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3324 (all A ((all B (r2_hidden(B,A) -> v1_funct_1(B) & v1_relat_1(B))) <-> v1_fraenkel(A))) # label(d1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3325 (all A ((exists B (p1_s10_fraenkel(B) & A = B & m1_subset_1(B,f1_s10_fraenkel))) <-> r2_hidden(A,a_0_18_fraenkel))) # label(fraenkel_a_0_18_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3326 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3327 v1_finset_1(f3_s25_fraenkel) & v1_finset_1(f4_s25_fraenkel) & (all A (m2_fraenkel(A,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (all B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (k7_relat_1(B,f3_s25_fraenkel) = k7_relat_1(A,f3_s25_fraenkel) -> f5_s25_fraenkel(A) = f5_s25_fraenkel(B)))))) -> v1_finset_1(a_0_40_fraenkel) # label(s25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3328 (exists A (-v1_xboole_0(A) & v1_fraenkel(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3329 (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> f3_s8_fraenkel(A,B) = f3_s8_fraenkel(B,A))))) & (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> (p2_s8_fraenkel(A,B) <-> p1_s8_fraenkel(A,B)))))) -> a_0_15_fraenkel = a_0_14_fraenkel # label(s8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3330 (all A (m1_subset_1(A,f1_s4_fraenkel) -> (all B (m1_subset_1(B,f2_s4_fraenkel) -> (p1_s4_fraenkel(A,B) <-> p2_s4_fraenkel(A,B)))))) -> a_0_7_fraenkel = a_0_6_fraenkel # label(s4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3331 (all A ((exists B exists C (m1_subset_1(C,f2_s20_fraenkel) & f4_s20_fraenkel = C & p1_s20_fraenkel(B,C) & f3_s20_fraenkel(B,C) = A & 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]. 87.57/85.60 3332 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3333 (all A (r2_hidden(A,a_0_9_fraenkel) <-> (exists B (m1_subset_1(B,f1_s5_fraenkel) & p1_s5_fraenkel(B) & A = f3_s5_fraenkel(B))))) # label(fraenkel_a_0_9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3334 (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]. 87.57/85.60 3335 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3336 (all A ((exists B (m1_subset_1(B,f1_s14_fraenkel) & B = A & p2_s14_fraenkel(B))) <-> r2_hidden(A,a_0_25_fraenkel))) # label(fraenkel_a_0_25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3337 (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]. 87.57/85.60 3338 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3339 (all A (r2_hidden(A,a_0_24_fraenkel) <-> (exists B (m1_subset_1(B,f1_s14_fraenkel) & r2_hidden(B,a_0_25_fraenkel) & p1_s14_fraenkel(B) & A = f2_s14_fraenkel(B))))) # label(fraenkel_a_0_24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3340 (all A ((exists B exists C (A = f3_s16_fraenkel(B,C) & 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]. 87.57/85.60 3341 (all A (r2_hidden(A,a_0_32_fraenkel) <-> (exists B (A = f3_s17_fraenkel(B) & p1_s17_fraenkel(B) & r2_hidden(f3_s17_fraenkel(B),f2_s17_fraenkel) & m1_subset_1(B,f1_s17_fraenkel))))) # label(fraenkel_a_0_32_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3342 (all A ((exists B (f2_s3_fraenkel(B) = A & p1_s3_fraenkel(B) & m1_subset_1(B,f1_s3_fraenkel))) <-> r2_hidden(A,a_0_4_fraenkel))) # label(fraenkel_a_0_4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3343 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3344 (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_2(A,f1_s26_fraenkel,f2_s26_fraenkel) & m2_relset_1(A,f1_s26_fraenkel,f2_s26_fraenkel) & (all B (m1_subset_1(B,f1_s26_fraenkel) -> (r2_hidden(B,f3_s26_fraenkel) -> p1_s26_fraenkel(B,k8_funct_2(f1_s26_fraenkel,f2_s26_fraenkel,A,B))))) & v1_funct_1(A))) # label(s26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3345 (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]. 87.57/85.60 3346 (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]. 87.57/85.60 3347 (all A ((exists B (f2_s6_fraenkel(B) = A & p1_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]. 87.57/85.60 3348 (all A ((exists B (m1_subset_1(B,f1_s21_fraenkel) & r2_hidden(B,f2_s21_fraenkel) & A = f3_s21_fraenkel(B))) <-> r2_hidden(A,a_0_38_fraenkel))) # label(fraenkel_a_0_38_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3349 (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]. 87.57/85.60 3350 (all A (r2_hidden(A,a_0_30_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s16_fraenkel) & p1_s16_fraenkel(B,C) & A = f3_s16_fraenkel(B,C) & m1_subset_1(B,f1_s16_fraenkel))))) # label(fraenkel_a_0_30_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3351 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3352 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3353 (all A ((exists B (m1_subset_1(B,f1_s18_fraenkel) & A = f3_s18_fraenkel(B) & p1_s18_fraenkel(B) & -r2_hidden(f3_s18_fraenkel(B),f2_s18_fraenkel))) <-> r2_hidden(A,a_0_33_fraenkel))) # label(fraenkel_a_0_33_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3354 (all A (m1_subset_1(A,f1_s19_fraenkel) -> (all B (m1_subset_1(B,f2_s19_fraenkel) -> (p2_s19_fraenkel(A,B) <-> p1_s19_fraenkel(A,B) & f4_s19_fraenkel = B))))) -> a_0_35_fraenkel = a_0_34_fraenkel # label(s19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3355 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3356 (all A ((exists B (p1_s5_fraenkel(B) & A = f2_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))) <-> r2_hidden(A,a_0_8_fraenkel))) # label(fraenkel_a_0_8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3357 (all A (r2_hidden(A,a_0_11_fraenkel) <-> (exists B (f3_s6_fraenkel(B) = A & p1_s6_fraenkel(B) & m1_subset_1(B,f1_s6_fraenkel))))) # label(fraenkel_a_0_11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3358 (all A (r2_hidden(A,a_0_16_fraenkel) <-> (exists B (m1_subset_1(B,f1_s9_fraenkel) & k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f4_s9_fraenkel,B) = A & p1_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel))))) # label(fraenkel_a_0_16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3359 (all A ((exists B exists C (m1_subset_1(C,f2_s19_fraenkel) & f3_s19_fraenkel(B,C) = A & p2_s19_fraenkel(B,C) & m1_subset_1(B,f1_s19_fraenkel))) <-> r2_hidden(A,a_0_34_fraenkel))) # label(fraenkel_a_0_34_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3360 (all A (r2_hidden(A,a_0_6_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s4_fraenkel) & f3_s4_fraenkel(B,C) = A & p1_s4_fraenkel(B,C) & m1_subset_1(C,f2_s4_fraenkel))))) # label(fraenkel_a_0_6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3361 (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]. 87.57/85.60 3362 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3363 (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]. 87.57/85.60 3364 (all A (v1_fraenkel(A) -> (all B (m1_subset_1(B,A) -> v1_funct_1(B) & v1_relat_1(B))))) # label(cc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3365 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3366 (all A (r2_hidden(A,a_0_21_fraenkel) <-> (exists B (A = B & p2_s13_fraenkel(B) & r2_hidden(B,a_0_22_fraenkel) & m1_subset_1(B,f3_s13_fraenkel))))) # label(fraenkel_a_0_21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3367 (all A ((exists B (m1_subset_1(B,f1_s19_fraenkel) & f3_s19_fraenkel(B,f4_s19_fraenkel) = A & 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]. 87.57/85.60 3368 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3369 (all A all B (-v1_xboole_0(B) -> k1_fraenkel(A,B) = k1_funct_2(A,B))) # label(redefinition_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.57/85.60 3370 (all A (m1_subset_1(A,f1_s23_fraenkel) -> p1_s23_fraenkel(A,A))) & (all A (m1_subset_1(A,f1_s23_fraenkel) -> (all B (m1_subset_1(B,f1_s23_fraenkel) -> (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(B,C) & p1_s23_fraenkel(A,B) -> p1_s23_fraenkel(A,C)))))))) -> (all A (m1_subset_1(A,f1_s23_fraenkel) -> -(r2_hidden(A,f2_s23_fraenkel) & (all B (m1_subset_1(B,f1_s23_fraenkel) -> -((all C (m1_subset_1(C,f1_s23_fraenkel) -> (r2_hidden(C,f2_s23_fraenkel) & p1_s23_fraenkel(C,B) -> p1_s23_fraenkel(B,C)))) & p1_s23_fraenkel(B,A) & r2_hidden(B,f2_s23_fraenkel))))))) # label(s23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3371 (all A ((exists B (p1_s1_fraenkel(B) & A = f2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel))) <-> r2_hidden(A,a_0_0_fraenkel))) # label(fraenkel_a_0_0_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3372 (all A (r2_hidden(A,a_0_14_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & m1_subset_1(C,f2_s8_fraenkel) & f3_s8_fraenkel(B,C) = A & p1_s8_fraenkel(B,C))))) # label(fraenkel_a_0_14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3373 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (all D (m2_fraenkel(D,A,B,C) -> v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B))))) # label(dt_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3374 (all A ((exists B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) & f5_s25_fraenkel(B) = A & r1_tarski(k2_funct_2(f1_s25_fraenkel,f2_s25_fraenkel,B,f3_s25_fraenkel),f4_s25_fraenkel))) <-> r2_hidden(A,a_0_40_fraenkel))) # label(fraenkel_a_0_40_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3375 (all A all B all C (-v1_xboole_0(C) & v1_fraenkel(C) -> (m1_fraenkel(C,A,B) <-> (all D (m1_subset_1(D,C) -> v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D)))))) # label(d2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3376 (all A ((exists B exists C (p1_s15_fraenkel(B,C) & r2_hidden(B,a_0_28_fraenkel) & f3_s15_fraenkel(B,C) = A & m1_subset_1(C,f2_s15_fraenkel) & m1_subset_1(B,f1_s15_fraenkel))) <-> r2_hidden(A,a_0_27_fraenkel))) # label(fraenkel_a_0_27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3377 (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]. 87.58/85.60 3378 (all A (m1_subset_1(A,f1_s9_fraenkel) -> (r2_hidden(A,f3_s9_fraenkel) -> (p2_s9_fraenkel(A) <-> p1_s9_fraenkel(A))))) & k7_relat_1(f4_s9_fraenkel,f3_s9_fraenkel) = k7_relat_1(f5_s9_fraenkel,f3_s9_fraenkel) -> a_0_17_fraenkel = a_0_16_fraenkel # label(s9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3379 (all A (r2_hidden(A,a_0_13_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & f4_s7_fraenkel(B,C) = A & p1_s7_fraenkel(B,C) & m1_subset_1(C,f2_s7_fraenkel))))) # label(fraenkel_a_0_13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3380 (all A (m1_subset_1(A,f1_s3_fraenkel) -> (p2_s3_fraenkel(A) <-> p1_s3_fraenkel(A)))) -> a_0_5_fraenkel = a_0_4_fraenkel # label(s3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3381 (all A ((exists B exists C (m1_subset_1(B,f1_s13_fraenkel) & A = f4_s13_fraenkel(B,C) & p2_s13_fraenkel(f4_s13_fraenkel(B,C)) & p1_s13_fraenkel(B,C) & m1_subset_1(C,f2_s13_fraenkel))) <-> r2_hidden(A,a_0_23_fraenkel))) # label(fraenkel_a_0_23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3382 v1_finset_1(f4_s22_fraenkel) & v1_finset_1(f3_s22_fraenkel) -> v1_finset_1(a_0_39_fraenkel) # label(s22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3383 (all A (r2_hidden(A,a_0_28_fraenkel) <-> (exists B (m1_subset_1(B,f1_s15_fraenkel) & B = A & p2_s15_fraenkel(B))))) # label(fraenkel_a_0_28_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3384 (all A ((exists B exists C (m1_subset_1(C,f2_s15_fraenkel) & p1_s15_fraenkel(B,C) & p2_s15_fraenkel(B) & f3_s15_fraenkel(B,C) = A & m1_subset_1(B,f1_s15_fraenkel))) <-> r2_hidden(A,a_0_29_fraenkel))) # label(fraenkel_a_0_29_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3385 (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 (k7_relat_1(F,C) = E & m2_fraenkel(F,B,A,k1_fraenkel(B,A)))))) | k1_funct_2(C,D) = k1_xboole_0)))) # label(t14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3386 (all A ((exists B exists C (m1_subset_1(C,f2_s11_fraenkel) & p1_s11_fraenkel(B,C) & f3_s11_fraenkel(B,C) = A & m1_subset_1(B,f1_s11_fraenkel))) <-> r2_hidden(A,a_0_19_fraenkel))) # label(fraenkel_a_0_19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3387 (all A (r2_hidden(A,a_0_39_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s22_fraenkel) & A = f5_s22_fraenkel(B,C) & r2_hidden(C,f4_s22_fraenkel) & r2_hidden(B,f3_s22_fraenkel) & m1_subset_1(B,f1_s22_fraenkel))))) # label(fraenkel_a_0_39_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3388 (all A (r2_hidden(A,a_0_12_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & m1_subset_1(C,f2_s7_fraenkel) & A = f3_s7_fraenkel(B,C) & p1_s7_fraenkel(B,C))))) # label(fraenkel_a_0_12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3389 (all A ((exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & A = f3_s8_fraenkel(C,B) & p2_s8_fraenkel(B,C) & m1_subset_1(C,f2_s8_fraenkel))) <-> r2_hidden(A,a_0_15_fraenkel))) # label(fraenkel_a_0_15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3390 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (k7_relat_1(C,E) = k7_relat_1(D,E) -> (all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k8_funct_2(A,B,C,F) = k8_funct_2(A,B,D,F)))))))))))))) # label(t3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3391 (all A (r2_hidden(A,a_0_20_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s12_fraenkel) & m1_subset_1(C,f2_s12_fraenkel) & p1_s12_fraenkel(B,C) & A = f3_s12_fraenkel(B,C))))) # label(fraenkel_a_0_20_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3392 (all A (m1_subset_1(A,f1_s7_fraenkel) -> (all B (m1_subset_1(B,f2_s7_fraenkel) -> f3_s7_fraenkel(A,B) = f4_s7_fraenkel(A,B))))) -> a_0_13_fraenkel = a_0_12_fraenkel # label(s7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3393 (all A (r2_hidden(A,a_0_0_numbers) <-> (exists B (A = B & np__0 = k1_funct_1(B,k13_arytm_3) & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)))))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3394 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3395 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3396 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3397 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3398 $T # label(d1_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3399 (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)) & (B = np__0 -> A = k5_arytm_0(A,B)))))) # label(d7_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3400 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k2_arytm_0(A,B),k1_numbers))) # label(dt_k2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3401 (all A (m1_subset_1(A,k2_arytm_2) -> (k12_arytm_3 != A -> r2_hidden(k4_tarski(k12_arytm_3,A),k1_numbers)))) # label(t2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 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(k2_arytm_0(A,B),C) = k2_arytm_0(A,k2_arytm_0(B,C)))))))) # label(t15_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3403 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k5_arytm_0(A,B),k2_numbers))) # label(dt_k5_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3404 (all A -(k12_arytm_3 = A & r2_hidden(k4_tarski(k12_arytm_3,A),k1_numbers))) # label(t3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3405 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (B = np__0 -> np__0 = k2_arytm_0(A,B)))))) # label(t14_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3406 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (np__0 = k1_arytm_0(k2_arytm_0(A,A),k2_arytm_0(B,B)) -> np__0 = A))))) # label(t19_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3407 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k2_arytm_0(B,A) = k2_arytm_0(A,B))) # label(commutativity_k2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3408 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (B != np__0 -> A = k2_arytm_0(k2_arytm_0(A,B),k4_arytm_0(B))))))) # label(t22_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3409 (all A all B k4_tarski(A,B) != k13_arytm_3) # label(t7_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3410 (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]. 87.58/85.60 3411 (all A (m1_subset_1(A,k1_numbers) -> A = k3_arytm_0(k3_arytm_0(A)))) # label(involutiveness_k3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3412 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k4_arytm_0(k2_arytm_0(A,B)) = k2_arytm_0(k4_arytm_0(A),k4_arytm_0(B)))))) # label(t24_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3413 (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]. 87.58/85.60 3414 (all A (m1_subset_1(A,k1_numbers) -> k4_arytm_0(k4_arytm_0(A)) = A)) # label(involutiveness_k4_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3415 $T # label(d6_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3416 (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]. 87.58/85.60 3417 (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]. 87.58/85.60 3418 $T # label(t9_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3419 (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) -> A = k12_arytm_3 | C = B))))))) # label(t8_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3420 (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]. 87.58/85.60 3421 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k1_arytm_0(k3_arytm_0(A),k3_arytm_0(B)) = k3_arytm_0(k1_arytm_0(A,B)))))) # label(t27_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3422 (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]. 87.58/85.60 3423 (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) -> np__0 = B))))) # label(t26_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3424 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (k2_arytm_0(A,C) = k13_arytm_3 & k2_arytm_0(A,B) = k13_arytm_3 -> C = B | A = np__0))))))) # label(t20_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3425 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_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) & D = A & k2_arytm_1(D,E) = C & B = k4_tarski(np__0,E))))) <-> C = k1_arytm_0(A,B))) & -(-(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_arytm_2)) & -(k1_arytm_0(A,B) = C <-> (exists D ((exists E (k4_tarski(np__0,E) = B & k4_tarski(np__0,k7_arytm_2(D,E)) = C & k4_tarski(np__0,D) = A & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,k2_arytm_2)))) & -(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_arytm_2)) & -(r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2))) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (C = k1_arytm_0(A,B) <-> (exists D ((exists E (C = k2_arytm_1(E,D) & E = B & A = k4_tarski(np__0,D) & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,k2_arytm_2))))) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2) -> ((exists D ((exists E (m1_subset_1(E,k2_arytm_2) & C = k7_arytm_2(D,E) & E = B & D = A)) & m1_subset_1(D,k2_arytm_2))) <-> C = k1_arytm_0(A,B))))))))) # label(d2_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3426 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2) -> (k2_arytm_0(A,B) = C <-> (exists D ((exists E (m1_subset_1(E,k2_arytm_2) & D = A & E = B & k8_arytm_2(D,E) = C)) & m1_subset_1(D,k2_arytm_2))))) & (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (C = k2_arytm_0(A,B) <-> (exists D ((exists E (m1_subset_1(E,k2_arytm_2) & D = A & k4_tarski(np__0,E) = B & k4_tarski(np__0,k8_arytm_2(D,E)) = C)) & m1_subset_1(D,k2_arytm_2)))) | np__0 = A) & -(-(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(k2_arytm_0(A,B) = C <-> np__0 = C) & -(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & np__0 != 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)) & A != np__0) & -(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)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (k2_arytm_0(A,B) = C <-> (exists D ((exists E (B = k4_tarski(np__0,E) & k8_arytm_2(E,D) = C & k4_tarski(np__0,D) = A & m1_subset_1(E,k2_arytm_2))) & m1_subset_1(D,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) & k4_tarski(np__0,D) = A & C = k4_tarski(np__0,k8_arytm_2(E,D)) & E = B)))) <-> k2_arytm_0(A,B) = C) | np__0 = B))))))) # label(d3_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3427 (all A (m1_subset_1(A,k2_numbers) -> (exists B ((exists C (m1_subset_1(C,k1_numbers) & k5_arytm_0(B,C) = A)) & m1_subset_1(B,k1_numbers))))) # label(t11_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3428 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k1_arytm_0(A,B) = k1_arytm_0(B,A))) # label(commutativity_k1_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3429 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (B = k3_arytm_0(A) <-> np__0 = k1_arytm_0(A,B)))))) # label(d4_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3430 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (np__0 = B -> k1_arytm_0(A,B) = A))))) # label(t13_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3431 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k2_arytm_0(k3_arytm_0(A),B) = k3_arytm_0(k2_arytm_0(A,B)))))) # label(t17_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3432 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> -(np__0 = k2_arytm_0(A,B) & np__0 != A & np__0 != B))))) # label(t23_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3433 (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]. 87.58/85.60 3434 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k1_arytm_0(k1_arytm_0(A,B),C) = k1_arytm_0(A,k1_arytm_0(B,C)))))))) # label(t25_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3435 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (A != np__0 -> (k2_arytm_0(A,B) = k13_arytm_3 <-> B = k4_arytm_0(A))) & (np__0 = A -> (B = np__0 <-> B = k4_arytm_0(A))))))) # label(d5_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3436 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k1_numbers) -> (k5_arytm_0(A,B) = k5_arytm_0(C,D) -> D = B & C = A))))))))) # label(t12_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3437 (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]. 87.58/85.60 3438 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k1_arytm_0(k2_arytm_0(A,B),k2_arytm_0(A,C)) = k2_arytm_0(A,k1_arytm_0(B,C)))))))) # label(t16_arytm_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3439 (all A all B (v1_xcmplx_0(A) & -v1_xboole_0(B) & v1_xcmplx_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc8_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3440 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 = k2_xcmplx_0(A,B) <-> B = k4_xcmplx_0(A)))))) # label(d6_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3441 $T # label(dt_k7_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3442 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)))) # label(dt_k5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3443 (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]. 87.58/85.60 3444 (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]. 87.58/85.60 3445 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A))) # label(commutativity_k3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3446 (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]. 87.58/85.60 3447 (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]. 87.58/85.60 3448 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)))) # label(dt_k4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3449 (all A (v1_xcmplx_0(A) -> A = k5_xcmplx_0(k5_xcmplx_0(A)))) # label(involutiveness_k5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3450 (all A (v4_ordinal2(A) -> v1_xcmplx_0(A))) # label(cc2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3451 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C ((exists D ((exists E ((exists F (m1_subset_1(F,k1_numbers) & (exists G (m1_subset_1(G,k1_numbers) & C = k5_arytm_0(k1_arytm_0(D,F),k1_arytm_0(E,G)) & B = k5_arytm_0(F,G) & k5_arytm_0(D,E) = A)))) & m1_subset_1(E,k1_numbers))) & m1_subset_1(D,k1_numbers))) <-> C = k2_xcmplx_0(A,B))))))) # label(d4_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3452 (all A (m1_subset_1(A,k1_numbers) -> v1_xcmplx_0(A))) # label(cc1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3453 (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]. 87.58/85.60 3454 $T # label(dt_k6_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3455 (all A (-v1_xboole_0(A) & v1_xcmplx_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & -v1_xboole_0(k4_xcmplx_0(A)))) # label(fc6_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3456 (all A (v1_xcmplx_0(A) <-> r2_hidden(A,k2_numbers))) # label(d2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.60 3457 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> k2_xcmplx_0(B,A) = k2_xcmplx_0(A,B))) # label(commutativity_k2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3458 $T # label(dt_k2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3459 (all A (v1_xcmplx_0(A) -> (v1_xboole_0(A) <-> A = np__0))) # label(d3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3460 (all A (-v1_xboole_0(A) & v1_xcmplx_0(A) -> -v1_xboole_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc7_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3461 (exists A v1_xcmplx_0(A)) # label(rc1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3462 $T # label(dt_k1_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3463 $T # label(dt_k3_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3464 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> (k3_xcmplx_0(A,B) = np__1 <-> B = k5_xcmplx_0(A))) & (A = np__0 -> (np__0 = B <-> B = k5_xcmplx_0(A))))))) # label(d7_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3465 (exists A (v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(rc2_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3466 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C ((exists D ((exists E ((exists F (m1_subset_1(F,k1_numbers) & (exists G (k5_arytm_0(D,E) = A & 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))) & m1_subset_1(G,k1_numbers))))) & m1_subset_1(E,k1_numbers))) & m1_subset_1(D,k1_numbers))) <-> C = k3_xcmplx_0(A,B))))))) # label(d5_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3467 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) & -v1_xboole_0(B) & -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]. 87.58/85.61 3468 (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]. 87.58/85.61 3469 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k3_xcmplx_0(A,k5_xcmplx_0(B)))))) # label(d9_xcmplx_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3470 (all A (v1_xcmplx_0(A) -> A = k2_xcmplx_0(A,np__0))) # label(t1_arithm) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3471 (all A (v1_xcmplx_0(A) -> np__0 = k7_xcmplx_0(np__0,A))) # label(t5_arithm) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3472 (all A (v1_xcmplx_0(A) -> A = k3_xcmplx_0(np__1,A))) # label(t3_arithm) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3473 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(A,np__0) = A)) # label(t4_arithm) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3474 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(A,np__1))) # label(t6_arithm) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3475 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(A,np__0) = np__0)) # label(t2_arithm) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3476 (all A (-v1_xboole_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3477 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> 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]. 87.58/85.61 3478 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3479 (exists A (v1_xboole_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3480 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(B,A)) & -v2_xreal_0(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3481 (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]. 87.58/85.61 3482 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc18_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3483 (all A (v1_xreal_0(A) & v3_xreal_0(A) -> -v2_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3484 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & v2_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(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3485 (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]. 87.58/85.61 3486 (exists A (v1_xcmplx_0(A) & -v3_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(A) & -v1_xboole_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3487 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3488 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) -> -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc23_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3489 (all A (v1_xboole_0(A) & v1_xreal_0(A) -> -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3490 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3491 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & 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]. 87.58/85.61 3492 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) -> -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3493 (all A (v1_xreal_0(A) & -v3_xreal_0(A) & -v1_xboole_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3494 (all A all B (v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & -v2_xreal_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3495 (all A (v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & -v3_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3496 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3497 (all A all B (v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(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)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3498 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) -> -v2_xreal_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & v1_xcmplx_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3499 (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]. 87.58/85.61 3500 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3501 (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]. 87.58/85.61 3502 (all A all B (v3_xreal_0(A) & -v2_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)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3503 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3504 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k2_xcmplx_0(B,A)) & -v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)))) # label(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3505 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & -v3_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc20_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3506 (all A (v1_xreal_0(A) & -v3_xreal_0(A) & -v2_xreal_0(A) -> v1_xboole_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3507 (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]. 87.58/85.61 3508 (all A (v1_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3509 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v3_xreal_0(A) -> -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3510 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) & -v2_xreal_0(A) & -v1_xboole_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3511 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) -> -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3512 (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]. 87.58/85.61 3513 (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]. 87.58/85.61 3514 (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]. 87.58/85.61 3515 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) -> -v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc15_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3516 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) -> -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(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3517 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3518 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> (r1_xreal_0(A,B) <-> (exists C ((exists D (k4_tarski(np__0,D) = B & r1_arytm_2(D,C) & A = k4_tarski(np__0,C) & m1_subset_1(D,k2_arytm_2))) & m1_subset_1(C,k2_arytm_2))))) & -(-(r2_hidden(A,k2_arytm_2) & 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))) & -(r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) <-> r1_xreal_0(A,B))) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (m1_subset_1(D,k2_arytm_2) & C = A & r1_arytm_2(C,D) & D = B)))))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3519 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & v3_xreal_0(A) -> -v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) & -v2_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3520 (all A all B (-v3_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3521 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & -v3_xreal_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3522 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,B) | r1_xreal_0(B,A))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3523 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3524 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (v3_xreal_0(B) & r1_xreal_0(A,B) -> v3_xreal_0(A)))))) # label(t2_real) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3525 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> v3_xreal_0(A) | v2_xreal_0(B) | v1_xboole_0(B)))))) # label(t5_real) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3526 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,B) & v2_xreal_0(A) & -v2_xreal_0(B)))))) # label(t4_real) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3527 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> v2_xreal_0(B) | v3_xreal_0(A) | v1_xboole_0(A)))))) # label(t6_real) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3528 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & v2_xreal_0(A) -> v2_xreal_0(B)))))) # label(t1_real) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3529 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,B) & -v3_xreal_0(B) & -v2_xreal_0(A)))))) # label(t8_real) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3530 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,B) & -v2_xreal_0(A) & -v3_xreal_0(B)))))) # label(t7_real) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3531 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,B) & -v3_xreal_0(A) & v3_xreal_0(B)))))) # label(t3_real) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3532 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,B) = k3_xcmplx_0(A,k7_xcmplx_0(np__1,B)))))) # label(t100_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3533 (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(C),B),A) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t165_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3534 (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]. 87.58/85.61 3535 (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]. 87.58/85.61 3536 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(B != np__0 & np__0 = k7_xcmplx_0(A,B) & np__0 != A))))) # label(t50_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3537 (all A (v1_xcmplx_0(A) -> A = k2_xcmplx_0(k4_xcmplx_0(A),k3_xcmplx_0(np__2,A)))) # label(t184_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3538 (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]. 87.58/85.61 3539 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_xcmplx_0(B) = k4_xcmplx_0(A) -> A = B))))) # label(t134_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3540 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k2_xcmplx_0(k6_xcmplx_0(A,B),B))))) # label(t27_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3541 (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]. 87.58/85.61 3542 (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]. 87.58/85.61 3543 (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]. 87.58/85.61 3544 (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]. 87.58/85.61 3545 (all A (v1_xcmplx_0(A) -> -(A != k4_xcmplx_0(np__1) & A != np__1 & A = k5_xcmplx_0(A) & np__0 != A))) # label(t225_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3546 (all A (v1_xcmplx_0(A) -> -(np__1 = k3_xcmplx_0(A,A) & k4_xcmplx_0(np__1) != A & np__1 != A))) # label(t183_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3547 (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]. 87.58/85.61 3548 (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]. 87.58/85.61 3549 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(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))) & B != np__0 & np__0 != A))))) # label(t213_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3550 (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]. 87.58/85.61 3551 (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]. 87.58/85.61 3552 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(B,k3_xcmplx_0(A,C)) = k3_xcmplx_0(k5_xcmplx_0(A),k7_xcmplx_0(B,C)))))))) # label(t222_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3553 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k6_xcmplx_0(A,B) = k2_xcmplx_0(A,k4_xcmplx_0(C)) -> C = B))))))) # label(t154_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3554 (all A (v1_xcmplx_0(A) -> -(A != np__0 & A != k4_xcmplx_0(np__1) & A != np__1 & A = k7_xcmplx_0(np__1,A)))) # label(t200_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3555 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k5_xcmplx_0(k3_xcmplx_0(A,B)))))) # label(t205_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3556 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k2_xcmplx_0(C,k4_xcmplx_0(B)) = k6_xcmplx_0(A,B) -> C = A))))))) # label(t153_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3557 (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) -> k2_xcmplx_0(A,D) = k2_xcmplx_0(B,C)))))))))) # label(t34_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3558 (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(k4_xcmplx_0(A),B),C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C))))))) # label(t174_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3559 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),A),B) = k6_xcmplx_0(k2_xcmplx_0(A,B),C))))))) # label(t155_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3560 (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]. 87.58/85.61 3561 (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]. 87.58/85.61 3562 (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]. 87.58/85.61 3563 (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]. 87.58/85.61 3564 (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]. 87.58/85.61 3565 (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) = k3_xcmplx_0(k6_xcmplx_0(B,A),k4_xcmplx_0(C)))))))) # label(t185_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3566 (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) = k4_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C)))))))) # label(t172_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3567 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != A & B != np__0 & 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))))))) # label(t214_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3568 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_xcmplx_0(A,k5_xcmplx_0(B)) = np__1 -> A = B))))) # label(t210_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3569 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(np__1,B),C),A) = k3_xcmplx_0(k7_xcmplx_0(A,B),C))))))) # label(t102_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3570 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k4_xcmplx_0(A),B) = k3_xcmplx_0(A,k4_xcmplx_0(B)))))) # label(t176_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3571 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != B & np__0 = k7_xcmplx_0(np__1,k3_xcmplx_0(A,B)) & np__0 != A))))) # label(t112_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3572 (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) -> k6_xcmplx_0(B,D) = k6_xcmplx_0(A,C)))))))))) # label(t24_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3573 (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),k6_xcmplx_0(C,B)) = k2_xcmplx_0(A,B))))))) # label(t31_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3574 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> k2_xcmplx_0(B,C) = k3_xcmplx_0(A,k2_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)))))))))) # label(t115_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3575 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != B & k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = np__0 & np__0 != A))))) # label(t209_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3576 (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]. 87.58/85.61 3577 (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(A,C) -> B = C))))))) # label(t20_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3578 (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]. 87.58/85.61 3579 (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]. 87.58/85.61 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(A,C),k2_xcmplx_0(B,C)) = k6_xcmplx_0(A,B))))))) # label(t32_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3581 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k4_xcmplx_0(B),A) = k4_xcmplx_0(k2_xcmplx_0(A,B)))))) # label(t161_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3582 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k7_xcmplx_0(C,A) = k7_xcmplx_0(D,B) -> np__0 = A | B = np__0 | k7_xcmplx_0(k2_xcmplx_0(C,D),k2_xcmplx_0(A,B)) = k7_xcmplx_0(C,A) | A = k4_xcmplx_0(B)))))))))) # label(t201_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3583 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(A,k4_xcmplx_0(B)) = k2_xcmplx_0(A,B))))) # label(t151_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 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) -> 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]. 87.58/85.61 3585 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k6_xcmplx_0(A,B),A) = k4_xcmplx_0(B))))) # label(t232_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3586 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,B) = k5_xcmplx_0(k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B))))))) # label(t207_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3587 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k7_xcmplx_0(D,B) = k7_xcmplx_0(C,A) -> B = A | k7_xcmplx_0(k6_xcmplx_0(C,D),k6_xcmplx_0(A,B)) = k7_xcmplx_0(C,A) | np__0 = B | np__0 = A))))))))) # label(t124_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3588 (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),k3_xcmplx_0(C,A)),A) = k6_xcmplx_0(B,C)))))))) # label(t130_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3589 (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]. 87.58/85.61 3590 (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]. 87.58/85.61 3591 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> k3_xcmplx_0(A,k2_xcmplx_0(np__1,k7_xcmplx_0(B,A))) = k2_xcmplx_0(A,B)))))) # label(t118_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3592 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(C,k7_xcmplx_0(A,B)))))))) # label(t82_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3593 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k2_xcmplx_0(k2_xcmplx_0(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(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D)))))))))) # label(t10_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3594 (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]. 87.58/85.61 3595 (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) -> k7_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(B,C),k7_xcmplx_0(D,E))) = k3_xcmplx_0(k7_xcmplx_0(E,C),k7_xcmplx_0(A,k3_xcmplx_0(B,D))))))))))))) # label(t87_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3596 (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]. 87.58/85.61 3597 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(np__1,k7_xcmplx_0(A,B)) = k7_xcmplx_0(B,A))))) # label(t57_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3598 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(B,A) = k5_xcmplx_0(k7_xcmplx_0(A,B)))))) # label(t215_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3599 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),A),B) = k4_xcmplx_0(B))))) # label(t231_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3600 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C)))))))) # label(t171_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3601 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(A,B) = k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B))))))) # label(t142_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3602 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != B & k3_xcmplx_0(A,k5_xcmplx_0(B)) = np__0 & A != np__0))))) # label(t208_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3603 (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]. 87.58/85.61 3604 (all A (v1_xcmplx_0(A) -> k4_xcmplx_0(k5_xcmplx_0(A)) = k5_xcmplx_0(k4_xcmplx_0(A)))) # label(t224_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3605 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),C),A) = k2_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t156_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3606 (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]. 87.58/85.61 3607 (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]. 87.58/85.61 3608 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = k7_xcmplx_0(A,B) -> np__1 = B | A = np__0))))) # label(t61_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3609 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k6_xcmplx_0(B,C) = k3_xcmplx_0(A,k6_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)))))))))) # label(t129_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3610 (all A (v1_xcmplx_0(A) -> A = k2_xcmplx_0(k7_xcmplx_0(A,np__2),k7_xcmplx_0(A,np__2)))) # label(t66_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3611 (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]. 87.58/85.61 3612 (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]. 87.58/85.61 3613 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(A,k6_xcmplx_0(B,B)) = A)))) # label(t25_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3614 (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]. 87.58/85.61 3615 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k3_xcmplx_0(B,C)))))))) # label(t4_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3616 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(B) = k6_xcmplx_0(k6_xcmplx_0(A,A),B))))) # label(t230_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3617 (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]. 87.58/85.61 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) -> k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) = k3_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),D))))))))) # label(t42_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3619 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k2_xcmplx_0(A,B) = A -> np__0 = B))))) # label(t3_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3620 $T # label(t212_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3621 (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]. 87.58/85.61 3622 (all A (v1_xcmplx_0(A) -> np__0 = k7_xcmplx_0(A,np__0))) # label(t49_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3623 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 = k6_xcmplx_0(A,B) -> A = B))))) # label(t15_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3624 (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]. 87.58/85.61 3625 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k6_xcmplx_0(A,k6_xcmplx_0(B,B)))))) # label(t17_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3626 (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) = k7_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A))))))))) # label(t55_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3627 (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) = k6_xcmplx_0(C,D) -> k6_xcmplx_0(C,B) = k2_xcmplx_0(A,D)))))))))) # label(t35_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3628 (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]. 87.58/85.61 3629 (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]. 87.58/85.61 3630 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k6_xcmplx_0(A,k6_xcmplx_0(A,B)) = B)))) # label(t18_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3631 (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]. 87.58/85.61 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) -> k3_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C)) = k3_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)))))))))) # label(t41_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3633 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(k3_xcmplx_0(A,B) = np__0 & np__0 != A & B != np__0))))) # label(t6_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3634 (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]. 87.58/85.61 3635 (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]. 87.58/85.61 3636 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_xcmplx_0(A) = k3_xcmplx_0(B,A) -> k4_xcmplx_0(np__1) = B | A = np__0))))) # label(t182_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3637 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(A,B) = k4_xcmplx_0(k3_xcmplx_0(A,k4_xcmplx_0(B))))))) # label(t178_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3638 (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]. 87.58/85.61 3639 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(A,A) = np__0)) # label(t14_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3640 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__1 = k3_xcmplx_0(A,B) -> k7_xcmplx_0(np__1,B) = A))))) # label(t74_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3641 (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]. 87.58/85.61 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(k7_xcmplx_0(B,k3_xcmplx_0(C,A)),A) = k7_xcmplx_0(B,C)))))))) # label(t93_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3643 (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]. 87.58/85.61 3644 (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]. 87.58/85.61 3645 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> B = k7_xcmplx_0(A,k7_xcmplx_0(A,B))))))) # label(t52_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3646 (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]. 87.58/85.61 3647 (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]. 87.58/85.61 3648 (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]. 87.58/85.61 3649 (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]. 87.58/85.61 3650 (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]. 87.58/85.61 3651 (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]. 87.58/85.61 3652 (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]. 87.58/85.61 3653 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,B) = k6_xcmplx_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)))))))) # label(t22_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3654 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(A,C) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),B))))))) # label(t229_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3655 (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]. 87.58/85.61 3656 (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]. 87.58/85.61 3657 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> k7_xcmplx_0(B,k3_xcmplx_0(A,k7_xcmplx_0(np__1,A))) = B))))) # label(t111_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3658 (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) -> A = np__0 | C = B))))))) # label(t53_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3659 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(k7_xcmplx_0(np__1,B),k7_xcmplx_0(A,C)) = k7_xcmplx_0(k7_xcmplx_0(A,B),C))))))) # label(t105_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3660 (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]. 87.58/85.61 3661 (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]. 87.58/85.61 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) -> 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]. 87.58/85.61 3663 (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]. 87.58/85.61 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,B),C) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),C),A))))))) # label(t158_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3665 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)))))))) # label(t8_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3666 (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]. 87.58/85.61 3667 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k5_xcmplx_0(A) = k5_xcmplx_0(B) -> B = A))))) # label(t202_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3668 (all A (v1_xcmplx_0(A) -> k4_xcmplx_0(A) = k7_xcmplx_0(A,k4_xcmplx_0(np__1)))) # label(t194_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3669 (all A (v1_xcmplx_0(A) -> k6_xcmplx_0(np__0,A) = k4_xcmplx_0(A))) # label(t150_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3670 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> k7_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,C)) = k7_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)))))))))) # label(t85_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3671 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(B,k3_xcmplx_0(C,A)) = k3_xcmplx_0(k7_xcmplx_0(np__1,A),k7_xcmplx_0(B,C)))))))) # label(t104_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3672 (all A (v1_xcmplx_0(A) -> A = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,np__3),k7_xcmplx_0(A,np__3)),k7_xcmplx_0(A,np__3)))) # label(t69_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3673 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(A,k2_xcmplx_0(B,C)))))))) # label(t36_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3674 (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(k2_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)))))))))) # label(t43_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3675 (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]. 87.58/85.61 3676 (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]. 87.58/85.61 3677 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(k4_xcmplx_0(A),B) = k7_xcmplx_0(A,k4_xcmplx_0(B)))))) # label(t193_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3678 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k7_xcmplx_0(k6_xcmplx_0(B,k3_xcmplx_0(C,A)),A) = k6_xcmplx_0(k7_xcmplx_0(B,A),C)))))))) # label(t127_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3679 (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]. 87.58/85.61 3680 (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]. 87.58/85.61 3681 (all A (v1_xcmplx_0(A) -> (np__0 = k4_xcmplx_0(A) -> A = np__0))) # label(t135_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3682 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> -(np__0 != A & 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)) & B != np__0))))))))) # label(t131_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3683 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(np__4,A) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A))) # label(t13_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3684 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> k3_xcmplx_0(B,k3_xcmplx_0(k7_xcmplx_0(np__1,A),A)) = B))))) # label(t109_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3685 (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]. 87.58/85.61 3686 (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]. 87.58/85.61 3687 (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 | B = np__0 | k7_xcmplx_0(D,A) = k3_xcmplx_0(C,B)))))))))) # label(t97_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3688 (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]. 87.58/85.61 3689 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> k7_xcmplx_0(k3_xcmplx_0(B,A),A) = B))))) # label(t90_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3690 (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]. 87.58/85.61 3691 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k7_xcmplx_0(A,k4_xcmplx_0(B)) = k4_xcmplx_0(k7_xcmplx_0(A,B)))))) # label(t189_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3692 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,B)) = k7_xcmplx_0(k2_xcmplx_0(A,C),B))))))) # label(t63_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3693 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k3_xcmplx_0(B,C) = k3_xcmplx_0(k3_xcmplx_0(B,A),k7_xcmplx_0(C,A))))))))) # label(t91_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3694 (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]. 87.58/85.61 3695 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k3_xcmplx_0(A,k6_xcmplx_0(B,C)) = k6_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)))))))) # label(t40_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3696 (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]. 87.58/85.61 3697 (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]. 87.58/85.61 3698 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(np__2,A) = k2_xcmplx_0(A,A))) # label(t11_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3699 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k3_xcmplx_0(A,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]. 87.58/85.61 3700 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_xcmplx_0(B,A) = A -> A = np__0 | np__1 = B))))) # label(t7_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.61 3701 (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]. 87.58/85.62 3702 (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]. 87.58/85.62 3703 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k4_xcmplx_0(A) = k7_xcmplx_0(A,B) -> A = np__0 | B = k4_xcmplx_0(np__1)))))) # label(t197_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3704 (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]. 87.58/85.62 3705 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(A,C),B))))))) # label(t29_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3706 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k2_xcmplx_0(A,B) = k2_xcmplx_0(C,B) -> A = C))))))) # label(t2_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 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) -> (k7_xcmplx_0(D,A) = k7_xcmplx_0(C,B) -> 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]. 87.58/85.62 3708 (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]. 87.58/85.62 3709 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != A -> B = k7_xcmplx_0(B,k7_xcmplx_0(A,A))))))) # label(t51_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3710 (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) | np__0 = B | np__0 = A))))))))) # label(t95_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3711 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = k6_xcmplx_0(A,B) -> B = np__0))))) # label(t16_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3712 (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]. 87.58/85.62 3713 (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]. 87.58/85.62 3714 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),A),B) = A)))) # label(t139_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3715 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(A != np__0 & B != np__0 & k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(B,A)) != np__1))))) # label(t113_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3716 (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]. 87.58/85.62 3717 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(np__0 != B & (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(B,C) != A))))))) # label(t234_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3718 (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]. 87.58/85.62 3719 (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]. 87.58/85.62 3720 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),B) = k6_xcmplx_0(A,C))))))) # label(t228_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3721 (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,C),B) = k7_xcmplx_0(k7_xcmplx_0(A,B),C))))))) # label(t48_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3722 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C)))))))) # label(t167_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3723 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (all D (v1_xcmplx_0(D) -> (k2_xcmplx_0(C,D) = k2_xcmplx_0(A,B) -> k6_xcmplx_0(D,B) = k6_xcmplx_0(A,C)))))))))) # label(t33_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3724 (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]. 87.58/85.62 3725 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C) = k4_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C)))))))) # label(t168_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3726 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k2_xcmplx_0(k2_xcmplx_0(A,B),k4_xcmplx_0(B)) = A)))) # label(t137_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3727 (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]. 87.58/85.62 3728 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(np__1,k5_xcmplx_0(A)))) # label(t218_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3729 (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]. 87.58/85.62 3730 (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]. 87.58/85.62 3731 (all A (v1_xcmplx_0(A) -> (A != np__0 -> k7_xcmplx_0(A,k4_xcmplx_0(A)) = k4_xcmplx_0(np__1)))) # label(t199_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3732 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(B) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),A))))) # label(t233_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3733 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k4_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(B,A),C)) = k3_xcmplx_0(k6_xcmplx_0(A,B),C))))))) # label(t186_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3734 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k7_xcmplx_0(A,k3_xcmplx_0(B,C)) = k7_xcmplx_0(k7_xcmplx_0(A,B),C))))))) # label(t79_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3735 (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),C),B) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),C))))))) # label(t146_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3736 (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]. 87.58/85.62 3737 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A != np__0 -> B = k3_xcmplx_0(B,k7_xcmplx_0(A,A))))))) # label(t89_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3738 (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]. 87.58/85.62 3739 (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]. 87.58/85.62 3740 (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]. 87.58/85.62 3741 (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]. 87.58/85.62 3742 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B),C) = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),A),B))))))) # label(t166_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3743 (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]. 87.58/85.62 3744 (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]. 87.58/85.62 3745 (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]. 87.58/85.62 3746 (all A (v1_xcmplx_0(A) -> A = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A),np__4))) # label(t70_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3747 (all A (v1_xcmplx_0(A) -> k7_xcmplx_0(k2_xcmplx_0(A,A),np__4) = k7_xcmplx_0(A,np__2))) # label(t73_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3748 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k6_xcmplx_0(B,k7_xcmplx_0(C,A)) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(B,A),C),A)))))))) # label(t128_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3749 (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]. 87.58/85.62 3750 (all A (v1_xcmplx_0(A) -> (A != np__0 -> np__1 = k7_xcmplx_0(A,A)))) # label(t60_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3751 (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]. 87.58/85.62 3752 (all A (v1_xcmplx_0(A) -> np__0 = k7_xcmplx_0(A,np__0))) # label(t62_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3753 (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]. 87.58/85.62 3754 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(A,B) = np__1 -> B = A))))) # label(t58_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3755 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(A),B)) = k3_xcmplx_0(A,B))))) # label(t179_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3756 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> A = k6_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))))))) # label(t152_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3757 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (np__0 != A -> 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]. 87.58/85.62 3758 (all A (v1_xcmplx_0(A) -> (np__0 != A -> k7_xcmplx_0(k4_xcmplx_0(A),A) = k4_xcmplx_0(np__1)))) # label(t198_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3759 (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]. 87.58/85.62 3760 (all A (v1_xcmplx_0(A) -> k3_xcmplx_0(np__3,A) = k2_xcmplx_0(k2_xcmplx_0(A,A),A))) # label(t12_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3761 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k7_xcmplx_0(np__1,B) = k7_xcmplx_0(np__1,A) -> B = A))))) # label(t59_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3762 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (k3_xcmplx_0(C,A) = k3_xcmplx_0(B,A) -> B = C | np__0 = A))))))) # label(t5_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3763 (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(A,k7_xcmplx_0(k7_xcmplx_0(B,A),C))))))))) # label(t98_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3764 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (all C (v1_xcmplx_0(C) -> (A != np__0 -> k7_xcmplx_0(B,C) = k3_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(A,C))))))))) # label(t99_xcmplx_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3765 (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]. 87.58/85.62 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) -> 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]. 87.58/85.62 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) -> 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]. 87.58/85.62 3768 (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]. 87.58/85.62 3769 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,k3_xcmplx_0(A,B)) & -r1_xreal_0(B,np__1) & -r1_xreal_0(np__0,A)))))) # label(t160_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3770 (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]. 87.58/85.62 3771 (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(t32_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3772 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k3_xcmplx_0(B,A),C) -> r1_xreal_0(A,np__0) | r1_xreal_0(B,k7_xcmplx_0(C,A))))))))) # label(t79_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3773 (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]. 87.58/85.62 3774 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(B,C) & r1_xreal_0(k2_xcmplx_0(A,C),B)))))))) # label(t41_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3775 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,B) & r1_xreal_0(k2_xcmplx_0(B,np__1),A)))))) # label(t147_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3776 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(np__0 != B & (all C (v1_xreal_0(C) -> A != k7_xcmplx_0(B,C)))))))) # label(t227_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3777 (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]. 87.58/85.62 3778 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(C,k6_xcmplx_0(B,A)) & -r1_xreal_0(C,B) & r1_xreal_0(np__0,A)))))))) # label(t53_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3779 (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]. 87.58/85.62 3780 (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(np__0,B) & r1_xreal_0(np__0,C) & -(np__0 = C & A = np__0) & -(np__0 = B & A = np__1) & -(np__0 = C & B = np__0) & np__0 = k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(k6_xcmplx_0(np__1,A),C)) & r1_xreal_0(A,np__1)))))))) # label(t172_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3781 (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]. 87.58/85.62 3782 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A)),np__0) & r1_xreal_0(np__0,A) -> r1_xreal_0(B,A) & r1_xreal_0(k4_xcmplx_0(A),B)))))) # label(t95_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3783 (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]. 87.58/85.62 3784 (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]. 87.58/85.62 3785 (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(t199_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3786 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,B) & r1_xreal_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)) & -r1_xreal_0(np__0,A)))))))) # label(t77_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3787 (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]. 87.58/85.62 3788 (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]. 87.58/85.62 3789 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,A) & r1_xreal_0(k7_xcmplx_0(B,A),np__1) & -r1_xreal_0(A,np__0)))))) # label(t189_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3790 (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,A) & r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & r1_xreal_0(B,D) & -r1_xreal_0(B,np__0) & r1_xreal_0(np__0,A)))))))))) # label(t99_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 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(D,C) & r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) & r1_xreal_0(A,B)))))))))) # label(t17_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3792 (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]. 87.58/85.62 3793 (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]. 87.58/85.62 3794 (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]. 87.58/85.62 3795 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,A) & -r1_xreal_0(B,C)))) & -r1_xreal_0(B,A)))))) # label(t7_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3796 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,C) & r1_xreal_0(A,np__0) -> r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A))))))))) # label(t75_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3797 (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]. 87.58/85.62 3798 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) -> r1_xreal_0(k5_xcmplx_0(A),np__0) | r1_xreal_0(B,A)))))) # label(t91_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3799 (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]. 87.58/85.62 3800 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(A,np__0) -> k3_xcmplx_0(A,B) = np__0))))) # label(t128_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3801 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(np__0,A) | r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B)) | r1_xreal_0(np__0,B)))))))))) # label(t105_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3802 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(A,np__3),np__0)))) # label(t224_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3803 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A))) | -r1_xreal_0(A,B) & -r1_xreal_0(B,k4_xcmplx_0(A))))))) # label(t96_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3804 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(k4_xcmplx_0(np__1),B) & r1_xreal_0(B,np__0) & r1_xreal_0(k4_xcmplx_0(np__1),A) -> r1_xreal_0(k3_xcmplx_0(A,B),np__1)))))) # label(t167_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3805 (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]. 87.58/85.62 3806 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,A) -> r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) | r1_xreal_0(np__0,A)))))) # label(t88_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3807 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(B,k3_xcmplx_0(C,A)) -> r1_xreal_0(C,k7_xcmplx_0(B,A)) | r1_xreal_0(np__0,A)))))))) # label(t82_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3808 (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]. 87.58/85.62 3809 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,k4_xcmplx_0(np__1)) & r1_xreal_0(A,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]. 87.58/85.62 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]. 87.58/85.62 3811 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1)) & -r1_xreal_0(k4_xcmplx_0(A),B)))))) # label(t201_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3812 (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(k3_xcmplx_0(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B))))))))))) # label(t114_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3813 (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]. 87.58/85.62 3814 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(np__0,A) & r1_xreal_0(C,B) -> r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) | r1_xreal_0(np__0,B)))))))) # label(t121_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3815 (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,np__0) | r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C))))))))) # label(t122_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3816 (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]. 87.58/85.62 3817 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(B,A) & -r1_xreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) & -r1_xreal_0(np__0,k5_xcmplx_0(A))))))) # label(t94_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3818 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(B,A) & -r1_xreal_0(np__0,C) & r1_xreal_0(k3_xcmplx_0(B,D),k3_xcmplx_0(A,C)) & -r1_xreal_0(C,D) & -r1_xreal_0(np__0,A)))))))))) # label(t72_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3819 (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]. 87.58/85.62 3820 (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]. 87.58/85.62 3821 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(A != B & r1_xreal_0(k6_xcmplx_0(A,B),np__0) & r1_xreal_0(k6_xcmplx_0(B,A),np__0)))))) # label(t57_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3822 (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(A,B)) & -r1_xreal_0(np__0,A)))))) # label(t143_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3823 (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]. 87.58/85.62 3824 (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(t202_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3825 (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]. 87.58/85.62 3826 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(k6_xcmplx_0(C,B),k6_xcmplx_0(C,A)) <-> r1_xreal_0(A,B)))))))) # label(t12_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3827 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,np__1) & r1_xreal_0(B,C) & 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]. 87.58/85.62 3828 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,np__1) & r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),B) & r1_xreal_0(np__0,A) -> np__0 = A | r1_xreal_0(C,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)))))))))) # label(t182_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3829 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__0) & r1_xreal_0(A,k4_xcmplx_0(B)) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t198_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3830 (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]. 87.58/85.62 3831 (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(k2_xcmplx_0(B,D),k2_xcmplx_0(A,C)) & r1_xreal_0(C,D)))))))))) # label(t10_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3832 (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]. 87.58/85.62 3833 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,k2_xcmplx_0(B,C)) <-> r1_xreal_0(k6_xcmplx_0(A,B),C)))))))) # label(t22_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3834 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(B,np__0) & r1_xreal_0(k7_xcmplx_0(C,A),k3_xcmplx_0(D,B)) & -r1_xreal_0(k3_xcmplx_0(D,A),k7_xcmplx_0(C,B))))))))))) # label(t118_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3835 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(np__0,A) | r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) | r1_xreal_0(B,np__0)))))))))) # label(t107_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3836 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(B,np__0) & r1_xreal_0(np__0,k7_xcmplx_0(B,A))))))) # label(t144_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3837 (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]. 87.58/85.62 3838 (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]. 87.58/85.62 3839 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (exists C (-r1_xreal_0(C,A) & -r1_xreal_0(C,B) & v1_xreal_0(C))))))) # label(t5_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3840 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(A,np__2),np__0)))) # label(t217_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3841 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,np__0) & r1_xreal_0(A,B) -> r1_xreal_0(k7_xcmplx_0(B,A),np__1)))))) # label(t186_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3842 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(k4_xcmplx_0(B),A) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t196_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.58/85.62 3843 (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]. 87.58/85.62 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(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]. 87.61/85.62 3845 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & -r1_xreal_0(np__1,C) & -r1_xreal_0(k3_xcmplx_0(A,C),B)))) -> r1_xreal_0(A,B)))))) # label(t170_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3846 (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]. 87.61/85.62 3847 (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,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) & r1_xreal_0(np__0,A)))))))))) # label(t178_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3848 (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]. 87.61/85.62 3849 (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(k7_xcmplx_0(B,A),C) | r1_xreal_0(A,np__0)))))))) # label(t81_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3850 (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]. 87.61/85.62 3851 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(k5_xcmplx_0(A),np__0) & -r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) & r1_xreal_0(A,B)))))) # label(t93_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3852 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,A) & -r1_xreal_0(np__1,A) & r1_xreal_0(np__0,B) & r1_xreal_0(B,np__1) & r1_xreal_0(np__1,k3_xcmplx_0(A,B))))))) # label(t164_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3853 (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]. 87.61/85.62 3854 (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]. 87.61/85.62 3855 (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(k3_xcmplx_0(A,B),A)))))) # label(t157_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3856 (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]. 87.61/85.62 3857 (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]. 87.61/85.62 3858 (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]. 87.61/85.62 3859 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r1_xreal_0(C,D) & r1_xreal_0(k6_xcmplx_0(B,C),k6_xcmplx_0(A,D)) & -r1_xreal_0(B,A)))))))))) # label(t16_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3860 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,k4_xcmplx_0(np__1)) & r1_xreal_0(k2_xcmplx_0(np__1,A),np__0)))) # label(t150_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3861 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) & -r1_xreal_0(B,C) & -r1_xreal_0(np__0,B)))))))) # label(t101_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3862 (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(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(np__0,B)))))))))) # label(t109_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3863 (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]. 87.61/85.62 3864 (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]. 87.61/85.62 3865 (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]. 87.61/85.62 3866 (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]. 87.61/85.62 3867 (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]. 87.61/85.62 3868 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(np__0,B) & r1_xreal_0(A,C) -> r1_xreal_0(A,np__0) | r1_xreal_0(k7_xcmplx_0(B,C),k7_xcmplx_0(B,A))))))))) # label(t120_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3869 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__1,B) & r1_xreal_0(np__1,A) -> r1_xreal_0(np__1,k3_xcmplx_0(A,B))))))) # label(t161_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3870 (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]. 87.61/85.62 3871 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k7_xcmplx_0(A,np__4),np__0)))) # label(t226_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3872 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__1,B) & r1_xreal_0(k3_xcmplx_0(A,B),A) & -r1_xreal_0(np__0,A)))))) # label(t158_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3873 (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]. 87.61/85.62 3874 (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]. 87.61/85.62 3875 (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]. 87.61/85.62 3876 (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]. 87.61/85.62 3877 (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]. 87.61/85.62 3878 (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(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & r1_xreal_0(A,C) & -r1_xreal_0(B,np__0) & -r1_xreal_0(A,np__0)))))))))) # label(t100_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3879 (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),B) & -r1_xreal_0(C,B) & r1_xreal_0(np__0,A)))))))) # label(t42_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3880 (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))) -> A = np__0 | 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]. 87.61/85.62 3881 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,k6_xcmplx_0(A,B)) & -r1_xreal_0(B,A)))))) # label(t51_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3882 (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]. 87.61/85.62 3883 (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(A,np__0) & -r1_xreal_0(B,np__0)) & -(-r1_xreal_0(np__0,B) & -r1_xreal_0(np__0,A))))))) # label(t136_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3884 (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]. 87.61/85.62 3885 (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(k7_xcmplx_0(B,A),np__1)))))) # label(t190_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3886 (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(B,A),k3_xcmplx_0(C,A)) & -r1_xreal_0(C,B)))))))) # label(t71_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3887 (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]. 87.61/85.62 3888 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k5_xcmplx_0(A),k4_xcmplx_0(np__1)) & -r1_xreal_0(k4_xcmplx_0(np__1),A)))) # label(t216_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3889 (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(k7_xcmplx_0(A,B),np__0)))))) # label(t140_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3890 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(B,np__0) & -r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A)) & r1_xreal_0(k3_xcmplx_0(C,B),k7_xcmplx_0(D,A))))))))))) # label(t116_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3891 (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(k4_xcmplx_0(B),A) & -r1_xreal_0(A,np__0)))))) # label(t208_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3892 (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]. 87.61/85.62 3893 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(k3_xcmplx_0(C,A),B) & r1_xreal_0(k7_xcmplx_0(B,A),C) & -r1_xreal_0(np__0,A)))))))) # label(t86_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3894 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(B,np__0) -> r1_xreal_0(k3_xcmplx_0(A,B),np__0)))))) # label(t133_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3895 (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]. 87.61/85.62 3896 (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]. 87.61/85.62 3897 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,B) & r1_xreal_0(np__0,k3_xcmplx_0(A,B)) & -r1_xreal_0(A,np__0)))))) # label(t134_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3898 (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]. 87.61/85.62 3899 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(np__0,B) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B))))))))))) # label(t110_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3900 (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]. 87.61/85.62 3901 (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]. 87.61/85.62 3902 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(k4_xcmplx_0(A),B) -> r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t195_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 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(np__0,A) & -r1_xreal_0(B,np__0) & -r1_xreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & r1_xreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(D,B))))))))))) # label(t111_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3904 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(k4_xcmplx_0(np__1),A) & r1_xreal_0(B,k4_xcmplx_0(np__1)) & r1_xreal_0(k3_xcmplx_0(A,B),np__1)))))) # label(t166_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3905 (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]. 87.61/85.62 3906 (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]. 87.61/85.62 3907 (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]. 87.61/85.62 3908 (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]. 87.61/85.62 3909 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(A,np__1) & r1_xreal_0(B,C) & r1_xreal_0(B,D) & 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]. 87.61/85.62 3910 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k4_xcmplx_0(A),B) -> r1_xreal_0(np__0,A) | r1_xreal_0(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))))))) # label(t205_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.62 3911 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,np__1) & r1_xreal_0(np__0,B) & r1_xreal_0(B,np__1) & r1_xreal_0(np__0,A) -> r1_xreal_0(k3_xcmplx_0(A,B),np__1)))))) # label(t162_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3912 (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]. 87.61/85.63 3913 (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]. 87.61/85.63 3914 (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]. 87.61/85.63 3915 (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]. 87.61/85.63 3916 (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(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C))))))))) # label(t8_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3917 (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,B) & r1_xreal_0(np__0,C) & r1_xreal_0(C,D) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D))))))))))) # label(t68_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3918 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(B,np__0) & -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(A,np__0)))))))))) # label(t113_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3919 (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]. 87.61/85.63 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]. 87.61/85.63 3921 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r1_xreal_0(k7_xcmplx_0(C,A),B) & -r1_xreal_0(C,k3_xcmplx_0(B,A)) & -r1_xreal_0(A,np__0)))))))) # label(t83_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3922 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(A,np__0) & -r1_xreal_0(np__1,A) & r1_xreal_0(B,C) & -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)))))))))) # label(t179_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3923 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(np__0,B) & -r1_xreal_0(B,C) & r1_xreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) & -r1_xreal_0(np__0,A)))))))) # label(t103_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3924 (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]. 87.61/85.63 3925 (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]. 87.61/85.63 3926 (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]. 87.61/85.63 3927 (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]. 87.61/85.63 3928 (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(A,np__0) & -r1_xreal_0(np__0,B)) & -(-r1_xreal_0(B,np__0) & -r1_xreal_0(np__0,A))))))) # label(t135_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3929 (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),k3_xcmplx_0(C,B)) & r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) & -r1_xreal_0(B,np__0)))))))))) # label(t108_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3930 (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]. 87.61/85.63 3931 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,np__0) & r1_xreal_0(k7_xcmplx_0(A,B),np__0) & -r1_xreal_0(A,np__0)))))) # label(t141_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3932 (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]. 87.61/85.63 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) -> -(np__0 = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) & np__0 != C & A != np__0 & r1_xreal_0(np__0,D) & r1_xreal_0(np__0,C) & r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A)))))))))) # label(t73_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3934 (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]. 87.61/85.63 3935 (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]. 87.61/85.63 3936 (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]. 87.61/85.63 3937 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(C,D) & r1_xreal_0(A,B) -> r1_xreal_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C))))))))))) # label(t15_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3938 (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]. 87.61/85.63 3939 (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]. 87.61/85.63 3940 (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]. 87.61/85.63 3941 (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(B,np__0) & -r1_xreal_0(A,np__0)))))) # label(t131_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3942 (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]. 87.61/85.63 3943 (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]. 87.61/85.63 3944 (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]. 87.61/85.63 3945 (all A (v1_xreal_0(A) -> -(r1_xreal_0(A,np__0) & -r1_xreal_0(k5_xcmplx_0(A),np__0)) & -(-r1_xreal_0(A,np__0) & r1_xreal_0(k5_xcmplx_0(A),np__0)))) # label(t124_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3946 (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]. 87.61/85.63 3947 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,k7_xcmplx_0(A,B)) & -(-r1_xreal_0(np__0,B) & -r1_xreal_0(A,np__0)) & -(-r1_xreal_0(B,np__0) & -r1_xreal_0(np__0,A))))))) # label(t145_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3948 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(np__0,A) & r1_xreal_0(A,np__1) & r1_xreal_0(B,C) -> r1_xreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(np__1,A),B),k3_xcmplx_0(A,C)),C)))))))) # label(t174_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3949 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__1) & r1_xreal_0(k3_xcmplx_0(A,B),np__1) & r1_xreal_0(np__1,B)))))) # label(t163_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3950 (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]. 87.61/85.63 3951 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(-r1_xreal_0(np__0,B) & -r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A)) & r1_xreal_0(k7_xcmplx_0(D,A),k3_xcmplx_0(C,B)) & -r1_xreal_0(np__0,A)))))))))) # label(t112_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3952 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (k2_xcmplx_0(A,B) = np__0 & r1_xreal_0(B,np__0) & r1_xreal_0(A,np__0) -> np__0 = A))))) # label(t30_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3953 (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]. 87.61/85.63 3954 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(D,B)) <-> r1_xreal_0(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D))))))))))) # label(t23_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3955 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,np__0) & r1_xreal_0(np__1,k7_xcmplx_0(A,B)) & -r1_xreal_0(A,B)))))) # label(t192_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3956 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(A,B) & r1_xreal_0(C,D) -> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D))))))))))) # label(t9_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 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(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]. 87.61/85.63 3958 (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(D,C) & r1_xreal_0(C,np__0) -> r1_xreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D))))))))))) # label(t69_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3959 (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]. 87.61/85.63 3960 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(A,B) & r1_xreal_0(B,k6_xcmplx_0(A,np__1))))))) # label(t149_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3961 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k6_xcmplx_0(B,A),np__0) & -r1_xreal_0(B,A)))))) # label(t52_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3962 (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,A) & -r1_xreal_0(D,B) & r1_xreal_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A)))))))))) # label(t98_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3963 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(k6_xcmplx_0(B,A),B) & -r1_xreal_0(np__0,A)))))) # label(t48_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 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(k7_xcmplx_0(B,A),k4_xcmplx_0(np__1))))))) # label(t206_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3965 (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(C,k2_xcmplx_0(B,A))))))))) # label(t39_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3966 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(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]. 87.61/85.63 3967 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(-r1_xreal_0(B,np__0) & r1_xreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(A,B)) & -r1_xreal_0(C,B) & -r1_xreal_0(np__0,A)))))))) # label(t102_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3968 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__1,k7_xcmplx_0(A,B)) & -r1_xreal_0(B,A) & r1_xreal_0(np__0,A)))))) # label(t191_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3969 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(A,np__0) & r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A)) & -r1_xreal_0(k4_xcmplx_0(A),B)))))) # label(t207_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3970 (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),k7_xcmplx_0(D,A)) & -r1_xreal_0(k7_xcmplx_0(D,B),k3_xcmplx_0(C,A)) & -r1_xreal_0(np__0,B) & -r1_xreal_0(A,np__0)))))))))) # label(t117_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3971 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,A) & -r1_xreal_0(B,k4_xcmplx_0(A)) & -r1_xreal_0(A,B) & r1_xreal_0(np__0,k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A)))))))) # label(t97_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3972 (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]. 87.61/85.63 3973 (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) & np__1 = k3_xcmplx_0(A,B) & r1_xreal_0(A,np__1) -> np__1 = A))))) # label(t152_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3974 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & r1_xreal_0(np__1,k7_xcmplx_0(B,A)) & -r1_xreal_0(B,A)))))) # label(t194_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3975 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) | r1_xreal_0(A,np__0)))))) # label(t87_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3976 (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]. 87.61/85.63 3977 (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]. 87.61/85.63 3978 (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]. 87.61/85.63 3979 (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]. 87.61/85.63 3980 (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]. 87.61/85.63 3981 (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,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) & -r1_xreal_0(A,np__0)))))))))) # label(t180_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3982 (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(k5_xcmplx_0(A),k5_xcmplx_0(B))))))) # label(t90_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3983 (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(k7_xcmplx_0(B,A),np__1)))))) # label(t187_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3984 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(B,A) & -r1_xreal_0(k5_xcmplx_0(B),np__0) & -r1_xreal_0(np__0,k5_xcmplx_0(A))))))) # label(t127_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3985 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) -> r1_xreal_0(A,B) | r1_xreal_0(np__0,k5_xcmplx_0(A))))))) # label(t92_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3986 (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(k6_xcmplx_0(C,A),B) & -r1_xreal_0(C,B)))))))) # label(t55_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3987 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(-r1_xreal_0(np__0,A) & -r1_xreal_0(B,k4_xcmplx_0(A)) & r1_xreal_0(k4_xcmplx_0(np__1),k7_xcmplx_0(B,A))))))) # label(t209_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3988 (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]. 87.61/85.63 3989 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> r1_xreal_0(np__0,k2_xcmplx_0(A,B))))))) # label(t35_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3990 (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]. 87.61/85.63 3991 (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(B,np__0) & -r1_xreal_0(A,np__0)) & -(-r1_xreal_0(np__0,A) & -r1_xreal_0(np__0,B))))))) # label(t146_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3992 (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]. 87.61/85.63 3993 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) -> r1_xreal_0(np__0,B) | r1_xreal_0(k7_xcmplx_0(D,B),k7_xcmplx_0(C,A)) | r1_xreal_0(A,np__0)))))))))) # label(t106_xreal_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3994 (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]. 87.61/85.63 3995 (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]. 87.61/85.63 3996 $T # label(t14_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3997 $T # label(t3_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3998 $T # label(t13_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 3999 $T # label(t2_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 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) -> (all D (v1_xreal_0(D) -> (r2_hidden(D,B) & r2_hidden(C,A) -> r1_xreal_0(C,D)))))) & (all C (v1_xreal_0(C) -> (exists D (v1_xreal_0(D) & (exists E (r2_hidden(D,A) & -(r1_xreal_0(C,E) & r1_xreal_0(D,C)) & r2_hidden(E,B) & v1_xreal_0(E)))))))))))) # label(t26_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4001 $T # label(t17_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4002 $T # label(t8_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4003 $T # label(t7_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4004 $T # label(t11_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4005 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (r2_hidden(np__0,A) & (all B (v1_xreal_0(B) -> (r2_hidden(B,A) -> r2_hidden(k2_xcmplx_0(B,np__1),A)))) -> r1_tarski(k5_numbers,A)))) # label(t29_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4006 $T # label(t1_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4007 $T # label(t21_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4008 $T # label(t12_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4009 (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]. 87.61/85.63 4010 $T # label(t25_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4011 $T # label(t4_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4012 $T # label(t16_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4013 $T # label(t24_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4014 $T # label(t27_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4015 $T # label(t5_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4016 (all A all B (v4_ordinal2(B) -> (r2_hidden(A,a_1_0_axioms(B)) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & C = A & -r1_xreal_0(B,C)))))) # label(fraenkel_a_1_0_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4017 $T # label(t9_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4018 $T # label(t6_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4019 (all A (v4_ordinal2(A) -> a_1_0_axioms(A) = A)) # label(t30_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4020 $T # label(t10_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4021 $T # label(t15_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4022 (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]. 87.61/85.63 4023 $T # label(t22_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4024 $T # label(t23_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4025 $T # label(t18_axioms) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4026 $T # label(t50_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4027 $T # label(t41_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4028 (all A (m1_subset_1(A,k1_numbers) -> k4_xcmplx_0(A) = k1_real_1(A))) # label(redefinition_k1_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4029 $T # label(t76_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4030 (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(C,D) & -r1_xreal_0(B,A))))))))))) # label(t92_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4031 $T # label(t4_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4032 $T # label(t43_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4033 $T # label(t40_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4034 $T # label(t52_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4035 $T # label(t31_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4036 $T # label(t59_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4037 $T # label(t29_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4038 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k3_real_1(A,B),k1_numbers))) # label(dt_k3_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4039 $T # label(t37_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4040 $T # label(t28_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4041 $T # label(t69_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4042 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k4_real_1(A,B),k1_numbers))) # label(dt_k4_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4043 $T # label(t14_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4044 $T # label(t6_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4045 $T # label(t86_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4046 (all A (m1_subset_1(A,k1_numbers) -> A = k2_real_1(k2_real_1(A)))) # label(involutiveness_k2_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4047 $T # label(t53_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4048 $T # label(t49_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4049 (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]. 87.61/85.63 4050 $T # label(t13_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4051 $T # label(t22_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4052 (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]. 87.61/85.63 4053 $T # label(t12_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4054 (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]. 87.61/85.63 4055 $T # label(t33_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4056 $T # label(t60_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4057 $T # label(t23_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4058 $T # label(t8_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4059 $T # label(t42_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4060 $T # label(t46_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4061 $T # label(t78_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4062 $T # label(t77_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4063 $T # label(t90_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4064 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k7_xcmplx_0(A,B) = k6_real_1(A,B))) # label(redefinition_k6_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4065 $T # label(t44_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4066 (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]. 87.61/85.63 4067 $T # label(d2_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4068 $T # label(t65_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4069 $T # label(t79_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4070 $T # label(t61_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4071 $T # label(t71_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4072 $T # label(t66_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4073 $T # label(t10_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4074 (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(k7_xcmplx_0(C,A),k7_xcmplx_0(B,A)) & -r1_xreal_0(C,B))))))))) # label(t73_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4075 $T # label(t67_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4076 $T # label(t54_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4077 $T # label(t70_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4078 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (-r1_xreal_0(np__0,A) -> -(-r1_xreal_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,A)) & r1_xreal_0(C,B)) & -(-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]. 87.61/85.63 4079 $T # label(t55_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4080 $T # label(t15_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4081 $T # label(t72_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4082 $T # label(t89_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4083 $T # label(t81_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4084 $T # label(t35_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4085 (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]. 87.61/85.63 4086 $T # label(t68_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4087 $T # label(t75_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4088 $T # label(d3_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4089 $T # label(t82_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4090 $T # label(t11_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4091 $T # label(t51_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4092 $T # label(t20_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4093 $T # label(d1_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4094 $T # label(t7_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4095 $T # label(t47_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4096 $T # label(t36_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4097 $T # label(t62_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4098 $T # label(d4_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4099 $T # label(t85_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4100 $T # label(t57_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4101 (all A (m1_subset_1(A,k1_numbers) -> v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc1_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4102 $T # label(t21_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4103 $T # label(t34_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4104 (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]. 87.61/85.63 4105 $T # label(t2_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4106 $T # label(t24_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4107 $T # label(t39_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4108 $T # label(t1_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4109 $T # label(t9_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4110 $T # label(t88_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4111 $T # label(t16_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4112 $T # label(t45_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4113 (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]. 87.61/85.63 4114 $T # label(t56_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4115 $T # label(t18_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4116 (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]. 87.61/85.63 4117 (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]. 87.61/85.63 4118 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k5_real_1(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k5_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4119 $T # label(t5_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4120 $T # label(t64_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4121 $T # label(t83_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4122 $T # label(t19_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4123 (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]. 87.61/85.63 4124 $T # label(t84_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4125 $T # label(t32_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4126 $T # label(t58_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4127 $T # label(t48_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4128 (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]. 87.61/85.63 4129 $T # label(t91_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4130 (all A (v1_xreal_0(A) -> A = k6_xcmplx_0(A,np__0))) # label(t25_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4131 $T # label(t3_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4132 $T # label(t63_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4133 $T # label(t80_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4134 $T # label(t87_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4135 $T # label(t30_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4136 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k3_real_1(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k3_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4137 $T # label(t27_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4138 $T # label(t38_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4139 $T # label(t17_real_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4140 $T # label(t18_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4141 $T # label(t27_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4142 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(B,A) -> k2_square_1(A,B) = A) & (-r1_xreal_0(B,A) -> B = k2_square_1(A,B)))))) # label(d2_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4143 $T # label(t22_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4144 (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]. 87.61/85.63 4145 (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]. 87.61/85.63 4146 (all A (v1_xcmplx_0(A) -> k5_square_1(A) = k5_square_1(k4_xcmplx_0(A)))) # label(t61_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4147 $T # label(t20_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4148 (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]. 87.61/85.63 4149 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> k2_square_1(k2_square_1(A,B),C) = k2_square_1(A,k2_square_1(B,C)))))))) # label(t51_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4150 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> k2_square_1(A,B) = k2_square_1(B,A))) # label(commutativity_k2_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4151 $T # label(t91_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4152 (all A (m1_subset_1(A,k1_numbers) -> k8_square_1(A) = k9_square_1(A))) # label(redefinition_k9_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4153 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(B,A) | k7_xcmplx_0(np__1,k2_xcmplx_0(k8_square_1(B),k8_square_1(A))) = k7_xcmplx_0(k6_xcmplx_0(k8_square_1(B),k8_square_1(A)),k6_xcmplx_0(B,A))))))) # label(t106_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4154 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k5_square_1(A),A) & -r1_xreal_0(A,np__1)))) # label(t76_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4155 $T # label(t100_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4156 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> A = k1_square_1(A,B)) & (-r1_xreal_0(A,B) -> k1_square_1(A,B) = B))))) # label(d1_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4157 $T # label(t11_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4158 (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]. 87.61/85.63 4159 $T # label(t81_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4160 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (r1_xreal_0(A,k1_square_1(B,C)) <-> r1_xreal_0(A,B) & r1_xreal_0(A,C)))))))) # label(t39_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4161 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> k1_square_1(A,B) = k1_square_1(B,A))) # label(commutativity_k1_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4162 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k2_square_1(A,B) = k4_square_1(A,B))) # label(redefinition_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4163 (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]. 87.61/85.63 4164 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A) -> A = B | k7_xcmplx_0(np__1,k2_xcmplx_0(k8_square_1(A),k8_square_1(B))) = k7_xcmplx_0(k6_xcmplx_0(k8_square_1(A),k8_square_1(B)),k6_xcmplx_0(A,B))))))) # label(t105_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4165 $T # label(t98_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4166 $T # label(t47_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4167 (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]. 87.61/85.63 4168 $T # label(t88_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4169 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> k1_square_1(A,k2_square_1(B,C)) = k2_square_1(k1_square_1(A,B),k1_square_1(A,C)))))))) # label(t56_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4170 (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]. 87.61/85.63 4171 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) & np__0 = k8_square_1(A) -> A = np__0))) # label(t92_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4172 (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(A,np__0) & r1_xreal_0(B,np__0)) & -(r1_xreal_0(np__0,B) & r1_xreal_0(np__0,A))))))) # label(t25_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4173 (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]. 87.61/85.63 4174 $T # label(t62_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4175 (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]. 87.61/85.63 4176 $T # label(t44_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4177 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k1_square_1(A,B)))) # label(dt_k1_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4178 (all A (m1_subset_1(A,k2_numbers) -> v1_xcmplx_0(A))) # label(cc1_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4179 (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]. 87.61/85.63 4180 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -(r1_xreal_0(np__0,A) & r1_xreal_0(k5_square_1(B),k5_square_1(A)) & -r1_xreal_0(B,A)))))) # label(t78_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4181 $T # label(t23_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4182 $T # label(t45_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4183 $T # label(t34_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4184 $T # label(t14_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4185 (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]. 87.61/85.63 4186 $T # label(t24_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4187 $T # label(t6_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4188 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k5_square_1(A)))) # label(fc1_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4189 (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]. 87.61/85.63 4190 $T # label(t43_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4191 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xreal_0(k2_square_1(A,B)))) # label(dt_k2_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4192 (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]. 87.61/85.63 4193 $T # label(t30_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4194 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k3_square_1(B,A) = k3_square_1(A,B))) # label(commutativity_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4195 $T # label(t29_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4196 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> B = k2_square_1(A,B) | A = k2_square_1(A,B))))) # label(t49_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4197 (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]. 87.61/85.63 4198 (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]. 87.61/85.63 4199 (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]. 87.61/85.63 4200 (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]. 87.61/85.63 4201 (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]. 87.61/85.63 4202 $T # label(t52_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4203 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != k6_xcmplx_0(k5_square_1(A),k5_square_1(B)) -> k7_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(k5_square_1(A),k5_square_1(B))) = k7_xcmplx_0(np__1,k6_xcmplx_0(A,B))))))) # label(t71_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4204 $T # label(t42_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4205 (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]. 87.61/85.63 4206 $T # label(t13_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4207 $T # label(t28_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4208 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 != k6_xcmplx_0(k5_square_1(A),k5_square_1(B)) -> k7_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(k5_square_1(A),k5_square_1(B))) = k7_xcmplx_0(np__1,k2_xcmplx_0(A,B))))))) # label(t70_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4209 $T # label(t4_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4210 $T # label(t37_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4211 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k3_square_1(A,B),k1_numbers))) # label(dt_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4212 (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]. 87.61/85.63 4213 (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]. 87.61/85.63 4214 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k4_square_1(A,B) = k4_square_1(B,A))) # label(commutativity_k4_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4215 (all A (v1_xreal_0(A) -> v1_xreal_0(k5_square_1(A)) & v1_xcmplx_0(k5_square_1(A)))) # label(fc2_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4216 (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]. 87.61/85.63 4217 (all A (v1_xcmplx_0(A) -> k2_xcmplx_0(k2_xcmplx_0(k5_square_1(A),k3_xcmplx_0(np__2,A)),np__1) = k5_square_1(k2_xcmplx_0(A,np__1)))) # label(t65_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4218 $T # label(t8_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4219 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,B) & k8_square_1(A) = k8_square_1(B) & r1_xreal_0(np__0,A) -> B = A))))) # label(t96_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4220 (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]. 87.61/85.63 4221 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_xcmplx_0(k5_square_1(A),k5_square_1(B)) = k5_square_1(k3_xcmplx_0(A,B)))))) # label(t68_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4222 (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]. 87.61/85.63 4223 $T # label(t41_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4224 (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]. 87.61/85.63 4225 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(A,B) -> r1_xreal_0(k8_square_1(A),k8_square_1(B))))))) # label(t94_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4226 $T # label(t9_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4227 $T # label(t1_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4228 $T # label(t79_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4229 (all A (v1_xreal_0(A) -> -(r1_xreal_0(A,k5_square_1(A)) & -r1_xreal_0(np__1,A) & -r1_xreal_0(A,np__0)))) # label(t75_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4230 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) & r1_xreal_0(np__0,B) -> k7_xcmplx_0(k8_square_1(A),k8_square_1(B)) = k8_square_1(k7_xcmplx_0(A,B))))))) # label(t99_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4231 $T # label(t5_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4232 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k1_square_1(A,B) = k3_square_1(A,B))) # label(redefinition_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4233 $T # label(dt_k5_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4234 $T # label(t7_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4235 $T # label(t32_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4236 $T # label(t87_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4237 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> (all B (v1_xreal_0(B) -> (B = k8_square_1(A) <-> r1_xreal_0(np__0,B) & k5_square_1(B) = A)))))) # label(d4_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4238 $T # label(t33_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4239 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(B,A) | k7_xcmplx_0(k2_xcmplx_0(k8_square_1(B),k8_square_1(A)),k6_xcmplx_0(B,A)) = k7_xcmplx_0(np__1,k6_xcmplx_0(k8_square_1(B),k8_square_1(A)))))))) # label(t108_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4240 (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 ((all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (p2_s1_square_1(C) & p1_s1_square_1(B) -> r1_xreal_0(B,A) & r1_xreal_0(A,C)))))) & v1_xreal_0(A))) # label(s1_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4241 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> A = k2_square_1(A,k1_square_1(A,B)))))) # label(t54_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4242 $T # label(t48_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4243 $T # label(t80_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4244 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> A = k3_square_1(A,A))) # label(idempotence_k3_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4245 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> k2_square_1(A,A) = A)) # label(idempotence_k2_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4246 (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]. 87.61/85.63 4247 $T # label(t12_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4248 $T # label(t21_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4249 (all A (v1_xreal_0(A) -> v1_xreal_0(k8_square_1(A)))) # label(dt_k8_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4250 $T # label(t3_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4251 $T # label(t31_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4252 (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]. 87.61/85.63 4253 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) & r1_xreal_0(np__0,A) -> r1_xreal_0(k5_square_1(A),k5_square_1(B))))))) # label(t77_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4254 $T # label(t15_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.63 4255 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k1_square_1(A,B) = A | k1_square_1(A,B) = B)))) # label(t38_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4256 $T # label(t16_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4257 (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]. 87.61/85.64 4258 (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]. 87.61/85.64 4259 $T # label(t58_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4260 $T # label(t10_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4261 (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(A,B) <-> r1_xreal_0(k2_square_1(A,C),B)))))))) # label(t50_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4262 (all A (v1_xreal_0(A) -> -(np__0 != A & r1_xreal_0(k5_square_1(A),np__0)))) # label(t74_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4263 $T # label(t26_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4264 (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]. 87.61/85.64 4265 $T # label(t36_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4266 (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]. 87.61/85.64 4267 $T # label(t17_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4268 (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]. 87.61/85.64 4269 $T # label(t19_square_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4270 (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]. 87.61/85.64 4271 (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]. 87.61/85.64 4272 -r1_xreal_0(f2_s8_nat_1,f3_s8_nat_1) & f2_s8_nat_1 = f1_s8_nat_1(np__0) & f3_s8_nat_1 = f1_s8_nat_1(np__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)))) & -r1_xreal_0(f3_s8_nat_1,np__0) -> (exists A (f1_s8_nat_1(A) = k6_nat_1(f2_s8_nat_1,f3_s8_nat_1) & np__0 = f1_s8_nat_1(k1_nat_1(A,np__1)) & m2_subset_1(A,k1_numbers,k5_numbers))) # label(s8_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4273 (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,k4_nat_1(B,C))))))))) # label(t58_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4274 $T # label(t48_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4275 (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]. 87.61/85.64 4276 $T # label(t31_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4277 (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]. 87.61/85.64 4278 $T # label(t30_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4279 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xreal_0(A) & -v3_xreal_0(A) & v1_xcmplx_0(A) & v2_ordinal1(A))) # label(cc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4280 $T # label(t5_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4281 (all A all B (v4_ordinal2(B) & -v1_xboole_0(B) & v4_ordinal2(A) -> v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)))) # label(fc4_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4282 (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]. 87.61/85.64 4283 (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]. 87.61/85.64 4284 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r1_nat_1(A,B) & r1_nat_1(A,k2_xcmplx_0(B,C)) -> r1_nat_1(A,C)))))))) # label(t57_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4285 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,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]. 87.61/85.64 4286 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(k2_xcmplx_0(B,np__1),A) <-> r1_xreal_0(A,B)))))) # label(t38_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4287 (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) | k4_nat_1(k2_xcmplx_0(A,B),C) = B | C = np__0))))))) # label(t66_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4288 (all A (v4_ordinal2(A) -> -(r1_xreal_0(A,np__0) & A != np__0))) # label(t19_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4289 $T # label(t8_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4290 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (A != np__0 -> k3_nat_1(k3_xcmplx_0(A,B),A) = B))))) # label(t68_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4291 (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]. 87.61/85.64 4292 (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]. 87.61/85.64 4293 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (np__0 = k2_xcmplx_0(A,B) -> B = np__0 & np__0 = A))))) # label(t23_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4294 (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]. 87.61/85.64 4295 (exists A (p1_s6_nat_1(A) & m2_subset_1(A,k1_numbers,k5_numbers))) & (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) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (p1_s6_nat_1(B) -> r1_xreal_0(B,A)))))) # label(s6_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4296 $T # label(t45_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4297 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_nat_1(B,A) & r1_nat_1(A,B) -> B = A))))) # label(t52_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4298 (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]. 87.61/85.64 4299 (exists A (m1_subset_1(A,k5_numbers) & v1_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4300 (exists A (m2_subset_1(A,k1_numbers,k5_numbers) & p1_s7_nat_1(A))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(p1_s7_nat_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r1_xreal_0(A,B) & p1_s7_nat_1(B)))) & A != np__0))) -> p1_s7_nat_1(np__0) # label(s7_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4301 (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(B,D) & r1_nat_1(A,D) -> r1_nat_1(C,D)))) & r1_nat_1(A,C) <-> C = k5_nat_1(A,B)))))))) # label(d4_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4302 (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]. 87.61/85.64 4303 $T # label(t16_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4304 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(r1_xreal_0(A,B) & r1_xreal_0(B,k2_xcmplx_0(A,np__1)) & A != B & B != k2_xcmplx_0(A,np__1)))))) # label(t27_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4305 (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]. 87.61/85.64 4306 (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]. 87.61/85.64 4307 (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(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)))) & r1_nat_1(C,A) <-> k6_nat_1(A,B) = C))))))) # label(d5_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4308 (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]. 87.61/85.64 4309 (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]. 87.61/85.64 4310 $T # label(t36_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4311 $T # label(t10_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4312 (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]. 87.61/85.64 4313 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (k4_nat_1(A,B) = np__0 -> 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]. 87.61/85.64 4314 $T # label(t6_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4315 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(A,np__0) -> k2_xcmplx_0(k3_xcmplx_0(A,k3_nat_1(B,A)),k4_nat_1(B,A)) = B))))) # label(t47_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4316 $T # label(t44_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4317 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (np__0 != B -> A = k3_nat_1(k2_nat_1(A,B),B)))))) # label(t72_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4318 (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]. 87.61/85.64 4319 $T # label(t9_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4320 (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]. 87.61/85.64 4321 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> ((exists C (B = k3_xcmplx_0(A,C) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r1_nat_1(A,B)))))) # label(d3_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4322 (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))))) & p1_s1_nat_1(np__0) -> (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]. 87.61/85.64 4323 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (-(-(B = np__0 & np__0 = C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(-r1_xreal_0(B,C) & k2_xcmplx_0(k3_xcmplx_0(B,D),C) = A)))) <-> C = k4_nat_1(A,B)))))))) # label(d2_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4324 $T # label(t33_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4325 (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]. 87.61/85.64 4326 $T # label(t4_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4327 $T # label(t34_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4328 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k3_xcmplx_0(A,B) = k2_nat_1(A,B))) # label(redefinition_k2_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4329 $T # label(t13_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4330 (all A (v4_ordinal2(A) -> np__0 = k4_nat_1(A,A))) # label(t77_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4331 $T # label(t32_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4332 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k2_xcmplx_0(A,B) = k1_nat_1(A,B))) # label(redefinition_k1_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4333 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(A != np__0 & np__1 != A & -r1_xreal_0(np__2,A)))) # label(t71_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4334 (all A (v4_ordinal2(A) -> np__0 = k4_nat_1(np__0,A))) # label(t78_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4335 (exists A (v3_ordinal1(A) & -v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)))) # label(rc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4336 (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]. 87.61/85.64 4337 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> m2_subset_1(k4_nat_1(A,B),k1_numbers,k5_numbers))) # label(dt_k4_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4338 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(np__0 != A & r1_xreal_0(k2_xcmplx_0(B,A),B)))))) # label(t41_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4339 (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) <-> -(-(A = np__0 & B = f1_s3_nat_1) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(k1_nat_1(C,np__1) = A & p1_s3_nat_1(C,D) & B = f2_s3_nat_1(A,D)))))))))))) -> (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) -> C = B))))))) & (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]. 87.61/85.64 4340 (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 & np__0 = k4_nat_1(A,C) -> k4_nat_1(B,C) = np__0))))))))) # label(t65_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4341 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> A = k6_nat_1(A,A))) # label(idempotence_k6_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4342 (all A (m1_subset_1(A,k5_numbers) -> v3_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4343 $T # label(t25_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4344 (exists A (m2_subset_1(A,k1_numbers,k5_numbers) & p1_s5_nat_1(A))) -> (exists A ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (p1_s5_nat_1(B) -> r1_xreal_0(A,B)))) & p1_s5_nat_1(A) & m2_subset_1(A,k1_numbers,k5_numbers))) # label(s5_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4345 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (C = k3_nat_1(A,B) <-> -(-(C = np__0 & B = np__0) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(-r1_xreal_0(B,D) & A = k2_xcmplx_0(k3_xcmplx_0(B,C),D)))))))))))) # label(d1_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4346 $T # label(t14_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4347 (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]. 87.61/85.64 4348 (all A (v4_ordinal2(A) -> k4_nat_1(A,np__2) = np__1 | np__0 = k4_nat_1(A,np__2))) # label(t62_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4349 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k2_nat_1(A,B) = k2_nat_1(B,A))) # label(commutativity_k2_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4350 (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]. 87.61/85.64 4351 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> k4_nat_1(k2_xcmplx_0(k4_nat_1(A,C),B),C) = k4_nat_1(k2_xcmplx_0(A,B),C))))))) # label(t74_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4352 $T # label(t12_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4353 $T # label(t50_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4354 $T # label(t15_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4355 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(r1_xreal_0(A,k4_nat_1(B,A)) & -r1_xreal_0(A,np__0)))))) # label(t46_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4356 (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]. 87.61/85.64 4357 (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]. 87.61/85.64 4358 (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) & A != k2_xcmplx_0(B,np__1)))))) # label(t26_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4359 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k5_nat_1(A,B) = k5_nat_1(B,A))) # label(commutativity_k5_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4360 (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) -> (A = k2_xcmplx_0(k3_xcmplx_0(B,C),E) & k2_xcmplx_0(k3_xcmplx_0(B,D),F) = A -> C = D & E = F | r1_xreal_0(B,F) | r1_xreal_0(B,E)))))))))))))) # label(t43_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4361 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> r1_nat_1(A,A))) # label(reflexivity_r1_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4362 $T # label(t3_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4363 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k6_nat_1(B,A) = k6_nat_1(A,B))) # label(commutativity_k6_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4364 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r1_xreal_0(k1_nat_1(B,np__1),A) & r1_xreal_0(B,A) & B != A))))) # label(t70_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4365 (all A (v4_ordinal2(A) -> (-r1_xreal_0(np__1,A) -> A = np__0))) # label(t39_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4366 $T # label(t1_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4367 (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]. 87.61/85.64 4368 (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]. 87.61/85.64 4369 (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]. 87.61/85.64 4370 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v4_ordinal2(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc2_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4371 $T # label(t11_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4372 (all A (v4_ordinal2(A) -> r1_xreal_0(np__0,A))) # label(t18_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4373 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)))) # label(fc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4374 (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]. 87.61/85.64 4375 $T # label(t17_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4376 (all A all B (v4_ordinal2(B) & -v1_xboole_0(B) & v4_ordinal2(A) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc3_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4377 (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]. 87.61/85.64 4378 $T # label(t7_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4379 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(np__1,B) <-> -r1_xreal_0(k2_xcmplx_0(A,B),A)))))) # label(t59_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4380 $T # label(t35_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4381 $T # label(t24_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4382 (exists A (-v1_xboole_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v4_ordinal2(A))) # label(rc1_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4383 (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]. 87.61/85.64 4384 (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]. 87.61/85.64 4385 (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) & B = k1_nat_1(k2_nat_1(A,C),D) & -r1_xreal_0(A,D)))))))))) # label(t42_nat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4386 (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]. 87.61/85.64 4387 (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]. 87.61/85.64 4388 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4389 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,k1_int_1(A)) & v1_int_1(A)) & -(-v1_int_1(A) & r1_xreal_0(A,k1_int_1(A))))) # label(t48_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4390 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4391 (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]. 87.61/85.64 4392 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> np__0 = k4_int_1(A)))) # label(t71_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4393 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 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]. 87.61/85.64 4395 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(D,E,C) & r1_int_1(A,B,C) -> r1_int_1(k2_xcmplx_0(A,D),k2_xcmplx_0(B,E),C)))))))))))) # label(t37_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4396 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> A = k2_int_1(A)))) # label(t54_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4397 (all A (v1_xreal_0(A) -> k3_int_1(A) = k6_xcmplx_0(A,k1_int_1(A)))) # label(d6_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4398 (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]. 87.61/85.64 4399 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k3_int_1(A)) & v1_xreal_0(k3_int_1(A)))) # label(fc10_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4400 (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]. 87.61/85.64 4401 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B = np__1 & np__1 = A | k1_real_1(np__1) = A & B = k1_real_1(np__1) <-> np__1 = k3_xcmplx_0(A,B)))))) # label(t22_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4402 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4403 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4404 (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]. 87.61/85.64 4405 (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]. 87.61/85.64 4406 (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]. 87.61/85.64 4407 (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]. 87.61/85.64 4408 (all A (v1_int_1(A) -> k5_int_1(A,np__0) = np__0)) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4409 (all A (v1_xreal_0(A) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> A != B & A != k1_real_1(B))) & v1_int_1(A)))) # label(t8_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4410 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) -> p1_s2_int_1(k2_xcmplx_0(A,np__1))))) -> (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(A)))) # label(s2_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4411 (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]. 87.61/85.64 4412 (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]. 87.61/85.64 4413 (all A (r2_hidden(A,k4_numbers) <-> v1_int_1(A))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4414 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k2_int_1(A),k1_int_1(A)) & -v1_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]. 87.61/85.64 4415 (all A (v1_int_1(A) -> r1_int_1(A,np__0,A) & r1_int_1(np__0,A,A))) # label(t33_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4416 (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]. 87.61/85.64 4417 (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))))) & p1_s4_int_1(f1_s4_int_1) -> (all A (v1_int_1(A) -> p1_s4_int_1(A))) # label(s4_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4418 (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) -> C = B | r1_xreal_0(C,k6_xcmplx_0(A,np__1)) | r1_xreal_0(B,k6_xcmplx_0(A,np__1))))))))) # label(t44_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4419 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4420 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(D,E,C) & r1_int_1(A,B,C) -> r1_int_1(k3_xcmplx_0(A,D),k3_xcmplx_0(B,E),C)))))))))))) # label(t39_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4421 (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]. 87.61/85.64 4422 (all A (v1_xreal_0(A) -> (all B (v4_ordinal2(B) -> (A = B | A = k4_xcmplx_0(B) -> v1_int_1(A)))))) # label(t7_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4423 (exists A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) & (all B (v1_int_1(B) -> (p1_s1_int_1(B) <-> r2_hidden(B,A)))))) # label(s1_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4424 (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]. 87.61/85.64 4425 (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]. 87.61/85.64 4426 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k6_int_1(A,B)))) # label(dt_k6_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4427 (all A (v1_xreal_0(A) -> (k2_int_1(A) = k1_int_1(A) <-> k2_int_1(A) != k2_xcmplx_0(k1_int_1(A),np__1)))) # label(t66_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4428 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc2_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4429 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4430 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> k5_int_1(A,B) = k1_int_1(k7_xcmplx_0(A,B)))))) # label(d7_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4431 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4432 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4433 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k5_int_1(A,B)))) # label(dt_k5_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4434 (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,B,C) & r1_int_1(B,D,C) -> r1_int_1(A,D,C)))))))))) # label(t36_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4435 (all A (v1_int_1(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc3_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4436 (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]. 87.61/85.64 4437 (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]. 87.61/85.64 4438 (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]. 87.61/85.64 4439 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4440 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (np__1 = B & A = k1_real_1(np__1) | A = np__1 & k1_real_1(np__1) = B <-> k3_xcmplx_0(A,B) = k1_real_1(np__1)))))) # label(t23_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4441 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4442 (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]. 87.61/85.64 4443 (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]. 87.61/85.64 4444 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4445 (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]. 87.61/85.64 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]. 87.61/85.64 4447 (all A (m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)))) # label(fc5_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4448 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4449 (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]. 87.61/85.64 4450 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4451 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4452 (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]. 87.61/85.64 4453 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_int_1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k2_int_1(A),B))))) # label(t58_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4454 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4455 (all A (v1_xreal_0(A) -> -r1_xreal_0(np__1,k4_int_1(A)) & r1_xreal_0(np__0,k4_int_1(A)))) # label(t69_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4456 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(A,B) & r1_xreal_0(A,C) -> r1_xreal_0(k2_xcmplx_0(A,np__1),C) | C = B | r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))))) # label(t45_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4457 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4458 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4459 (all A (v1_xreal_0(A) -> (np__0 != A -> k1_int_1(k7_xcmplx_0(A,A)) = np__1))) # label(t74_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4460 (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]. 87.61/85.64 4461 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4462 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4463 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4464 (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]. 87.61/85.64 4465 (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]. 87.61/85.64 4466 (all A (v1_int_1(A) -> (p1_s3_int_1(A) & r1_xreal_0(A,f1_s3_int_1) -> 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]. 87.61/85.64 4467 (all A (v1_xreal_0(A) -> (v1_int_1(A) -> v1_int_1(k2_xcmplx_0(A,np__1)) & v1_int_1(k6_xcmplx_0(A,np__1))))) # label(t17_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4468 (all A (v1_xreal_0(A) -> (k1_int_1(A) = A <-> v1_int_1(A)))) # label(t47_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4469 (all A (v1_xreal_0(A) -> k1_int_1(k4_int_1(A)) = np__0)) # label(t70_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4470 (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]. 87.61/85.64 4471 (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) & p1_s6_int_1(A))) -> (exists A (v1_int_1(A) & p1_s6_int_1(A) & (all B (v1_int_1(B) -> (p1_s6_int_1(B) -> r1_xreal_0(B,A)))))) # label(s6_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4472 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(A,np__1),k1_int_1(A)) & -r1_xreal_0(A,k6_xcmplx_0(k1_int_1(A),np__1)))) # label(t50_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4473 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4474 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4475 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4476 (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]. 87.61/85.64 4477 (exists A (v1_xreal_0(A) & v1_int_1(A) & v1_xcmplx_0(A) & m1_subset_1(A,k1_numbers))) # label(rc1_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4478 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4479 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4480 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> ((exists D (v1_int_1(D) & k3_xcmplx_0(C,D) = k6_xcmplx_0(A,B))) <-> r1_int_1(A,B,C)))))))) # label(d3_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4481 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B = np__0 -> np__0 = k6_int_1(A,B)) & (B != np__0 -> 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]. 87.61/85.64 4482 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4483 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4484 (all A (v1_int_1(A) -> (A != np__0 -> k5_int_1(A,A) = np__1))) # label(t76_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4485 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4486 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> v1_int_1(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc6_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4487 (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]. 87.61/85.64 4488 (all A (v1_int_1(A) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4489 (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) <-> k2_int_1(A) = B))))) # label(d5_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4490 (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]. 87.61/85.64 4491 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4492 (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]. 87.61/85.64 4493 (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]. 87.61/85.64 4494 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4495 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)))) # label(fc7_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4496 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 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]. 87.61/85.64 4498 (all A (k4_numbers = A <-> (all B (-(all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B != C & k1_real_1(C) != B)) <-> r2_hidden(B,A))))) # label(d1_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4499 (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]. 87.61/85.64 4500 (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]. 87.61/85.64 4501 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4502 (all A (v1_int_1(A) -> np__0 = k6_int_1(A,A))) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4503 (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]. 87.61/85.64 4504 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v2_ordinal1(A) & -v3_xreal_0(A) & v1_int_1(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v3_ordinal1(A))) # label(cc2_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4505 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)))) # label(fc8_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4506 (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]. 87.61/85.64 4507 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k2_int_1(A)) & r1_xreal_0(np__0,k1_int_1(A)) & m2_subset_1(k2_int_1(A),k1_numbers,k5_numbers) & m2_subset_1(k1_int_1(A),k1_numbers,k5_numbers)))) # label(t80_int_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4508 $T # label(t12_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4509 $T # label(t57_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4510 (all A (v1_rat_1(A) <-> r2_hidden(A,k3_numbers))) # label(d2_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4511 $T # label(t70_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4512 $T # label(t20_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4513 (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]. 87.61/85.64 4514 (all A all B (v1_int_1(A) & 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(fc9_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4515 (all A all B (v1_rat_1(A) & v1_int_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(fc4_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4516 $T # label(t56_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4517 (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]. 87.61/85.64 4518 (all A (v1_rat_1(A) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc1_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4519 (all A all B (v1_rat_1(A) & m1_subset_1(B,k5_numbers) -> 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(fc12_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4520 (exists A v1_rat_1(A)) # label(rc2_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4521 (all A (v1_rat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B = k1_rat_1(A) <-> (all C (v1_int_1(C) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (A = k7_xcmplx_0(C,D) -> r1_xreal_0(B,D) | D = np__0))))) & (exists C (A = k7_xcmplx_0(C,B) & v1_int_1(C))) & np__0 != B))))) # label(d3_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4522 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (k7_xcmplx_0(np__1,A) = B -> r1_xreal_0(A,np__0) | k2_rat_1(B) = k1_rat_1(A) & k1_rat_1(B) = k2_rat_1(A)) & (k2_rat_1(B) = k1_rat_1(A) & k2_rat_1(A) = k1_rat_1(B) -> B = k7_xcmplx_0(np__1,A) & -r1_xreal_0(A,np__0)))))) # label(t88_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4523 $T # label(t43_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4524 (all A (v1_rat_1(A) -> (r1_xreal_0(k2_rat_1(A),k1_rat_1(A)) <-> r1_xreal_0(A,np__1)))) # label(t73_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4525 (all A (v1_rat_1(A) -> (r1_xreal_0(k2_rat_1(A),np__0) <-> r1_xreal_0(A,np__0)))) # label(t77_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4526 (all A (v1_int_1(A) -> v1_rat_1(A))) # label(t7_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4527 $T # label(t52_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4528 $T # label(t55_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4529 $T # label(t18_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4530 (all A (v1_rat_1(A) -> k2_rat_1(k4_xcmplx_0(A)) = k4_xcmplx_0(k2_rat_1(A)) & k1_rat_1(A) = k1_rat_1(k4_xcmplx_0(A)))) # label(t87_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4531 $T # label(t54_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4532 (all A (v1_rat_1(A) -> -(r1_xreal_0(k1_real_1(k1_rat_1(A)),k2_rat_1(A)) & -r1_xreal_0(k1_real_1(np__1),A)) & -(-r1_xreal_0(k1_real_1(k1_rat_1(A)),k2_rat_1(A)) & r1_xreal_0(k1_real_1(np__1),A)))) # label(t64_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4533 (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]. 87.61/85.64 4534 $T # label(t31_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4535 (all A (v1_rat_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))) & -v1_int_1(A)))) # label(t46_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4536 (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]. 87.61/85.64 4537 (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]. 87.61/85.64 4538 (all A (v1_rat_1(A) -> v1_int_1(k2_rat_1(A)))) # label(dt_k2_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4539 (all A ((exists B (v1_int_1(B) & (exists C (v1_int_1(C) & k7_xcmplx_0(B,C) = A)))) -> v1_rat_1(A))) # label(t6_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4540 (all A (v1_rat_1(A) -> (exists B (v1_int_1(B) & (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (all D (v1_int_1(D) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (k7_xcmplx_0(D,E) = A -> r1_xreal_0(C,E) | np__0 = E))))) & A = k7_xcmplx_0(B,C) & C != np__0)))))) # label(t25_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4541 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_rat_1(C) -> -(C = k7_xcmplx_0(B,A) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(B = k3_xcmplx_0(k2_rat_1(C),D) & A = k2_nat_1(k1_rat_1(C),D)))) & np__0 != A))))))) # label(t60_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.64 4542 (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]. 87.61/85.65 4543 $T # label(t39_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4544 $T # label(t10_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4545 (all A all B (v1_int_1(B) & v1_rat_1(A) -> 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(fc6_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4546 (all A -((all B (v1_int_1(B) -> (all C (v1_int_1(C) -> -(np__0 != C & k7_xcmplx_0(B,C) = A))))) & r2_hidden(A,k3_numbers))) # label(t1_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4547 $T # label(t85_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4548 $T # label(t69_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4549 (all A (v1_rat_1(A) -> v1_rat_1(k5_xcmplx_0(A)))) # label(t21_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4550 (all A (v1_rat_1(A) -> (k2_rat_1(A) = k1_rat_1(A) <-> A = np__1))) # label(t47_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4551 (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]. 87.61/85.65 4552 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_rat_1(C) -> -(k7_xcmplx_0(A,B) = C & np__0 != B & (all D (v1_int_1(D) -> -(k3_xcmplx_0(k1_rat_1(C),D) = B & A = k3_xcmplx_0(k2_rat_1(C),D))))))))))) # label(t61_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4553 (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]. 87.61/85.65 4554 $T # label(t59_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4555 $T # label(t58_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4556 (all A (v1_rat_1(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_rat_1(k5_xcmplx_0(A)))) # label(fc18_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4557 (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]. 87.61/85.65 4558 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> -((all C (v1_rat_1(C) -> -(-r1_xreal_0(C,A) & -r1_xreal_0(B,C)))) & -r1_xreal_0(B,A)))))) # label(t22_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4559 (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]. 87.61/85.65 4560 (all A all B (v1_rat_1(B) & v1_int_1(A) -> v1_rat_1(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc8_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4561 (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]. 87.61/85.65 4562 (all A (v1_rat_1(A) -> (k1_rat_1(A) = np__1 | A = k2_rat_1(A) -> v1_int_1(A)))) # label(t41_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4563 (all A (v1_rat_1(A) -> (r1_xreal_0(A,k1_real_1(np__1)) <-> r1_xreal_0(k1_rat_1(A),k4_xcmplx_0(k2_rat_1(A)))))) # label(t67_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4564 (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]. 87.61/85.65 4565 (all A (v1_int_1(A) -> (all B (v1_rat_1(B) -> (np__0 != A -> 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]. 87.61/85.65 4566 (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]. 87.61/85.65 4567 $T # label(t19_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4568 $T # label(t14_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4569 (all A all B (m1_subset_1(A,k5_numbers) & v1_rat_1(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_rat_1(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc14_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4570 $T # label(t26_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4571 $T # label(t71_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4572 (all A (v1_rat_1(A) -> (k2_rat_1(A) = k1_real_1(k1_rat_1(A)) <-> A = k1_real_1(np__1)))) # label(t48_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4573 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v1_rat_1(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc3_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4574 (all A all B (m1_subset_1(A,k5_numbers) & v1_rat_1(B) -> v1_rat_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc15_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4575 (all A (v1_rat_1(A) -> (v1_int_1(A) -> A = k2_rat_1(A) & np__1 = k1_rat_1(A)))) # label(t40_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4576 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (k1_real_1(k1_rat_1(A)) = k2_rat_1(B) & k4_xcmplx_0(k2_rat_1(A)) = k1_rat_1(B) -> k7_xcmplx_0(np__1,A) = B & -r1_xreal_0(np__0,A)) & (k7_xcmplx_0(np__1,A) = B -> r1_xreal_0(np__0,A) | k2_rat_1(B) = k1_real_1(k1_rat_1(A)) & k1_rat_1(B) = k4_xcmplx_0(k2_rat_1(A))))))) # label(t89_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4577 (all A (v1_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)) & -(r1_xreal_0(k1_real_1(np__1),A) & -r1_xreal_0(k4_xcmplx_0(k2_rat_1(A)),k1_rat_1(A))))) # label(t66_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4578 (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) & k2_nat_1(D,B) = k1_rat_1(A) & k2_rat_1(A) = k3_xcmplx_0(C,B)))))))))) # label(t62_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4579 $T # label(t28_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4580 $T # label(t4_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4581 $T # label(t79_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4582 $T # label(t11_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4583 (all A -(v1_rat_1(A) & (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> -(C != np__0 & k7_xcmplx_0(B,C) = A))))))) # label(t3_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4584 $T # label(t75_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4585 (all A (v1_rat_1(A) -> (k2_rat_1(A) = np__0 <-> np__0 = A))) # label(t36_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4586 (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]. 87.61/85.65 4587 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v1_rat_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc1_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4588 $T # label(t15_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4589 $T # label(t51_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4590 (all A (v1_rat_1(A) -> (r1_xreal_0(np__0,A) -> k1_rat_1(A) != np__1 & k2_rat_1(A) != A | m2_subset_1(A,k1_numbers,k5_numbers)))) # label(t44_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4591 (all A (v1_rat_1(A) -> A = k3_xcmplx_0(k2_real_1(k1_rat_1(A)),k2_rat_1(A)) & A = k3_xcmplx_0(k2_rat_1(A),k2_real_1(k1_rat_1(A))) & k7_xcmplx_0(k2_rat_1(A),k1_rat_1(A)) = A)) # label(t37_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4592 (all A (k3_numbers = A <-> (all B (r2_hidden(B,A) <-> (exists C ((exists D (v1_int_1(D) & k7_xcmplx_0(C,D) = B)) & v1_int_1(C))))))) # label(d1_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4593 (all A all B (v1_rat_1(A) & m1_subset_1(B,k5_numbers) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_rat_1(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc11_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4594 $T # label(t9_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4595 (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]. 87.61/85.65 4596 $T # label(t53_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4597 (all A (v1_rat_1(A) -> (A != np__0 -> k7_xcmplx_0(k2_rat_1(A),A) = k1_rat_1(A)))) # label(t38_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4598 $T # label(t32_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4599 $T # label(t2_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4600 $T # label(t83_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4601 (all A (v1_xreal_0(A) -> (all B (v1_rat_1(B) -> (r1_xreal_0(k3_xcmplx_0(A,k1_rat_1(B)),k2_rat_1(B)) <-> r1_xreal_0(A,B)))))) # label(t81_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4602 (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]. 87.61/85.65 4603 $T # label(t5_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4604 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_rat_1(C) -> (C = k7_xcmplx_0(B,A) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -((exists E (v1_int_1(E) & (exists F (k2_nat_1(F,D) = A & B = k3_xcmplx_0(E,D) & m2_subset_1(F,k1_numbers,k5_numbers))))) & -r1_xreal_0(D,np__1)))) -> A = np__0 | k1_rat_1(C) = A & k2_rat_1(C) = B))))))) # label(t63_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4605 (all A (v1_xreal_0(A) -> (all B (v1_rat_1(B) -> -(-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))) & -r1_xreal_0(B,A)))))) # label(t80_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4606 (all A (v1_rat_1(A) -> (A = k1_real_1(np__1) <-> k4_xcmplx_0(k2_rat_1(A)) = k1_rat_1(A)))) # label(t49_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4607 (all A all B (m1_subset_1(A,k5_numbers) & v1_rat_1(B) -> 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(fc13_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4608 $T # label(t13_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4609 $T # label(t78_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4610 $T # label(t35_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4611 $T # label(t74_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4612 (all A (v1_rat_1(A) -> k3_xcmplx_0(k1_rat_1(A),A) = k2_rat_1(A))) # label(d4_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4613 $T # label(t82_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4614 $T # label(t8_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4615 (all A (v1_rat_1(A) -> (exists B ((exists C (np__0 != C & A = k7_xcmplx_0(B,C) & m2_subset_1(C,k1_numbers,k5_numbers))) & v1_int_1(B))))) # label(t24_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4616 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & v1_rat_1(k7_xcmplx_0(A,B)))) # label(fc17_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4617 $T # label(t17_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4618 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> -(-r1_xreal_0(B,A) & r1_xreal_0(k3_xcmplx_0(k2_rat_1(B),k1_rat_1(A)),k3_xcmplx_0(k2_rat_1(A),k1_rat_1(B)))) & -(-r1_xreal_0(k3_xcmplx_0(k2_rat_1(B),k1_rat_1(A)),k3_xcmplx_0(k2_rat_1(A),k1_rat_1(B))) & r1_xreal_0(B,A)))))) # label(t86_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4619 $T # label(t68_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4620 (all A (v1_rat_1(A) -> (all B (v1_rat_1(B) -> (k2_rat_1(B) = k2_rat_1(A) & k1_rat_1(B) = k1_rat_1(A) -> A = B))))) # label(t84_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4621 (all A all B (v1_int_1(B) & v1_rat_1(A) -> 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(fc5_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4622 $T # label(t33_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4623 (all A all B (v1_rat_1(A) & m1_subset_1(B,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(fc10_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4624 $T # label(t23_rat_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4625 (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]. 87.61/85.65 4626 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k6_binop_2(A,B),k2_numbers))) # label(dt_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4627 (all A (v1_funct_2(A,k1_numbers,k1_numbers) & m2_relset_1(A,k1_numbers,k1_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k1_numbers) -> k8_funct_2(k1_numbers,k1_numbers,A,B) = k7_binop_2(B))) <-> A = k31_binop_2))) # label(d7_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4628 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> (A = k28_binop_2 <-> (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)))))))) # label(d4_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4629 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> m1_subset_1(k18_binop_2(A,B),k3_numbers))) # label(dt_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4630 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> m1_subset_1(k21_binop_2(A,B),k4_numbers))) # label(dt_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4631 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k3_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4632 (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]. 87.61/85.65 4633 (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) -> (A = k30_binop_2 <-> (all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k6_binop_2(B,C) = k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C)))))))) # label(d6_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4634 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k7_xcmplx_0(A,B) = k12_binop_2(A,B))) # label(redefinition_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4635 (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) -> (k45_binop_2 = 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)))))))) # label(d21_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4636 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k3_binop_2(B,A) = k3_binop_2(A,B))) # label(commutativity_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4637 (all A (m1_subset_1(A,k3_numbers) -> v1_rat_1(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc1_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4638 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k3_xcmplx_0(A,B) = k5_binop_2(A,B))) # label(redefinition_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4639 (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]. 87.61/85.65 4640 (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]. 87.61/85.65 4641 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> k3_xcmplx_0(A,B) = k22_binop_2(A,B))) # label(redefinition_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4642 (all A (m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k9_binop_2(B,C))))) <-> A = k33_binop_2))) # label(d9_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4643 (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]. 87.61/85.65 4644 (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]. 87.61/85.65 4645 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> k21_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4646 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k7_xcmplx_0(A,B) = k18_binop_2(A,B))) # label(redefinition_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4647 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k5_binop_2(B,A) = k5_binop_2(A,B))) # label(commutativity_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4648 (all A (m2_relset_1(A,k2_numbers,k2_numbers) & v1_funct_2(A,k2_numbers,k2_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k2_numbers) -> k1_binop_2(B) = k8_funct_2(k2_numbers,k2_numbers,A,B))) <-> k25_binop_2 = A))) # label(d1_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4649 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> m1_subset_1(k22_binop_2(A,B),k4_numbers))) # label(dt_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4650 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) -> (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]. 87.61/85.65 4651 (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]. 87.61/85.65 4652 (all A (m1_subset_1(A,k1_numbers) -> k4_xcmplx_0(A) = k7_binop_2(A))) # label(redefinition_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4653 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k5_binop_2(A,B),k2_numbers))) # label(dt_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4654 (all A (m1_subset_1(A,k3_numbers) -> k5_xcmplx_0(A) = k14_binop_2(A))) # label(redefinition_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4655 (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 = k34_binop_2 <-> (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]. 87.61/85.65 4656 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k17_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4657 (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]. 87.61/85.65 4658 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k3_binop_2(A,B),k2_numbers))) # label(dt_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4659 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k20_binop_2(A,B) = k20_binop_2(B,A))) # label(commutativity_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4660 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k3_xcmplx_0(A,B) = k24_binop_2(A,B))) # label(redefinition_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 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) -> (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]. 87.61/85.65 4662 (all 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) & v1_funct_1(A) -> (all B (v1_funct_1(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) -> ((all C (m1_subset_1(C,f1_s1_binop_2) -> k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,A,C) = f3_s1_binop_2(C))) & (all C (m1_subset_1(C,f1_s1_binop_2) -> k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,B,C) = f3_s1_binop_2(C))) -> B = A))))) # label(s1_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4663 (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]. 87.61/85.65 4664 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) -> (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]. 87.61/85.65 4665 (all A (m1_subset_1(A,k3_numbers) -> k14_binop_2(k14_binop_2(A)) = A)) # label(involutiveness_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4666 (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]. 87.61/85.65 4667 (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]. 87.61/85.65 4668 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k23_binop_2(A,B) = k23_binop_2(B,A))) # label(commutativity_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4669 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k22_binop_2(A,B) = k22_binop_2(B,A))) # label(commutativity_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4670 (all A (v1_funct_1(A) & m2_relset_1(A,k1_numbers,k1_numbers) & v1_funct_2(A,k1_numbers,k1_numbers) -> ((all B (m1_subset_1(B,k1_numbers) -> k8_binop_2(B) = k8_funct_2(k1_numbers,k1_numbers,A,B))) <-> k32_binop_2 = A))) # label(d8_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4671 (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]. 87.61/85.65 4672 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k11_binop_2(A,B),k1_numbers))) # label(dt_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4673 (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]. 87.61/85.65 4674 (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]. 87.61/85.65 4675 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k4_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4676 (all A (m2_relset_1(A,k3_numbers,k3_numbers) & v1_funct_2(A,k3_numbers,k3_numbers) & v1_funct_1(A) -> (A = k38_binop_2 <-> (all B (m1_subset_1(B,k3_numbers) -> k14_binop_2(B) = k8_funct_2(k3_numbers,k3_numbers,A,B)))))) # label(d14_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4677 (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]. 87.61/85.65 4678 (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]. 87.61/85.65 4679 (all A (v1_funct_1(A) & v1_funct_2(A,k2_numbers,k2_numbers) & m2_relset_1(A,k2_numbers,k2_numbers) -> ((all B (m1_subset_1(B,k2_numbers) -> k2_binop_2(B) = k8_funct_2(k2_numbers,k2_numbers,A,B))) <-> A = k26_binop_2))) # label(d2_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4680 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k17_binop_2(B,A) = k17_binop_2(A,B))) # label(commutativity_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4681 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k23_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4682 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k15_binop_2(B,A) = k15_binop_2(A,B))) # label(commutativity_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4683 (all A (m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_1(A) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k24_binop_2(B,C) = k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C))))) <-> A = k48_binop_2))) # label(d24_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4684 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k2_xcmplx_0(A,B) = k20_binop_2(A,B))) # label(redefinition_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4685 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k9_binop_2(A,B) = k9_binop_2(B,A))) # label(commutativity_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4686 (all A (m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_1(A) -> (A = k42_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) = k18_binop_2(B,C)))))))) # label(d18_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4687 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k7_xcmplx_0(A,B) = k6_binop_2(A,B))) # label(redefinition_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4688 (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]. 87.61/85.65 4689 (all A (m1_subset_1(A,k1_numbers) -> k7_binop_2(k7_binop_2(A)) = A)) # label(involutiveness_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4690 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> ((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]. 87.61/85.65 4691 (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]. 87.61/85.65 4692 (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]. 87.61/85.65 4693 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> m1_subset_1(k17_binop_2(A,B),k3_numbers))) # label(dt_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4694 (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) & m2_relset_1(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_2(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) -> ((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]. 87.61/85.65 4695 (all A (v1_funct_1(A) & m2_relset_1(A,k4_numbers,k4_numbers) & v1_funct_2(A,k4_numbers,k4_numbers) -> ((all B (m1_subset_1(B,k4_numbers) -> k8_funct_2(k4_numbers,k4_numbers,A,B) = k19_binop_2(B))) <-> A = k43_binop_2))) # label(d19_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4696 (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]. 87.61/85.65 4697 (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]. 87.61/85.65 4698 (all A (m1_subset_1(A,k1_numbers) -> k8_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4699 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> m1_subset_1(k20_binop_2(A,B),k4_numbers))) # label(dt_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4700 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k9_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4701 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k6_xcmplx_0(A,B) = k16_binop_2(A,B))) # label(redefinition_k16_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4702 (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]. 87.61/85.65 4703 (all A (m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k16_binop_2(B,C))))) <-> A = k40_binop_2))) # label(d16_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4704 (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]. 87.61/85.65 4705 (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]. 87.61/85.65 4706 (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) -> (k35_binop_2 = A <-> (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)))))))) # label(d11_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4707 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k24_binop_2(A,B) = k24_binop_2(B,A))) # label(commutativity_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4708 (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]. 87.61/85.65 4709 (all A (v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k12_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C))))) <-> A = k36_binop_2))) # label(d12_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4710 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) -> (A = k46_binop_2 <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k22_binop_2(B,C)))))))) # label(d22_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4711 (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]. 87.61/85.65 4712 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k3_xcmplx_0(A,B) = k11_binop_2(A,B))) # label(redefinition_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4713 (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) -> k17_binop_2(B,C) = k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C))))) <-> A = k41_binop_2))) # label(d17_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4714 (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]. 87.61/85.65 4715 (all A (v1_funct_1(A) & m2_relset_1(A,k3_numbers,k3_numbers) & v1_funct_2(A,k3_numbers,k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> k8_funct_2(k3_numbers,k3_numbers,A,B) = k13_binop_2(B))) <-> k37_binop_2 = A))) # label(d13_binop_2) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4716 (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]. 87.61/85.65 4717 (all A (v1_membered(A) -> ((all B (v1_xcmplx_0(B) -> r2_hidden(B,A))) -> A = k2_numbers))) # label(t11_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4718 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_int_1(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4719 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4720 (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]. 87.61/85.65 4721 (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]. 87.61/85.65 4722 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4723 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> v1_membered(k2_tarski(A,B)))) # label(fc12_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4724 (all A all B (v5_membered(A) & v5_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4725 (all A all B (v5_membered(A) -> v5_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4726 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (r1_tarski(A,B) <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d10_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4727 (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]. 87.61/85.65 4728 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4729 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4730 (all A all B (v4_membered(A) & v4_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4731 (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]. 87.61/85.65 4732 (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]. 87.61/85.65 4733 (all A (v3_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v3_membered(B) & v1_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4734 (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]. 87.61/85.65 4735 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4736 (all A (v1_xreal_0(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4737 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4738 (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]. 87.61/85.65 4739 (all A all B (v3_membered(A) -> v3_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4740 (all A (v1_membered(A) & -v1_xboole_0(A) -> (exists B (v1_xcmplx_0(B) & r2_hidden(B,A))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4741 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4742 (all A (v4_membered(A) & -v1_xboole_0(A) -> (exists B (v1_int_1(B) & r2_hidden(B,A))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4743 (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]. 87.61/85.65 4744 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4745 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4746 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v4_membered(A) & v5_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4747 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4748 (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]. 87.61/85.65 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]. 87.61/85.65 4750 (all A all B all C (v1_int_1(C) & v1_int_1(B) & v1_int_1(A) -> v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4751 (all A all B all C (v1_xreal_0(C) & v1_xreal_0(B) & v1_xreal_0(A) -> v2_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc18_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4752 (all A (v2_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc11_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4753 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> A = B))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4754 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4755 (all A all B (v4_membered(B) & r2_hidden(B,A) -> v4_membered(k1_setfam_1(A)))) # label(t29_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4756 (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]. 87.61/85.65 4757 (exists A ((all B (v1_rat_1(B) -> (p1_s3_membered(B) <-> r2_hidden(B,A)))) & v3_membered(A))) # label(s3_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4758 (all A all B (v4_membered(A) & v4_membered(B) -> v1_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4759 (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]. 87.61/85.65 4760 (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]. 87.61/85.65 4761 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4762 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4763 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4764 (all A (v3_membered(A) <-> (all B (r2_hidden(B,A) -> v1_rat_1(B))))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4765 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4766 (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]. 87.61/85.65 4767 (all A all B (v2_membered(A) & v2_membered(B) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4768 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v1_membered(A) & v2_membered(A) & v4_membered(A) & v3_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4769 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4770 (all A all B (v3_membered(A) -> v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4771 (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]. 87.61/85.65 4772 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4773 (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]. 87.61/85.65 4774 (all A ((all B (r2_hidden(B,A) -> v1_int_1(B))) <-> v4_membered(A))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4775 (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]. 87.61/85.65 4776 (exists A ((all B (v1_xcmplx_0(B) -> (r2_hidden(B,A) <-> p1_s1_membered(B)))) & v1_membered(A))) # label(s1_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4777 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v2_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4778 (all A ((all B (r2_hidden(B,A) -> v1_xcmplx_0(B))) <-> v1_membered(A))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4779 (all A all B (v1_int_1(B) & v1_int_1(A) -> v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4780 (all A all B (v3_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4781 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (B = A <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4782 (all A (v2_membered(A) <-> (all B (r2_hidden(B,A) -> v1_xreal_0(B))))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4783 (all A (v5_membered(A) & -v1_xboole_0(A) -> (exists B (v4_ordinal2(B) & r2_hidden(B,A))))) # label(t10_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4784 (all A all B all C (v4_ordinal2(B) & v4_ordinal2(C) & v4_ordinal2(A) -> v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4785 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4786 (all A all B (v5_membered(B) & v5_membered(A) -> v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4787 (all A (v1_rat_1(A) -> v1_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4788 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v4_ordinal2(B) & v1_int_1(B) & v1_rat_1(B) & v1_xreal_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4789 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> B = A))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4790 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> -(r2_hidden(C,A) & r2_hidden(C,B)))) <-> r1_xboole_0(A,B)))))) # label(d20_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.65 4791 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xcmplx_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d16_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4792 (exists A (v5_membered(A) & (all B (v4_ordinal2(B) -> (p1_s5_membered(B) <-> r2_hidden(B,A)))))) # label(s5_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4793 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4794 (all A all B (v2_membered(A) & v2_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4795 (all A ((all B (r2_hidden(B,A) -> v4_ordinal2(B))) <-> v5_membered(A))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4796 (all A all B all C (v1_rat_1(A) & v1_rat_1(B) & v1_rat_1(C) -> v1_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4797 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_rat_1(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d18_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4798 (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]. 87.61/85.66 4799 (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]. 87.61/85.66 4800 (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]. 87.61/85.66 4801 (all A all B (v3_membered(B) & v3_membered(A) -> v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc24_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4802 (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]. 87.61/85.66 4803 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B) & v5_membered(B) & v4_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4804 (all A (v2_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_xreal_0(B))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4805 (exists A ((all B (v1_int_1(B) -> (p1_s4_membered(B) <-> r2_hidden(B,A)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4806 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4807 (all A all B all C (v1_xcmplx_0(C) & v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4808 (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]. 87.61/85.66 4809 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4810 (exists A (-v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v5_membered(A) & v4_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4811 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (A = B <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4812 (all A all B (v5_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4813 (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]. 87.61/85.66 4814 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xreal_0(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4815 (all A all B (v2_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc30_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4816 (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]. 87.61/85.66 4817 (all A (v3_membered(A) -> (all B (m1_subset_1(B,A) -> v1_rat_1(B) & v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4818 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4819 (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]. 87.61/85.66 4820 (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]. 87.61/85.66 4821 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v3_membered(B) & v4_membered(B) & v2_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4822 (exists A (v2_membered(A) & (all B (v1_xreal_0(B) -> (r2_hidden(B,A) <-> p1_s2_membered(B)))))) # label(s2_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4823 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d7_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4824 (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]. 87.61/85.66 4825 (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]. 87.61/85.66 4826 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4827 (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]. 87.61/85.66 4828 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4829 (all A (v1_xboole_0(A) -> v5_membered(A) & v4_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4830 (all A all B (v1_rat_1(B) & v1_rat_1(A) -> v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc14_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4831 (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]. 87.61/85.66 4832 (all A (v1_int_1(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4833 (all A (v1_xcmplx_0(A) -> v1_xreal_0(k16_complex1(A)) & v1_xcmplx_0(k16_complex1(A)))) # label(fc4_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4834 (all A (v1_xcmplx_0(A) -> m1_subset_1(k18_complex1(A),k1_numbers))) # label(dt_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4835 $T # label(t85_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4836 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k11_complex1(A,B) = 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)))))) # label(d12_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4837 $T # label(t6_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4838 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k16_complex1(A)))) # label(dt_k16_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4839 $T # label(t88_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4840 $T # label(t20_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4841 $T # label(t76_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4842 (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]. 87.61/85.66 4843 (all A (v1_xcmplx_0(A) -> r1_xreal_0(np__0,k17_complex1(A)))) # label(t132_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4844 (all A (m1_subset_1(A,k2_numbers) -> k4_real_1(np__2,k4_real_1(k3_complex1(A),k4_complex1(A))) = k4_complex1(k9_complex1(A,A)) & k5_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))) = k3_complex1(k9_complex1(A,A)))) # label(t32_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4845 $T # label(t7_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4846 (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]. 87.61/85.66 4847 (all A (v1_xcmplx_0(A) -> k17_complex1(k4_xcmplx_0(A)) = k17_complex1(A))) # label(t138_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4848 (all A (m1_subset_1(A,k2_numbers) -> k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))) = k3_complex1(k9_complex1(A,k15_complex1(A))) & np__0 = k4_complex1(k9_complex1(A,k15_complex1(A))))) # label(t126_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4849 (all A (m1_subset_1(A,k2_numbers) -> k15_complex1(k10_complex1(A)) = k10_complex1(k15_complex1(A)))) # label(t119_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4850 (all A (m1_subset_1(A,k2_numbers) -> v1_xcmplx_0(A))) # label(cc1_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4851 (all A (v1_xcmplx_0(A) -> k4_complex1(A) = k2_complex1(A))) # label(redefinition_k4_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4852 $T # label(dt_k1_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4853 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k2_complex1(A)) & v1_xreal_0(k2_complex1(A)))) # label(fc2_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4854 $T # label(t99_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4855 (all A (v1_xcmplx_0(A) -> k16_complex1(A) = k16_complex1(k16_complex1(A)))) # label(projectivity_k16_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4856 $T # label(t51_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4857 $T # label(t23_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4858 $T # label(t44_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4859 $T # label(t50_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4860 $T # label(d1_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4861 $T # label(t81_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4862 $T # label(t21_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4863 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k11_complex1(A,B),k2_numbers))) # label(dt_k11_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4864 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (k2_xcmplx_0(k5_square_1(A),k5_square_1(B)) = np__0 <-> np__0 = A & np__0 = B))))) # label(t2_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4865 (all A (v1_xcmplx_0(A) -> (k15_complex1(A) = np__0 -> np__0 = A))) # label(t114_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4866 (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]. 87.61/85.66 4867 $T # label(t73_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4868 (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]. 87.61/85.66 4869 (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]. 87.61/85.66 4870 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 = k17_complex1(k6_xcmplx_0(A,B)) <-> B = A))))) # label(t147_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4871 $T # label(t69_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4872 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_complex1(A) = np__0 & k3_complex1(B) = np__0 -> k1_real_1(k4_real_1(k4_complex1(A),k4_complex1(B))) = k3_complex1(k3_xcmplx_0(A,B)) & k4_complex1(k3_xcmplx_0(A,B)) = np__0))))) # label(t31_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4873 (all A (v1_xcmplx_0(A) -> (k3_complex1(A) = np__0 -> k17_complex1(A) = k17_complex1(k4_complex1(A))))) # label(t137_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4874 $T # label(t65_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4875 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (k3_complex1(B) = k3_complex1(A) & k4_complex1(A) = k4_complex1(B) -> A = B))))) # label(t9_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4876 (all A (v1_xcmplx_0(A) -> k3_complex1(k4_xcmplx_0(A)) = k1_real_1(k3_complex1(A)) & k1_real_1(k4_complex1(A)) = k4_complex1(k4_xcmplx_0(A)))) # label(t34_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4877 $T # label(t58_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4878 $T # label(t100_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4879 $T # label(t97_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4880 $T # label(t52_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4881 $T # label(t61_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4882 $T # label(t86_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4883 $T # label(t83_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4884 (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]. 87.61/85.66 4885 $T # label(t94_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4886 (all A (v1_xcmplx_0(A) -> r1_xreal_0(k3_complex1(A),k17_complex1(A)))) # label(t140_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4887 $T # label(t101_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4888 $T # label(t22_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4889 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) = k5_arytm_0(A,B))))) # label(t27_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4890 $T # label(t102_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4891 $T # label(t39_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4892 (all A (v1_xcmplx_0(A) -> m1_subset_1(k3_complex1(A),k1_numbers))) # label(dt_k3_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4893 $T # label(t4_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4894 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k1_complex1(A)) & v1_xreal_0(k1_complex1(A)))) # label(fc1_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4895 $T # label(t96_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4896 $T # label(t77_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4897 $T # label(t14_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4898 $T # label(t95_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4899 (all A (v1_xcmplx_0(A) -> (np__0 = k17_complex1(A) -> A = np__0))) # label(t131_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4900 (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]. 87.61/85.66 4901 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k6_real_1(k3_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B)))) = k3_complex1(k13_complex1(A,B)) & k4_complex1(k13_complex1(A,B)) = k6_real_1(k5_real_1(k4_real_1(k3_complex1(B),k4_complex1(A)),k4_real_1(k3_complex1(A),k4_complex1(B))),k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B)))))))) # label(t82_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4902 $T # label(t108_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4903 $T # label(t38_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4904 $T # label(t84_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4905 $T # label(t105_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4906 $T # label(t117_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4907 (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]. 87.61/85.66 4908 (all A (v1_xreal_0(A) -> (r1_xreal_0(A,np__0) -> k17_complex1(A) = k4_xcmplx_0(A)))) # label(t156_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4909 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k4_complex1(k11_complex1(A,B)) = k5_real_1(k4_complex1(A),k4_complex1(B)) & k5_real_1(k3_complex1(A),k3_complex1(B)) = k3_complex1(k11_complex1(A,B)))))) # label(t48_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4910 $T # label(t71_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4911 (all A (v1_xcmplx_0(A) -> k18_complex1(A) = k18_complex1(k18_complex1(A)))) # label(projectivity_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4912 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k2_xcmplx_0(A,B) = k8_complex1(A,B))) # label(redefinition_k8_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4913 (all A (v1_xcmplx_0(A) -> v1_xcmplx_0(k14_complex1(A)))) # label(dt_k14_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4914 $T # label(t74_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4915 (all A (v1_xcmplx_0(A) -> r1_xreal_0(k4_complex1(A),k17_complex1(A)))) # label(t141_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4916 $T # label(dt_k2_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4917 (all A (m1_subset_1(A,k1_numbers) -> k4_complex1(k3_xcmplx_0(A,k7_complex1)) = A)) # label(t26_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4918 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k15_complex1(k13_complex1(A,B)) = k13_complex1(k15_complex1(A),k15_complex1(B)))))) # label(t123_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4919 (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]. 87.61/85.66 4920 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k11_complex1(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k11_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4921 (all A (m1_subset_1(A,k2_numbers) -> k10_complex1(k10_complex1(A)) = A)) # label(involutiveness_k10_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4922 (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]. 87.61/85.66 4923 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> A = k17_complex1(A)))) # label(t129_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4924 $T # label(t8_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4925 $T # label(t67_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4926 (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]. 87.61/85.66 4927 $T # label(t111_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4928 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> -(r1_xreal_0(k17_complex1(k6_xcmplx_0(A,B)),np__0) & A != B) & -(-r1_xreal_0(k17_complex1(k6_xcmplx_0(A,B)),np__0) & A = B))))) # label(t148_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4929 $T # label(t18_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4930 $T # label(t78_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4931 (all A (m1_subset_1(A,k2_numbers) -> (k4_complex1(A) = np__0 -> k4_complex1(k12_complex1(A)) = np__0 & k2_real_1(k3_complex1(A)) = k3_complex1(k12_complex1(A)) | np__0 = k3_complex1(A)))) # label(t79_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4932 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> 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)) = k9_complex1(A,B))))) # label(d10_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4933 $T # label(t35_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4934 $T # label(t41_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4935 $T # label(t1_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4936 $T # label(t98_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4937 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k4_complex1(k3_xcmplx_0(A,B)) = k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k3_complex1(B),k4_complex1(A))) & 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)))))) # label(t24_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4938 (all A (v1_xcmplx_0(A) -> (all B ((-r2_hidden(A,k1_numbers) -> (B = k2_complex1(A) <-> (exists C (m2_relset_1(C,np__2,k1_numbers) & k1_funct_1(C,np__1) = B & A = C & v1_funct_2(C,np__2,k1_numbers) & v1_funct_1(C))))) & (r2_hidden(A,k1_numbers) -> (k2_complex1(A) = B <-> np__0 = B)))))) # label(d3_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4939 $T # label(t16_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4940 (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]. 87.61/85.66 4941 (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]. 87.61/85.66 4942 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (np__0 = k4_complex1(A) & k4_complex1(B) = np__0 -> 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]. 87.61/85.66 4943 (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]. 87.61/85.66 4944 (all A (v1_xcmplx_0(A) -> k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))) = k17_complex1(k3_xcmplx_0(A,A)))) # label(t154_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4945 $T # label(t89_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4946 (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]. 87.61/85.66 4947 (all A (v1_xcmplx_0(A) -> k15_complex1(k15_complex1(A)) = A)) # label(involutiveness_k15_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4948 $T # label(t56_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4949 (all A (v1_xcmplx_0(A) -> m1_subset_1(k15_complex1(A),k2_numbers))) # label(dt_k15_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4950 (all A (v1_xreal_0(A) -> k17_complex1(A) = k4_xcmplx_0(A) | k17_complex1(A) = A)) # label(t157_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4951 (all A (m1_subset_1(A,k2_numbers) -> np__0 = k4_complex1(k8_complex1(A,k15_complex1(A))) & k3_complex1(k8_complex1(A,k15_complex1(A))) = k4_real_1(np__2,k3_complex1(A)))) # label(t127_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4952 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> k3_complex1(k2_xcmplx_0(A,B)) = k3_real_1(k3_complex1(A),k3_complex1(B)) & k4_complex1(k2_xcmplx_0(A,B)) = k3_real_1(k4_complex1(A),k4_complex1(B)))))) # label(t19_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4953 (all A (m1_subset_1(A,k2_numbers) -> k3_complex1(k11_complex1(A,k15_complex1(A))) = np__0 & k4_real_1(np__2,k4_complex1(A)) = k4_complex1(k11_complex1(A,k15_complex1(A))))) # label(t128_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4954 $T # label(t53_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4955 $T # label(t42_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4956 $T # label(t103_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4957 $T # label(t55_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4958 (all A (v1_funct_1(A) & m2_relset_1(A,np__2,k1_numbers) & v1_funct_2(A,np__2,k1_numbers) -> (exists B (m1_subset_1(B,k1_numbers) & (exists C (A = k5_funct_4(k1_numbers,np__0,np__1,B,C) & m1_subset_1(C,k1_numbers))))))) # label(t5_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4959 $T # label(t62_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4960 (all A (v1_xcmplx_0(A) -> k15_complex1(A) = k14_complex1(A))) # label(redefinition_k15_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4961 (all A (v1_xcmplx_0(A) -> m1_subset_1(k4_complex1(A),k1_numbers))) # label(dt_k4_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4962 $T # label(t11_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4963 $T # label(t107_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4964 (all A (v1_xcmplx_0(A) -> k17_complex1(A) = k16_complex1(A))) # label(redefinition_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4965 (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]. 87.61/85.66 4966 (all A (m1_subset_1(A,k2_numbers) -> k12_complex1(k12_complex1(A)) = A)) # label(involutiveness_k12_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4967 $T # label(t90_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4968 (all A (v1_xcmplx_0(A) -> -(r1_xreal_0(k17_complex1(A),np__0) & A != np__0) & -(A = np__0 & -r1_xreal_0(k17_complex1(A),np__0)))) # label(t133_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4969 (all A (v1_xcmplx_0(A) -> k3_complex1(k15_complex1(A)) = k3_complex1(A) & k4_complex1(k15_complex1(A)) = k1_real_1(k4_complex1(A)))) # label(t112_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4970 (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]. 87.61/85.66 4971 (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]. 87.61/85.66 4972 (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]. 87.61/85.66 4973 (all A (v1_xcmplx_0(A) -> m1_subset_1(k17_complex1(A),k1_numbers))) # label(dt_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4974 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k8_complex1(A,B),k2_numbers))) # label(dt_k8_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4975 $T # label(t92_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4976 (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]. 87.61/85.66 4977 (all A (v1_xcmplx_0(A) -> A = k14_complex1(k14_complex1(A)))) # label(involutiveness_k14_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4978 (all A (v1_xcmplx_0(A) -> k17_complex1(k5_xcmplx_0(A)) = k2_real_1(k17_complex1(A)))) # label(t152_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4979 $T # label(t93_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4980 $T # label(d4_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4981 $T # label(t106_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4982 (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]. 87.61/85.66 4983 (all A (v1_xcmplx_0(A) -> k18_complex1(A) = k16_complex1(A))) # label(redefinition_k18_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4984 $T # label(t63_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4985 $T # label(t45_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4986 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k1_numbers) -> (k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) = k2_xcmplx_0(C,k3_xcmplx_0(D,k7_complex1)) -> B = D & A = C))))))))) # label(t163_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4987 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k2_square_1(A,B) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),k17_complex1(k6_xcmplx_0(A,B))),np__2))))) # label(t160_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4988 (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]. 87.61/85.66 4989 (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]. 87.61/85.66 4990 $T # label(t33_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4991 (all A (v1_xcmplx_0(A) -> k9_square_1(k3_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A)))) = k16_complex1(A))) # label(d16_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4992 $T # label(t60_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4993 $T # label(t87_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4994 (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]. 87.61/85.66 4995 (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]. 87.61/85.66 4996 (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]. 87.61/85.66 4997 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k4_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = B & k3_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = A)))) # label(t28_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 4998 (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]. 87.61/85.66 4999 $T # label(t49_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5000 $T # label(t70_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5001 $T # label(t43_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5002 $T # label(t46_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5003 $T # label(t54_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5004 $T # label(t75_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5005 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k7_xcmplx_0(A,B) = k13_complex1(A,B))) # label(redefinition_k13_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5006 (all A (v1_xreal_0(A) -> k5_square_1(A) = k7_square_1(k17_complex1(A)))) # label(t161_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5007 (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]. 87.61/85.66 5008 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k11_complex1(k15_complex1(A),k15_complex1(B)) = k15_complex1(k11_complex1(A,B)))))) # label(t120_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5009 (all A (v1_xcmplx_0(A) -> k1_complex1(A) = k3_complex1(A))) # label(redefinition_k3_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5010 $T # label(t3_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5011 (all A (v1_xcmplx_0(A) -> k17_complex1(A) = k17_complex1(k15_complex1(A)))) # label(t139_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5012 (all A (m1_subset_1(A,k2_numbers) -> (np__0 = k3_complex1(A) -> k1_real_1(k2_real_1(k4_complex1(A))) = k4_complex1(k12_complex1(A)) & k3_complex1(k12_complex1(A)) = np__0 | k4_complex1(A) = np__0))) # label(t80_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5013 $T # label(t66_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5014 (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]. 87.61/85.66 5015 (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]. 87.61/85.66 5016 $T # label(t47_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5017 $T # label(t68_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5018 (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]. 87.61/85.66 5019 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> (np__0 = k3_complex1(B) & np__0 = k3_complex1(A) -> k3_complex1(k13_complex1(A,B)) = k6_real_1(k4_complex1(A),k4_complex1(B)) & np__0 = k4_complex1(k13_complex1(A,B)) | np__0 = k4_complex1(B)))))) # label(t110_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5020 $T # label(t10_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5021 (all A (v1_xcmplx_0(A) -> (all B ((-r2_hidden(A,k1_numbers) -> ((exists C (v1_funct_2(C,np__2,k1_numbers) & C = A & k1_funct_1(C,np__0) = B & m2_relset_1(C,np__2,k1_numbers) & v1_funct_1(C))) <-> B = k1_complex1(A))) & (r2_hidden(A,k1_numbers) -> (k1_complex1(A) = B <-> B = A)))))) # label(d2_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5022 (all A (v1_xcmplx_0(A) -> k17_complex1(A) = k17_complex1(k17_complex1(A)))) # label(projectivity_k17_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5023 $T # label(t91_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5024 $T # label(t59_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5025 $T # label(t40_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5026 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> (np__0 = k4_complex1(A) & np__0 = k4_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)) | np__0 = k3_complex1(B)))))) # label(t109_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5027 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k3_xcmplx_0(A,B) = k9_complex1(A,B))) # label(redefinition_k9_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5028 (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]. 87.61/85.66 5029 (all A (v1_xcmplx_0(A) -> (all B (v1_xcmplx_0(B) -> (A = B <-> k4_complex1(A) = k4_complex1(B) & k3_complex1(B) = k3_complex1(A)))))) # label(d5_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5030 (all A (m1_subset_1(A,k2_numbers) -> (all B (m1_subset_1(B,k2_numbers) -> k9_complex1(k15_complex1(A),k15_complex1(B)) = k15_complex1(k9_complex1(A,B)))))) # label(t121_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5031 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k9_complex1(A,B) = k9_complex1(B,A))) # label(commutativity_k9_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5032 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k8_complex1(B,A) = k8_complex1(A,B))) # label(commutativity_k8_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5033 $T # label(t104_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5034 $T # label(t36_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5035 $T # label(t57_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5036 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k9_complex1(A,B),k2_numbers))) # label(dt_k9_complex1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5037 (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]. 87.61/85.66 5038 $T # label(t8_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5039 (all A (v1_xreal_0(A) -> k1_absvalue(k1_absvalue(A)) = k1_absvalue(A))) # label(t36_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5040 (all A (v1_xreal_0(A) -> (A != np__0 -> 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]. 87.61/85.66 5041 (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]. 87.61/85.66 5042 (all A (v1_xreal_0(A) -> -(r1_xreal_0(A,np__0) & np__1 = k1_absvalue(A)))) # label(t31_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5043 (all A (v1_xreal_0(A) -> (-r1_xreal_0(A,np__0) -> k1_absvalue(A) = np__1) & (-r1_xreal_0(np__0,A) -> k1_absvalue(A) = k1_real_1(np__1)) & (r1_xreal_0(np__0,A) & r1_xreal_0(A,np__0) -> k1_absvalue(A) = np__0))) # label(d2_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5044 (all A (v1_xreal_0(A) -> A = k3_xcmplx_0(k18_complex1(A),k1_absvalue(A)))) # label(t34_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5045 $T # label(t4_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5046 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(k18_complex1(A),B) & r1_xreal_0(k18_complex1(C),D) -> r1_xreal_0(k18_complex1(k2_xcmplx_0(A,C)),k2_xcmplx_0(B,D))))))))))) # label(t21_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5047 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (k18_complex1(k2_xcmplx_0(A,B)) = k3_real_1(k18_complex1(A),k18_complex1(B)) -> r1_xreal_0(np__0,k3_xcmplx_0(A,B))))))) # label(t25_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5048 (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]. 87.61/85.66 5049 (all A (v1_xreal_0(A) -> k18_complex1(A) = k4_xcmplx_0(A) | k18_complex1(A) = A)) # label(t1_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5050 $T # label(t16_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5051 (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]. 87.61/85.66 5052 (all A (v1_xreal_0(A) -> (k18_complex1(A) = np__0 <-> A = np__0))) # label(t7_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5053 (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]. 87.61/85.66 5054 (all A (v1_xreal_0(A) -> (np__0 != A -> np__1 = k4_real_1(k18_complex1(A),k18_complex1(k7_xcmplx_0(np__1,A)))))) # label(t14_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5055 $T # label(t29_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5056 $T # label(t3_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5057 $T # label(t19_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5058 $T # label(dt_k1_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5059 $T # label(t5_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5060 (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]. 87.61/85.66 5061 (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]. 87.61/85.66 5062 (all A (v1_xreal_0(A) -> k1_absvalue(k7_xcmplx_0(np__1,A)) = k7_xcmplx_0(np__1,k1_absvalue(A)))) # label(t39_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5063 $T # label(t18_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5064 (all A (v1_xreal_0(A) -> -(k1_real_1(np__1) = k1_absvalue(A) & r1_xreal_0(np__0,A)))) # label(t32_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5065 $T # label(t6_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5066 (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]. 87.61/85.66 5067 (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]. 87.61/85.66 5068 (all A (m1_subset_1(A,k1_numbers) -> k1_absvalue(A) = k2_absvalue(A))) # label(redefinition_k2_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5069 (all A (v1_xreal_0(A) -> -(r1_xreal_0(np__0,A) & A != np__0 & k4_xcmplx_0(A) = k18_complex1(A)))) # label(t9_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5070 $T # label(t27_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5071 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k7_xcmplx_0(k1_absvalue(A),k1_absvalue(B)) = k1_absvalue(k7_xcmplx_0(A,B)))))) # label(t42_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5072 $T # label(t30_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5073 (all A (v1_xreal_0(A) -> r1_xreal_0(A,k18_complex1(A)) & r1_xreal_0(k1_real_1(k18_complex1(A)),A))) # label(t11_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5074 (all A (v1_xreal_0(A) -> (np__0 = k1_absvalue(A) -> A = np__0))) # label(t33_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5075 (all A (v1_xreal_0(A) -> (-r1_xreal_0(np__0,A) -> k4_xcmplx_0(A) = k16_complex1(A)) & (r1_xreal_0(np__0,A) -> k16_complex1(A) = A))) # label(d1_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5076 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (-r1_xreal_0(k7_xcmplx_0(A,B),np__0) -> k6_real_1(k9_square_1(k18_complex1(A)),k9_square_1(k18_complex1(B))) = k8_square_1(k7_xcmplx_0(A,B))))))) # label(t23_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5077 $T # label(t10_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5078 $T # label(t28_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5079 $T # label(t13_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5080 (all A (v1_xreal_0(A) -> k18_complex1(k7_xcmplx_0(np__1,A)) = k6_real_1(np__1,k18_complex1(A)))) # label(t15_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5081 $T # label(t22_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5082 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> k1_absvalue(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k1_absvalue(A),k1_absvalue(B)))))) # label(t35_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5083 $T # label(t17_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5084 $T # label(t2_absvalue) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5085 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_relat_1(B)) -> r2_wellord2(A,k9_relat_1(B,A))))) # label(t60_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5086 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5087 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(A,B) <-> -r1_tarski(B,A)))))) # label(t14_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5088 (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]. 87.61/85.66 5089 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5090 (all A (v1_finset_1(A) -> v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_ordinal1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5091 (all A (k1_xboole_0 = A <-> r2_wellord2(A,k1_xboole_0))) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5092 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5093 (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]. 87.61/85.66 5094 (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]. 87.61/85.66 5095 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5096 (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]. 87.61/85.66 5097 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5098 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> r2_wellord2(k4_xboole_0(B,k1_tarski(A)),k4_xboole_0(B,k1_tarski(C))))) # label(t59_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5099 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5100 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5101 (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]. 87.61/85.66 5102 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5103 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5104 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5105 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(A,B) -> A = B))))) # label(t64_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5106 (all A all B all C all D (r2_wellord2(A,B) & r2_hidden(C,A) & r2_hidden(D,B) -> r2_wellord2(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(B,k1_tarski(D))))) # label(t61_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5107 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5108 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5109 (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]. 87.61/85.66 5110 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5111 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (B = A <-> r2_wellord2(A,B)))))) # label(t8_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5112 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5113 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5114 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5115 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5116 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5117 (all A (m1_subset_1(A,k5_numbers) -> v3_ordinal1(A) & v1_xreal_0(A) & v1_card_1(A) & -v3_xreal_0(A) & v1_finset_1(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5118 (all A ((exists B (v3_ordinal1(B) & (all C (v3_ordinal1(C) -> (r2_wellord2(C,B) -> r1_ordinal1(B,C)))) & A = B)) <-> v1_card_1(A))) # label(d1_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5119 (all A all B (v1_card_1(B) -> ((all C (v1_card_1(C) -> (r2_hidden(k1_card_1(A),C) -> r1_tarski(B,C)))) & r2_hidden(k1_card_1(A),B) <-> k2_card_1(A) = B))) # label(d6_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5120 (all A all B ((exists C (v1_funct_1(C) & r1_tarski(k2_relat_1(C),B) & A = k1_relat_1(C) & v2_funct_1(C) & v1_relat_1(C))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t26_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5121 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5122 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5123 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5124 (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]. 87.61/85.66 5125 (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]. 87.61/85.66 5126 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.66 5127 (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]. 87.61/85.67 5128 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k3_card_1(A),k3_card_1(B)) <-> r2_hidden(A,B)))))) # label(t41_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5129 (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]. 87.61/85.67 5130 (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]. 87.61/85.67 5131 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) <-> r1_ordinal1(A,B)))))) # label(t56_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5132 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5133 (all A (v1_finset_1(A) -> k1_card_1(A) = k4_card_1(A))) # label(redefinition_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5134 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | k1_funct_1(C,D) = k1_card_1(k8_ordinal2(k2_ordinal1(C,D)))))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k2_card_1(k3_tarski(k1_tarski(k1_funct_1(C,D)))) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = k1_card_1(k5_numbers) & B = k1_ordinal2(C) & v1_funct_1(C))) <-> B = k3_card_1(A))))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5135 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5136 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5137 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5138 (exists A (v1_ordinal1(A) & v1_card_1(A) & v1_finset_1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5139 (all A all B (v1_card_1(B) -> (k1_card_1(A) = B <-> r2_wellord2(A,B)))) # label(d5_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5140 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5141 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5142 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5143 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(A,B) <-> r1_tarski(A,B) & B != A))))) # label(t13_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5144 (all A (v1_card_1(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(cc1_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5145 (all A (v3_ordinal1(A) -> v1_card_1(k3_card_1(A)) & v3_ordinal1(k3_card_1(A)) & v2_ordinal1(k3_card_1(A)) & v1_ordinal1(k3_card_1(A)))) # label(fc1_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5146 (all A all B (r1_tarski(k1_zfmisc_1(A),B) -> -r2_wellord2(A,B) & r2_hidden(k1_card_1(A),k1_card_1(B)))) # label(t45_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5147 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5148 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5149 (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]. 87.61/85.67 5150 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5151 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5152 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5153 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5154 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(A) = k1_card_1(B) -> A = B))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5155 (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]. 87.61/85.67 5156 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> v1_finset_1(k1_card_1(A)) & v1_finset_1(A))) # label(t69_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5157 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5158 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r2_wellord2(A,B) -> k4_card_1(A) = k4_card_1(B)))))) # label(t81_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5159 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5160 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) <-> B = k4_card_1(A)))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5161 (all A all B (r2_wellord2(A,k1_tarski(B)) <-> (exists C k1_tarski(C) = A))) # label(t48_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5162 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(k3_card_1(A),k3_card_1(B)) <-> r1_ordinal1(A,B)))))) # label(t43_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5163 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5164 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5165 (all A (v1_card_1(A) -> (p1_s1_card_1(A) -> p1_s1_card_1(k2_card_1(A))))) & (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s1_card_1(B)))) & v2_card_1(A) -> A = k1_xboole_0 | p1_s1_card_1(A)))) & p1_s1_card_1(k1_xboole_0) -> (all A (v1_card_1(A) -> p1_s1_card_1(A))) # label(s1_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5166 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5167 (all A all B (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> (exists C (v1_funct_1(C) & r1_tarski(A,k2_relat_1(C)) & k1_relat_1(C) = B & v1_relat_1(C))))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5168 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5169 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5170 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k3_card_1(C) = k1_funct_1(B,C)))) & A = k1_relat_1(B) -> k1_card_1(k8_ordinal2(B)) = k3_card_1(A))))))) # label(t40_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5171 (all A all B (k1_card_1(B) = k1_card_1(A) -> k2_card_1(A) = k2_card_1(B))) # label(t34_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5172 (all A all B all C all D (r1_xboole_0(C,D) & r2_wellord2(B,D) & r2_wellord2(A,C) & r1_xboole_0(A,B) -> r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)))) # label(t58_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5173 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5174 (all A (v1_card_1(A) -> (v2_card_1(A) <-> (all B (v1_card_1(B) -> A != k2_card_1(B)))))) # label(d7_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5175 (all A (v1_finset_1(A) & v1_card_1(A) -> (exists B (k1_card_1(B) = A & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(t86_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5176 (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]. 87.61/85.67 5177 (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]. 87.61/85.67 5178 (all A -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,B))) & v1_finset_1(A))) # label(t74_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5179 (all A (m1_subset_1(A,k5_numbers) -> v3_ordinal1(A) & v1_xcmplx_0(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_xreal_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5180 (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]. 87.61/85.67 5181 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5182 (all A all B ((exists C k1_tarski(C) = A) <-> k1_card_1(k1_tarski(B)) = k1_card_1(A))) # label(t49_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5183 (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]. 87.61/85.67 5184 (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]. 87.61/85.67 5185 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5186 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5187 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5188 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k3_card_1(B) = k3_card_1(A) -> B = A))))) # label(t42_card_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5189 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s2_finseq_1)) -> k1_funct_1(A,B) = f2_s2_finseq_1(B)))) & k3_finseq_1(A) = f1_s2_finseq_1)) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5190 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5191 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5192 (exists A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5193 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k3_finseq_1(B) = k3_finseq_1(A) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) -> B = A))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5194 (all A all B (m1_finseq_1(B,A) -> v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(dt_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5195 (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]. 87.61/85.67 5196 (all A k5_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5197 (all A (v1_finset_1(A) <-> (exists B (v1_relat_1(B) & A = k2_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B))))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5198 (all A all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (np__2 = k3_finseq_1(C) & k1_funct_1(C,np__2) = B & k1_funct_1(C,np__1) = A <-> k10_finseq_1(A,B) = C))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5199 (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]. 87.61/85.67 5200 (all A (v1_relat_1(A) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k2_finseq_1(B) = k1_relat_1(A))) <-> v1_finseq_1(A)))) # label(d2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5201 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t84_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5202 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5203 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5204 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5205 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5206 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5207 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5208 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k3_finseq_1(A) = np__0 <-> A = k1_xboole_0))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5209 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> A = k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),np__1)))) # label(t59_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5210 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> -((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(A = D & r2_hidden(k1_nat_1(k3_finseq_1(C),D),k4_finseq_1(k7_finseq_1(C,B)))))) & r2_hidden(A,k4_finseq_1(B))))))) # label(t40_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5211 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> A = k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),np__1))) # label(t58_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5212 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))) & -r2_hidden(C,k4_finseq_1(A)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(C = k1_nat_1(k3_finseq_1(A),D) & r2_hidden(D,k4_finseq_1(B)))))))))))) # label(t38_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5213 (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]. 87.61/85.67 5214 (all A (v4_ordinal2(A) -> A = k4_card_1(k2_finseq_1(A)))) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5215 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (k2_relat_1(B) = k2_relat_1(A) & v2_funct_1(A) & v2_funct_1(B) -> k3_finseq_1(B) = k3_finseq_1(A)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5216 (all A exists B (m1_finseq_1(B,A) & v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v2_funct_1(B) & v1_relat_1(B))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5217 (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]. 87.61/85.67 5218 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k1_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5219 (all A k9_finseq_1(A) = k5_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5220 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k3_finseq_1(A) = np__0 <-> A = k6_finseq_1(B))))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5221 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(A = k4_tarski(C,k1_funct_1(B,C)) & r2_hidden(C,k4_finseq_1(B))))) & r2_hidden(A,B)))) # label(t16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5222 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) -> v1_finset_1(k1_relat_1(A)))) # label(fc17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5223 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> -(r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) & (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> C != k7_finseq_1(A,E))) & k7_finseq_1(A,B) = k7_finseq_1(C,D)))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5224 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5225 (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]. 87.61/85.67 5226 (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]. 87.61/85.67 5227 (all A (v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)))) # label(dt_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5228 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k4_finseq_1(A) = k1_relat_1(A))) # label(redefinition_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5229 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5230 p1_s3_finseq_1(k1_xboole_0) & (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (p1_s3_finseq_1(A) -> p1_s3_finseq_1(k7_finseq_1(A,k9_finseq_1(B))))))) -> (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5231 (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]. 87.61/85.67 5232 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (p1_s1_finseq_1(A,B) & p1_s1_finseq_1(A,C) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) -> C = B)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((all B -p1_s1_finseq_1(A,B)) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1))))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_1)) -> p1_s1_finseq_1(B,k1_funct_1(A,B))))) & k4_finseq_1(A) = k2_finseq_1(f1_s1_finseq_1))) # label(s1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5233 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k9_finseq_1(A) <-> k1_funct_1(B,np__1) = A & k1_relat_1(B) = k2_finseq_1(np__1)))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5234 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5235 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)) & v1_finseq_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5236 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k1_xboole_0 = A <-> k1_xboole_0 = k2_relat_1(A)))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5237 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & -v1_xboole_0(B) & v1_finseq_1(A) & v1_funct_1(A) -> -v1_xboole_0(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5238 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> A = k7_finseq_1(k1_xboole_0,A) & A = k7_finseq_1(A,k1_xboole_0))) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5239 (exists A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5240 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5241 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_relat_1(A) = k2_finseq_1(B) <-> B = k3_finseq_1(A)))))) # label(d3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5242 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5243 (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]. 87.61/85.67 5244 (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]. 87.61/85.67 5245 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(k1_nat_1(k3_finseq_1(C),A),k4_finseq_1(k7_finseq_1(C,B)))))))))) # label(t41_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5246 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5247 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C))) -> r2_hidden(B,k2_finseq_1(k2_xcmplx_0(A,C))) & r2_hidden(B,k2_finseq_1(A)) | r1_xreal_0(B,np__0)))))))) # label(t82_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5248 (all A all B (m1_finseq_1(B,A) -> v1_xboole_0(k16_finseq_1(A,B,np__0)) & v1_funct_1(k16_finseq_1(A,B,np__0)) & v1_finset_1(k16_finseq_1(A,B,np__0)) & v1_finseq_1(k16_finseq_1(A,B,np__0)) & v2_funct_1(k16_finseq_1(A,B,np__0)) & v1_relat_1(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5249 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(B)) -> k1_funct_1(B,C) = k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C))))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5250 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((all B (m1_subset_1(B,f1_s5_finseq_1) -> -p1_s5_finseq_1(A,B))) & r2_hidden(A,k2_finseq_1(f2_s5_finseq_1))))) -> (exists A (k4_finseq_1(A) = k2_finseq_1(f2_s5_finseq_1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f2_s5_finseq_1)) -> p1_s5_finseq_1(B,k1_funct_1(A,B))))) & m2_finseq_1(A,f1_s5_finseq_1))) # label(s5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5251 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> v1_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A))))))) # label(t20_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5252 (all A (v4_ordinal2(A) -> A = np__0 | r2_hidden(A,k2_finseq_1(A)))) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5253 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> A = k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)))))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5254 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5255 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(k2_finseq_1(A),k2_finseq_1(B)) -> A = B))))) # label(t74_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5256 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (exists C (A = k3_finseq_1(C) & m2_finseq_1(C,B))))))) # label(t24_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5257 (all A k1_tarski(k4_tarski(np__1,A)) = k9_finseq_1(A)) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5258 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (C = k7_finseq_1(A,B) <-> k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) = k4_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D))))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(A,D) = k1_funct_1(C,D))))))))))) # label(d7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5259 (all A ((exists B (v4_ordinal2(B) & r1_tarski(A,k2_finseq_1(B)))) -> (all B (m2_finseq_1(B,k5_numbers) -> (k2_relat_1(B) = A & (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(-r1_xreal_0(D,C) & r1_xreal_0(F,E) & F = k1_funct_1(B,D) & E = k1_funct_1(B,C) & r1_xreal_0(D,k3_finseq_1(B)) & r1_xreal_0(np__1,C)))))))))) <-> B = k14_finseq_1(A)))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5260 (all A all B all C (m1_finseq_1(B,A) & m1_finseq_1(C,A) -> k7_finseq_1(B,C) = k8_finseq_1(A,B,C))) # label(redefinition_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5261 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5262 (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]. 87.61/85.67 5263 (all A (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)))) # label(fc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5264 (all A exists B (m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5265 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5266 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) <-> r1_xreal_0(A,B)))))) # label(t7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5267 (all A all B all C (v1_relat_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)) & v1_finset_1(k11_finseq_1(A,B,C)))) # label(fc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5268 (all A all B all C (k7_finseq_1(k9_finseq_1(A),k10_finseq_1(B,C)) = k11_finseq_1(A,B,C) & k7_finseq_1(k10_finseq_1(A,B),k9_finseq_1(C)) = k11_finseq_1(A,B,C))) # label(t60_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5269 (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]. 87.61/85.67 5270 (exists A (v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) & -v1_xboole_0(A))) # label(rc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5271 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5272 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)))))) # label(t35_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5273 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (m2_finseq_1(k7_finseq_1(A,B),C) -> m2_finseq_1(B,C) & m2_finseq_1(A,C))))))) # label(t50_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5274 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,np__1)),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5275 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5276 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> k15_finseq_1(A) = k5_relat_1(k14_finseq_1(k1_relat_1(A)),A))) # label(d14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5277 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (A = k1_funct_1(B,np__1) & np__1 = k3_finseq_1(B) <-> k9_finseq_1(A) = B))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5278 (all A ((exists B (r1_tarski(A,k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) -> (A = k1_xboole_0 <-> k1_xboole_0 = k14_finseq_1(A)))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5279 (all A all B (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)))) # label(dt_k7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5280 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B))) -> r1_xreal_0(C,k3_finseq_1(A)) | k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A)))))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5281 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) & v1_xboole_0(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5282 (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]. 87.61/85.67 5283 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5284 (exists A all B (r2_hidden(B,A) <-> (exists C (r2_hidden(C,k13_finseq_1(f1_s4_finseq_1)) & p1_s4_finseq_1(C) & C = B & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5285 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5286 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5287 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = k17_finseq_1(A) <-> (all C all D (r2_hidden(C,k3_relat_1(A)) & (exists E (v1_relat_1(E) & C = k1_funct_1(E,np__1) & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,F) -> r1_xreal_0(k3_finseq_1(E),F) | r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,k1_nat_1(F,np__1))),A)))) & k1_funct_1(E,k3_finseq_1(E)) = D & r1_xreal_0(np__1,k3_finseq_1(E)) & v1_finseq_1(E) & v1_funct_1(E))) & r2_hidden(D,k3_relat_1(A)) <-> r2_hidden(k4_tarski(C,D),B)))))))) # label(d16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5288 (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]. 87.61/85.67 5289 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5290 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5291 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k7_relat_1(B,k2_finseq_1(A))) & v1_funct_1(k7_relat_1(B,k2_finseq_1(A))) & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))))))) # label(t19_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5292 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5293 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k2_relat_1(k14_finseq_1(k1_relat_1(A))))) # label(t71_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5294 (all A all B all C (v1_relat_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)))) # label(fc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5295 (all A k1_xboole_0 = k6_finseq_1(A)) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5296 (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]. 87.61/85.67 5297 (all A all B all C all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> (B = k1_funct_1(D,np__2) & k1_funct_1(D,np__3) = C & A = k1_funct_1(D,np__1) & np__3 = k3_finseq_1(D) <-> D = k11_finseq_1(A,B,C)))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5298 (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]. 87.61/85.67 5299 (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]. 87.61/85.67 5300 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5301 (all A all B (v1_relat_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)))) # label(fc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5302 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B)))) <-> v2_finseq_1(A)))) # label(d12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5303 (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]. 87.61/85.67 5304 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5305 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A))) # label(cc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5306 (exists A (-v1_xboole_0(A) & v1_finseq_1(A) & v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5307 (all A (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)))) # label(fc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5308 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5309 (all A (v4_ordinal2(A) -> k2_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))) = k2_finseq_1(k2_xcmplx_0(A,np__1)))) # label(t11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5310 (all A all B (v4_ordinal2(B) -> ((exists C (r1_xreal_0(np__1,C) & r1_xreal_0(C,B) & A = C & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_0_finseq_1(B))))) # label(fraenkel_a_1_0_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5311 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)))) # label(dt_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5312 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)))))))) # label(t45_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5313 (all A (-v1_xboole_0(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5314 (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]. 87.61/85.67 5315 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.67 5316 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_tarski(A) = k2_relat_1(B) & k4_finseq_1(B) = k2_finseq_1(np__1) <-> B = k9_finseq_1(A)))) # label(t55_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5317 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (k7_finseq_1(C,B) = k7_finseq_1(A,B) | k7_finseq_1(B,C) = k7_finseq_1(B,A) -> A = C))))))) # label(t46_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5318 (all A all B (v1_funct_1(A) & -v1_xboole_0(B) & v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_finseq_1(A) & v1_relat_1(A) -> -v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5319 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))))))) # label(t39_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5320 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(B)) -> C = k3_finseq_1(k16_finseq_1(A,B,C))))))) # label(t80_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5321 (all A all B k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)) = k10_finseq_1(A,B)) # label(d9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5322 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (m1_finseq_1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5323 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(k1_nat_1(k3_finseq_1(A),np__1),C) & r1_xreal_0(C,k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) -> k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A)))))))))) # label(t36_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5324 (all A (v1_finset_1(A) & v1_relat_1(A) -> v1_finset_1(k2_relat_1(A)))) # label(fc11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5325 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = a_1_0_finseq_1(A))) # label(d1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5326 (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]. 87.61/85.68 5327 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> -(k1_xboole_0 != A & (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C k7_finseq_1(B,k9_finseq_1(C)) != A)))))) # label(t63_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5328 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5329 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(A),k2_finseq_1(B)) -> r1_xreal_0(A,B)))))) # label(t10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5330 (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]. 87.61/85.68 5331 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> v1_funct_1(k7_relat_1(B,A)) & v1_relat_1(k8_relat_1(A,B)) & v2_finseq_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)) & v2_finseq_1(k7_relat_1(B,A)) & v1_relat_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5332 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k7_finseq_1(A,B)))))) # label(t44_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5333 (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]. 87.61/85.68 5334 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k3_finseq_1(A) = k1_card_1(A))) # label(redefinition_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5335 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5336 (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]. 87.61/85.68 5337 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (r1_xreal_0(A,k3_finseq_1(B)) & C = k7_relat_1(B,k2_finseq_1(A)) -> k2_finseq_1(A) = k4_finseq_1(C) & k3_finseq_1(C) = A))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5338 (all A (v1_fraenkel(k13_finseq_1(A)) & -v1_xboole_0(k13_finseq_1(A)))) # label(fc16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5339 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5340 (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]. 87.61/85.68 5341 (all A (v1_relat_1(A) & v1_funct_1(A) -> -((all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> -r1_tarski(A,B))) & (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B))))))) # label(t15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5342 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k7_finseq_1(A,B) = k1_xboole_0 -> A = k1_xboole_0 & B = k1_xboole_0))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5343 (all A all B (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) -> v1_finset_1(k10_relat_1(A,B)))) # label(fc18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5344 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k1_xboole_0 = A <-> k1_xboole_0 = k4_finseq_1(A)))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5345 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) & k4_finseq_1(B) = k4_finseq_1(A) -> B = A))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5346 (all A all B (m2_finseq_1(B,A) <-> m1_finseq_1(B,A))) # label(redefinition_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5347 (all A all B (m2_finseq_1(B,A) -> v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A))) # label(dt_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5348 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k1_tarski(A) = k2_relat_1(B) & np__1 = k3_finseq_1(B) <-> B = k9_finseq_1(A)))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5349 (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]. 87.61/85.68 5350 $T # label(t3_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5351 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_zf_lang(k21_zf_lang(A)) & m2_finseq_1(k21_zf_lang(A),k5_numbers))) # label(dt_k21_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 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 (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> k17_zf_lang(A,B,C,D) = k13_zf_lang(A,k15_zf_lang(B,C,D)) & k16_zf_lang(A,B,C,D) = k8_zf_lang(A,k14_zf_lang(B,C,D)))))))))) # label(t24_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5353 (all A (m2_finseq_1(A,k5_numbers) -> k6_zf_lang(A) = k8_finseq_1(k5_numbers,k12_finseq_1(k5_numbers,np__2),A))) # label(d5_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5354 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v7_zf_lang(A) -> k19_zf_lang(A) = k1_funct_1(A,np__3) & k1_funct_1(A,np__2) = k18_zf_lang(A)))) # label(t52_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5355 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r3_zf_lang(A,k6_zf_lang(B)) -> r2_zf_lang(A,B)))))) # label(t90_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5356 (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]. 87.61/85.68 5357 $T # label(t9_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5358 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (k1_funct_1(A,np__1) = np__4 -> v6_zf_lang(A)))) # label(t45_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5359 (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(D,B) = k8_zf_lang(C,A) -> C = D & B = A))))))))) # label(t12_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5360 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m2_finseq_1(k26_zf_lang(A),k5_numbers) & v1_zf_lang(k26_zf_lang(A)))) # label(dt_k26_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5361 (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) <-> k22_zf_lang(A) = B | B = k21_zf_lang(A))))))) # label(t76_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5362 $T # label(t20_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5363 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> k2_xboole_0(k29_zf_lang(A),k1_tarski(k6_zf_lang(A))) = k29_zf_lang(k6_zf_lang(A)))) # label(t104_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5364 (all A all B (m1_finseq_1(A,k5_numbers) & m1_finseq_1(B,k5_numbers) -> m2_finseq_1(k7_zf_lang(A,B),k5_numbers))) # label(dt_k7_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5365 (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) -> (k27_zf_lang(A) = B <-> (exists C (A = k12_zf_lang(B,C) & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))))))))) # label(d37_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5366 (all A all B (m1_subset_1(A,k1_zf_lang) & m1_finseq_1(B,k5_numbers) -> m2_finseq_1(k8_zf_lang(A,B),k5_numbers))) # label(dt_k8_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5367 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v7_zf_lang(A) -> k1_funct_1(A,np__2) = k18_zf_lang(A)))) # label(d28_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5368 $T # label(t21_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5369 (all A all B (m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) -> v1_zf_lang(k4_zf_lang(A,B)) & v1_finseq_1(k4_zf_lang(A,B)) & v1_finset_1(k4_zf_lang(A,B)) & v1_funct_1(k4_zf_lang(A,B)) & v1_relat_1(k4_zf_lang(A,B)))) # label(fc2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5370 (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) -> r1_tarski(k29_zf_lang(A),k29_zf_lang(B))))))) # label(t101_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5371 (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) -> (v6_zf_lang(B) -> -((all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> k8_zf_lang(A,D) != B)) & A = k23_zf_lang(B)) & -((all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> k8_zf_lang(D,C) != B)) & C = k24_zf_lang(B)) & ((exists D (B = k8_zf_lang(D,C) & m2_subset_1(D,k5_numbers,k1_zf_lang))) -> k24_zf_lang(B) = C) & ((exists D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) & k8_zf_lang(A,D) = B)) -> A = k23_zf_lang(B))))))))) # label(t60_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5372 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v5_zf_lang(A) -> k29_zf_lang(A) = k2_xboole_0(k2_xboole_0(k29_zf_lang(k21_zf_lang(A)),k29_zf_lang(k22_zf_lang(A))),k1_tarski(A))))) # label(t109_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5373 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m2_finseq_1(k27_zf_lang(A),k5_numbers) & v1_zf_lang(k27_zf_lang(A)))) # label(dt_k27_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5374 (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]. 87.61/85.68 5375 $T # label(t15_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5376 (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)) -> k21_zf_lang(A) = B) & ((exists C (v1_zf_lang(C) & A = k10_zf_lang(C,B) & m2_finseq_1(C,k5_numbers))) -> k22_zf_lang(A) = B) & -(B = k22_zf_lang(A) & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> A != k10_zf_lang(C,B)))) & -(k21_zf_lang(A) = B & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> A != k10_zf_lang(B,C))))))))) # label(t57_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5377 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> ((exists B (v1_zf_lang(B) & (exists C (v1_zf_lang(C) & A = k10_zf_lang(B,C) & m2_finseq_1(C,k5_numbers))) & m2_finseq_1(B,k5_numbers))) <-> v8_zf_lang(A)))) # label(d20_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5378 (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]. 87.61/85.68 5379 $T # label(t1_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5380 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> np__3 = k1_funct_1(k7_zf_lang(A,B),np__1))))) # label(t33_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5381 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r1_zf_lang(B,k8_zf_lang(A,C)) <-> B = C))))))) # label(t73_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5382 (all A all B (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) & m1_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> 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]. 87.61/85.68 5383 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v6_zf_lang(A) -> k2_xboole_0(k29_zf_lang(k24_zf_lang(A)),k1_tarski(A)) = k29_zf_lang(A)))) # label(t110_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5384 (all A all B (m1_finseq_1(B,k5_numbers) & v1_zf_lang(B) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> v1_zf_lang(k10_zf_lang(A,B)) & m2_finseq_1(k10_zf_lang(A,B),k5_numbers))) # label(dt_k10_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5385 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v10_zf_lang(A) -> -((all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> A != k12_zf_lang(B,C))) & B = k27_zf_lang(A)) & -((all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> A != k12_zf_lang(C,B))) & k28_zf_lang(A) = B) & ((exists C (m2_finseq_1(C,k5_numbers) & A = k12_zf_lang(C,B) & v1_zf_lang(C))) -> B = k28_zf_lang(A)) & ((exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & A = k12_zf_lang(B,C))) -> B = k27_zf_lang(A))))))) # label(t66_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5386 (all A all B (m1_subset_1(B,k1_zf_lang) & m1_subset_1(A,k1_zf_lang) -> v1_relat_1(k5_zf_lang(A,B)) & v1_zf_lang(k5_zf_lang(A,B)) & v1_finseq_1(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]. 87.61/85.68 5387 (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_xreal_0(k3_finseq_1(B),k3_finseq_1(A))))))) # label(t83_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5388 (all A all B (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(B) & m1_finseq_1(B,k5_numbers) -> v1_finseq_1(k7_zf_lang(A,B)) & v1_zf_lang(k7_zf_lang(A,B)) & v1_finset_1(k7_zf_lang(A,B)) & v1_funct_1(k7_zf_lang(A,B)) & v1_relat_1(k7_zf_lang(A,B)))) # label(fc5_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5389 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (v11_zf_lang(B) -> -((all D (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> B != k13_zf_lang(A,D))) & A = k23_zf_lang(B)) & ((exists D (B = k13_zf_lang(D,C) & m2_subset_1(D,k5_numbers,k1_zf_lang))) -> k24_zf_lang(B) = C) & -(k24_zf_lang(B) = C & (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> B != k13_zf_lang(D,C)))) & ((exists D (m2_finseq_1(D,k5_numbers) & k13_zf_lang(A,D) = B & v1_zf_lang(D))) -> k23_zf_lang(B) = A)))))))) # label(t61_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5390 (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]. 87.61/85.68 5391 (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) -> (r2_zf_lang(C,k4_zf_lang(A,B)) <-> k4_zf_lang(A,B) = C))))))) # label(t97_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5392 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m2_finseq_1(k28_zf_lang(A),k5_numbers) & v1_zf_lang(k28_zf_lang(A)))) # label(dt_k28_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5393 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> -r1_zf_lang(C,k5_zf_lang(A,B)))))))) # label(t70_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5394 (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]. 87.61/85.68 5395 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v9_zf_lang(A) -> -(B = k25_zf_lang(A) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> A != k11_zf_lang(B,C)))) & ((exists C (v1_zf_lang(C) & k11_zf_lang(C,B) = A & m2_finseq_1(C,k5_numbers))) -> B = k26_zf_lang(A)) & -(k26_zf_lang(A) = B & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> A != k11_zf_lang(C,B)))) & ((exists C (m2_finseq_1(C,k5_numbers) & k11_zf_lang(B,C) = A & v1_zf_lang(C))) -> k25_zf_lang(A) = B)))))) # label(t64_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5396 (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]. 87.61/85.68 5397 $T # label(t19_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5398 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v3_zf_lang(A) | v2_zf_lang(A) <-> v7_zf_lang(A)))) # label(d15_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5399 $T # label(t13_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5400 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v9_zf_lang(A) -> k11_zf_lang(k25_zf_lang(A),k26_zf_lang(A)) = A))) # label(t65_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5401 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -((all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> k4_zf_lang(B,C) != A)))) & v2_zf_lang(A)) & ((exists B ((exists C (m2_subset_1(C,k5_numbers,k1_zf_lang) & k5_zf_lang(B,C) = A)) & m2_subset_1(B,k5_numbers,k1_zf_lang))) -> v3_zf_lang(A)) & -(v5_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) -> A != k7_zf_lang(B,C)))))) & -((all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> A != k8_zf_lang(B,C))))) & v6_zf_lang(A)) & ((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 (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) & (exists C (A = k7_zf_lang(B,C) & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))))) -> v5_zf_lang(A)) & ((exists B (v1_zf_lang(B) & A = k6_zf_lang(B) & m2_finseq_1(B,k5_numbers))) -> v4_zf_lang(A)) & -((all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k6_zf_lang(B) != A)) & 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))))) & ((exists B ((exists C (A = k4_zf_lang(B,C) & m2_subset_1(C,k5_numbers,k1_zf_lang))) & m2_subset_1(B,k5_numbers,k1_zf_lang))) -> v2_zf_lang(A)))) # label(t16_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5402 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -(-(k1_funct_1(A,np__1) = np__0 & v2_zf_lang(A)) & -(np__3 = k1_funct_1(A,np__1) & v5_zf_lang(A)) & -(v6_zf_lang(A) & np__4 = k1_funct_1(A,np__1)) & -(np__2 = k1_funct_1(A,np__1) & v4_zf_lang(A)) & -(v3_zf_lang(A) & k1_funct_1(A,np__1) = np__1)))) # label(t40_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5403 (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]. 87.61/85.68 5404 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (r3_zf_lang(B,C) & r3_zf_lang(A,B) -> r3_zf_lang(A,C)))))))) # label(t85_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5405 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> m2_subset_1(k23_zf_lang(A),k5_numbers,k1_zf_lang))) # label(dt_k23_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5406 $T # label(t5_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5407 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v5_zf_lang(A) | v8_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v5_zf_lang(A) -> ((exists C (m2_finseq_1(C,k5_numbers) & k7_zf_lang(B,C) = A & v1_zf_lang(C))) <-> B = k21_zf_lang(A))) & (-v5_zf_lang(A) -> (B = k21_zf_lang(A) <-> (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & A = k10_zf_lang(B,C)))))))))) # label(d31_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5408 (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]. 87.61/85.68 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 (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))))))))) # label(d27_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5410 (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_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (k12_zf_lang(C,D) = k12_zf_lang(A,B) -> A = C & B = D))))))))) # label(t50_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5411 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -(-v4_zf_lang(A) & -v6_zf_lang(A) & -v5_zf_lang(A) & -v7_zf_lang(A)))) # label(t26_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.68 5412 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v4_zf_lang(A) -> k29_zf_lang(A) = k2_xboole_0(k29_zf_lang(k20_zf_lang(A)),k1_tarski(A))))) # label(t108_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5413 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) <-> r2_hidden(A,k9_zf_lang))) # label(t14_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5414 $T # label(t11_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5415 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v11_zf_lang(A) | v6_zf_lang(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (-v6_zf_lang(A) -> (k23_zf_lang(A) = B <-> (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k13_zf_lang(B,C) = A)))) & (v6_zf_lang(A) -> ((exists C (m2_finseq_1(C,k5_numbers) & k8_zf_lang(B,C) = A & v1_zf_lang(C))) <-> k23_zf_lang(A) = B))))))) # label(d33_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5416 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v9_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> ((exists C (m2_finseq_1(C,k5_numbers) & k11_zf_lang(B,C) = A & v1_zf_lang(C))) <-> B = k25_zf_lang(A))))))) # label(d35_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5417 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (k13_zf_lang(B,D) = k13_zf_lang(A,C) -> A = B & D = C))))))))) # label(t51_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5418 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v5_zf_lang(A) -> A = k7_zf_lang(k21_zf_lang(A),k22_zf_lang(A))))) # label(t58_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5419 $T # label(t80_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5420 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v7_zf_lang(A) <-> k29_zf_lang(A) = k1_tarski(A)))) # label(t107_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5421 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v11_zf_lang(A) -> k13_zf_lang(k23_zf_lang(A),k24_zf_lang(A)) = A))) # label(t63_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5422 (all A all B all C all D (m1_subset_1(A,k1_zf_lang) & m1_subset_1(C,k1_zf_lang) & m1_finseq_1(D,k5_numbers) & v1_zf_lang(D) & m1_subset_1(B,k1_zf_lang) -> v1_zf_lang(k16_zf_lang(A,B,C,D)) & m2_finseq_1(k16_zf_lang(A,B,C,D),k5_numbers))) # label(dt_k16_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5423 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v3_zf_lang(A) -> np__1 = k1_funct_1(A,np__1)))) # label(t36_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5424 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> 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]. 87.61/85.71 5425 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> -(-v5_zf_lang(A) & -v6_zf_lang(A) & -v4_zf_lang(A) & -v3_zf_lang(A) & -v2_zf_lang(A)))) # label(t25_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5426 (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) & r2_zf_lang(B,A) -> B = A))))) # label(t87_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5427 (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]. 87.61/85.71 5428 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> -r3_zf_lang(C,k5_zf_lang(A,B)))))))) # label(t89_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5429 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v5_zf_lang(A) & p1_s1_zf_lang(k21_zf_lang(A)) & p1_s1_zf_lang(k22_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) -> (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) -> (v7_zf_lang(A) -> p1_s1_zf_lang(A)))) -> (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> p1_s1_zf_lang(A))) # label(s1_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5430 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> ((exists C ((exists D (v1_relat_1(D) & v1_finseq_1(D) & r1_xreal_0(np__1,C) & k3_finseq_1(D) = C & A = k1_funct_1(D,np__1) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> -(r1_xreal_0(np__1,E) & -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) -> -(r1_zf_lang(F,G) & k1_funct_1(D,k1_nat_1(E,np__1)) = G & F = k1_funct_1(D,E))))))))) & B = k1_funct_1(D,C) & v1_funct_1(D))) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_zf_lang(A,B)))))) # label(d40_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5431 $T # label(t68_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5432 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v6_zf_lang(A) | v11_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (v6_zf_lang(A) -> (B = k24_zf_lang(A) <-> (exists C (A = k8_zf_lang(C,B) & m2_subset_1(C,k5_numbers,k1_zf_lang))))) & (-v6_zf_lang(A) -> ((exists C (A = k13_zf_lang(C,B) & m2_subset_1(C,k5_numbers,k1_zf_lang))) <-> B = k24_zf_lang(A)))))))) # label(d34_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5433 (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_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (A = k7_finseq_1(B,C) -> B = A))))))) # label(t46_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5434 (exists A (m1_finseq_1(A,k5_numbers) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_zf_lang(A))) # label(rc1_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5435 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k29_zf_lang(k8_zf_lang(A,B)) = k2_xboole_0(k29_zf_lang(B),k1_tarski(k8_zf_lang(A,B))))))) # label(t106_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5436 (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) -> B = D & C = A))))))))) # label(t7_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5437 (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) & k12_zf_lang(B,C) = A)) & v1_zf_lang(B))) <-> v10_zf_lang(A)))) # label(d22_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5438 (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]. 87.61/85.71 5439 (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 (m2_finseq_1(D,k5_numbers) & v1_zf_lang(D) -> (k10_zf_lang(A,B) = k10_zf_lang(C,D) -> B = D & C = A))))))))) # label(t48_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5440 (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]. 87.61/85.71 5441 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k6_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B))) = k10_zf_lang(A,B))))) # label(d16_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5442 (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]. 87.61/85.71 5443 (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]. 87.61/85.71 5444 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> -(v7_zf_lang(A) & r1_zf_lang(B,A)))))) # label(t74_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5445 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r1_zf_lang(A,B) -> r3_zf_lang(A,B)))))) # label(t82_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5446 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> -(r3_zf_lang(A,B) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> -r1_zf_lang(C,B)))))))) # label(t84_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5447 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v5_zf_lang(A) <-> (exists B (v1_zf_lang(B) & (exists C (k7_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) & m2_finseq_1(B,k5_numbers)))))) # label(d13_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5448 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (k7_zf_lang(A,B) = k7_zf_lang(C,D) -> B = D & A = C))))))))) # label(t47_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5449 (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]. 87.61/85.71 5450 $T # label(t4_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5451 (all A all B (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(B) & m1_finseq_1(B,k5_numbers) -> v1_zf_lang(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]. 87.61/85.71 5452 (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]. 87.61/85.71 5453 $T # label(dt_k29_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5454 (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_zf_lang(A,B) & r2_zf_lang(B,C) -> r2_zf_lang(A,C)))))))) # label(t86_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5455 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k1_funct_1(k8_zf_lang(A,B),np__1) = np__4)))) # label(t34_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5456 (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]. 87.61/85.71 5457 (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]. 87.61/85.71 5458 $T # label(t18_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5459 (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) & r1_xreal_0(k3_finseq_1(B),k3_finseq_1(A))))))) # label(t81_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5460 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (r3_zf_lang(A,B) <-> B != A & r2_zf_lang(A,B)))))) # label(d41_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.71 5461 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,A)) = k12_zf_lang(A,B))))) # label(d18_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.72 5462 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> ((exists B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) & (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k11_zf_lang(B,C) = A)))) -> v9_zf_lang(A)) & ((exists B (m2_subset_1(B,k5_numbers,k1_zf_lang) & (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & k13_zf_lang(B,C) = A)))) -> 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 (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) & (exists C (k12_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))))) -> v10_zf_lang(A)) & -(v10_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) -> k12_zf_lang(B,C) != 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) -> k11_zf_lang(B,C) != A)))) & v9_zf_lang(A)) & ((exists B (m2_finseq_1(B,k5_numbers) & (exists C (v1_zf_lang(C) & k10_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers))) & 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) -> k10_zf_lang(B,C) != A)))) & v8_zf_lang(A)))) # label(t22_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.72 5463 (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]. 87.61/85.72 5464 (all A all B all C (m1_finseq_1(C,k5_numbers) & v1_zf_lang(C) & m1_subset_1(B,k1_zf_lang) & m1_subset_1(A,k1_zf_lang) -> m2_finseq_1(k15_zf_lang(A,B,C),k5_numbers) & v1_zf_lang(k15_zf_lang(A,B,C)))) # label(dt_k15_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.72 5465 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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) & k4_zf_lang(B,C) = A))))))) # label(d10_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.72 5466 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> v1_zf_lang(k20_zf_lang(A)) & m2_finseq_1(k20_zf_lang(A),k5_numbers))) # label(dt_k20_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.72 5467 (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(A,B) = k4_zf_lang(C,D) -> A = C & D = B))))))))) # label(t6_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.72 5468 (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]. 87.61/85.72 5469 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v8_zf_lang(A) -> k10_zf_lang(k21_zf_lang(A),k22_zf_lang(A)) = A))) # label(t59_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.72 5470 (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]. 87.61/85.72 5471 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v9_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (B = k26_zf_lang(A) <-> (exists C (A = k11_zf_lang(C,B) & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))))))))) # label(d36_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.72 5472 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> (k11_zf_lang(A,B) = k11_zf_lang(C,D) -> B = D & A = C))))))))) # label(t49_zf_lang) # label(axiom) # label(non_clause). [assumption]. 87.61/85.72 5473 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (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]. 91.58/89.67 5474 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v11_zf_lang(A) <-> (exists B (m2_subset_1(B,k5_numbers,k1_zf_lang) & (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & A = k13_zf_lang(B,C)))))))) # label(d23_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5475 $T # label(t55_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5476 (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]. 91.58/89.67 5477 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v6_zf_lang(A) -> np__4 = k1_funct_1(A,np__1)))) # label(t39_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5478 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> k1_funct_1(k6_zf_lang(A),np__1) = np__2)) # label(t32_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5479 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k2_zf_lang(A) = k1_nat_1(np__5,A))) # label(d2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5480 (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_finset_1(k8_zf_lang(A,B)) & v1_zf_lang(k8_zf_lang(A,B)) & v1_finseq_1(k8_zf_lang(A,B)) & v1_funct_1(k8_zf_lang(A,B)))) # label(fc6_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5481 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v10_zf_lang(A) -> k12_zf_lang(k27_zf_lang(A),k28_zf_lang(A)) = A))) # label(t67_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5482 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> ((all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (r3_zf_lang(B,A) -> p1_s2_zf_lang(B)))) -> p1_s2_zf_lang(A)))) -> (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> p1_s2_zf_lang(A))) # label(s2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5483 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> m2_finseq_1(k25_zf_lang(A),k5_numbers) & v1_zf_lang(k25_zf_lang(A)))) # label(dt_k25_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5484 (all A (-v1_xboole_0(A) -> (A = k9_zf_lang <-> (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_lang(B,C),A) & r2_hidden(k4_zf_lang(B,C),A))))) & (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_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(k5_zf_lang(C,D),B) & r2_hidden(k4_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(C,B) & r2_hidden(D,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) -> (r2_hidden(B,A) -> r2_hidden(k6_zf_lang(B),A)))) & (all B (r2_hidden(B,A) -> m2_finseq_1(B,k5_numbers)))))) # label(d8_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5485 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v5_zf_lang(A) -> k1_funct_1(A,np__1) = np__3))) # label(t38_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5486 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (-(k6_zf_lang(A) != B & (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> k8_zf_lang(C,A) != B)) & (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> B != k7_zf_lang(C,A) & k7_zf_lang(A,C) != B))) <-> r1_zf_lang(A,B)))))) # label(d39_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5487 (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))) <-> k28_zf_lang(A) = B)))))) # label(d38_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5488 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> ((exists B ((exists C (m2_subset_1(C,k5_numbers,k1_zf_lang) & A = k5_zf_lang(B,C))) & m2_subset_1(B,k5_numbers,k1_zf_lang))) <-> v3_zf_lang(A)))) # label(d11_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5489 (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]. 91.58/89.67 5490 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (v6_zf_lang(A) -> (r1_zf_lang(B,A) <-> B = k24_zf_lang(A))))))) # label(t77_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5491 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v4_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (k6_zf_lang(B) = A <-> B = k20_zf_lang(A))))))) # label(d30_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5492 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v3_zf_lang(A) -> A = k5_zf_lang(k18_zf_lang(A),k19_zf_lang(A))))) # label(t54_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5493 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v9_zf_lang(A) <-> (exists B (m2_finseq_1(B,k5_numbers) & (exists C (v1_zf_lang(C) & k11_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers))) & v1_zf_lang(B)))))) # label(d21_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5494 (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(A,k7_zf_lang(B,C)) & -r2_zf_lang(A,C) & -r2_zf_lang(A,B)))))))) # label(t91_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5495 (all A all B all C (m1_finseq_1(C,k5_numbers) & v1_zf_lang(C) & m1_subset_1(B,k1_zf_lang) & m1_subset_1(A,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]. 91.58/89.67 5496 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v2_zf_lang(A) -> k4_zf_lang(k18_zf_lang(A),k19_zf_lang(A)) = A))) # label(t53_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5497 (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) -> -((all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> A != k7_zf_lang(B,C))) & B = k21_zf_lang(A)) & ((exists C (k7_zf_lang(B,C) = A & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))) -> B = k21_zf_lang(A)) & -(k22_zf_lang(A) = B & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> k7_zf_lang(C,B) != A))) & ((exists C (m2_finseq_1(C,k5_numbers) & A = k7_zf_lang(C,B) & v1_zf_lang(C))) -> B = k22_zf_lang(A))))))) # label(t56_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5498 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v7_zf_lang(A) -> np__3 = k3_finseq_1(A)))) # label(t27_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5499 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v7_zf_lang(A) -> k1_funct_1(A,np__3) = k19_zf_lang(A)))) # label(d29_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5500 (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_hidden(B,k29_zf_lang(C)) -> r2_hidden(A,k29_zf_lang(C)) | -r1_zf_lang(A,B) & -r2_zf_lang(A,B) & -r3_zf_lang(A,B)))))))) # label(t111_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5501 (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]. 91.58/89.67 5502 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k11_zf_lang(A,B) = k6_zf_lang(k7_zf_lang(A,k6_zf_lang(B))))))) # label(d17_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5503 (all A (v1_zf_lang(A) & m1_finseq_1(A,k5_numbers) -> v1_finset_1(k6_zf_lang(A)) & v1_finseq_1(k6_zf_lang(A)) & v1_zf_lang(k6_zf_lang(A)) & v1_funct_1(k6_zf_lang(A)) & v1_relat_1(k6_zf_lang(A)))) # label(fc4_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5504 (all A (m2_subset_1(A,k5_numbers,k1_zf_lang) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> k13_zf_lang(A,B) = k6_zf_lang(k8_zf_lang(A,k6_zf_lang(B))))))) # label(d19_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5505 (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]. 91.58/89.67 5506 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v6_zf_lang(A) <-> (exists B ((exists C (v1_zf_lang(C) & A = k8_zf_lang(B,C) & m2_finseq_1(C,k5_numbers))) & m2_subset_1(B,k5_numbers,k1_zf_lang)))))) # label(d14_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5507 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (np__3 = k3_finseq_1(A) -> v7_zf_lang(A)))) # label(t30_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5508 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v4_zf_lang(A) -> np__2 = k1_funct_1(A,np__1)))) # label(t37_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5509 $T # label(t78_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.58/89.67 5510 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (v4_zf_lang(A) -> (k20_zf_lang(A) = B <-> r1_zf_lang(B,A))))))) # label(t75_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5511 (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]. 91.66/89.67 5512 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v2_zf_lang(A) -> k1_funct_1(A,np__1) = np__0))) # label(t35_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5513 (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)) & 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]. 91.66/89.67 5514 (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]. 91.66/89.67 5515 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (v8_zf_lang(A) | v5_zf_lang(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> (v5_zf_lang(A) -> (B = k22_zf_lang(A) <-> (exists C (k7_zf_lang(C,B) = A & m2_finseq_1(C,k5_numbers) & v1_zf_lang(C))))) & (-v5_zf_lang(A) -> (B = k22_zf_lang(A) <-> (exists C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) & A = k10_zf_lang(C,B)))))))))) # label(d32_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5516 (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]. 91.66/89.67 5517 (all A ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_xreal_0(np__5,B) & A = B)) <-> r2_hidden(A,a_0_0_zf_lang))) # label(fraenkel_a_0_0_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5518 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (B = k29_zf_lang(A) <-> (all C ((exists D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) & r2_zf_lang(D,A) & D = C)) <-> r2_hidden(C,B))))))) # label(d42_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5519 (all A all B all C all D (m1_subset_1(C,k1_zf_lang) & v1_zf_lang(D) & m1_finseq_1(D,k5_numbers) & m1_subset_1(B,k1_zf_lang) & m1_subset_1(A,k1_zf_lang) -> m2_finseq_1(k17_zf_lang(A,B,C,D),k5_numbers) & v1_zf_lang(k17_zf_lang(A,B,C,D)))) # label(dt_k17_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5520 $T # label(t8_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5521 $T # label(t17_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5522 (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) -> 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]. 91.66/89.67 5523 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (v6_zf_lang(A) -> r3_zf_lang(k24_zf_lang(A),A)))) # label(t96_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5524 (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]. 91.66/89.67 5525 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> r1_xreal_0(np__3,k3_finseq_1(A)))) # label(t29_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5526 (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]. 91.66/89.67 5527 (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]. 91.66/89.67 5528 $T # label(t2_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5529 (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(k4_zf_lang(A,B),np__1) = np__0 & k1_funct_1(k5_zf_lang(A,B),np__1) = np__1)))) # label(t31_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5530 (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) -> (r1_zf_lang(A,k7_zf_lang(B,C)) <-> B = A | A = C))))))) # label(t72_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5531 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> ((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]. 91.66/89.67 5532 (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(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]. 91.66/89.67 5533 (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]. 91.66/89.67 5534 $T # label(t99_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5535 (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) -> 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]. 91.66/89.67 5536 (all A (m1_subset_1(A,k1_zf_lang) -> k5_finseq_1(A) = k3_zf_lang(A))) # label(redefinition_k3_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.66/89.67 5537 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> -(-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]. 91.72/89.76 5538 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (v1_zf_lang(B) & m2_finseq_1(B,k5_numbers) -> (B = A <-> r1_zf_lang(A,k6_zf_lang(B))))))) # label(t71_zf_lang) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5539 (all A (-v1_xboole_0(A) -> (v1_ordinal1(A) & r2_zf_model(A,k9_zf_model) & (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))))) & r2_zf_model(A,k10_zf_model) & r2_zf_model(A,k8_zf_model) & r2_zf_model(A,k7_zf_model) <-> v1_zf_model(A)))) # label(d12_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5540 (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 (m1_subset_1(D,k3_zf_model(B)) & (all E (m2_relset_1(E,k1_zf_lang,B) & v1_funct_2(E,k1_zf_lang,B) & v1_funct_1(E) -> (E = D -> k8_funct_2(k1_zf_lang,B,E,k19_zf_lang(C)) = k8_funct_2(k1_zf_lang,B,E,k18_zf_lang(C))))) & A = D))))) # label(fraenkel_a_2_0_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5541 (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,C) = k8_funct_2(k1_zf_lang,A,B,D) <-> r1_zf_model(A,B,k4_zf_lang(C,D))))))))))) # label(t12_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5542 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k1_zf_lang,A) & v1_funct_2(B,k1_zf_lang,A) & v1_funct_1(B) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (r1_zf_model(A,B,k13_zf_lang(D,C)) <-> (exists E ((all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,B,F) -> F = D))) & r1_zf_model(A,E,C) & m2_relset_1(E,k1_zf_lang,A) & v1_funct_2(E,k1_zf_lang,A) & v1_funct_1(E)))))))))))) # label(t20_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5543 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (k1_zf_model(A) = B <-> (exists 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) -> (v2_zf_lang(D) -> k2_tarski(k18_zf_lang(D),k19_zf_lang(D)) = E) & (v3_zf_lang(D) -> E = k2_tarski(k18_zf_lang(D),k19_zf_lang(D))) & -(v6_zf_lang(D) & (all F -(r2_hidden(k4_tarski(k24_zf_lang(D),F),C) & k4_xboole_0(k3_tarski(k1_tarski(F)),k1_tarski(k23_zf_lang(D))) = E))) & -(v5_zf_lang(D) & (all F all G -(r2_hidden(k4_tarski(k22_zf_lang(D),G),C) & r2_hidden(k4_tarski(k21_zf_lang(D),F),C) & k3_tarski(k2_tarski(F,G)) = E))) & -((all F -(F = E & r2_hidden(k4_tarski(k20_zf_lang(D),F),C))) & v4_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(k4_zf_lang(D,E),k2_tarski(D,E)),C) & r2_hidden(k4_tarski(k5_zf_lang(D,E),k2_tarski(D,E)),C))))))))))) # label(d1_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5544 (all A (-v1_xboole_0(A) -> (all B (k3_zf_model(A) = B <-> (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,B))))))) # label(d2_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5545 $T # label(t24_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5546 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k1_zf_lang,A) & v1_funct_2(B,k1_zf_lang,A) & v1_funct_1(B) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (r1_zf_model(A,B,k5_zf_lang(C,D)) <-> r2_hidden(k8_funct_2(k1_zf_lang,A,B,C),k8_funct_2(k1_zf_lang,A,B,D))))))))))) # label(t13_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5547 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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 = f1_s3_zf_model(k18_zf_lang(D),k19_zf_lang(D))) & -((all F -(f3_s3_zf_model(F) = E & r2_hidden(k4_tarski(k20_zf_lang(D),F),C))) & v4_zf_lang(D)) & -((all F all G -(r2_hidden(k4_tarski(k21_zf_lang(D),F),C) & r2_hidden(k4_tarski(k22_zf_lang(D),G),C) & E = f4_s3_zf_model(F,G))) & v5_zf_lang(D)) & -((all F -(r2_hidden(k4_tarski(k24_zf_lang(D),F),C) & f5_s3_zf_model(k23_zf_lang(D),F) = E)) & v6_zf_lang(D)) & (v3_zf_lang(D) -> E = f2_s3_zf_model(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(k4_zf_lang(D,E),f1_s3_zf_model(D,E)),C) & r2_hidden(k4_tarski(k5_zf_lang(D,E),f2_s3_zf_model(D,E)),C))))))) <-> B = f7_s3_zf_model(A))))) -> (v2_zf_lang(f6_s3_zf_model) -> f1_s3_zf_model(k18_zf_lang(f6_s3_zf_model),k19_zf_lang(f6_s3_zf_model)) = f7_s3_zf_model(f6_s3_zf_model)) & (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))) & (v5_zf_lang(f6_s3_zf_model) -> (all A all B (f7_s3_zf_model(k22_zf_lang(f6_s3_zf_model)) = B & A = f7_s3_zf_model(k21_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)) & (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)) # label(s3_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5548 (all A (m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> k1_zf_model(A) = k2_zf_model(A))) # label(redefinition_k2_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5549 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,k5_numbers) & v1_zf_lang(B) -> ((all C (v1_funct_2(C,k1_zf_lang,A) & m2_relset_1(C,k1_zf_lang,A) & v1_funct_1(C) -> r1_zf_model(A,C,B))) <-> r2_zf_model(A,B)))))) # label(d5_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5550 (all A (-v1_xboole_0(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_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]. 91.72/89.76 5551 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k1_zf_lang,A) & v1_funct_2(B,k1_zf_lang,A) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> ((all E (v1_funct_2(E,k1_zf_lang,A) & m2_relset_1(E,k1_zf_lang,A) & v1_funct_1(E) -> ((all F (m2_subset_1(F,k5_numbers,k1_zf_lang) -> (k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,B,F) -> F = D))) -> r1_zf_model(A,E,C)))) <-> r1_zf_model(A,B,k8_zf_lang(D,C))))))))))) # label(t16_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5552 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k1_zf_lang,A) & v1_funct_2(B,k1_zf_lang,A) & v1_funct_1(B) -> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (v1_zf_lang(D) & m2_finseq_1(D,k5_numbers) -> ((r1_zf_model(A,B,D) <-> r1_zf_model(A,B,C)) <-> r1_zf_model(A,B,k12_zf_lang(C,D))))))))))) # label(t19_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5553 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (v5_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(k22_zf_lang(A),B)) & r2_hidden(C,k5_zf_model(k21_zf_lang(A),B)) <-> r2_hidden(C,k5_zf_model(A,B)))))))))) # label(t10_zf_model) # label(axiom) # label(non_clause). [assumption]. 91.72/89.76 5554 (all A all B all C (-v1_xboole_0(B) & v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> ((exists D (m1_subset_1(D,k3_zf_model(B)) & (all E (v1_funct_2(E,k1_zf_lang,B) & m2_relset_1(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)))))) & D = A)) <-> r2_hidden(A,a_2_1_zf_model(B,C))))) # label(fraenkel_a_2_1_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.79 5555 (all A all B all C all D (-v1_xboole_0(B) & m2_subset_1(C,k5_numbers,k1_zf_lang) & m2_subset_1(D,k5_numbers,k1_zf_lang) -> ((exists E (E = A & (all F (m2_relset_1(F,k1_zf_lang,B) & v1_funct_2(F,k1_zf_lang,B) & v1_funct_1(F) -> (E = F -> k8_funct_2(k1_zf_lang,B,F,D) = k8_funct_2(k1_zf_lang,B,F,C)))) & m1_subset_1(E,k3_zf_model(B)))) <-> r2_hidden(A,a_3_0_zf_model(B,C,D))))) # label(fraenkel_a_3_0_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.79 5556 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (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) -> (v3_zf_lang(D) -> f2_s4_zf_model(k18_zf_lang(D),k19_zf_lang(D)) = E) & -(v4_zf_lang(D) & (all F -(E = f3_s4_zf_model(F) & r2_hidden(k4_tarski(k20_zf_lang(D),F),C)))) & -((all F all G -(r2_hidden(k4_tarski(k21_zf_lang(D),F),C) & r2_hidden(k4_tarski(k22_zf_lang(D),G),C) & E = f4_s4_zf_model(F,G))) & v5_zf_lang(D)) & -((all F -(r2_hidden(k4_tarski(k24_zf_lang(D),F),C) & f5_s4_zf_model(k23_zf_lang(D),F) = E)) & v6_zf_lang(D)) & (v2_zf_lang(D) -> f1_s4_zf_model(k18_zf_lang(D),k19_zf_lang(D)) = E))))) & (all D (m2_subset_1(D,k5_numbers,k1_zf_lang) -> (all E (m2_subset_1(E,k5_numbers,k1_zf_lang) -> r2_hidden(k4_tarski(k5_zf_lang(D,E),f2_s4_zf_model(D,E)),C) & r2_hidden(k4_tarski(k4_zf_lang(D,E),f1_s4_zf_model(D,E)),C))))))) <-> f6_s4_zf_model(A) = B)))) & (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 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 (p1_s4_zf_model(A) -> p1_s4_zf_model(f3_s4_zf_model(A)))) & (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(f2_s4_zf_model(A,B)) & p1_s4_zf_model(f1_s4_zf_model(A,B)))))) -> p1_s4_zf_model(f6_s4_zf_model(f7_s4_zf_model)) # label(s4_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.79 5557 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (C = k4_zf_model(A,B) <-> (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 (v1_zf_lang(E) & m2_finseq_1(E,k5_numbers) -> (all F (r2_hidden(k4_tarski(E,F),D) -> (v2_zf_lang(E) -> a_2_0_zf_model(B,E) = F) & (v3_zf_lang(E) -> F = a_2_1_zf_model(B,E)) & -((all G -(r2_hidden(k4_tarski(k20_zf_lang(E),G),D) & F = k4_xboole_0(k3_zf_model(B),k3_tarski(k1_tarski(G))))) & v4_zf_lang(E)) & -((all G all H -(F = k3_xboole_0(k3_tarski(k1_tarski(G)),k3_tarski(k1_tarski(H))) & r2_hidden(k4_tarski(k22_zf_lang(E),H),D) & r2_hidden(k4_tarski(k21_zf_lang(E),G),D))) & v5_zf_lang(E)) & -((all G -(F = a_3_2_zf_model(B,E,G) & r2_hidden(k4_tarski(k24_zf_lang(E),G),D))) & v6_zf_lang(E)))))) & r2_hidden(k4_tarski(A,C),D))))))))) # label(d3_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.79 5558 (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(k5_zf_lang(C,D),f2_s1_zf_model(C,D)),B) & r2_hidden(k4_tarski(k4_zf_lang(C,D),f1_s1_zf_model(C,D)),B))))) & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (all D (r2_hidden(k4_tarski(C,D),B) -> -((all E all F -(D = f4_s1_zf_model(E,F) & r2_hidden(k4_tarski(k21_zf_lang(C),E),B) & r2_hidden(k4_tarski(k22_zf_lang(C),F),B))) & v5_zf_lang(C)) & -((all E -(D = f5_s1_zf_model(k23_zf_lang(C),E) & r2_hidden(k4_tarski(k24_zf_lang(C),E),B))) & v6_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)))) & (v3_zf_lang(C) -> D = f2_s1_zf_model(k18_zf_lang(C),k19_zf_lang(C))) & (v2_zf_lang(C) -> D = f1_s1_zf_model(k18_zf_lang(C),k19_zf_lang(C))))))) & r2_hidden(k4_tarski(f6_s1_zf_model,A),B))) # label(s1_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.80 5559 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (all B (-v1_xboole_0(B) -> (v2_zf_lang(A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k1_zf_lang,B) & v1_funct_2(C,k1_zf_lang,B) -> (k8_funct_2(k1_zf_lang,B,C,k19_zf_lang(A)) = k8_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)) <-> r2_hidden(C,k5_zf_model(A,B)))))))))) # label(t7_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.80 5560 (all A all B (-v1_xboole_0(B) & m1_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> k5_zf_model(A,B) = k4_zf_model(A,B))) # label(redefinition_k5_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.80 5561 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,A) & m2_relset_1(D,k1_zf_lang,A) -> (r2_hidden(D,k5_zf_model(k5_zf_lang(B,C),A)) <-> r2_hidden(k8_funct_2(k1_zf_lang,A,D,B),k8_funct_2(k1_zf_lang,A,D,C))))))))))) # label(t3_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.80 5562 (all A all B all C all D (-v1_xboole_0(B) & m2_subset_1(C,k5_numbers,k1_zf_lang) & m2_subset_1(D,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_2(F,k1_zf_lang,B) & m2_relset_1(F,k1_zf_lang,B) & v1_funct_1(F) -> (F = E -> r2_hidden(k8_funct_2(k1_zf_lang,B,F,C),k8_funct_2(k1_zf_lang,B,F,D))))) & E = A))))) # label(fraenkel_a_3_1_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.80 5563 (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) -> (-r1_zf_model(A,B,k6_zf_lang(C)) <-> r1_zf_model(A,B,C)))))))) # label(t14_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.80 5564 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_zf_lang,A) & v1_funct_2(D,k1_zf_lang,A) -> (r2_hidden(D,k5_zf_model(k4_zf_lang(B,C),A)) <-> k8_funct_2(k1_zf_lang,A,D,B) = k8_funct_2(k1_zf_lang,A,D,C)))))))))) # label(t2_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.80 5565 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (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(k8_zf_lang(B,C),A)) <-> (all E (v1_funct_1(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) -> (k8_funct_2(k1_zf_lang,A,E,F) != k8_funct_2(k1_zf_lang,A,D,F) -> F = B))) -> r2_hidden(E,k5_zf_model(C,A))))) & r2_hidden(D,k5_zf_model(C,A))))))))))) # label(t6_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.80 5566 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> k11_zf_model(A) = k11_zf_lang(k8_zf_lang(k2_zf_lang(np__3),k13_zf_lang(k2_zf_lang(np__0),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(A,k4_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__0)))))),k8_zf_lang(k2_zf_lang(np__1),k13_zf_lang(k2_zf_lang(np__2),k8_zf_lang(k2_zf_lang(np__4),k12_zf_lang(k5_zf_lang(k2_zf_lang(np__4),k2_zf_lang(np__2)),k13_zf_lang(k2_zf_lang(np__3),k7_zf_lang(k5_zf_lang(k2_zf_lang(np__3),k2_zf_lang(np__1)),A))))))))) # label(d11_zf_model) # label(axiom) # label(non_clause). [assumption]. 101.75/99.80 5567 (all A (v1_zf_lang(A) & m2_finseq_1(A,k5_numbers) -> (all B (m2_subset_1(B,k5_numbers,k1_zf_lang) -> (all C (m2_subset_1(C,k5_numbers,k1_zf_lang) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k1_zf_lang,D) & v1_funct_2(E,k1_zf_lang,D) -> ((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) -> -(B != G & G != C & k8_funct_2(k1_zf_lang,D,F,G) != k8_funct_2(k1_zf_lang,D,E,G)))) -> r1_zf_model(D,F,A)))Alarm clock 122.01/120.10 Prover9 interrupted 122.01/120.11 EOF