0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.33 % Computer : n025.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 960 0.12/0.33 % WCLimit : 120 0.12/0.33 % DateTime : Tue Aug 9 06:37:11 EDT 2022 0.12/0.33 % CPUTime : 3.15/3.68 ============================== Prover9 =============================== 3.15/3.68 Prover9 (32) version 2009-11A, November 2009. 3.15/3.68 Process 21189 was started by sandbox2 on n025.cluster.edu, 3.15/3.68 Tue Aug 9 06:37:14 2022 3.15/3.68 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_21035_n025.cluster.edu". 3.15/3.68 ============================== end of head =========================== 3.15/3.68 3.15/3.68 ============================== INPUT ================================= 3.15/3.68 3.15/3.68 % Reading from file /tmp/Prover9_21035_n025.cluster.edu 3.15/3.68 3.15/3.68 set(prolog_style_variables). 3.15/3.68 set(auto2). 3.15/3.68 % set(auto2) -> set(auto). 3.15/3.68 % set(auto) -> set(auto_inference). 3.15/3.68 % set(auto) -> set(auto_setup). 3.15/3.68 % set(auto_setup) -> set(predicate_elim). 3.15/3.68 % set(auto_setup) -> assign(eq_defs, unfold). 3.15/3.68 % set(auto) -> set(auto_limits). 3.15/3.68 % set(auto_limits) -> assign(max_weight, "100.000"). 3.15/3.68 % set(auto_limits) -> assign(sos_limit, 20000). 3.15/3.68 % set(auto) -> set(auto_denials). 3.15/3.68 % set(auto) -> set(auto_process). 3.15/3.68 % set(auto2) -> assign(new_constants, 1). 3.15/3.68 % set(auto2) -> assign(fold_denial_max, 3). 3.15/3.68 % set(auto2) -> assign(max_weight, "200.000"). 3.15/3.68 % set(auto2) -> assign(max_hours, 1). 3.15/3.68 % assign(max_hours, 1) -> assign(max_seconds, 3600). 3.15/3.68 % set(auto2) -> assign(max_seconds, 0). 3.15/3.68 % set(auto2) -> assign(max_minutes, 5). 3.15/3.68 % assign(max_minutes, 5) -> assign(max_seconds, 300). 3.15/3.68 % set(auto2) -> set(sort_initial_sos). 3.15/3.68 % set(auto2) -> assign(sos_limit, -1). 3.15/3.68 % set(auto2) -> assign(lrs_ticks, 3000). 3.15/3.68 % set(auto2) -> assign(max_megs, 400). 3.15/3.68 % set(auto2) -> assign(stats, some). 3.15/3.68 % set(auto2) -> clear(echo_input). 3.15/3.68 % set(auto2) -> set(quiet). 3.15/3.68 % set(auto2) -> clear(print_initial_clauses). 3.15/3.68 % set(auto2) -> clear(print_given). 3.15/3.68 assign(lrs_ticks,-1). 3.15/3.68 assign(sos_limit,10000). 3.15/3.68 assign(order,kbo). 3.15/3.68 set(lex_order_vars). 3.15/3.68 clear(print_given). 3.15/3.68 3.15/3.68 % formulas(sos). % not echoed (2539 formulas) 3.15/3.68 3.15/3.68 ============================== end of input ========================== 3.15/3.68 3.15/3.68 % From the command line: assign(max_seconds, 960). 3.15/3.68 3.15/3.68 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 3.15/3.68 3.15/3.68 % Formulas that are not ordinary clauses: 3.15/3.68 1 (all A all B all F (mem(F,arr(A,B)) -> (all G (mem(G,arr(A,B)) -> ((all X (mem(X,A) -> ap(G,X) = ap(F,X))) -> F = G))))) # label(funcext) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 2 (all A all B all F (mem(F,arr(A,B)) -> (all X (mem(X,A) -> mem(ap(F,X),B))))) # label(ap_tp) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 3 (all A all X (mem(X,A) -> ap(i(A),X) = X)) # label(ibeta) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 4 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 5 (all A all Y all X (mem(X,A) -> Y = ap(k(A,Y),X))) # label(kbeta) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 6 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(Q) <-> p(R)) -> R = Q))))) # label(boolext) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 7 (all A_27a (ne(A_27a) -> mem(c_2Emin_2E_40(A_27a),arr(arr(A_27a,bool),A_27a)))) # label(mem_c_2Emin_2E_40) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 8 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R)) <-> (p(Q) -> p(R))))))) # label(ax_imp_p) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 9 (all A_27a (ne(A_27a) -> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))))) # label(mem_c_2Emin_2E_3D) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 10 (all A (ne(A) -> (all X (mem(X,A) -> (all Y (mem(Y,A) -> (Y = X <-> p(ap(ap(c_2Emin_2E_3D(A),X),Y))))))))) # label(ax_eq_p) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 11 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> (exists V1x (V1x = V0a & mem(V1x,A_27a))))))) # label(conj_thm_2Ebool_2EEXISTS__REFL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 12 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((p(V1B) | p(V0A) <-> p(V0A)) <-> (p(V1B) -> p(V0A))))))) # label(conj_thm_2Ebool_2EOR__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.68 13 (all A_27a all V0t (mem(V0t,bool) -> (all V1t1 ap(f17(A_27a,V0t),V1t1) = f16(A_27a,V0t,V1t1)))) # label(lameq_f17) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 14 (all A_27a all V0x ap(f33(A_27a),V0x) = f32(A_27a,V0x)) # label(lameq_f33) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 15 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0b (mem(V0b,A_27b) -> V0b = ap(ap(c_2Ebool_2Eitself__case(A_27a,A_27b),c_2Ebool_2Ethe__value(A_27a)),V0b))))))) # label(ax_thm_2Ebool_2Eitself__case__thm) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 16 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (all V1v (mem(V1v,A_27a) -> (p(ap(V0f,V1v)) <-> (all V2x (mem(V2x,A_27a) -> (V1v = V2x -> p(ap(V0f,V2x)))))))))))) # label(conj_thm_2Ebool_2EUNWIND__FORALL__THM2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 17 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) -> p(V1t2) | p(V0t1)))))) # label(conj_thm_2Ebool_2EOR__INTRO__THM1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 18 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_3F_21(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_3F_21) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 19 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x ap(c_2Ebool_2E_21(A_27a),f10(A_27a,V0P,V1x)) = ap(f11(A_27a,V0P),V1x)))) # label(lameq_f11) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 20 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V1B) | p(V0A) <-> p(V0A) | p(V1B)))))) # label(conj_thm_2Ebool_2EDISJ__COMM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 21 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> ((p(V2C) | p(V0A)) & (p(V0A) | p(V1B)) <-> p(V0A) | p(V1B) & p(V2C)))))))) # label(conj_thm_2Ebool_2ERIGHT__OR__OVER__AND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 22 (all V0P (mem(V0P,arr(arr(bool,bool),bool)) -> (p(ap(V0P,k(bool,c_2Ebool_2ET))) & p(ap(V0P,f65)) & p(ap(V0P,i(bool))) & p(ap(V0P,k(bool,c_2Ebool_2EF))) -> (all V5f (mem(V5f,arr(bool,bool)) -> p(ap(V0P,V5f))))))) # label(conj_thm_2Ebool_2EBOOL__FUN__INDUCT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 23 (all A_27a all A_27b all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V4x (mem(V4x,A_27a) -> (all V5x_27 ap(f27(A_27a,A_27b,V1rep,V4x),V5x_27) = ap(ap(c_2Emin_2E_3D(A_27a),V4x),ap(V1rep,V5x_27))))))) # label(lameq_f27) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 24 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ebool_2ELET(A_27a,A_27b) = f14(A_27b,A_27a))))) # label(ax_thm_2Ebool_2ELET__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 25 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & (p(V0t) | p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)) & ($T <-> p(V0t) | $T) & ($T | p(V0t) <-> $T))) # label(conj_thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 26 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & ((p(V0t) -> $T) <-> $T) & ($T <-> ($F -> p(V0t))) & (-p(V0t) <-> -p(V0t)) & ($T <-> (p(V0t) -> p(V0t))))) # label(conj_thm_2Ebool_2EIMP__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 27 (all A_27b all A_27a all V0f f13(A_27b,A_27a,V0f) = ap(f14(A_27b,A_27a),V0f)) # label(lameq_f14) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 28 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> ((exists V2x ((p(V0P) -> p(V1Q)) & mem(V2x,A_27a))) <-> ((all V3x (mem(V3x,A_27a) -> p(V0P))) -> (exists V4x (p(V1Q) & mem(V4x,A_27a))))))))))) # label(conj_thm_2Ebool_2EBOTH__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 29 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> ap(V0f,V1x) = ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V0f),V1x))))))))) # label(conj_thm_2Ebool_2ELET__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 30 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2Eitself__case(A_27a,A_27b),arr(ty_2Ebool_2Eitself(A_27a),arr(A_27b,A_27b))))))) # label(mem_c_2Ebool_2Eitself__case) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 31 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (all V2t3 (mem(V2t3,bool) -> (p(V0t1) & p(V1t2) & p(V2t3) <-> p(V2t3) & p(V1t2) & p(V0t1)))))))) # label(conj_thm_2Ebool_2ECONJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 32 (all V0t (mem(V0t,bool) -> -(p(V0t) & -p(V0t)))) # label(conj_thm_2Ebool_2ENOT__AND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 33 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> V0t1 = ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2))))) & (all V2t1 (mem(V2t1,A_27a) -> (all V3t2 (mem(V3t2,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V2t1),V3t2) = V3t2)))))) # label(conj_thm_2Ebool_2Ebool__case__thm) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 34 (all A_27a all V0x (mem(V0x,A_27a) -> (all V1y ap(ap(c_2Emin_2E_3D(A_27a),V1y),V0x) = ap(f50(A_27a,V0x),V1y)))) # label(lameq_f50) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 35 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EF__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 36 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> p(ap(c_2Ebool_2E_3F_21(A_27a),f57(A_27a,V0a))))))) # label(conj_thm_2Ebool_2EEXISTS__UNIQUE__REFL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 37 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0N (mem(V0N,arr(A_27a,arr(A_27b,A_27c))) -> (all V1M (mem(V1M,A_27a) -> (all V2b (mem(V2b,A_27b) -> ap(ap(ap(c_2Ebool_2Eliteral__case(A_27a,arr(A_27b,A_27c)),f55(A_27c,A_27b,A_27a,V0N)),V1M),V2b) = ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27c),f56(A_27b,A_27c,A_27a,V0N,V2b)),V1M))))))))))))) # label(conj_thm_2Ebool_2Eliteral__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 38 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> (all V2x (mem(V2x,A_27a) -> (all V3x_27 (mem(V3x_27,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5y_27 (mem(V5y_27,A_27a) -> ((p(V1Q) <-> p(V0P)) & (-p(V1Q) -> V5y_27 = V4y) & (p(V1Q) -> V3x_27 = V2x) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0P),V2x),V4y) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1Q),V3x_27),V5y_27)))))))))))))))) # label(conj_thm_2Ebool_2Ebool__case__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 39 (all A_27a (ne(A_27a) -> c_2Ebool_2ECOND(A_27a) = f18(A_27a))) # label(ax_thm_2Ebool_2ECOND__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 40 (all A_27a (ne(A_27a) -> c_2Ebool_2ERES__FORALL(A_27a) = f36(A_27a))) # label(ax_thm_2Ebool_2ERES__FORALL__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 41 (all V0t (mem(V0t,bool) -> ((p(V0t) <-> $F) <-> -p(V0t)))) # label(conj_thm_2Ebool_2EIMP__F__EQ__F) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 42 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) <-> p(Q) | p(R)))))) # label(ax_or_p) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 43 (all A_27b all A_27c all A_27a all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V0P (mem(V0P,arr(A_27b,A_27c)) -> (all V4x ap(V0P,ap(V1N,V4x)) = ap(f66(A_27b,A_27c,A_27a,V1N,V0P),V4x)))))) # label(lameq_f66) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 44 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Ebool_2E_5C_2F,ap(V0P,V2x)),ap(V1Q,V2x)) = ap(f58(A_27a,V0P,V1Q),V2x)))))) # label(lameq_f58) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 45 (all A_27a (ne(A_27a) -> (all V0b (mem(V0b,bool) -> (all V1t (mem(V1t,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0b),V1t),V1t) = V1t)))))) # label(conj_thm_2Ebool_2Ebool__case__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 46 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = V0x)))) # label(conj_thm_2Ebool_2EEQ__REFL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 47 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x ap(V0P,V1x) = ap(f49(A_27a,V0P),V1x)))) # label(lameq_f49) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 48 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V1y = V0x <-> V0x = V1y))))))) # label(conj_thm_2Ebool_2EEQ__SYM__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 49 (all A_27a all A_27b all V0f ap(f24(A_27a,A_27b),V0f) = ap(c_2Ebool_2E_21(A_27b),f23(A_27a,A_27b,V0f))) # label(lameq_f24) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 50 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> ap(V1g,V2x) = ap(V0f,V2x))) -> V0f = V1g))))))))) # label(conj_thm_2Ebool_2EEQ__EXT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 51 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (p(ap(c_2Ebool_2E_21(A_27a),V0f)) <-> (all V1x (mem(V1x,A_27a) -> p(ap(V0f,V1x))))))))) # label(conj_thm_2Ebool_2EFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 52 (all A_27b all A_27a all V0M (mem(V0M,arr(A_27a,A_27b)) -> (all V1x ap(V0M,V1x) = ap(f47(A_27b,A_27a,V0M),V1x)))) # label(lameq_f47) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 53 (all A_27a all V0t (mem(V0t,bool) -> (all V1t1 (mem(V1t1,A_27a) -> (all V2t2 ap(c_2Emin_2E_40(A_27a),f15(A_27a,V1t1,V2t2,V0t)) = ap(f16(A_27a,V0t,V1t1),V2t2)))))) # label(lameq_f16) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 54 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x)) = ap(f37(A_27a,V0p,V1m),V2x)))))) # label(lameq_f37) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 55 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($T <-> p(ap(c_2Ebool_2EDATATYPE(A_27a),V0x))))))) # label(conj_thm_2Ebool_2EDATATYPE__TAG__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 56 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((exists V1rep (mem(V1rep,arr(A_27b,A_27a)) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b),V0P),V1rep)))) -> (exists V2rep (mem(V2rep,arr(A_27b,A_27a)) & (exists V3abs ((all V5r (mem(V5r,A_27a) -> (ap(V2rep,ap(V3abs,V5r)) = V5r <-> p(ap(V0P,V5r))))) & (all V4a (mem(V4a,A_27b) -> V4a = ap(V3abs,ap(V2rep,V4a)))) & mem(V3abs,arr(A_27a,A_27b))))))))))))) # label(conj_thm_2Ebool_2EABS__REP__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 57 (all A_27a all V0P ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_3F(A_27a),V0P)),ap(c_2Ebool_2E_21(A_27a),f11(A_27a,V0P))) = ap(f12(A_27a),V0P)) # label(lameq_f12) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 58 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> ((all V2x (mem(V2x,A_27a) -> (p(V0P) -> p(V1Q)))) <-> ((exists V3x (p(V0P) & mem(V3x,A_27a))) -> (all V4x (mem(V4x,A_27a) -> p(V1Q))))))))))) # label(conj_thm_2Ebool_2EBOTH__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 59 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1y (mem(V1y,A_27a) -> ap(f48(A_27b,A_27a,V0f),V1y) = ap(V0f,V1y))))))))) # label(conj_thm_2Ebool_2EBETA__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 60 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2ELET(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))))))) # label(mem_c_2Ebool_2ELET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 61 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V0A) | p(V1B) <-> (-p(V0A) -> p(V1B))))))) # label(conj_thm_2Ebool_2EDISJ__EQ__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 62 (all V0P (mem(V0P,arr(bool,bool)) -> ((all V1b (mem(V1b,bool) -> p(ap(V0P,V1b)))) <-> p(ap(V0P,c_2Ebool_2ET)) & p(ap(V0P,c_2Ebool_2EF))))) # label(conj_thm_2Ebool_2EFORALL__BOOL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 63 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3x ap(f59(A_27a,V0P),V3x) = ap(V0P,V3x)))) # label(lameq_f59) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 64 (all A_27a all V0p f43(A_27a,V0p) = ap(f44(A_27a),V0p)) # label(lameq_f44) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 65 (all A_27b all A_27a all V1t (mem(V1t,A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V2u (mem(V2u,A_27b) -> (all V3x ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V0a)),V1t),V2u) = ap(f67(A_27b,A_27a,V1t,V0a,V2u),V3x)))))))) # label(lameq_f67) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 66 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> p(ap(V1Q,V3x))))) & (exists V2x (p(ap(V0P,V2x)) & mem(V2x,A_27a))) -> p(ap(V1Q,ap(c_2Emin_2E_40(A_27a),V0P)))))))))) # label(conj_thm_2Ebool_2ESELECT__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 67 (all A_27a all V0t ap(f18(A_27a),V0t) = f17(A_27a,V0t)) # label(lameq_f18) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 68 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0b (mem(V0b,bool) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2g (mem(V2g,arr(A_27a,A_27b)) -> (all V3x (mem(V3x,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27b),V0b),ap(V1f,V3x)),ap(V2g,V3x)) = ap(ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,A_27b)),V0b),V1f),V2g),V3x))))))))))))) # label(conj_thm_2Ebool_2ECOND__RATOR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 69 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ebool_2EONTO(A_27a,A_27b) = f24(A_27a,A_27b))))) # label(ax_thm_2Ebool_2EONTO__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 70 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2EDATATYPE(A_27a),arr(A_27a,bool)))) # label(mem_c_2Ebool_2EDATATYPE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 71 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> (all V2x ap(f64(A_27a,V0P,V1f),V2x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P)),ap(V1f,V2x))))))) # label(lameq_f64) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 72 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1b (mem(V1b,bool) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ap(V0f,ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1b),V2x),V3y)) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),V1b),ap(V0f,V2x)),ap(V0f,V3y)))))))))))))) # label(conj_thm_2Ebool_2ECOND__RAND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 73 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(V0P,V2x)) -> p(ap(V1Q,V2x))))) -> ((all V3x (mem(V3x,A_27a) -> p(ap(V0P,V3x)))) -> (all V4x (mem(V4x,A_27a) -> p(ap(V1Q,V4x)))))))))))) # label(conj_thm_2Ebool_2EMONO__ALL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 74 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((exists V2x (p(ap(V1Q,V2x)) & mem(V2x,A_27a))) | p(V0P) <-> (exists V3x (mem(V3x,A_27a) & (p(ap(V1Q,V3x)) | p(V0P))))))))))) # label(conj_thm_2Ebool_2ERIGHT__OR__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 75 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((exists V2x (p(ap(V0P,V2x)) & mem(V2x,A_27a))) <-> p(ap(V0P,ap(c_2Emin_2E_40(A_27a),f49(A_27a,V0P))))))))) # label(conj_thm_2Ebool_2ESELECT__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 76 (all A_27a (ne(A_27a) -> f46(A_27a) = c_2Ebool_2ERES__SELECT(A_27a))) # label(ax_thm_2Ebool_2ERES__SELECT__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 77 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V3p (mem(V3p,arr(A_27a,bool)) -> (all V4m1 (mem(V4m1,arr(A_27a,A_27b)) -> (all V5m2 (mem(V5m2,arr(A_27a,A_27b)) -> ((all V6x (mem(V6x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V6x),V3p)) -> ap(V4m1,V6x) = ap(V5m2,V6x)))) -> ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V3p),V4m1) = ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V3p),V5m2)))))))) & (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,A_27b)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)) -> ap(ap(ap(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),V0p),V1m),V2x) = ap(V1m,V2x)))))))))))) # label(ax_thm_2Ebool_2ERES__ABSTRACT__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 78 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Ebool_2E_2F_5C,Q),R)) <-> p(R) & p(Q)))))) # label(ax_and_p) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 79 (all A_27a (ne(A_27a) -> (all V0b (mem(V0b,bool) -> (all V1t (mem(V1t,A_27a) -> V1t = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0b),V1t),V1t))))))) # label(conj_thm_2Ebool_2ECOND__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 80 (all V0t1 ap(f8,V0t1) = f7(V0t1)) # label(lameq_f8) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 81 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,bool) -> ((exists V1x (p(V0t) & mem(V1x,A_27a))) <-> p(V0t)))))) # label(conj_thm_2Ebool_2EEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 82 (all A_27a all V0a (mem(V0a,A_27a) -> (all V1x ap(f57(A_27a,V0a),V1x) = ap(ap(c_2Emin_2E_3D(A_27a),V1x),V0a)))) # label(lameq_f57) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 83 $T # label(conj_thm_2Ebool_2ETRUTH) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 84 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) & p(V1t2) -> p(V1t2)))))) # label(conj_thm_2Ebool_2EAND2__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 85 (all A_27a all V0P ap(f2(A_27a),V0P) = ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P))) # label(lameq_f2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 86 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(V0P,V1x)) -> p(ap(V0P,ap(c_2Emin_2E_40(A_27a),V0P)))))))))) # label(ax_thm_2Ebool_2ESELECT__AX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 87 (all A_27a (ne(A_27a) -> c_2Ebool_2E_3F_21(A_27a) = f12(A_27a))) # label(ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 88 (all V1t2 (mem(V1t2,bool) -> (all V0t1 (mem(V0t1,bool) -> (all V2t ap(f3(V1t2,V0t1),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t))),V2t)))))) # label(lameq_f3) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 89 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_3F) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 90 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> ((p(V0A) | p(V1B)) & (p(V0A) | p(V2C)) <-> p(V1B) & p(V2C) | p(V0A)))))))) # label(conj_thm_2Ebool_2ELEFT__OR__OVER__AND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 91 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b),V0P),V1rep)) <-> (all V2x_27 (mem(V2x_27,A_27b) -> (all V3x_27_27 (mem(V3x_27_27,A_27b) -> (ap(V1rep,V2x_27) = ap(V1rep,V3x_27_27) -> V3x_27_27 = V2x_27))))) & (all V4x (mem(V4x,A_27a) -> ((exists V5x_27 (mem(V5x_27,A_27b) & ap(V1rep,V5x_27) = V4x)) <-> p(ap(V0P,V4x)))))))))))))) # label(conj_thm_2Ebool_2ETYPE__DEFINITION__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 92 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y ap(f10(A_27a,V0P,V1x),V2y) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V1x)),ap(V0P,V2y))),ap(ap(c_2Emin_2E_3D(A_27a),V1x),V2y))))))) # label(lameq_f10) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 93 (all A_27a all V1f (mem(V1f,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (all V4y ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V1f,V3x)),ap(V1f,V4y))),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V4y)) = ap(f62(A_27a,V1f,V3x),V4y)))))) # label(lameq_f62) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 94 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2Ethe__value(A_27a),ty_2Ebool_2Eitself(A_27a)))) # label(mem_c_2Ebool_2Ethe__value) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 95 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (-(p(V0A) -> p(V1B)) <-> -p(V1B) & p(V0A)))))) # label(conj_thm_2Ebool_2ENOT__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 96 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,bool)) -> (all V3g (mem(V3g,arr(A_27a,bool)) -> (V1Q = V0P -> ((all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1Q)) -> (p(ap(V2f,V4x)) <-> p(ap(V3g,V4x)))))) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),V2f)) <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V1Q),V3g))))))))))))))) # label(conj_thm_2Ebool_2ERES__FORALL__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 97 (all V4b ap(f65,V4b) = ap(c_2Ebool_2E_7E,V4b)) # label(lameq_f65) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 98 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1a (mem(V1a,A_27a) -> ((exists V2x (p(ap(V0P,V2x)) & V2x = V1a & mem(V2x,A_27a))) <-> p(ap(V0P,V1a))))))))) # label(conj_thm_2Ebool_2EUNWIND__THM1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 99 (all A_27a (ne(A_27a) -> c_2Ebool_2EIN(A_27a) = f33(A_27a))) # label(ax_thm_2Ebool_2EIN__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 100 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V0x = V1y -> V1y = V0x))))))) # label(conj_thm_2Ebool_2EEQ__SYM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 101 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (all V4y ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_2F_5C,ap(V1m,V3x)),ap(V1m,V4y))),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V4y)) = ap(f41(A_27a,V1m,V3x),V4y)))))) # label(lameq_f41) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 102 (all V0t (mem(V0t,bool) -> p(V0t) | -p(V0t))) # label(conj_thm_2Ebool_2EEXCLUDED__MIDDLE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 103 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),V1f)) <-> (exists V2x (mem(V2x,A_27a) & p(ap(V1f,V2x)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P))))))))))) # label(conj_thm_2Ebool_2ERES__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 104 (all A_27a all V1f (mem(V1f,arr(A_27a,bool)) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3x ap(f63(A_27a,V1f,V0P),V3x) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f62(A_27a,V1f,V3x))))))) # label(lameq_f63) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 105 (all V0v (mem(V0v,bool) -> ($T <-> p(ap(c_2Ebool_2EBOUNDED,V0v))))) # label(conj_thm_2Ebool_2EBOUNDED__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 106 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ebool_2Eliteral__case(A_27a,A_27b) = f14(A_27b,A_27a))))) # label(ax_thm_2Ebool_2Eliteral__case__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 107 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0M (mem(V0M,arr(A_27a,A_27b)) -> f47(A_27b,A_27a,V0M) = V0M)))))) # label(conj_thm_2Ebool_2EETA__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 108 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2EARB(A_27a),A_27a))) # label(mem_c_2Ebool_2EARB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 109 i(bool) = i(bool) <-> $T # label(ax_thm_2Ebool_2ET__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 110 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(c_2Ebool_2E_3F(A_27a),f37(A_27a,V0p,V1m)) = ap(f38(A_27a,V0p),V1m)))) # label(lameq_f38) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 111 (all V0x (mem(V0x,bool) -> (all V1y (mem(V1y,bool) -> (all V2z (mem(V2z,bool) -> (all V3w (mem(V3w,bool) -> ((p(V2z) -> p(V3w)) & (p(V0x) -> p(V1y)) -> (p(V2z) | p(V0x) -> p(V3w) | p(V1y))))))))))) # label(conj_thm_2Ebool_2EMONO__OR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 112 (all A_27a all V0x (mem(V0x,A_27a) -> (all V1y ap(ap(c_2Emin_2E_3D(A_27a),V0x),V1y) = ap(f51(A_27a,V0x),V1y)))) # label(lameq_f51) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 113 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & ($F <-> p(V0t) & $F) & (p(V0t) & p(V0t) <-> p(V0t)) & (p(V0t) & $F <-> $F) & (p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 114 (all A0 (ne(A0) -> ne(ty_2Ebool_2Eitself(A0)))) # label(ne_ty_2Ebool_2Eitself) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 115 (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> (all V2R (mem(V2R,bool) -> ((p(V0P) -> p(V1Q) & p(V2R)) <-> (p(V0P) -> p(V2R)) & (p(V0P) -> p(V1Q))))))))) # label(conj_thm_2Ebool_2EIMP__CONJ__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 116 (all A_27a all V0p ap(f46(A_27a),V0p) = f45(A_27a,V0p)) # label(lameq_f46) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 117 (all V0t1 f4(V0t1) = ap(f5,V0t1)) # label(lameq_f5) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 118 (all A_27a all A_27b all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V2x_27 (mem(V2x_27,A_27b) -> (all V3x_27_27 ap(f25(A_27a,A_27b,V1rep,V2x_27),V3x_27_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27a),ap(V1rep,V2x_27)),ap(V1rep,V3x_27_27))),ap(ap(c_2Emin_2E_3D(A_27b),V2x_27),V3x_27_27))))))) # label(lameq_f25) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 119 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2EONTO(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)))))) # label(mem_c_2Ebool_2EONTO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 120 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__EXISTS(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2ERES__EXISTS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 121 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1 & V1t2 = ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2))))))) # label(conj_thm_2Ebool_2ECOND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 122 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> p(ap(V0P,V3x)))) & (all V4x (mem(V4x,A_27a) -> p(ap(V1Q,V4x)))) <-> (all V2x (mem(V2x,A_27a) -> p(ap(V1Q,V2x)) & p(ap(V0P,V2x))))))))))) # label(conj_thm_2Ebool_2EFORALL__AND__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 123 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (V0f = V1g <-> (all V2x (mem(V2x,A_27a) -> ap(V1g,V2x) = ap(V0f,V2x)))))))))))) # label(conj_thm_2Ebool_2EFUN__EQ__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 124 (all V0f (mem(V0f,arr(bool,bool)) -> V0f = f65 | i(bool) = V0f | k(bool,c_2Ebool_2EF) = V0f | k(bool,c_2Ebool_2ET) = V0f)) # label(conj_thm_2Ebool_2EBOOL__FUN__CASES__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 125 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,bool) -> (p(V0t) <-> (all V1x (mem(V1x,A_27a) -> p(V0t)))))))) # label(conj_thm_2Ebool_2EFORALL__SIMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 126 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((exists V1x (mem(V1x,A_27a) & (exists V2y (mem(V2y,A_27b) & p(ap(ap(V0P,V1x),V2y)))))) <-> (exists V3y (mem(V3y,A_27b) & (exists V4x (mem(V4x,A_27a) & p(ap(ap(V0P,V4x),V3y))))))))))))) # label(conj_thm_2Ebool_2ESWAP__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 127 (all Q (mem(Q,bool) -> (p(ap(c_2Ebool_2E_7E,Q)) <-> -p(Q)))) # label(ax_neg_p) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 128 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V3x (mem(V3x,A_27a) & (p(V1Q) | p(ap(V0P,V3x))))) <-> p(V1Q) | (exists V2x (mem(V2x,A_27a) & p(ap(V0P,V2x))))))))))) # label(conj_thm_2Ebool_2ELEFT__OR__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 129 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27a))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> ap(ap(V0f,V1x),ap(ap(V0f,V2y),V3z)) = ap(ap(V0f,ap(ap(V0f,V1x),V2y)),V3z))))))) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> ap(ap(V0f,V5y),V4x) = ap(ap(V0f,V4x),V5y))))) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (all V8z (mem(V8z,A_27a) -> ap(ap(V0f,V7y),ap(ap(V0f,V6x),V8z)) = ap(ap(V0f,V6x),ap(ap(V0f,V7y),V8z)))))))))))))) # label(conj_thm_2Ebool_2ELCOMM__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 130 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((all V3y (mem(V3y,A_27b) -> (all V4x (mem(V4x,A_27a) -> p(ap(ap(V0P,V4x),V3y)))))) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> p(ap(ap(V0P,V1x),V2y))))))))))))) # label(conj_thm_2Ebool_2ESWAP__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 131 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0N (mem(V0N,arr(A_27a,arr(A_27b,A_27c))) -> (all V1M (mem(V1M,A_27a) -> (all V2b (mem(V2b,A_27b) -> ap(ap(ap(c_2Ebool_2ELET(A_27a,arr(A_27b,A_27c)),f55(A_27c,A_27b,A_27a,V0N)),V1M),V2b) = ap(ap(c_2Ebool_2ELET(A_27a,A_27c),f56(A_27b,A_27c,A_27a,V0N,V2b)),V1M))))))))))))) # label(conj_thm_2Ebool_2ELET__RATOR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 132 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 133 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0b (mem(V0b,bool) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2g (mem(V2g,arr(A_27a,A_27b)) -> f52(A_27b,A_27a,V0b,V1f,V2g) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,A_27b)),V0b),V1f),V2g))))))))))) # label(conj_thm_2Ebool_2ECOND__ABS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 134 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V2x (p(V1Q) & p(ap(V0P,V2x)) & mem(V2x,A_27a))) <-> p(V1Q) & (exists V3x (p(ap(V0P,V3x)) & mem(V3x,A_27a)))))))))) # label(conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 135 (all A_27b all A_27a all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V3x ap(V1N,V3x) = ap(f53(A_27b,A_27a,V1N),V3x)))) # label(lameq_f53) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 136 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (all V2M (mem(V2M,A_27a) -> (all V3N (mem(V3N,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (V3N = V4x -> ap(V0f,V4x) = ap(V1g,V4x)))) & V2M = V3N -> ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),V0f),V2M) = ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),V1g),V3N)))))))))))))) # label(conj_thm_2Ebool_2Eliteral__case__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 137 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V1t2) -> p(V0t1) | p(V1t2)))))) # label(conj_thm_2Ebool_2EOR__INTRO__THM2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 138 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27b,bool)) -> (all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V2M (mem(V2M,A_27a) -> (p(ap(ap(c_2Ebool_2ELET(A_27a,bool),f54(A_27b,A_27a,V1N,V0P)),V2M)) <-> p(ap(V0P,ap(ap(c_2Ebool_2ELET(A_27a,A_27b),f53(A_27b,A_27a,V1N)),V2M)))))))))))))) # label(conj_thm_2Ebool_2ELET__RAND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 139 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2Eliteral__case(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))))))) # label(mem_c_2Ebool_2Eliteral__case) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 140 (all A_27a all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V4x ap(f60(A_27a,V1Q),V4x) = ap(V1Q,V4x)))) # label(lameq_f60) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 141 (all V0t (mem(V0t,bool) -> (p(V0t) <-> $F) | (p(V0t) <-> $T))) # label(ax_thm_2Ebool_2EBOOL__CASES__AX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 142 (all A_27a (ne(A_27a) -> (all V0i (mem(V0i,ty_2Ebool_2Eitself(A_27a)) -> c_2Ebool_2Ethe__value(A_27a) = V0i)))) # label(conj_thm_2Ebool_2EITSELF__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 143 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f30(A_27b,A_27a) = c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b))))) # label(ax_thm_2Ebool_2ETYPE__DEFINITION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 144 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V1t2) & p(V0t1) -> p(V0t1)))))) # label(conj_thm_2Ebool_2EAND1__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 145 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0t (mem(V0t,arr(A_27a,A_27b)) -> V0t = f31(A_27b,A_27a,V0t))))))) # label(ax_thm_2Ebool_2EETA__AX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 146 (all V0P (mem(V0P,arr(bool,bool)) -> (p(ap(V0P,c_2Ebool_2ET)) & p(ap(V0P,c_2Ebool_2EF)) -> (all V1b (mem(V1b,bool) -> p(ap(V0P,V1b))))))) # label(conj_thm_2Ebool_2Ebool__INDUCT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 147 (all V0t (mem(V0t,bool) -> p(V0t))) <-> $F # label(ax_thm_2Ebool_2EF__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 148 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2ERES__ABSTRACT(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27a,A_27b),arr(A_27a,A_27b)))))))) # label(mem_c_2Ebool_2ERES__ABSTRACT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 149 (all A_27b all A_27c all A_27a all V0N (mem(V0N,arr(A_27a,arr(A_27b,A_27c))) -> (all V2b (mem(V2b,A_27b) -> (all V4x ap(f56(A_27b,A_27c,A_27a,V0N,V2b),V4x) = ap(ap(V0N,V4x),V2b)))))) # label(lameq_f56) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 150 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(f43(A_27a,V0p),V1m) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0p),f40(A_27a,V1m))),ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f42(A_27a,V1m,V0p)))))) # label(lameq_f43) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 151 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__FORALL(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2ERES__FORALL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 152 -$T <-> $F # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 153 -$F <-> $T # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 154 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 155 (all A_27a (ne(A_27a) -> f1(A_27a) = c_2Ebool_2E_21(A_27a))) # label(ax_thm_2Ebool_2EFORALL__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 156 (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> (all V2R (mem(V2R,bool) -> ((p(V1Q) -> p(V2R)) & (p(V0P) -> p(V2R)) <-> (p(V0P) | p(V1Q) -> p(V2R))))))))) # label(conj_thm_2Ebool_2EDISJ__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 157 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (-(p(V0A) | p(V1B)) <-> -p(V1B) & -p(V0A)) & (-(p(V1B) & p(V0A)) <-> -p(V0A) | -p(V1B)))))) # label(conj_thm_2Ebool_2EDE__MORGAN__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 158 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Ebool_2E_21) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 159 (all V0t1 (mem(V0t1,bool) -> (all V1t2 ap(f7(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f6(V0t1,V1t2))))) # label(lameq_f7) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 160 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1a (mem(V1a,A_27a) -> (p(ap(V0P,V1a)) <-> (exists V2x (V2x = V1a & p(ap(V0P,V2x)) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Ebool_2EUNWIND__THM2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 161 (all V0y (mem(V0y,bool) -> (all V1x (mem(V1x,bool) -> ((-p(V1x) -> -p(V0y)) <-> (p(V0y) -> p(V1x))))))) # label(conj_thm_2Ebool_2EMONO__NOT__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 162 (all V0t1 (mem(V0t1,bool) -> (all V1t2 ap(f4(V0t1),V1t2) = ap(c_2Ebool_2E_21(bool),f3(V1t2,V0t1))))) # label(lameq_f4) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 163 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2EIN(A_27a),arr(A_27a,arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2EIN) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 164 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1y (mem(V1y,A_27b) -> (all V2x ap(ap(c_2Emin_2E_3D(A_27b),V1y),ap(V0f,V2x)) = ap(f22(A_27b,A_27a,V0f,V1y),V2x)))))) # label(lameq_f22) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 165 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (all V2t3 (mem(V2t3,bool) -> ((p(V0t1) -> (p(V1t2) -> p(V2t3))) <-> (p(V1t2) & p(V0t1) -> p(V2t3))))))))) # label(conj_thm_2Ebool_2EAND__IMP__INTRO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 166 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> -p(ap(V0P,V2x)))) <-> -(exists V1x (p(ap(V0P,V1x)) & mem(V1x,A_27a)))))))) # label(conj_thm_2Ebool_2ENOT__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 167 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Ebool_2Eitself(A_27a),bool)) -> (p(ap(V0P,c_2Ebool_2Ethe__value(A_27a))) -> (all V1i (mem(V1i,ty_2Ebool_2Eitself(A_27a)) -> p(ap(V0P,V1i))))))))) # label(conj_thm_2Ebool_2Eitself__induction) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 168 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x ap(V0f,V1x) = ap(f13(A_27b,A_27a,V0f),V1x)))) # label(lameq_f13) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 169 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V5x (p(ap(V0P,V5x)) & p(V1Q) & mem(V5x,A_27a))) <-> (exists V4x (mem(V4x,A_27a) & p(ap(V0P,V4x)))) & p(V1Q)) & ((exists V7x (p(ap(V0P,V7x)) & p(V1Q) & mem(V7x,A_27a))) <-> p(V1Q) & (exists V6x (mem(V6x,A_27a) & p(ap(V0P,V6x))))) & ((all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> p(V1Q)))) <-> ((exists V2x (mem(V2x,A_27a) & p(ap(V0P,V2x)))) -> p(V1Q))))))))) # label(conj_thm_2Ebool_2EPULL__EXISTS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 170 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) -> (p(V3y_27) <-> p(V2y))) & (p(V1x_27) <-> p(V0x)) -> ((p(V0x) -> p(V2y)) <-> (p(V1x_27) -> p(V3y_27)))))))))))) # label(conj_thm_2Ebool_2EIMP__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 171 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V1t2) & p(V0t1) <-> p(V1t2) & p(V0t1)))))) # label(conj_thm_2Ebool_2ECONJ__COMM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 172 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (V0x = V0x <-> $T))))) # label(conj_thm_2Ebool_2EREFL__CLAUSE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 173 (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> (((p(V0P) -> p(V1Q)) -> p(V0P)) -> p(V0P)))))) # label(conj_thm_2Ebool_2EPEIRCE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 174 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Ebool_2Eitself(A_27a),bool)) -> (p(ap(V0P,c_2Ebool_2Ethe__value(A_27a))) <-> (all V1x (mem(V1x,ty_2Ebool_2Eitself(A_27a)) -> p(ap(V0P,V1x))))))))) # label(conj_thm_2Ebool_2EFORALL__itself) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 175 (all A_27b all A_27a all V0P f29(A_27b,A_27a,V0P) = ap(f30(A_27b,A_27a),V0P)) # label(lameq_f30) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 176 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V0A) | p(V1B) | p(V2C) <-> p(V0A) | p(V1B) | p(V2C)))))))) # label(conj_thm_2Ebool_2EDISJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 177 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Emin_2E_40(A_27a),f50(A_27a,V0x)) = V0x)))) # label(conj_thm_2Ebool_2ESELECT__REFL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 178 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> ((p(V1t2) <-> p(V0t1)) <-> -p(V0t1) & -p(V1t2) | p(V1t2) & p(V0t1)))))) # label(conj_thm_2Ebool_2EEQ__EXPAND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 179 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((p(V0P) -> (exists V3x (mem(V3x,A_27a) & p(ap(V1Q,V3x))))) <-> (exists V2x ((p(V0P) -> p(ap(V1Q,V2x))) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Ebool_2ERIGHT__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 180 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(V0P,V2x)) -> p(ap(V1Q,V2x))))) -> ((exists V3x (p(ap(V0P,V3x)) & mem(V3x,A_27a))) -> (exists V4x (mem(V4x,A_27a) & p(ap(V1Q,V4x)))))))))))) # label(conj_thm_2Ebool_2EMONO__EXISTS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 181 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V4x ap(ap(c_2Emin_2E_3D(bool),ap(V0P,V4x)),ap(c_2Ebool_2E_3F(A_27b),f27(A_27a,A_27b,V1rep,V4x))) = ap(f28(A_27b,A_27a,V0P,V1rep),V4x)))))) # label(lameq_f28) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 182 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (-(all V1x (mem(V1x,A_27a) -> p(ap(V0P,V1x)))) <-> (exists V2x (mem(V2x,A_27a) & -p(ap(V0P,V2x))))))))) # label(conj_thm_2Ebool_2ENOT__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 183 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V2x (mem(V2x,A_27a) & (p(ap(V0P,V2x)) -> p(V1Q)))) <-> ((all V3x (mem(V3x,A_27a) -> p(ap(V0P,V3x)))) -> p(V1Q))))))))) # label(conj_thm_2Ebool_2ELEFT__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 184 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (all V2M (mem(V2M,A_27a) -> (all V3N (mem(V3N,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (V3N = V4x -> ap(V1g,V4x) = ap(V0f,V4x)))) & V3N = V2M -> ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V0f),V2M) = ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V1g),V3N)))))))))))))) # label(conj_thm_2Ebool_2ELET__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 185 (all A_27a (ne(A_27a) -> (exists V0rep (p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(A_27a,ty_2Ebool_2Eitself(A_27a)),ap(c_2Emin_2E_3D(A_27a),c_2Ebool_2EARB(A_27a))),V0rep)) & mem(V0rep,arr(ty_2Ebool_2Eitself(A_27a),A_27a)))))) # label(ax_thm_2Ebool_2Eitself__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 186 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__SELECT(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),A_27a))))) # label(mem_c_2Ebool_2ERES__SELECT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 187 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V2x ap(f48(A_27b,A_27a,V0f),V2x) = ap(V0f,V2x)))) # label(lameq_f48) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 188 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ($T <-> p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),k(A_27a,c_2Ebool_2ET)))))))) # label(conj_thm_2Ebool_2ERES__FORALL__TRUE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 189 (all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1y ap(c_2Ebool_2E_3F(A_27a),f22(A_27b,A_27a,V0f,V1y)) = ap(f23(A_27a,A_27b,V0f),V1y)))) # label(lameq_f23) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 190 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> ((all V2y (mem(V2y,A_27a) -> (V1x = V2y <-> p(ap(V0P,V2y))))) -> V1x = ap(c_2Emin_2E_40(A_27a),V0P)))))))) # label(conj_thm_2Ebool_2ESELECT__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 191 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27b) -> ap(k(A_27b,V0t1),V1t2) = V0t1)))))))) # label(conj_thm_2Ebool_2EABS__SIMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 192 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),V0P),V1f)) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),f61(A_27a,V1f))) & p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),f63(A_27a,V1f,V0P)))))))))) # label(conj_thm_2Ebool_2ERES__EXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 193 (all A_27a all V1f (mem(V1f,arr(A_27a,bool)) -> (all V2x ap(f61(A_27a,V1f),V2x) = ap(V1f,V2x)))) # label(lameq_f61) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 194 (all V0P (mem(V0P,bool) -> (all V1P_27 (mem(V1P_27,bool) -> (all V2Q (mem(V2Q,bool) -> (all V3Q_27 (mem(V3Q_27,bool) -> ((p(V0P) <-> p(V1P_27)) & (-p(V1P_27) -> (p(V3Q_27) <-> p(V2Q))) -> (p(V3Q_27) | p(V1P_27) <-> p(V2Q) | p(V0P))))))))))) # label(conj_thm_2Ebool_2ELEFT__OR__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.69 195 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,A_27a),bool))))))) # label(mem_c_2Ebool_2ETYPE__DEFINITION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 196 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V2C) & p(V0A) | p(V1B) & p(V0A) <-> p(V0A) & (p(V1B) | p(V2C))))))))) # label(conj_thm_2Ebool_2ERIGHT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 197 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(c_2Emin_2E_40(A_27a),f37(A_27a,V0p,V1m)) = ap(f45(A_27a,V0p),V1m)))) # label(lameq_f45) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 198 (all V0x (mem(V0x,bool) -> (all V1y (mem(V1y,bool) -> (all V2z (mem(V2z,bool) -> (all V3w (mem(V3w,bool) -> ((p(V0x) -> p(V1y)) & (p(V2z) -> p(V3w)) -> (p(V2z) & p(V0x) -> p(V1y) & p(V3w))))))))))) # label(conj_thm_2Ebool_2EMONO__AND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 199 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (p(ap(c_2Ebool_2EONTO(A_27a,A_27b),V0f)) <-> (all V1y (mem(V1y,A_27b) -> (exists V2x (ap(V0f,V2x) = V1y & mem(V2x,A_27a)))))))))))) # label(conj_thm_2Ebool_2EONTO__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 200 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) -> (p(V1t2) -> p(V1t2) & p(V0t1))))))) # label(conj_thm_2Ebool_2EAND__INTRO__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 201 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,bool) -> (p(ap(c_2Ebool_2E_3F_21(A_27a),k(A_27a,V0t))) <-> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> V2x = V3y)))) & p(V0t)))))) # label(conj_thm_2Ebool_2EUEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 202 (all A_27b all A_27a all V0f ap(c_2Ebool_2E_21(A_27a),f20(A_27b,A_27a,V0f)) = ap(f21(A_27b,A_27a),V0f)) # label(lameq_f21) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 203 (all V0P (mem(V0P,bool) -> (all V1P_27 (mem(V1P_27,bool) -> (all V2Q (mem(V2Q,bool) -> (all V3Q_27 (mem(V3Q_27,bool) -> ((-p(V1P_27) -> (p(V3Q_27) <-> p(V2Q))) & (-p(V2Q) -> (p(V1P_27) <-> p(V0P))) -> (p(V2Q) | p(V0P) <-> p(V3Q_27) | p(V1P_27))))))))))) # label(conj_thm_2Ebool_2EOR__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 204 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (p(V0P) & (all V2x (mem(V2x,A_27a) -> p(ap(V1Q,V2x)))) <-> (all V3x (mem(V3x,A_27a) -> p(ap(V1Q,V3x)) & p(V0P)))))))))) # label(conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 205 (exists V0f (-p(ap(c_2Ebool_2EONTO(ind,ind),V0f)) & p(ap(c_2Ebool_2EONE__ONE(ind,ind),V0f)) & mem(V0f,arr(ind,ind)))) # label(ax_thm_2Ebool_2EINFINITY__AX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 206 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ((all V1x1 (mem(V1x1,A_27a) -> (all V2x2 (mem(V2x2,A_27a) -> (ap(V0f,V1x1) = ap(V0f,V2x2) -> V1x1 = V2x2))))) <-> p(ap(c_2Ebool_2EONE__ONE(A_27a,A_27b),V0f))))))))) # label(conj_thm_2Ebool_2EONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 207 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EIMP__F) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 208 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2EONE__ONE(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)))))) # label(mem_c_2Ebool_2EONE__ONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 209 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> ((exists X (mem(X,A) & p(ap(Q,X)))) <-> p(ap(c_2Ebool_2E_3F(A),Q))))))) # label(ax_ex_p) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 210 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V0A) & p(V2C) | p(V0A) & p(V1B) <-> (p(V1B) | p(V2C)) & p(V0A)))))))) # label(conj_thm_2Ebool_2ELEFT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 211 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),k(A_27a,c_2Ebool_2EF))) <-> $F))))) # label(conj_thm_2Ebool_2ERES__EXISTS__FALSE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 212 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(c_2Ebool_2E_21(A_27a),f34(A_27a,V0p,V1m)) = ap(f35(A_27a,V0p),V1m)))) # label(lameq_f35) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 213 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((all V3x (mem(V3x,A_27a) -> p(ap(V0P,V3x)) & p(V1Q))) <-> (all V2x (mem(V2x,A_27a) -> p(ap(V0P,V2x)))) & p(V1Q)))))))) # label(conj_thm_2Ebool_2ELEFT__AND__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 214 (all A_27b all A_27a all V0b (mem(V0b,bool) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2g (mem(V2g,arr(A_27a,A_27b)) -> (all V3x ap(ap(ap(c_2Ebool_2ECOND(A_27b),V0b),ap(V1f,V3x)),ap(V2g,V3x)) = ap(f52(A_27b,A_27a,V0b,V1f,V2g),V3x)))))))) # label(lameq_f52) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 215 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Ebool_2ERES__EXISTS__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 216 (all V0P (mem(V0P,bool) -> (all V1P_27 (mem(V1P_27,bool) -> (all V2Q (mem(V2Q,bool) -> (all V3Q_27 (mem(V3Q_27,bool) -> ((p(V1P_27) -> (p(V3Q_27) <-> p(V2Q))) & (p(V0P) <-> p(V1P_27)) -> (p(V3Q_27) & p(V1P_27) <-> p(V0P) & p(V2Q))))))))))) # label(conj_thm_2Ebool_2ELEFT__AND__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 217 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> (exists V2fn (V1t2 = ap(V2fn,c_2Ebool_2EF) & V0t1 = ap(V2fn,c_2Ebool_2ET) & mem(V2fn,arr(bool,A_27a)))))))))) # label(conj_thm_2Ebool_2EboolAxiom) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 218 (all A_27a (ne(A_27a) -> c_2Ebool_2ERES__EXISTS(A_27a) = f39(A_27a))) # label(ax_thm_2Ebool_2ERES__EXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 219 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2z (mem(V2z,A_27a) -> (V2z = V1y & V0x = V1y -> V2z = V0x))))))))) # label(conj_thm_2Ebool_2EEQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 220 (all A_27a all V1t1 (mem(V1t1,A_27a) -> (all V2t2 (mem(V2t2,A_27a) -> (all V0t (mem(V0t,bool) -> (all V3x ap(f15(A_27a,V1t1,V2t2,V0t),V3x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2ET)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V1t1))),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(bool),V0t),c_2Ebool_2EF)),ap(ap(c_2Emin_2E_3D(A_27a),V3x),V2t2)))))))))) # label(lameq_f15) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 221 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> ((all X (mem(X,A) -> p(ap(Q,X)))) <-> p(ap(c_2Ebool_2E_21(A),Q))))))) # label(ax_all_p) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 222 (all V0t ap(ap(c_2Emin_2E_3D_3D_3E,V0t),c_2Ebool_2EF) = ap(f9,V0t)) # label(lameq_f9) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 223 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (p(V0P) | (all V3x (mem(V3x,A_27a) -> p(ap(V1Q,V3x)))) <-> (all V2x (mem(V2x,A_27a) -> p(V0P) | p(ap(V1Q,V2x))))))))))) # label(conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 224 (all V0bool (mem(V0bool,arr(bool,arr(bool,bool))) -> (p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(V0bool,c_2Ebool_2ET),c_2Ebool_2EF))) <-> $T))) # label(conj_thm_2Ebool_2EDATATYPE__BOOL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 225 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(V0P) -> p(ap(V1Q,V2x))))) <-> (p(V0P) -> (all V3x (mem(V3x,A_27a) -> p(ap(V1Q,V3x)))))))))))) # label(conj_thm_2Ebool_2ERIGHT__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 226 (all V0y (mem(V0y,bool) -> (all V1x (mem(V1x,bool) -> (all V2z (mem(V2z,bool) -> (all V3w (mem(V3w,bool) -> ((p(V0y) -> p(V1x)) & (p(V2z) -> p(V3w)) -> ((p(V1x) -> p(V2z)) -> (p(V0y) -> p(V3w)))))))))))) # label(conj_thm_2Ebool_2EMONO__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 227 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> (all V2x (mem(V2x,A_27a) -> (all V3x_27 (mem(V3x_27,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5y_27 (mem(V5y_27,A_27a) -> ((p(V1Q) -> V2x = V3x_27) & (-p(V1Q) -> V4y = V5y_27) & (p(V1Q) <-> p(V0P)) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0P),V2x),V4y) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V1Q),V3x_27),V5y_27)))))))))))))))) # label(conj_thm_2Ebool_2ECOND__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 228 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1t (mem(V1t,A_27a) -> ((all V2x (mem(V2x,A_27a) -> (V1t = V2x -> p(ap(V0P,V2x))))) -> p(ap(c_2Ebool_2E_3F(A_27a),V0P))))))))) # label(conj_thm_2Ebool_2EJRH__INDUCT__UTIL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 229 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> (((exists V3x (p(ap(V0P,V3x)) & mem(V3x,A_27a))) -> p(V1Q)) <-> (all V2x (mem(V2x,A_27a) -> (p(ap(V0P,V2x)) -> p(V1Q))))))))))) # label(conj_thm_2Ebool_2ELEFT__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 230 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (p(ap(c_2Ebool_2E_3F_21(A_27a),f49(A_27a,V0P))) <-> (exists V2x (mem(V2x,A_27a) & p(ap(V0P,V2x)))) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(V0P,V4y)) & p(ap(V0P,V3x)) -> V3x = V4y)))))))))) # label(conj_thm_2Ebool_2EEXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 231 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((all V1x (mem(V1x,A_27a) -> (exists V2y (p(ap(ap(V0P,V1x),V2y)) & mem(V2y,A_27b))))) <-> (exists V3f (mem(V3f,arr(A_27a,A_27b)) & (all V4x (mem(V4x,A_27a) -> p(ap(ap(V0P,V4x),ap(V3f,V4x)))))))))))))) # label(conj_thm_2Ebool_2ESKOLEM__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 232 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V3x ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f41(A_27a,V1m,V3x)) = ap(f42(A_27a,V1m,V0p),V3x)))))) # label(lameq_f42) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 233 (all V0x (mem(V0x,bool) -> (all V1y (mem(V1y,bool) -> (all V2z (mem(V2z,bool) -> (all V3w (mem(V3w,bool) -> (all V4b (mem(V4b,bool) -> ((p(V0x) -> p(V1y)) -> ((p(V2z) -> p(V3w)) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V4b),V0x),V2z)) -> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V4b),V1y),V3w))))))))))))))) # label(conj_thm_2Ebool_2EMONO__COND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 234 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (p(ap(c_2Ebool_2E_3F_21(A_27a),f58(A_27a,V0P,V1Q))) -> p(ap(c_2Ebool_2E_3F_21(A_27a),f60(A_27a,V1Q))) | p(ap(c_2Ebool_2E_3F_21(A_27a),f59(A_27a,V0P)))))))))) # label(conj_thm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 235 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V0A) | p(V1B) <-> p(V0A) | p(V1B)))))) # label(conj_thm_2Ebool_2EDISJ__SYM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 236 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) & p(V1t2) <-> p(V1t2) & p(V0t1)))))) # label(conj_thm_2Ebool_2ECONJ__SYM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 237 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (p(ap(c_2Ebool_2E_3F(A_27a),V0f)) <-> (exists V1x (p(ap(V0f,V1x)) & mem(V1x,A_27a)))))))) # label(conj_thm_2Ebool_2EEXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 238 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ebool_2EONE__ONE(A_27a,A_27b) = f21(A_27b,A_27a))))) # label(ax_thm_2Ebool_2EONE__ONE__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 239 (all A_27c all A_27b all A_27a all V0N (mem(V0N,arr(A_27a,arr(A_27b,A_27c))) -> (all V3x ap(V0N,V3x) = ap(f55(A_27c,A_27b,A_27a,V0N),V3x)))) # label(lameq_f55) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 240 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (all V1v (mem(V1v,A_27a) -> (p(ap(V0f,V1v)) <-> (all V2x (mem(V2x,A_27a) -> (V2x = V1v -> p(ap(V0f,V2x)))))))))))) # label(conj_thm_2Ebool_2EUNWIND__FORALL__THM1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 241 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27b) -> (exists V1f (mem(V1f,arr(ty_2Ebool_2Eitself(A_27a),A_27b)) & V0e = ap(V1f,c_2Ebool_2Ethe__value(A_27a)))))))))) # label(conj_thm_2Ebool_2Eitself__Axiom) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 242 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> ((exists V4x (p(V1Q) & mem(V4x,A_27a))) & (exists V3x (mem(V3x,A_27a) & p(V0P))) <-> (exists V2x (mem(V2x,A_27a) & p(V0P) & p(V1Q)))))))))) # label(conj_thm_2Ebool_2EBOTH__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 243 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x1 ap(f20(A_27b,A_27a,V0f),V1x1) = ap(c_2Ebool_2E_21(A_27a),f19(A_27b,A_27a,V0f,V1x1))))) # label(lameq_f20) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 244 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(f40(A_27a,V1m),V2x) = ap(V1m,V2x)))) # label(lameq_f40) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 245 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x)) = ap(f34(A_27a,V0p,V1m),V2x)))))) # label(lameq_f34) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 246 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1rep ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_21(A_27b),f26(A_27a,A_27b,V1rep))),ap(c_2Ebool_2E_21(A_27a),f28(A_27b,A_27a,V0P,V1rep))) = ap(f29(A_27b,A_27a,V0P),V1rep)))) # label(lameq_f29) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 247 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0P),V1f)) <-> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P)) -> p(ap(V1f,V2x)))))))))))) # label(conj_thm_2Ebool_2ERES__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 248 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> ((p(V1t2) <-> p(V0t1)) <-> (p(V0t1) -> p(V1t2)) & (p(V1t2) -> p(V0t1))))))) # label(conj_thm_2Ebool_2EEQ__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 249 (all V0t (mem(V0t,bool) -> (all V1t1 (mem(V1t1,bool) -> (all V2t2 (mem(V2t2,bool) -> (p(V1t1) | p(V2t2) -> ((p(V1t1) -> p(V0t)) -> ((p(V2t2) -> p(V0t)) -> p(V0t)))))))))) # label(conj_thm_2Ebool_2EOR__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 250 -($T <-> $F) # label(conj_thm_2Ebool_2EBOOL__EQ__DISTINCT_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 251 -($F <-> $T) # label(conj_thm_2Ebool_2EBOOL__EQ__DISTINCT_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 252 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(A_27b,A_27c)) -> (all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V2M (mem(V2M,A_27a) -> ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27c),f66(A_27b,A_27c,A_27a,V1N,V0P)),V2M) = ap(V0P,ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),f53(A_27b,A_27a,V1N)),V2M)))))))))))))) # label(conj_thm_2Ebool_2Eliteral__case__RAND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 253 (all A_27b all A_27a all V0t (mem(V0t,arr(A_27a,A_27b)) -> (all V1x ap(f31(A_27b,A_27a,V0t),V1x) = ap(V0t,V1x)))) # label(lameq_f31) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 254 (all A_27a (ne(A_27a) -> c_2Ebool_2EDATATYPE(A_27a) = k(A_27a,c_2Ebool_2ET))) # label(ax_thm_2Ebool_2EDATATYPE__TAG__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 255 (all A_27a all A_27b all V1rep (mem(V1rep,arr(A_27b,A_27a)) -> (all V2x_27 ap(f26(A_27a,A_27b,V1rep),V2x_27) = ap(c_2Ebool_2E_21(A_27b),f25(A_27a,A_27b,V1rep,V2x_27))))) # label(lameq_f26) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 256 (all A_27b all A_27a all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V0P (mem(V0P,arr(A_27b,bool)) -> (all V4x ap(V0P,ap(V1N,V4x)) = ap(f54(A_27b,A_27a,V1N,V0P),V4x)))))) # label(lameq_f54) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 257 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x1 (mem(V1x1,A_27a) -> (all V2x2 ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D(A_27b),ap(V0f,V1x1)),ap(V0f,V2x2))),ap(ap(c_2Emin_2E_3D(A_27a),V1x1),V2x2)) = ap(f19(A_27b,A_27a,V0f,V1x1),V2x2)))))) # label(lameq_f19) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 258 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (all V2t ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),V2t)),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t)),V2t)) = ap(f6(V0t1,V1t2),V2t)))))) # label(lameq_f6) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 259 (all A_27a (ne(A_27a) -> mem(c_2Ebool_2ECOND(A_27a),arr(bool,arr(A_27a,arr(A_27a,A_27a)))))) # label(mem_c_2Ebool_2ECOND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 260 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V1B) | -p(V0A) <-> (p(V0A) -> p(V1B))))))) # label(conj_thm_2Ebool_2EIMP__DISJ__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 261 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (p(V0P) & (exists V3x (p(ap(V1Q,V3x)) & mem(V3x,A_27a))) <-> (exists V2x (mem(V2x,A_27a) & p(V0P) & p(ap(V1Q,V2x))))))))))) # label(conj_thm_2Ebool_2ERIGHT__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 262 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> ((all V2x (mem(V2x,A_27a) -> p(V1Q) | p(V0P))) <-> (all V4x (mem(V4x,A_27a) -> p(V1Q))) | (all V3x (mem(V3x,A_27a) -> p(V0P)))))))))) # label(conj_thm_2Ebool_2EBOTH__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 263 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> ap(ap(c_2Ebool_2ERES__SELECT(A_27a),V0P),V1f) = ap(c_2Emin_2E_40(A_27a),f64(A_27a,V0P,V1f)))))))) # label(conj_thm_2Ebool_2ERES__SELECT__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 264 (all V0t (mem(V0t,bool) -> (-p(V0t) -> ($F <-> p(V0t))))) # label(conj_thm_2Ebool_2ENOT__F) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 265 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(c_2Emin_2E_40(A_27a),f51(A_27a,V0x)))))) # label(conj_thm_2Ebool_2ESELECT__REFL__2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 266 (all V0b (mem(V0b,bool) -> (all V1t1 (mem(V1t1,bool) -> (all V2t2 (mem(V2t2,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0b),V1t1),V2t2)) <-> p(V0b) & p(V1t1) | p(V2t2) & -p(V0b)))))))) # label(conj_thm_2Ebool_2ECOND__EXPAND__OR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 267 (all A_27a all V0x (mem(V0x,A_27a) -> (all V1f ap(f32(A_27a,V0x),V1f) = ap(V1f,V0x)))) # label(lameq_f32) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 268 (all A_27a (ne(A_27a) -> f2(A_27a) = c_2Ebool_2E_3F(A_27a))) # label(ax_thm_2Ebool_2EEXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 269 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,bool)) -> (all V3g (mem(V3g,arr(A_27a,bool)) -> (V0P = V1Q -> ((all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1Q)) -> (p(ap(V3g,V4x)) <-> p(ap(V2f,V4x)))))) -> (p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V1Q),V3g)) <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),V2f))))))))))))))) # label(conj_thm_2Ebool_2ERES__EXISTS__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 270 (all A_27a (ne(A_27a) -> (all V0Q (mem(V0Q,bool) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> p(V0Q) | p(ap(V1P,V2x)))) <-> (all V3x (mem(V3x,A_27a) -> p(ap(V1P,V3x)))) | p(V0Q)))))))) # label(conj_thm_2Ebool_2ELEFT__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 271 (all V0b (mem(V0b,bool) -> (all V1t1 (mem(V1t1,bool) -> (all V2t2 (mem(V2t2,bool) -> ((p(V1t1) | -p(V0b)) & (p(V0b) | p(V2t2)) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0b),V1t1),V2t2))))))))) # label(conj_thm_2Ebool_2ECOND__EXPAND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 272 (all V0b (mem(V0b,bool) -> (all V1t1 (mem(V1t1,bool) -> (all V2t2 (mem(V2t2,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0b),V1t1),V2t2)) <-> (p(V0b) -> p(V1t1)) & (-p(V0b) -> p(V2t2))))))))) # label(conj_thm_2Ebool_2ECOND__EXPAND__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 273 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> (p(V1Q) & (all V6x (mem(V6x,A_27a) -> p(ap(V0P,V6x)))) <-> (all V7x (mem(V7x,A_27a) -> p(V1Q) & p(ap(V0P,V7x))))) & ((all V4x (mem(V4x,A_27a) -> p(ap(V0P,V4x)))) & p(V1Q) <-> (all V5x (mem(V5x,A_27a) -> p(V1Q) & p(ap(V0P,V5x))))) & ((all V3x (mem(V3x,A_27a) -> (p(V1Q) -> p(ap(V0P,V3x))))) <-> (p(V1Q) -> (all V2x (mem(V2x,A_27a) -> p(ap(V0P,V2x)))))))))))) # label(conj_thm_2Ebool_2EPULL__FORALL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 274 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V1t (mem(V1t,A_27b) -> (all V2u (mem(V2u,A_27b) -> V1t = ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),f67(A_27b,A_27a,V1t,V0a,V2u)),V0a))))))))))) # label(conj_thm_2Ebool_2Eliteral__case__id) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 275 (all V0y (mem(V0y,bool) -> (all V1x (mem(V1x,bool) -> ((p(V0y) -> p(V1x)) -> (-p(V1x) -> -p(V0y))))))) # label(conj_thm_2Ebool_2EMONO__NOT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 276 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> ((p(V0t1) -> p(V1t2)) -> ((p(V1t2) -> p(V0t1)) -> (p(V1t2) <-> p(V0t1)))))))) # label(conj_thm_2Ebool_2EIMP__ANTISYM__AX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 277 (all A_27a all V0p f38(A_27a,V0p) = ap(f39(A_27a),V0p)) # label(lameq_f39) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 278 (all A_27a all V0p ap(f36(A_27a),V0p) = f35(A_27a,V0p)) # label(lameq_f36) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 279 (all A_27a all V0P ap(ap(c_2Emin_2E_3D(arr(A_27a,bool)),V0P),k(A_27a,c_2Ebool_2ET)) = ap(f1(A_27a),V0P)) # label(lameq_f1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 280 (all V0P (mem(V0P,bool) -> (all V1P_27 (mem(V1P_27,bool) -> (all V2Q (mem(V2Q,bool) -> (all V3Q_27 (mem(V3Q_27,bool) -> ((p(V2Q) -> (p(V0P) <-> p(V1P_27))) & (p(V1P_27) -> (p(V2Q) <-> p(V3Q_27))) -> (p(V2Q) & p(V0P) <-> p(V1P_27) & p(V3Q_27))))))))))) # label(conj_thm_2Ebool_2EAND__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 281 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Ebool_2Eitself(A_27a),bool)) -> ((exists V1x (mem(V1x,ty_2Ebool_2Eitself(A_27a)) & p(ap(V0P,V1x)))) <-> p(ap(V0P,c_2Ebool_2Ethe__value(A_27a)))))))) # label(conj_thm_2Ebool_2EEXISTS__itself) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 282 (all A_27a (ne(A_27a) -> f44(A_27a) = c_2Ebool_2ERES__EXISTS__UNIQUE(A_27a))) # label(ax_thm_2Ebool_2ERES__EXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 283 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),V0f),V1x) = ap(V0f,V1x))))))))) # label(conj_thm_2Ebool_2Eliteral__case__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 284 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((exists V2x ((p(ap(V1Q,V2x)) | p(ap(V0P,V2x))) & mem(V2x,A_27a))) <-> (exists V4x (mem(V4x,A_27a) & p(ap(V1Q,V4x)))) | (exists V3x (mem(V3x,A_27a) & p(ap(V0P,V3x))))))))))) # label(conj_thm_2Ebool_2EEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 285 (all V0t (mem(V0t,bool) -> (p(V0t) <-> ($T <-> p(V0t))) & (p(V0t) <-> ($T <-> p(V0t))) & (-p(V0t) <-> (p(V0t) <-> $F)) & (-p(V0t) <-> ($F <-> p(V0t))))) # label(conj_thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 286 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t) | p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 287 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V1x),c_2Ebool_2ET)) <-> (p(V0c) -> p(V1x))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__FT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 288 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) -> (p(V2y) -> p(V3y_27))) & (p(V2y) -> (p(V0x) -> p(V1x_27))) -> (p(V2y) & p(V0x) -> p(V3y_27) & p(V1x_27))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__conj__weaken) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 289 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__X) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 290 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V1x),c_2Ebool_2EF)) <-> p(V0c) & p(V1x)))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__FF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 291 -$F <-> $T # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__F) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 292 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((-p(V1x_27) -> (p(V3y_27) -> p(V2y))) & (-p(V2y) -> (p(V1x_27) -> p(V0x))) -> (p(V3y_27) | p(V1x_27) -> p(V0x) | p(V2y))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__disj__strengthen) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 293 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (p(V1x) & -p(V0c) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),c_2Ebool_2EF),V1x))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__TF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 294 (all V0t (mem(V0t,bool) -> ($F <-> p(V0t) & $F))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 295 (all V0t (mem(V0t,bool) -> ($T <-> (p(V0t) -> p(V0t))))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 296 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V0x) -> (p(V2y) -> p(V3y_27))) & (-p(V3y_27) -> (p(V1x_27) -> p(V0x))) -> ((p(V0x) -> p(V2y)) -> (p(V1x_27) -> p(V3y_27)))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 297 (all V0t (mem(V0t,bool) -> (-p(V0t) <-> -p(V0t)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 298 (all V0t (mem(V0t,bool) -> ($T <-> p(V0t) | $T))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 299 -$T <-> $F # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__T) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 300 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2ET),V0t1),V1t2) = V0t1)))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__CT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 301 (all V0t (mem(V0t,bool) -> (($F -> p(V0t)) <-> $T))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 302 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) -> (p(V2y) -> p(V3y_27))) & (p(V1x_27) -> p(V0x)) -> ((p(V0x) -> p(V2y)) -> (p(V1x_27) -> p(V3y_27)))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 303 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) -> (p(V3y_27) -> p(V2y))) & (p(V0x) -> p(V1x_27)) -> ((p(V1x_27) -> p(V3y_27)) -> (p(V0x) -> p(V2y)))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__simple__imp__strengthen) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 304 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 305 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V2y) -> (p(V1x_27) -> p(V0x))) & (p(V1x_27) -> (p(V3y_27) -> p(V2y))) -> (p(V1x_27) & p(V3y_27) -> p(V2y) & p(V0x))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__conj__strengthen) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 306 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t) & p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 307 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> ((-p(V0c) -> p(V1x)) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),c_2Ebool_2ET),V1x))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__TT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 308 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 309 (all V0y (mem(V0y,bool) -> (all V1x (mem(V1x,bool) -> (p(V1x) <-> p(ap(ap(c_2EConseqConv_2EASM__MARKER,V0y),V1x))))))) # label(conj_thm_2EConseqConv_2EASM__MARKER__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 310 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2s (mem(V2s,A_27a) -> (p(ap(V0P,V2s)) <-> p(ap(V1Q,V2s))))) -> ((all V3s (mem(V3s,A_27a) -> p(ap(V0P,V3s)))) <-> (all V4s (mem(V4s,A_27a) -> p(ap(V1Q,V4s)))))))))))) # label(conj_thm_2EConseqConv_2Eforall__eq__thm) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 311 (all A_27a (ne(A_27a) -> (all V0b (mem(V0b,bool) -> (all V1t (mem(V1t,A_27a) -> V1t = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0b),V1t),V1t))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 312 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((-p(V3y_27) -> (p(V0x) -> p(V1x_27))) & (p(V0x) -> (p(V3y_27) -> p(V2y))) -> ((p(V1x_27) -> p(V3y_27)) -> (p(V0x) -> p(V2y)))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__imp__strengthen) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 313 (all V0t (mem(V0t,bool) -> ($T <-> (p(V0t) -> $T)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 314 (all V0t (mem(V0t,bool) -> (p(V0t) -> $T))) # label(conj_thm_2EConseqConv_2Etrue__imp) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 315 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (all V2x_27 (mem(V2x_27,bool) -> (all V3y (mem(V3y,bool) -> (all V4y_27 (mem(V4y_27,bool) -> ((p(V0c) -> (p(V2x_27) -> p(V1x))) & (-p(V0c) -> (p(V4y_27) -> p(V3y))) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V2x_27),V4y_27)) -> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V1x),V3y)))))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__cond) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 316 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2)))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__CF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 317 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 318 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2EConseqConv_2Efalse__imp) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 319 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (all V2x_27 (mem(V2x_27,bool) -> (all V3y (mem(V3y,bool) -> (all V4y_27 (mem(V4y_27,bool) -> ((p(V4y_27) -> p(V3y)) & (p(V2x_27) -> p(V1x)) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V2x_27),V4y_27)) -> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V1x),V3y)))))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__cond__simple) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 320 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V2s (mem(V2s,A_27a) -> (p(ap(V0P,V2s)) <-> p(ap(V1Q,V2s))))) -> ((exists V3s (p(ap(V0P,V3s)) & mem(V3s,A_27a))) <-> (exists V4s (mem(V4s,A_27a) & p(ap(V1Q,V4s)))))))))))) # label(conj_thm_2EConseqConv_2Eexists__eq__thm) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 321 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((-p(V1x_27) -> (p(V2y) -> p(V3y_27))) & (-p(V2y) -> (p(V0x) -> p(V1x_27))) -> (p(V0x) | p(V2y) -> p(V1x_27) | p(V3y_27))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__disj__weaken) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 322 (all V0t (mem(V0t,bool) -> ($F <-> $F & p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 323 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 324 (all V0t (mem(V0t,bool) -> ($T <-> p(V0t) | $T))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 325 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 326 (all V0p (mem(V0p,bool) -> (--p(V0p) -> p(V0p)))) # label(conj_thm_2Esat_2Epth__nn) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 327 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V0p) | p(V1q)) -> -p(V0p)))))) # label(conj_thm_2Esat_2Epth__no1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 328 (all V0t (mem(V0t,bool) -> (p(V0t) <-> --p(V0t)))) # label(conj_thm_2Esat_2ENOT__NOT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 329 (all V0A (mem(V0A,bool) -> ($F <-> -p(V0A) & p(V0A)))) # label(conj_thm_2Esat_2EAND__INV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 330 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> ((-p(V0p) | -p(V1q)) & (p(V1q) | p(V0p)) <-> (-p(V1q) <-> p(V0p))))))) # label(conj_thm_2Esat_2Edc__neg) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 331 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V1q) | p(V2r) <-> p(V0p)) <-> (p(V0p) | -p(V1q)) & (-p(V2r) | p(V0p)) & (-p(V0p) | p(V2r) | p(V1q))))))))) # label(conj_thm_2Esat_2Edc__disj) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 332 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> (((p(V1q) -> p(V2r)) <-> p(V0p)) <-> (p(V0p) | p(V1q)) & (-p(V0p) | p(V2r) | -p(V1q)) & (-p(V2r) | p(V0p))))))))) # label(conj_thm_2Esat_2Edc__imp) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 333 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (p(V0p) & p(V1q) -> p(V0p)))))) # label(conj_thm_2Esat_2Epth__an1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 334 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> (all V3s (mem(V3s,bool) -> ((p(ap(ap(ap(c_2Ebool_2ECOND(bool),V1q),V2r),V3s)) <-> p(V0p)) <-> (p(V0p) | -p(V3s) | p(V1q)) & (-p(V1q) | p(V2r) | -p(V0p)) & (p(V1q) | -p(V0p) | p(V3s)) & (-p(V2r) | -p(V3s) | p(V0p)) & (p(V0p) | -p(V1q) | -p(V2r))))))))))) # label(conj_thm_2Esat_2Edc__cond) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 335 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V0p) -> p(V1q)) -> p(V0p)))))) # label(conj_thm_2Esat_2Epth__ni1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 336 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V0p) -> p(V1q)) -> -p(V1q)))))) # label(conj_thm_2Esat_2Epth__ni2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 337 (all V0A (mem(V0A,bool) -> (--p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 338 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((-p(V0p) | p(V1q)) & (-p(V0p) | p(V2r)) & (p(V0p) | -p(V2r) | -p(V1q)) <-> (p(V0p) <-> p(V2r) & p(V1q))))))))) # label(conj_thm_2Esat_2Edc__conj) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 339 (all V0b (mem(V0b,bool) -> (-p(V0b) -> (p(V0b) <-> $F)))) # label(conj_thm_2Esat_2EEQF__Imp1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 340 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((-p(V0A) -> --p(V1B)) <-> --(p(V0A) | p(V1B))))))) # label(conj_thm_2Esat_2EOR__DUAL2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 341 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V0p) | p(V1q)) -> -p(V1q)))))) # label(conj_thm_2Esat_2Epth__no2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 342 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (p(V0p) & p(V1q) -> p(V1q)))))) # label(conj_thm_2Esat_2Epth__an2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 343 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((-p(V0A) -> --p(V1B)) <-> --(p(V1B) | p(V0A))))))) # label(conj_thm_2Esat_2EOR__DUAL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 344 (all V0b (mem(V0b,bool) -> (p(V0b) -> (p(V0b) <-> $T)))) # label(conj_thm_2Esat_2EEQT__Imp1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 345 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((p(V0A) -> --p(V1B)) <-> --(-p(V0A) | p(V1B))))))) # label(conj_thm_2Esat_2EOR__DUAL3) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 346 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V0p) <-> (p(V1q) <-> p(V2r))) <-> (p(V2r) | -p(V0p) | -p(V1q)) & (-p(V2r) | -p(V0p) | p(V1q)) & (p(V0p) | -p(V1q) | -p(V2r)) & (p(V0p) | p(V2r) | p(V1q))))))))) # label(conj_thm_2Esat_2Edc__eq) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 347 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> ((p(V0A) -> (p(V1B) -> p(V2C))) <-> (p(V0A) & p(V1B) -> p(V2C))))))))) # label(conj_thm_2Esat_2EAND__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 348 (all V0A (mem(V0A,bool) -> (p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 349 (all V0A (mem(V0A,bool) -> (p(V0A) <-> --p(V0A)))) # label(conj_thm_2Esat_2ENOT__ELIM2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 350 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,A_27b),A_27a))))))) # label(mem_c_2EnormalForms_2EEXT__POINT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 351 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (p(ap(V0p,ap(c_2EnormalForms_2EUNIV__POINT(A_27a),V0p))) <-> (all V1x (mem(V1x,A_27a) -> p(ap(V0p,V1x))))))))) # label(conj_thm_2EnormalForms_2EUNIV__POINT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 352 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (p(ap(V0p,ap(c_2EnormalForms_2EUNIV__POINT(A_27a),V0p))) -> (all V1x (mem(V1x,A_27a) -> p(ap(V0p,V1x))))))))) # label(ax_thm_2EnormalForms_2EUNIV__POINT__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 353 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (V0f = V1g <-> ap(V1g,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g)) = ap(V0f,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g))))))))))) # label(conj_thm_2EnormalForms_2EEXT__POINT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 354 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (ap(V0f,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g)) = ap(V1g,ap(ap(c_2EnormalForms_2EEXT__POINT(A_27a,A_27b),V0f),V1g)) -> V0f = V1g))))))))) # label(ax_thm_2EnormalForms_2EEXT__POINT__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 355 (all A_27a (ne(A_27a) -> mem(c_2EnormalForms_2EUNIV__POINT(A_27a),arr(arr(A_27a,bool),A_27a)))) # label(mem_c_2EnormalForms_2EUNIV__POINT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 356 $T <-> p(c_2Emarker_2EIfCases) # label(ax_thm_2Emarker_2EIfCases__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 357 (all A_27a (ne(A_27a) -> mem(c_2Emarker_2Estmarker(A_27a),arr(A_27a,A_27a)))) # label(mem_c_2Emarker_2Estmarker) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 358 (all V0x (mem(V0x,bool) -> (p(ap(c_2Emarker_2EAbbrev,V0x)) <-> p(V0x)))) # label(ax_thm_2Emarker_2EAbbrev__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 359 (all A_27a (ne(A_27a) -> mem(c_2Emarker_2Eunint(A_27a),arr(A_27a,A_27a)))) # label(mem_c_2Emarker_2Eunint) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 360 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2m (mem(V2m,bool) -> (p(V0p) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V1q) <-> p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V0p) & p(V1q)) & (p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V1q) & p(V0p) <-> p(V0p) & p(V1q) & p(ap(c_2Emarker_2Estmarker(bool),V2m))) & (p(V0p) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) <-> p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V0p)))))))) # label(conj_thm_2Emarker_2Emove__left__conj) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 361 (all V0x (mem(V0x,bool) -> (p(ap(c_2Emarker_2ECong,V0x)) <-> p(V0x)))) # label(ax_thm_2Emarker_2ECong__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 362 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(c_2Emarker_2Estmarker(A_27a),V0x))))) # label(ax_thm_2Emarker_2Estmarker__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 363 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Emarker_2Eunint(A_27a),V0x) = V0x)))) # label(ax_thm_2Emarker_2Eunint__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 364 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2m (mem(V2m,bool) -> (p(V0p) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) <-> p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V0p)) & (p(V0p) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V1q) <-> p(V1q) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V0p)) & (p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V1q) & p(V0p) <-> p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V1q) & p(V0p)))))))) # label(conj_thm_2Emarker_2Emove__right__conj) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 365 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2m (mem(V2m,bool) -> (p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) <-> p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V0p)) & (p(V1q) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V0p) <-> p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V1q)) & (p(V1q) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V0p) <-> p(V1q) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V0p)))))))) # label(conj_thm_2Emarker_2Emove__right__disj) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 366 (all V0lab (mem(V0lab,ind) -> (all V1argument (mem(V1argument,bool) -> (p(ap(ap(c_2Emarker_2E_3A_2D,V0lab),V1argument)) <-> p(V1argument)))))) # label(ax_thm_2Emarker_2Elabel__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 367 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2m (mem(V2m,bool) -> (p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V0p) <-> p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m))) & (p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V1q) <-> p(V1q) | p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m))) & (p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V1q) | p(V0p) <-> p(V0p) | p(V1q) | p(ap(c_2Emarker_2Estmarker(bool),V2m))))))))) # label(conj_thm_2Emarker_2Emove__left__disj) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 368 (all V0b1 (mem(V0b1,bool) -> (all V1b2 (mem(V1b2,bool) -> (p(ap(ap(c_2Emarker_2EAC,V0b1),V1b2)) <-> p(V1b2) & p(V0b1)))))) # label(ax_thm_2Emarker_2EAC__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 369 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> (all V3c (mem(V3c,A_27b) -> (all V4d (mem(V4d,A_27b) -> (V2b != V1a -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2b),V4d),V0f)) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2b),V4d),ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f))))))))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__COMMUTES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 370 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27c,A_27d)) -> (all V1f1 (mem(V1f1,A_27a) -> (all V2f2 (mem(V2f2,A_27b) -> (all V3a (mem(V3a,A_27c) -> (all V4b (mem(V4b,A_27d) -> (all V5c (mem(V5c,A_27d) -> (V5c != V4b -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27c,A_27d),V3a),V4b),V0f) != ap(ap(ap(c_2Ecombin_2EUPDATE(A_27c,A_27d),V3a),V5c),V0f)))))))))))))))))))))) # label(conj_thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 371 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(A_27b,A_27a)) -> (all V1f (mem(V1f,arr(A_27c,A_27b)) -> (all V2v (mem(V2v,A_27c) -> ap(V0P,ap(ap(c_2Ebool_2Eliteral__case(A_27c,A_27b),V1f),V2v)) = ap(ap(c_2Ebool_2Eliteral__case(A_27c,A_27a),ap(ap(c_2Ecombin_2Eo(A_27c,A_27a,A_27b),V0P),V1f)),V2v))))))))))))) # label(conj_thm_2Ecombin_2EGEN__literal__case__RAND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 372 (all A_27a (ne(A_27a) -> mem(c_2Ecombin_2EMONOID(A_27a),arr(arr(A_27a,arr(A_27a,A_27a)),arr(A_27a,bool))))) # label(mem_c_2Ecombin_2EMONOID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 373 (all A_27c all A_27b all A_27a all V1g (mem(V1g,arr(A_27a,A_27c)) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V3x ap(f83(A_27c,A_27b,A_27a,V1g,V0f),V3x) = ap(V0f,ap(V1g,V3x))))))) # label(lameq_f83) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 374 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f1 (mem(V0f1,arr(A_27a,A_27b)) -> (all V1f2 (mem(V1f2,arr(A_27a,A_27b)) -> (all V2a (mem(V2a,A_27a) -> (all V3b (mem(V3b,A_27b) -> (all V4c (mem(V4c,A_27b) -> (ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V3b),V0f1) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V4c),V1f2) -> V4c = V3b & (all V5v (mem(V5v,A_27b) -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V5v),V0f1) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V5v),V1f2)))))))))))))))))) # label(conj_thm_2Ecombin_2EUPD__SAME__KEY__UNWIND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 375 (all A_27b all A_27c all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V2x ap(f84(A_27b,A_27c,A_27a,V0f),V2x) = ap(V0f,V2x)))) # label(lameq_f84) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 376 (all A_27a all A_27c all A_27b all V1g (mem(V1g,arr(A_27b,A_27a)) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V3x ap(V0f,ap(V1g,V3x)) = ap(f81(A_27a,A_27c,A_27b,V1g,V0f),V3x)))))) # label(lameq_f81) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 377 (all A_27c all A_27a all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V2x ap(V0f,V2x) = ap(f80(A_27c,A_27a,V0f),V2x)))) # label(lameq_f80) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 378 (all A_27c all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V1y (mem(V1y,A_27c) -> (all V3x ap(ap(V0f,V3x),V1y) = ap(f86(A_27c,A_27b,A_27a,V0f,V1y),V3x)))))) # label(lameq_f86) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 379 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(c_2Ecombin_2EI(A_27a),V0x))))) # label(conj_thm_2Ecombin_2EI__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 380 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27c,A_27a)) -> (all V2h (mem(V2h,arr(A_27d,A_27c)) -> ap(ap(c_2Ecombin_2Eo(A_27d,A_27b,A_27a),V0f),ap(ap(c_2Ecombin_2Eo(A_27d,A_27a,A_27c),V1g),V2h)) = ap(ap(c_2Ecombin_2Eo(A_27d,A_27b,A_27c),ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),V1g)),V2h))))))))))))))) # label(conj_thm_2Ecombin_2Eo__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 381 (all A_27c all A_27a all A_27b all V0f f70(A_27c,A_27a,A_27b,V0f) = ap(f71(A_27c,A_27a,A_27b),V0f)) # label(lameq_f71) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 382 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Ecombin_2ES(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,A_27c)),arr(arr(A_27a,A_27b),arr(A_27a,A_27c)))))))))) # label(mem_c_2Ecombin_2ES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 383 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ecombin_2EFAIL(A_27a,A_27b) = f68(A_27b,A_27a))))) # label(ax_thm_2Ecombin_2EFAIL__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.70 384 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27a))) -> (p(ap(ap(c_2Ecombin_2EFCOMM(A_27a,A_27a,A_27a),V0f),V0f)) <-> p(ap(c_2Ecombin_2EASSOC(A_27a),V0f))))))) # label(conj_thm_2Ecombin_2EFCOMM__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 385 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27a))) -> (p(ap(c_2Ecombin_2EASSOC(A_27a),V0f)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> ap(ap(V0f,V1x),ap(ap(V0f,V2y),V3z)) = ap(ap(V0f,ap(ap(V0f,V1x),V2y)),V3z)))))))))))) # label(ax_thm_2Ecombin_2EASSOC__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 386 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> ap(ap(c_2Ecombin_2ES(A_27a,A_27c,A_27b),V0f),f82(A_27c,A_27a,V1g)) = f85(A_27c,A_27b,A_27a,V0f,V1g))))))))))) # label(conj_thm_2Ecombin_2ES__ABS__R) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 387 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Ecombin_2EFCOMM(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,A_27a)),arr(arr(A_27c,arr(A_27a,A_27a)),bool))))))))) # label(mem_c_2Ecombin_2EFCOMM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 388 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> (all A_27f (ne(A_27f) -> (all V2f (mem(V2f,arr(A_27d,A_27e)) -> (all V3v (mem(V3v,A_27d) -> ap(c_2Ecombin_2EK(A_27e,A_27f),ap(V2f,V3v)) = ap(ap(c_2Ecombin_2Eo(A_27f,A_27e,A_27d),V2f),ap(c_2Ecombin_2EK(A_27d,A_27f),V3v)))))) & (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1v (mem(V1v,A_27c) -> ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),ap(c_2Ecombin_2EK(A_27c,A_27b),V1v)),V0f) = ap(c_2Ecombin_2EK(A_27c,A_27a),V1v))))))))))))))))) # label(conj_thm_2Ecombin_2EK__o__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 389 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> V0x = ap(ap(c_2Ecombin_2EFAIL(A_27a,A_27b),V0x),V1y))))))))) # label(conj_thm_2Ecombin_2EFAIL__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 390 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2ELEFT__ID(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,A_27b)),arr(A_27a,bool))))))) # label(mem_c_2Ecombin_2ELEFT__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 391 (all A_27b all A_27a all V0x k(A_27b,V0x) = ap(f68(A_27b,A_27a),V0x)) # label(lameq_f68) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 392 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> f85(A_27c,A_27b,A_27a,V0f,V1g) = ap(ap(c_2Ecombin_2ES(A_27a,A_27c,A_27b),f84(A_27b,A_27c,A_27a,V0f)),V1g))))))))))) # label(conj_thm_2Ecombin_2ES__ABS__L) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 393 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> f83(A_27c,A_27b,A_27a,V1g,V0f) = ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),V0f),f82(A_27c,A_27a,V1g)))))))))))) # label(conj_thm_2Ecombin_2Eo__ABS__R) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 394 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f76(A_27b,A_27a) = c_2Ecombin_2EW(A_27a,A_27b))))) # label(ax_thm_2Ecombin_2EW__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 395 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27b) -> (all V3c (mem(V3c,A_27b) -> (V2b = V3c <-> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V2b),V0f)))))))))))))) # label(conj_thm_2Ecombin_2EUPD11__SAME__KEY__AND__BASE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 396 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),arr(arr(A_27c,A_27b),arr(arr(A_27a,A_27c),arr(A_27a,A_27b)))))))))) # label(mem_c_2Ecombin_2Eo) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 397 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> V0x = ap(ap(c_2Ecombin_2EK(A_27a,A_27b),V0x),V1y))))))))) # label(conj_thm_2Ecombin_2EK__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 398 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> V0f = ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27a),V0f),c_2Ecombin_2EI(A_27a)) & ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27b),c_2Ecombin_2EI(A_27b)),V0f) = V0f)))))) # label(conj_thm_2Ecombin_2EI__o__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 399 (all A_27a (ne(A_27a) -> mem(c_2Ecombin_2EASSOC(A_27a),arr(arr(A_27a,arr(A_27a,A_27a)),bool)))) # label(mem_c_2Ecombin_2EASSOC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 400 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27b))) -> (all V1x ap(ap(V0f,V1x),V1x) = ap(f75(A_27b,A_27a,V0f),V1x)))) # label(lameq_f75) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 401 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (all V1v (mem(V1v,A_27a) -> (p(ap(c_2Ebool_2E_21(A_27a),ap(ap(c_2Ecombin_2ES(A_27a,bool,bool),ap(ap(c_2Ecombin_2Eo(A_27a,arr(bool,bool),bool),c_2Emin_2E_3D_3D_3E),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Emarker_2EAbbrev),ap(ap(c_2Ecombin_2EC(A_27a,A_27a,bool),c_2Emin_2E_3D(A_27a)),V1v)))),V0f))) <-> p(ap(ap(c_2Ebool_2ELET(A_27a,bool),V0f),V1v))))))))) # label(conj_thm_2Ecombin_2ELET__FORALL__ELIM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 402 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27b) -> (V2b = ap(V0f,V1a) <-> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V2b),V0f) = V0f))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__APPLY__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 403 (all A_27b all A_27a all V1b (mem(V1b,A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V2f ap(f79(A_27b,A_27a,V1b,V0a),V2f) = f78(A_27b,A_27a,V1b,V0a,V2f)))))) # label(lameq_f79) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 404 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> (all V3c (mem(V3c,A_27b) -> (all V4d (mem(V4d,A_27b) -> (V2b != V1a & ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2b),V4d),V0f) = V0f & V0f = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f) | V4d = V3c & V1a = V2b <-> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2b),V4d),V0f) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f)))))))))))))))) # label(conj_thm_2Ecombin_2EUPD11__SAME__BASE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 405 (all A_27a all A_27c all A_27b all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x f72(A_27b,A_27c,A_27a,V0f,V1x) = ap(f73(A_27a,A_27c,A_27b,V0f),V1x)))) # label(lameq_f73) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 406 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27b) -> (all V3c (mem(V3c,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(A_27a),V1a),V3c)),V2b),ap(V0f,V3c)) = ap(ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V2b),V0f),V3c))))))))))))) # label(conj_thm_2Ecombin_2EAPPLY__UPDATE__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 407 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f68(A_27b,A_27a) = c_2Ecombin_2EK(A_27a,A_27b))))) # label(ax_thm_2Ecombin_2EK__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 408 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27b))) -> (all V1e (mem(V1e,A_27a) -> (p(ap(ap(c_2Ecombin_2ELEFT__ID(A_27a,A_27b),V0f),V1e)) <-> (all V2x (mem(V2x,A_27b) -> ap(ap(V0f,V1e),V2x) = V2x))))))))))) # label(ax_thm_2Ecombin_2ELEFT__ID__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 409 (all A_27b all A_27a all V1b (mem(V1b,A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (all V3c ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(A_27a),V0a),V3c)),V1b),ap(V2f,V3c)) = ap(f78(A_27b,A_27a,V1b,V0a,V2f),V3c)))))))) # label(lameq_f78) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 410 (all A_27a (ne(A_27a) -> ap(ap(c_2Ecombin_2ES(A_27a,arr(A_27a,A_27a),A_27a),c_2Ecombin_2EK(A_27a,arr(A_27a,A_27a))),c_2Ecombin_2EK(A_27a,A_27a)) = c_2Ecombin_2EI(A_27a))) # label(ax_thm_2Ecombin_2EI__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 411 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27c,A_27a)) -> (all V2x (mem(V2x,A_27c) -> ap(V0f,ap(V1g,V2x)) = ap(ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),V1g),V2x))))))))))))) # label(conj_thm_2Ecombin_2Eo__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 412 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),V0f),V1g) = f77(A_27c,A_27b,A_27a,V1g,V0f))))))))))) # label(ax_thm_2Ecombin_2Eo__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 413 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V3a (mem(V3a,A_27c) -> (all V4b (mem(V4b,A_27c) -> (all V5x (mem(V5x,A_27d) -> (all V6f (mem(V6f,arr(A_27c,A_27d)) -> (V3a != V4b -> ap(V6f,V4b) = ap(ap(ap(ap(c_2Ecombin_2EUPDATE(A_27c,A_27d),V3a),V5x),V6f),V4b)))))))))) & (all V0a (mem(V0a,A_27a) -> (all V1x (mem(V1x,A_27b) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> V1x = ap(ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V0a),V1x),V2f),V0a))))))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__APPLY) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 414 (all A_27c all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1g ap(f70(A_27c,A_27a,A_27b,V0f),V1g) = f69(A_27b,A_27c,A_27a,V0f,V1g)))) # label(lameq_f70) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 415 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27b) -> (all V3c (mem(V3c,A_27b) -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V2b),V0f)))))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 416 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2ERIGHT__ID(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,A_27a)),arr(A_27b,bool))))))) # label(mem_c_2Ecombin_2ERIGHT__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 417 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27c,A_27a))) -> (all V1v (mem(V1v,A_27b) -> (all V2x (mem(V2x,A_27c) -> ap(ap(ap(c_2Ebool_2ELET(A_27b,arr(A_27c,A_27a)),V0f),V1v),V2x) = ap(ap(c_2Ebool_2ELET(A_27b,A_27a),ap(ap(c_2Ecombin_2EC(A_27b,A_27c,A_27a),V0f),V2x)),V1v))))))))))))) # label(conj_thm_2Ecombin_2EGEN__LET__RATOR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 418 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27c,A_27a))) -> (all V1v (mem(V1v,A_27b) -> (all V2x (mem(V2x,A_27c) -> ap(ap(c_2Ebool_2Eliteral__case(A_27b,A_27a),ap(ap(c_2Ecombin_2EC(A_27b,A_27c,A_27a),V0f),V2x)),V1v) = ap(ap(ap(c_2Ebool_2Eliteral__case(A_27b,arr(A_27c,A_27a)),V0f),V1v),V2x))))))))))))) # label(conj_thm_2Ecombin_2EGEN__literal__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 419 (all A_27b all A_27c all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x (mem(V1x,A_27b) -> (all V2y ap(f72(A_27b,A_27c,A_27a,V0f,V1x),V2y) = ap(ap(V0f,V2y),V1x)))))) # label(lameq_f72) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 420 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(ap(c_2Ecombin_2ES(A_27a,A_27b,A_27c),V0f),V1g),V2x) = ap(ap(V0f,V2x),ap(V1g,V2x)))))))))))))) # label(conj_thm_2Ecombin_2ES__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 421 (all A_27c all A_27a all V1g (mem(V1g,arr(A_27a,A_27c)) -> (all V2x ap(V1g,V2x) = ap(f82(A_27c,A_27a,V1g),V2x)))) # label(lameq_f82) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 422 (all A_27b all A_27a all V0f f75(A_27b,A_27a,V0f) = ap(f76(A_27b,A_27a),V0f)) # label(lameq_f76) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 423 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27a))) -> (all V1g (mem(V1g,arr(A_27c,arr(A_27a,A_27a))) -> ((all V2x (mem(V2x,A_27c) -> (all V3y (mem(V3y,A_27a) -> (all V4z (mem(V4z,A_27b) -> ap(ap(V0f,ap(ap(V1g,V2x),V3y)),V4z) = ap(ap(V1g,V2x),ap(ap(V0f,V3y),V4z)))))))) <-> p(ap(ap(c_2Ecombin_2EFCOMM(A_27a,A_27b,A_27c),V0f),V1g))))))))))))) # label(ax_thm_2Ecombin_2EFCOMM__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 424 (all A_27c all A_27b all A_27a all V1g (mem(V1g,arr(A_27a,A_27c)) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V2x ap(f77(A_27c,A_27b,A_27a,V1g,V0f),V2x) = ap(V0f,ap(V1g,V2x))))))) # label(lameq_f77) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 425 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2EUPDATE(A_27a,A_27b),arr(A_27a,arr(A_27b,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))))))))) # label(mem_c_2Ecombin_2EUPDATE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 426 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (all V1v (mem(V1v,A_27a) -> (p(ap(c_2Ebool_2E_21(A_27a),ap(ap(c_2Ecombin_2ES(A_27a,bool,bool),ap(ap(c_2Ecombin_2Eo(A_27a,arr(bool,bool),bool),c_2Emin_2E_3D_3D_3E),ap(ap(c_2Ecombin_2Eo(A_27a,bool,bool),c_2Emarker_2EAbbrev),ap(ap(c_2Ecombin_2EC(A_27a,A_27a,bool),c_2Emin_2E_3D(A_27a)),V1v)))),V0f))) <-> p(ap(ap(c_2Ebool_2Eliteral__case(A_27a,bool),V0f),V1v))))))))) # label(conj_thm_2Ecombin_2Eliteral__case__FORALL__ELIM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 427 (all A_27b all A_27c all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1g (mem(V1g,arr(A_27a,A_27b)) -> (all V2x ap(f69(A_27b,A_27c,A_27a,V0f,V1g),V2x) = ap(ap(V0f,V2x),ap(V1g,V2x))))))) # label(lameq_f69) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 428 (all A_27c all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> (all V3x ap(f85(A_27c,A_27b,A_27a,V0f,V1g),V3x) = ap(ap(V0f,V3x),ap(V1g,V3x))))))) # label(lameq_f85) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 429 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27a))) -> (all V1e (mem(V1e,A_27b) -> ((all V2x (mem(V2x,A_27a) -> V2x = ap(ap(V0f,V2x),V1e))) <-> p(ap(ap(c_2Ecombin_2ERIGHT__ID(A_27a,A_27b),V0f),V1e))))))))))) # label(ax_thm_2Ecombin_2ERIGHT__ID__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 430 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1b (mem(V1b,A_27b) -> (all V2a (mem(V2a,A_27a) -> (ap(V0f,V2a) = V1b -> V0f = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V1b),V0f)))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__APPLY__IMP__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 431 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27a)) -> f81(A_27a,A_27c,A_27b,V1g,V0f) = ap(ap(c_2Ecombin_2Eo(A_27b,A_27c,A_27a),f80(A_27c,A_27a,V0f)),V1g))))))))))) # label(conj_thm_2Ecombin_2Eo__ABS__L) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 432 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27a))) -> (all V1e (mem(V1e,A_27a) -> (p(ap(c_2Ecombin_2EASSOC(A_27a),V0f)) & p(ap(ap(c_2Ecombin_2ELEFT__ID(A_27a,A_27a),V0f),V1e)) & p(ap(ap(c_2Ecombin_2ERIGHT__ID(A_27a,A_27a),V0f),V1e)) <-> p(ap(ap(c_2Ecombin_2EMONOID(A_27a),V0f),V1e))))))))) # label(ax_thm_2Ecombin_2EMONOID__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 433 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V1y (mem(V1y,A_27c) -> f86(A_27c,A_27b,A_27a,V0f,V1y) = ap(ap(c_2Ecombin_2EC(A_27a,A_27c,A_27b),f84(A_27b,A_27c,A_27a,V0f)),V1y))))))))))) # label(conj_thm_2Ecombin_2EC__ABS__L) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 434 (all A_27a (ne(A_27a) -> mem(c_2Ecombin_2EI(A_27a),arr(A_27a,A_27a)))) # label(mem_c_2Ecombin_2EI) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 435 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27a))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> ap(ap(V0f,V1x),ap(ap(V0f,V2y),V3z)) = ap(ap(V0f,ap(ap(V0f,V1x),V2y)),V3z))))))) <-> p(ap(c_2Ecombin_2EASSOC(A_27a),V0f))))))) # label(conj_thm_2Ecombin_2EASSOC__SYM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 436 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x (mem(V1x,A_27b) -> (all V2y (mem(V2y,A_27a) -> ap(ap(ap(c_2Ecombin_2EC(A_27a,A_27b,A_27c),V0f),V1x),V2y) = ap(ap(V0f,V2y),V1x))))))))))))) # label(conj_thm_2Ecombin_2EC__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 437 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1a (mem(V1a,A_27a) -> V0f = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),ap(V0f,V1a)),V0f))))))))) # label(conj_thm_2Ecombin_2EAPPLY__UPDATE__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 438 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2ECOMM(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,A_27b)),bool)))))) # label(mem_c_2Ecombin_2ECOMM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 439 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2E_3A_3E(A_27a,A_27b),arr(A_27b,arr(arr(A_27b,A_27a),A_27a))))))) # label(mem_c_2Ecombin_2E_3A_3E) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 440 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2EW(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,A_27b)),arr(A_27a,A_27b))))))) # label(mem_c_2Ecombin_2EW) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 441 (all A_27a all A_27c all A_27b all V0f f73(A_27a,A_27c,A_27b,V0f) = ap(f74(A_27a,A_27c,A_27b),V0f)) # label(lameq_f74) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 442 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2EK(A_27a,A_27b),arr(A_27a,arr(A_27b,A_27a))))))) # label(mem_c_2Ecombin_2EK) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 443 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27b))) -> (p(ap(c_2Ecombin_2ECOMM(A_27a,A_27b),V0f)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> ap(ap(V0f,V2y),V1x) = ap(ap(V0f,V1x),V2y)))))))))))) # label(ax_thm_2Ecombin_2ECOMM__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 444 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(A_27b,A_27a)) -> (all V1f (mem(V1f,arr(A_27c,A_27b)) -> (all V2v (mem(V2v,A_27c) -> ap(ap(c_2Ebool_2ELET(A_27c,A_27a),ap(ap(c_2Ecombin_2Eo(A_27c,A_27a,A_27b),V0P),V1f)),V2v) = ap(V0P,ap(ap(c_2Ebool_2ELET(A_27c,A_27b),V1f),V2v)))))))))))))) # label(conj_thm_2Ecombin_2EGEN__LET__RAND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 445 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> f74(A_27a,A_27c,A_27b) = c_2Ecombin_2EC(A_27a,A_27b,A_27c))))))) # label(ax_thm_2Ecombin_2EC__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 446 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27b) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> ap(ap(c_2Ecombin_2E_3A_3E(A_27a,A_27b),V0x),V1f) = ap(V1f,V0x))))))))) # label(ax_thm_2Ecombin_2EAPP__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 447 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Ecombin_2EC(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,A_27c)),arr(A_27b,arr(A_27a,A_27c)))))))))) # label(mem_c_2Ecombin_2EC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 448 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V1b (mem(V1b,A_27b) -> ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V0a),V1b) = f79(A_27b,A_27a,V1b,V0a))))))))) # label(ax_thm_2Ecombin_2EUPDATE__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 449 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> f71(A_27c,A_27a,A_27b) = c_2Ecombin_2ES(A_27a,A_27b,A_27c))))))) # label(ax_thm_2Ecombin_2ES__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 450 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ecombin_2EFAIL(A_27a,A_27b),arr(A_27a,arr(A_27b,A_27a))))))) # label(mem_c_2Ecombin_2EFAIL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 451 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27a,A_27b))) -> (all V1x (mem(V1x,A_27a) -> ap(ap(V0f,V1x),V1x) = ap(ap(c_2Ecombin_2EW(A_27a,A_27b),V0f),V1x))))))))) # label(conj_thm_2Ecombin_2EW__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 452 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,V0n) != c_2Enum_2E0)) # label(conj_thm_2Enum_2ENOT__SUC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 453 (all V0a (mem(V0a,ty_2Enum_2Enum) -> ap(c_2Enum_2EABS__num,ap(c_2Enum_2EREP__num,V0a)) = V0a)) # label(ax_thm_2Enum_2Enum__ISO__DEF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 454 (all V1r (mem(V1r,ind) -> (V1r = ap(c_2Enum_2EREP__num,ap(c_2Enum_2EABS__num,V1r)) <-> p(ap(c_2Enum_2EIS__NUM__REP,V1r))))) # label(ax_thm_2Enum_2Enum__ISO__DEF_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 455 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Enum_2ESUC,V0m) = ap(c_2Enum_2ESUC,V1n) -> V0m = V1n))))) # label(conj_thm_2Enum_2EINV__SUC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 456 (all V0y (mem(V0y,ind) -> ap(c_2Enum_2ESUC__REP,V0y) != c_2Enum_2EZERO__REP)) # label(ax_thm_2Enum_2EZERO__REP__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 457 (all V0m (mem(V0m,ind) -> (p(ap(c_2Enum_2EIS__NUM__REP,V0m)) <-> (all V1P (mem(V1P,arr(ind,bool)) -> ((all V2n (mem(V2n,ind) -> (p(ap(V1P,V2n)) -> p(ap(V1P,ap(c_2Enum_2ESUC__REP,V2n)))))) & p(ap(V1P,c_2Enum_2EZERO__REP)) -> p(ap(V1P,V0m)))))))) # label(ax_thm_2Enum_2EIS__NUM__REP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 458 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(c_2Enum_2EABS__num,ap(c_2Enum_2ESUC__REP,ap(c_2Enum_2EREP__num,V0m))) = ap(c_2Enum_2ESUC,V0m))) # label(ax_thm_2Enum_2ESUC__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 459 (exists V0rep (p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ind,ty_2Enum_2Enum),c_2Enum_2EIS__NUM__REP),V0rep)) & mem(V0rep,arr(ty_2Enum_2Enum,ind)))) # label(ax_thm_2Enum_2Enum__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 460 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (p(ap(V0P,c_2Enum_2E0)) & (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(V0P,V1n)) -> p(ap(V0P,ap(c_2Enum_2ESUC,V1n)))))) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(V0P,V2n))))))) # label(conj_thm_2Enum_2EINDUCTION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 461 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Eone_2Eone)) -> (all V1g (mem(V1g,arr(A_27a,ty_2Eone_2Eone)) -> V0f = V1g)))))) # label(conj_thm_2Eone_2Eone__axiom) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 462 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (exists V1fn (ap(V1fn,c_2Eone_2Eone) = V0e & mem(V1fn,arr(ty_2Eone_2Eone,A_27a)))))))) # label(conj_thm_2Eone_2Eone__prim__rec) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 463 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(ap(c_2Eone_2Eone__CASE(A_27a),c_2Eone_2Eone),V0x))))) # label(conj_thm_2Eone_2Eone__case__thm) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 464 (exists V0rep (mem(V0rep,arr(ty_2Eone_2Eone,bool)) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(bool,ty_2Eone_2Eone),i(bool)),V0rep)))) # label(ax_thm_2Eone_2Eone__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 465 (all A_27a all V0e (mem(V0e,A_27a) -> (all V1fn ap(f87(A_27a,V0e),V1fn) = ap(ap(c_2Emin_2E_3D(A_27a),ap(V1fn,c_2Eone_2Eone)),V0e)))) # label(lameq_f87) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 466 (all V0v (mem(V0v,ty_2Eone_2Eone) -> c_2Eone_2Eone = V0v)) # label(conj_thm_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 467 (all V0P (mem(V0P,arr(ty_2Eone_2Eone,bool)) -> (p(ap(V0P,c_2Eone_2Eone)) -> (all V1x (mem(V1x,ty_2Eone_2Eone) -> p(ap(V0P,V1x))))))) # label(conj_thm_2Eone_2Eone__induction) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 468 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> p(ap(c_2Ebool_2E_3F_21(arr(ty_2Eone_2Eone,A_27a)),f87(A_27a,V0e))))))) # label(conj_thm_2Eone_2Eone__Axiom) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 469 (all A_27a (ne(A_27a) -> mem(c_2Eone_2Eone__CASE(A_27a),arr(ty_2Eone_2Eone,arr(A_27a,A_27a))))) # label(mem_c_2Eone_2Eone__CASE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 470 (all A_27a (ne(A_27a) -> (all V0u (mem(V0u,ty_2Eone_2Eone) -> (all V1x (mem(V1x,A_27a) -> V1x = ap(ap(c_2Eone_2Eone__CASE(A_27a),V0u),V1x))))))) # label(ax_thm_2Eone_2Eone__case__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 471 (all V0P (mem(V0P,arr(ty_2Eone_2Eone,bool)) -> (p(ap(V0P,c_2Eone_2Eone)) <-> (all V1x (mem(V1x,ty_2Eone_2Eone) -> p(ap(V0P,V1x))))))) # label(conj_thm_2Eone_2EFORALL__ONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 472 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27b) -> ap(c_2Esum_2EOUTR(A_27a,A_27b),ap(c_2Esum_2EINR(A_27a,A_27b),V0x)) = V0x)))))) # label(ax_thm_2Esum_2EOUTR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 473 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0ss (mem(V0ss,ty_2Esum_2Esum(A_27a,A_27b)) -> (exists V1x (V0ss = ap(c_2Esum_2EINL(A_27a,A_27b),V1x) & mem(V1x,A_27a))) | (exists V2y (mem(V2y,A_27b) & ap(c_2Esum_2EINR(A_27a,A_27b),V2y) = V0ss)))))))) # label(conj_thm_2Esum_2Esum__CASES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 474 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EINR(A_27a,A_27b),arr(A_27b,ty_2Esum_2Esum(A_27a,A_27b))))))) # label(mem_c_2Esum_2EINR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 475 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> ap(c_2Esum_2EINL(A_27a,A_27b),V0x) != ap(c_2Esum_2EINR(A_27a,A_27b),V1y))))))))) # label(conj_thm_2Esum_2Esum__distinct1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 476 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V2y (mem(V2y,A_27b) -> (all V3x (mem(V3x,A_27b) -> (V3x = V2y <-> ap(c_2Esum_2EINR(A_27a,A_27b),V3x) = ap(c_2Esum_2EINR(A_27a,A_27b),V2y)))))) & (all V0y (mem(V0y,A_27a) -> (all V1x (mem(V1x,A_27a) -> (V1x = V0y <-> ap(c_2Esum_2EINL(A_27a,A_27b),V0y) = ap(c_2Esum_2EINL(A_27a,A_27b),V1x)))))))))) # label(conj_thm_2Esum_2EINR__INL__11) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 477 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27b) -> ap(c_2Esum_2EINR(A_27a,A_27b),V0e) = ap(c_2Esum_2EABS__sum(A_27a,A_27b),f95(A_27b,A_27a,V0e)))))))) # label(ax_thm_2Esum_2EINR__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 478 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EISR(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),bool)))))) # label(mem_c_2Esum_2EISR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 479 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27a,A_27b),c_2Ecombin_2EI(A_27a)),c_2Ecombin_2EI(A_27b)) = c_2Ecombin_2EI(ty_2Esum_2Esum(A_27a,A_27b)))))) # label(conj_thm_2Esum_2ESUM__MAP__I) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 480 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27c)) -> p(ap(c_2Ebool_2E_3F_21(arr(ty_2Esum_2Esum(A_27a,A_27b),A_27c)),f96(A_27a,A_27b,A_27c,V0f,V1g))))))))))))) # label(conj_thm_2Esum_2Esum__axiom) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 481 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EREP__sum(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),arr(bool,arr(A_27a,arr(A_27b,bool))))))))) # label(mem_c_2Esum_2EREP__sum) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 482 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> mem(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),arr(arr(A_27a,A_27c),arr(arr(A_27b,A_27d),arr(ty_2Esum_2Esum(A_27a,A_27b),ty_2Esum_2Esum(A_27c,A_27d))))))))))))) # label(mem_c_2Esum_2E_2B_2B) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 483 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0v1 (mem(V0v1,A_27a) -> (all V1v2 (mem(V1v2,A_27b) -> ap(c_2Esum_2EINR(A_27a,A_27b),V1v2) != ap(c_2Esum_2EINL(A_27a,A_27b),V0v1))))))))) # label(conj_thm_2Esum_2EINR__neq__INL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 484 (all A_27a all A_27b all V0e (mem(V0e,A_27a) -> (all V1b ap(f93(A_27a,A_27b,V0e),V1b) = f92(A_27b,A_27a,V0e,V1b)))) # label(lameq_f93) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 485 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Esum_2Esum(A_27a,A_27b),bool)) -> ((all V2y (mem(V2y,A_27b) -> p(ap(V0P,ap(c_2Esum_2EINR(A_27a,A_27b),V2y))))) & (all V1x (mem(V1x,A_27a) -> p(ap(V0P,ap(c_2Esum_2EINL(A_27a,A_27b),V1x))))) -> (all V3s (mem(V3s,ty_2Esum_2Esum(A_27a,A_27b)) -> p(ap(V0P,V3s))))))))))) # label(conj_thm_2Esum_2Esum__INDUCT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 486 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),arr(ty_2Esum_2Esum(A_27a,A_27b),arr(arr(A_27a,A_27c),arr(arr(A_27b,A_27c),A_27c)))))))))) # label(mem_c_2Esum_2Esum__CASE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 487 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Esum_2Esum(A_27a,A_27b),bool)) -> ((all V1s (mem(V1s,ty_2Esum_2Esum(A_27a,A_27b)) -> p(ap(V0P,V1s)))) <-> (all V2x (mem(V2x,A_27a) -> p(ap(V0P,ap(c_2Esum_2EINL(A_27a,A_27b),V2x))))) & (all V3y (mem(V3y,A_27b) -> p(ap(V0P,ap(c_2Esum_2EINR(A_27a,A_27b),V3y)))))))))))) # label(conj_thm_2Esum_2EFORALL__SUM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 488 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) -> p(ap(c_2Esum_2EISL(A_27a,A_27b),V0x)) | p(ap(c_2Esum_2EISR(A_27a,A_27b),V0x)))))))) # label(conj_thm_2Esum_2EISL__OR__ISR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 489 (all A_27b all V2v2 (mem(V2v2,A_27b) -> (all V6b (mem(V6b,bool) -> (all V8y ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27b),V8y),V2v2)),ap(c_2Ebool_2E_7E,V6b)) = ap(f90(A_27b,V2v2,V6b),V8y)))))) # label(lameq_f90) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 490 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(c_2Esum_2EOUTL(A_27a,A_27b),ap(c_2Esum_2EINL(A_27a,A_27b),V0x)))))))) # label(ax_thm_2Esum_2EOUTL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 491 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (exists V0rep (mem(V0rep,arr(ty_2Esum_2Esum(A_27a,A_27b),arr(bool,arr(A_27a,arr(A_27b,bool))))) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(arr(bool,arr(A_27a,arr(A_27b,bool))),ty_2Esum_2Esum(A_27a,A_27b)),c_2Esum_2EIS__SUM__REP(A_27a,A_27b)),V0rep)))))))) # label(ax_thm_2Esum_2Esum__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 492 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(V0P,V2x)) <-> p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V0P),V1Q),ap(c_2Esum_2EINL(A_27a,A_27b),V2x)))))))))) & (all V3P (mem(V3P,arr(A_27a,bool)) -> (all V4Q (mem(V4Q,arr(A_27b,bool)) -> (all V5y (mem(V5y,A_27b) -> (p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V3P),V4Q),ap(c_2Esum_2EINR(A_27a,A_27b),V5y))) <-> p(ap(V4Q,V5y))))))))))))) # label(ax_thm_2Esum_2ESUM__ALL__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 493 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) -> (p(ap(c_2Esum_2EISL(A_27a,A_27b),V0x)) -> ap(c_2Esum_2EINL(A_27a,A_27b),ap(c_2Esum_2EOUTL(A_27a,A_27b),V0x)) = V0x))))))) # label(conj_thm_2Esum_2EINL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 494 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27d)) -> (all V2z (mem(V2z,ty_2Esum_2Esum(A_27a,A_27b)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27c,A_27d)),ap(c_2Esum_2EISL(A_27a,A_27b),V2z)),ap(c_2Esum_2EINL(A_27c,A_27d),ap(V0f,ap(c_2Esum_2EOUTL(A_27a,A_27b),V2z)))),ap(c_2Esum_2EINR(A_27c,A_27d),ap(V1g,ap(c_2Esum_2EOUTR(A_27a,A_27b),V2z)))) = ap(ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),V0f),V1g),V2z))))))))))))))) # label(conj_thm_2Esum_2ESUM__MAP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 495 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27b) -> (all V1y (mem(V1y,A_27b) -> (ap(c_2Esum_2EINR(A_27a,A_27b),V1y) = ap(c_2Esum_2EINR(A_27a,A_27b),V0x) <-> V1y = V0x))))))))) # label(conj_thm_2Esum_2EINR__11) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 496 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all A_27e (ne(A_27e) -> (all A_27f (ne(A_27f) -> (all A_27g (ne(A_27g) -> (all A_27h (ne(A_27h) -> (all V0P (mem(V0P,bool) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> (all V3z (mem(V3z,A_27a) -> (p(V0P) & V1x = V3z <-> ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27b,A_27a)),V0P),ap(c_2Esum_2EINR(A_27b,A_27a),V1x)),ap(c_2Esum_2EINL(A_27b,A_27a),V2y)) = ap(c_2Esum_2EINR(A_27b,A_27a),V3z)))))))) & (all V4x (mem(V4x,A_27c) -> (all V5y (mem(V5y,A_27d) -> (all V6z (mem(V6z,A_27d) -> (ap(c_2Esum_2EINL(A_27d,A_27c),V6z) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27d,A_27c)),V0P),ap(c_2Esum_2EINR(A_27d,A_27c),V4x)),ap(c_2Esum_2EINL(A_27d,A_27c),V5y)) <-> -p(V0P) & V5y = V6z))))))) & (all V7x (mem(V7x,A_27e) -> (all V8y (mem(V8y,A_27f) -> (all V9z (mem(V9z,A_27e) -> (V7x = V9z & p(V0P) <-> ap(c_2Esum_2EINL(A_27e,A_27f),V9z) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27e,A_27f)),V0P),ap(c_2Esum_2EINL(A_27e,A_27f),V7x)),ap(c_2Esum_2EINR(A_27e,A_27f),V8y))))))))) & (all V10x (mem(V10x,A_27g) -> (all V11y (mem(V11y,A_27h) -> (all V12z (mem(V12z,A_27h) -> (ap(c_2Esum_2EINR(A_27g,A_27h),V12z) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Esum_2Esum(A_27g,A_27h)),V0P),ap(c_2Esum_2EINL(A_27g,A_27h),V10x)),ap(c_2Esum_2EINR(A_27g,A_27h),V11y)) <-> -p(V0P) & V12z = V11y))))))))))))))))))))))))) # label(conj_thm_2Esum_2Econd__sum__expand) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 497 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27c)) -> (exists V2h (mem(V2h,arr(ty_2Esum_2Esum(A_27a,A_27b),A_27c)) & (all V3x (mem(V3x,A_27a) -> ap(V0f,V3x) = ap(V2h,ap(c_2Esum_2EINL(A_27a,A_27b),V3x)))) & (all V4y (mem(V4y,A_27b) -> ap(V1g,V4y) = ap(V2h,ap(c_2Esum_2EINR(A_27a,A_27b),V4y)))))))))))))))) # label(conj_thm_2Esum_2Esum__Axiom) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 498 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) -> (-p(ap(c_2Esum_2EISL(A_27a,A_27b),V0x)) <-> p(ap(c_2Esum_2EISR(A_27a,A_27b),V0x))))))))) # label(conj_thm_2Esum_2ENOT__ISL__ISR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 499 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2ESUM__ALL(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(ty_2Esum_2Esum(A_27a,A_27b),bool)))))))) # label(mem_c_2Esum_2ESUM__ALL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 500 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0s (mem(V0s,ty_2Esum_2Esum(A_27a,A_27b)) -> (all V1s_27 (mem(V1s_27,ty_2Esum_2Esum(A_27a,A_27b)) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (all V3P_27 (mem(V3P_27,arr(A_27a,bool)) -> (all V4Q (mem(V4Q,arr(A_27b,bool)) -> (all V5Q_27 (mem(V5Q_27,arr(A_27b,bool)) -> (V1s_27 = V0s & (all V6a (mem(V6a,A_27a) -> (V1s_27 = ap(c_2Esum_2EINL(A_27a,A_27b),V6a) -> (p(ap(V2P,V6a)) <-> p(ap(V3P_27,V6a)))))) & (all V7b (mem(V7b,A_27b) -> (V1s_27 = ap(c_2Esum_2EINR(A_27a,A_27b),V7b) -> (p(ap(V5Q_27,V7b)) <-> p(ap(V4Q,V7b)))))) -> (p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V3P_27),V5Q_27),V1s_27)) <-> p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V2P),V4Q),V0s)))))))))))))))))))) # label(conj_thm_2Esum_2ESUM__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 501 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EOUTR(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),A_27b)))))) # label(mem_c_2Esum_2EOUTR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 502 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> ap(c_2Esum_2EINL(A_27a,A_27b),V0x) != ap(c_2Esum_2EINR(A_27a,A_27b),V1y))))))))) # label(conj_thm_2Esum_2Esum__distinct) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 503 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) -> (-p(ap(c_2Esum_2EISR(A_27a,A_27b),V0x)) <-> p(ap(c_2Esum_2EISL(A_27a,A_27b),V0x))))))))) # label(conj_thm_2Esum_2ENOT__ISR__ISL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 504 (all A_27a all A_27b all A_27c all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27c)) -> (all V2h ap(f96(A_27a,A_27b,A_27c,V0f,V1g),V2h) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(arr(A_27a,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,ty_2Esum_2Esum(A_27a,A_27b)),V2h),c_2Esum_2EINL(A_27a,A_27b))),V0f)),ap(ap(c_2Emin_2E_3D(arr(A_27b,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27b,A_27c,ty_2Esum_2Esum(A_27a,A_27b)),V2h),c_2Esum_2EINR(A_27a,A_27b))),V1g))))))) # label(lameq_f96) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 505 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EISL(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),bool)))))) # label(mem_c_2Esum_2EISL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 506 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0sum (mem(V0sum,arr(arr(A_27a,ty_2Esum_2Esum(A_27a,A_27b)),arr(arr(A_27b,ty_2Esum_2Esum(A_27a,A_27b)),A_27c))) -> p(ap(c_2Ebool_2EDATATYPE(A_27c),ap(ap(V0sum,c_2Esum_2EINL(A_27a,A_27b)),c_2Esum_2EINR(A_27a,A_27b)))))))))))) # label(conj_thm_2Esum_2Edatatype__sum) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 507 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EIS__SUM__REP(A_27a,A_27b),arr(arr(bool,arr(A_27a,arr(A_27b,bool))),bool)))))) # label(mem_c_2Esum_2EIS__SUM__REP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 508 (all A_27b all A_27a all V1v1 (mem(V1v1,A_27a) -> (all V3b (mem(V3b,bool) -> (all V4x ap(f88(A_27b,A_27a,V1v1,V3b),V4x) = k(A_27b,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V4x),V1v1)),V3b))))))) # label(lameq_f88) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 509 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27d)) -> (all V2z (mem(V2z,ty_2Esum_2Esum(A_27a,A_27b)) -> ap(ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),V0f),V1g),V2z) = ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,ty_2Esum_2Esum(A_27c,A_27d)),V2z),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Esum_2Esum(A_27c,A_27d),A_27c),c_2Esum_2EINL(A_27c,A_27d)),V0f)),ap(ap(c_2Ecombin_2Eo(A_27b,ty_2Esum_2Esum(A_27c,A_27d),A_27d),c_2Esum_2EINR(A_27c,A_27d)),V1g)))))))))))))))) # label(conj_thm_2Esum_2ESUM__MAP__CASE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 510 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V1y = V0x <-> ap(c_2Esum_2EINL(A_27a,A_27b),V0x) = ap(c_2Esum_2EINL(A_27a,A_27b),V1y)))))))))) # label(conj_thm_2Esum_2EINL__11) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 511 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27a) -> ap(c_2Esum_2EABS__sum(A_27a,A_27b),f93(A_27a,A_27b,V0e)) = ap(c_2Esum_2EINL(A_27a,A_27b),V0e))))))) # label(ax_thm_2Esum_2EINL__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 512 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1P_27 (mem(V1P_27,arr(A_27a,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V3Q_27 (mem(V3Q_27,arr(A_27b,bool)) -> (all V4s (mem(V4s,ty_2Esum_2Esum(A_27a,A_27b)) -> ((all V5x (mem(V5x,A_27a) -> (p(ap(V0P,V5x)) -> p(ap(V1P_27,V5x))))) & (all V6y (mem(V6y,A_27b) -> (p(ap(V2Q,V6y)) -> p(ap(V3Q_27,V6y))))) -> (p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V0P),V2Q),V4s)) -> p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V1P_27),V3Q_27),V4s)))))))))))))))))) # label(conj_thm_2Esum_2ESUM__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 513 (all A_27b all V0e (mem(V0e,A_27b) -> (all V1b (mem(V1b,bool) -> (all V3y ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27b),V3y),V0e)),ap(c_2Ebool_2E_7E,V1b)) = ap(f94(A_27b,V0e,V1b),V3y)))))) # label(lameq_f94) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 514 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V1y (mem(V1y,A_27a) -> -p(ap(c_2Esum_2EISR(A_27a,A_27b),ap(c_2Esum_2EINL(A_27a,A_27b),V1y))))) & (all V0x (mem(V0x,A_27b) -> p(ap(c_2Esum_2EISR(A_27a,A_27b),ap(c_2Esum_2EINR(A_27a,A_27b),V0x))))))))) # label(ax_thm_2Esum_2EISR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 515 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,ty_2Esum_2Esum(A_27a,A_27b)) -> V0a = ap(c_2Esum_2EABS__sum(A_27a,A_27b),ap(c_2Esum_2EREP__sum(A_27a,A_27b),V0a)))) & (all V1r (mem(V1r,arr(bool,arr(A_27a,arr(A_27b,bool)))) -> (V1r = ap(c_2Esum_2EREP__sum(A_27a,A_27b),ap(c_2Esum_2EABS__sum(A_27a,A_27b),V1r)) <-> p(ap(c_2Esum_2EIS__SUM__REP(A_27a,A_27b),V1r))))))))) # label(ax_thm_2Esum_2Esum__ISO__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 516 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27c)) -> (all V2f1 (mem(V2f1,arr(A_27b,A_27c)) -> ap(V1f,V0x) = ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),ap(c_2Esum_2EINL(A_27a,A_27b),V0x)),V1f),V2f1))))))) & (all V3y (mem(V3y,A_27b) -> (all V4f (mem(V4f,arr(A_27a,A_27c)) -> (all V5f1 (mem(V5f1,arr(A_27b,A_27c)) -> ap(V5f1,V3y) = ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),ap(c_2Esum_2EINR(A_27a,A_27b),V3y)),V4f),V5f1))))))))))))) # label(ax_thm_2Esum_2Esum__case__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 517 (all A_27a all A_27b all V1v1 (mem(V1v1,A_27a) -> (all V3b f88(A_27b,A_27a,V1v1,V3b) = ap(f89(A_27a,A_27b,V1v1),V3b)))) # label(lameq_f89) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 518 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Esum_2Esum(A_27a,A_27b)) -> (p(ap(c_2Esum_2EISR(A_27a,A_27b),V0x)) -> ap(c_2Esum_2EINR(A_27a,A_27b),ap(c_2Esum_2EOUTR(A_27a,A_27b),V0x)) = V0x))))))) # label(conj_thm_2Esum_2EINR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 519 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27d)) -> (all V2a (mem(V2a,A_27a) -> ap(c_2Esum_2EINL(A_27c,A_27d),ap(V0f,V2a)) = ap(ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),V0f),V1g),ap(c_2Esum_2EINL(A_27a,A_27b),V2a)))))))) & (all V3f (mem(V3f,arr(A_27a,A_27c)) -> (all V4g (mem(V4g,arr(A_27b,A_27d)) -> (all V5b (mem(V5b,A_27b) -> ap(ap(ap(c_2Esum_2E_2B_2B(A_27a,A_27b,A_27c,A_27d),V3f),V4g),ap(c_2Esum_2EINR(A_27a,A_27b),V5b)) = ap(c_2Esum_2EINR(A_27c,A_27d),ap(V4g,V5b)))))))))))))))) # label(ax_thm_2Esum_2ESUM__MAP__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 520 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EABS__sum(A_27a,A_27b),arr(arr(bool,arr(A_27a,arr(A_27b,bool))),ty_2Esum_2Esum(A_27a,A_27b))))))) # label(mem_c_2Esum_2EABS__sum) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 521 (all A_27b all A_27a all V0e (mem(V0e,A_27b) -> (all V1b ap(f95(A_27b,A_27a,V0e),V1b) = k(A_27a,f94(A_27b,V0e,V1b))))) # label(lameq_f95) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 522 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EINL(A_27a,A_27b),arr(A_27a,ty_2Esum_2Esum(A_27a,A_27b))))))) # label(mem_c_2Esum_2EINL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 523 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> p(ap(c_2Esum_2EISL(A_27a,A_27b),ap(c_2Esum_2EINL(A_27a,A_27b),V0x))))) & (all V1y (mem(V1y,A_27b) -> -p(ap(c_2Esum_2EISL(A_27a,A_27b),ap(c_2Esum_2EINR(A_27a,A_27b),V1y))))))))) # label(ax_thm_2Esum_2EISL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 524 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Esum_2Esum(A_27a,A_27b),bool)) -> ((exists V1s (p(ap(V0P,V1s)) & mem(V1s,ty_2Esum_2Esum(A_27a,A_27b)))) <-> (exists V2x (mem(V2x,A_27a) & p(ap(V0P,ap(c_2Esum_2EINL(A_27a,A_27b),V2x))))) | (exists V3y (p(ap(V0P,ap(c_2Esum_2EINR(A_27a,A_27b),V3y))) & mem(V3y,A_27b)))))))))) # label(conj_thm_2Esum_2EEXISTS__SUM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 525 (all A0 (ne(A0) -> (all A1 (ne(A1) -> ne(ty_2Esum_2Esum(A0,A1)))))) # label(ne_ty_2Esum_2Esum) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 526 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(bool,arr(A_27a,arr(A_27b,bool)))) -> ((exists V1v1 (mem(V1v1,A_27a) & (exists V2v2 (mem(V2v2,A_27b) & (V0f = f89(A_27a,A_27b,V1v1) | f91(A_27b,A_27a,V2v2) = V0f))))) <-> p(ap(c_2Esum_2EIS__SUM__REP(A_27a,A_27b),V0f))))))))) # label(ax_thm_2Esum_2EIS__SUM__REP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 527 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f_27 (mem(V0f_27,arr(A_27a,A_27c)) -> (all V1f1_27 (mem(V1f1_27,arr(A_27b,A_27c)) -> (all V2M (mem(V2M,ty_2Esum_2Esum(A_27a,A_27b)) -> (all V3M_27 (mem(V3M_27,ty_2Esum_2Esum(A_27a,A_27b)) -> (all V4f (mem(V4f,arr(A_27a,A_27c)) -> (all V5f1 (mem(V5f1,arr(A_27b,A_27c)) -> ((all V6x (mem(V6x,A_27a) -> (ap(c_2Esum_2EINL(A_27a,A_27b),V6x) = V3M_27 -> ap(V0f_27,V6x) = ap(V4f,V6x)))) & (all V7y (mem(V7y,A_27b) -> (ap(c_2Esum_2EINR(A_27a,A_27b),V7y) = V3M_27 -> ap(V5f1,V7y) = ap(V1f1_27,V7y)))) & V2M = V3M_27 -> ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),V3M_27),V0f_27),V1f1_27) = ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),V2M),V4f),V5f1)))))))))))))))))))) # label(conj_thm_2Esum_2Esum__case__cong) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 528 (all A_27b all A_27a all V0e (mem(V0e,A_27a) -> (all V1b (mem(V1b,bool) -> (all V2x ap(f92(A_27b,A_27a,V0e,V1b),V2x) = k(A_27b,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V2x),V0e)),V1b))))))) # label(lameq_f92) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 529 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Esum_2EOUTL(A_27a,A_27b),arr(ty_2Esum_2Esum(A_27a,A_27b),A_27a)))))) # label(mem_c_2Esum_2EOUTL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 530 (all A_27b all A_27a all V2v2 (mem(V2v2,A_27b) -> (all V6b k(A_27a,f90(A_27b,V2v2,V6b)) = ap(f91(A_27b,A_27a,V2v2),V6b)))) # label(lameq_f91) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 531 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V1R2),V0R1) = ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),V1R2))))))))) # label(conj_thm_2Erelation_2ERUNION__COMM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 532 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0y (mem(V0y,A_27a) -> (all V1R (mem(V1R,arr(A_27b,arr(A_27a,bool))) -> ((exists V2x (mem(V2x,A_27b) & p(ap(ap(V1R,V2x),V0y)))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Erelation_2ERRANGE(A_27b,A_27a),V1R)))))))))))) # label(conj_thm_2Erelation_2EIN__RRANGE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 533 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> ((all V3Q (mem(V3Q,arr(A_27a,bool)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V3Q,V5y)) & p(ap(ap(V0R,V4x),V5y)) -> p(ap(V3Q,V4x))))))) & p(ap(V3Q,V2b)) -> p(ap(V3Q,V1a))))) <-> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1a),V2b))))))))))) # label(conj_thm_2Erelation_2ERTC__ALT__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.71 534 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERDOM(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,bool))))))) # label(mem_c_2Erelation_2ERDOM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 535 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),ap(ap(c_2Erelation_2EO(A_27a,A_27a,A_27a),V0R),V0R)),V0R)) <-> p(ap(c_2Erelation_2Etransitive(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Etransitive__O__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 536 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> p(ap(c_2Ebool_2E_3F_21(arr(A_27a,A_27b)),f106(A_27b,A_27a,V1M,V0R)))))))))))) # label(conj_thm_2Erelation_2EWF__RECURSION__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 537 (all A_27a (ne(A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R1)) & p(ap(c_2Erelation_2Etransitive(A_27a),V1R2)) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R1),V1R2)))))))))) # label(conj_thm_2Erelation_2Etransitive__RINTER) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 538 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <-> V2y = V1x | (exists V3u (p(ap(ap(V0R,V3u),V2y)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V3u)) & mem(V3u,A_27a)))))))))))) # label(conj_thm_2Erelation_2ERTC__CASES2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 539 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etrichotomous(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) <-> p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Etrichotomous__RC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 540 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(V1P,V4x),V5y)) & p(ap(ap(V0R,V5y),V6z)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) -> p(ap(ap(V1P,V4x),V6z))))))))) -> (all V7u (mem(V7u,A_27a) -> (all V8v (mem(V8v,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) -> p(ap(ap(V1P,V7u),V8v)))))))))))))) # label(conj_thm_2Erelation_2ETC__STRONG__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 541 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__EQC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 542 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EOrder(A_27a),V0R)) & p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R)) <-> p(ap(c_2Erelation_2ELinearOrder(A_27a),V0R))))))) # label(ax_thm_2Erelation_2ELinearOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 543 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0y (mem(V0y,arr(A_27a,arr(A_27b,bool))) -> (all V1z (mem(V1z,arr(A_27a,arr(A_27b,bool))) -> (V0y = V1z <-> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0y),V1z)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V1z),V0y))))))))))) # label(conj_thm_2Erelation_2EEqIsBothRSUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 544 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2z (mem(V2z,A_27a) -> (p(ap(ap(V0R,V1x),V2z)) | (exists V3y (mem(V3y,A_27a) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V3y)) & p(ap(ap(V0R,V3y),V2z)))) <-> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z))))))))))) # label(conj_thm_2Erelation_2ETC__CASES2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 545 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R))) <-> p(ap(c_2Erelation_2EWF(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EWF__TC__EQN) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 546 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (p(ap(ap(V0R,V1x),V2y)) -> V2y != V1x)))))))))) # label(conj_thm_2Erelation_2EWF__NOT__REFL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 547 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> p(ap(ap(V1P,V2x),V2x)))) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(V0R,V3x),V4y)) & p(ap(ap(V1P,V4y),V5z)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V4y),V5z)) -> p(ap(ap(V1P,V3x),V5z))))))))) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) -> p(ap(ap(V1P,V6x),V7y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 548 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ediamond(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))) <-> p(ap(c_2Erelation_2ECR(A_27a),V0R))))))) # label(ax_thm_2Erelation_2ECR__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 549 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Ereflexive__RC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 550 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERC__RTC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 551 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R) & ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R))))) # label(conj_thm_2Erelation_2Einv__EQC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 552 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2a (mem(V2a,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (all V4z (mem(V4z,A_27a) -> (p(ap(ap(V0R,V3y),V4z)) & p(ap(V1Q,V3y)) -> p(ap(V1Q,V4z))))))) & p(ap(V1Q,V2a)) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2a),V5z)) -> p(ap(V1Q,V5z)))))))))))))) # label(conj_thm_2Erelation_2ERTC__ALT__RIGHT__INDUCT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 553 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (c_2Erelation_2ERUNIV(A_27a,A_27b) = V0R <-> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),c_2Erelation_2ERUNIV(A_27a,A_27b)),V0R))) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0R),c_2Erelation_2ERUNIV(A_27a,A_27b))))))))) # label(conj_thm_2Erelation_2ERUNIV__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 554 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27a) -> ((all V2y (mem(V2y,A_27b) -> -p(ap(ap(V0R,V1x),V2y)))) <-> p(ap(ap(c_2Erelation_2Enf(A_27a,A_27b),V0R),V1x))))))))))) # label(ax_thm_2Erelation_2Enf__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 555 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERRANGE(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27b,bool))))))) # label(mem_c_2Erelation_2ERRANGE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 556 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27b,bool))) -> (all V2M (mem(V2M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (p(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V0R),V1P),V2M)) <-> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> (all V4x (mem(V4x,A_27a) -> ((all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V5y),V4x)) -> p(ap(ap(V1P,V5y),ap(V3f,V5y)))))) -> p(ap(ap(V1P,V4x),ap(ap(V2M,V3f),V4x))))))))))))))))))) # label(ax_thm_2Erelation_2EINDUCTIVE__INVARIANT__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 557 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27b,arr(A_27b,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(ap(V0R,V3x),V4y)) -> p(ap(ap(V1Q,ap(V2f,V3x)),ap(V2f,V4y)))))))) & p(ap(c_2Erelation_2Etransitive(A_27b),V1Q)) & p(ap(c_2Erelation_2Ereflexive(A_27b),V1Q)) -> (all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V5x),V6y)) -> p(ap(ap(V1Q,ap(V2f,V5x)),ap(V2f,V6y))))))))))))))))))) # label(conj_thm_2Erelation_2ERTC__lifts__reflexive__transitive__relations) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 558 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ESTRORD(A_27a),V0R),V1a),V2b)) <-> V2b != V1a & p(ap(ap(V0R,V1a),V2b))))))))))) # label(ax_thm_2Erelation_2ESTRORD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 559 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2Einv__image(A_27a,A_27b),arr(arr(A_27b,arr(A_27b,bool)),arr(arr(A_27a,A_27b),arr(A_27a,arr(A_27a,bool))))))))) # label(mem_c_2Erelation_2Einv__image) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 560 (all A_27g (ne(A_27g) -> (all V0Z (mem(V0Z,arr(A_27g,arr(A_27g,bool))) -> (p(ap(c_2Erelation_2Eantisymmetric(A_27g),V0Z)) & p(ap(c_2Erelation_2Etransitive(A_27g),V0Z)) <-> p(ap(c_2Erelation_2EOrder(A_27g),V0Z))))))) # label(ax_thm_2Erelation_2EOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 561 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),bool))))))))) # label(mem_c_2Erelation_2EINDUCTIVE__INVARIANT__ON) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 562 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R)) <-> p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Eantisymmetric__RC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 563 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V1x)))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (all V4z (mem(V4z,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3y),V4z)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V4z))))))))))))) # label(conj_thm_2Erelation_2ERTC__RULES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 564 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y)) <-> V2y = V1x | p(ap(ap(V0R,V1x),V2y))))))))))) # label(ax_thm_2Erelation_2ERC__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 565 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) -> V2y != V1x)))))))))) # label(conj_thm_2Erelation_2EWF__noloops) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 566 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) -> p(ap(c_2Erelation_2Etransitive(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f)))))))))))) # label(conj_thm_2Erelation_2Etransitive__inv__image) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 567 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27b,arr(A_27b,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (p(ap(c_2Erelation_2Etransitive(A_27b),V1Q)) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(ap(V0R,V3x),V4y)) -> p(ap(ap(V1Q,ap(V2f,V3x)),ap(V2f,V4y)))))))) -> (all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V5x),V6y)) -> p(ap(ap(V1Q,ap(V2f,V5x)),ap(V2f,V6y))))))))))))))))))) # label(conj_thm_2Erelation_2ETC__lifts__transitive__relations) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 568 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2EWF__TC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 569 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ERTC__REFLEXIVE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 570 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (all V4z (mem(V4z,A_27a) -> (p(ap(ap(V0R,V3y),V4z)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V4z))))))))) & (all V1x (mem(V1x,A_27a) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V1x)))))))) # label(conj_thm_2Erelation_2ERTC__RULES__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 571 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> (p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1a)) <-> (all V2P (mem(V2P,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> ((all V4y (mem(V4y,A_27a) -> (p(ap(ap(V0R,V4y),V3x)) -> p(ap(V2P,V4y))))) -> p(ap(V2P,V3x))))) -> p(ap(V2P,V1a)))))))))))) # label(ax_thm_2Erelation_2EWFP__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 572 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ERTC__TRANSITIVE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 573 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EWFP(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,bool))))) # label(mem_c_2Erelation_2EWFP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 574 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EStrongOrder(A_27a),V0R)) -> p(ap(c_2Erelation_2EOrder(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EStrongOrd__Ord) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 575 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) -> p(ap(c_2Erelation_2Esymmetric(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f)))))))))))) # label(conj_thm_2Erelation_2Esymmetric__inv__image) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 576 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> V0R = ap(ap(c_2Erelation_2EO(A_27a,A_27a,A_27b),V0R),c_2Emin_2E_3D(A_27a)))))))) # label(conj_thm_2Erelation_2EO__Id) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 577 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EINVOL(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2Einv(A_27a,A_27a))))) # label(conj_thm_2Erelation_2Einv__INVOL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 578 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V1P,V2x),V3y)) -> p(ap(ap(V0R,V2x),V3y))))))) -> p(ap(c_2Erelation_2EWF(A_27a),V1P))))))))) # label(conj_thm_2Erelation_2EWF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 579 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EIDEM(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2ERTC(A_27a))))) # label(conj_thm_2Erelation_2EIDEM__RTC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 580 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ESTRORD(A_27a),V0R) = ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R),ap(c_2Erelation_2ERCOMPL(A_27a,A_27a),c_2Emin_2E_3D(A_27a))))))) # label(conj_thm_2Erelation_2ESTRORD__AND__NOT__Id) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 581 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ETC(A_27a),V0R))))) # label(conj_thm_2Erelation_2ETC__IDEM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 582 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R))) = ap(c_2Erelation_2EEQC(A_27a),V0R))))) # label(ax_thm_2Erelation_2EEQC__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 583 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Etransitive(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Etransitive) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 584 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V2y),V1x))))))))))) # label(conj_thm_2Erelation_2EEQC__SYM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 585 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2Q (mem(V2Q,arr(A_27a,bool)) -> ((all V3y (mem(V3y,A_27a) -> (p(ap(ap(V1R,V0a),V3y)) -> p(ap(V2Q,V3y))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V1R,V4x),V5y)) & p(ap(V2Q,V4x)) -> p(ap(V2Q,V5y))))))) -> (all V6b (mem(V6b,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1R),V0a),V6b)) -> p(ap(V2Q,V6b)))))))))))))) # label(conj_thm_2Erelation_2ETC__INDUCT__ALT__RIGHT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 586 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V1M) = f104(A_27b,A_27a,V1M,V0R))))))))) # label(ax_thm_2Erelation_2EWFREC__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 587 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V1x != V2y & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) -> (exists V3z (V3z != V1x & p(ap(ap(V0R,V1x),V3z)) & mem(V3z,A_27a)))))))))))) # label(conj_thm_2Erelation_2ETC__implies__one__step) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 588 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) -> V0R = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ESTRORD(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ERC__STRORD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 589 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R)) & p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) <-> p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EWeakLinearOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 590 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EIDEM(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2ERC(A_27a))))) # label(conj_thm_2Erelation_2EIDEM__RC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 591 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> p(ap(c_2Erelation_2EWeakOrder(arr(A_27a,arr(A_27b,bool))),c_2Erelation_2ERSUBSET(A_27a,A_27b))))))) # label(conj_thm_2Erelation_2ERSUBSET__WeakOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 592 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) -> ap(c_2Erelation_2Einv(A_27a,A_27a),V0R) = V0R))))) # label(conj_thm_2Erelation_2Esymmetric__inv__identity) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 593 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EEQC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2EEQC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 594 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2R3 (mem(V2R3,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V1R2),V2R3)) = ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),V1R2)),V2R3))))))))))) # label(conj_thm_2Erelation_2ERUNION__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 595 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1R_27 (mem(V1R_27,arr(A_27c,arr(A_27a,bool))) -> ap(c_2Erelation_2Einv(A_27c,A_27b),ap(ap(c_2Erelation_2EO(A_27c,A_27a,A_27b),V0R),V1R_27)) = ap(ap(c_2Erelation_2EO(A_27b,A_27a,A_27c),ap(c_2Erelation_2Einv(A_27c,A_27a),V1R_27)),ap(c_2Erelation_2Einv(A_27a,A_27b),V0R)))))))))))) # label(conj_thm_2Erelation_2Einv__O) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 596 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EWeakLinearOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2EWeakLinearOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 597 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <-> (exists V3u (mem(V3u,A_27a) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3u),V2y)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V3u))))))))))))) # label(conj_thm_2Erelation_2ERTC__CASES__RTC__TWICE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 598 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(V0R,V4y),V5z)) & p(ap(ap(V1P,V3x),V4y)) -> p(ap(ap(V1P,V3x),V5z))))))))) & (all V2x (mem(V2x,A_27a) -> p(ap(ap(V1P,V2x),V2x)))) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) -> p(ap(ap(V1P,V6x),V7y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 599 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V3y),V2x)) -> p(ap(V1P,V3y))))) -> p(ap(V1P,V2x))))) -> (all V4x (mem(V4x,A_27a) -> p(ap(V1P,V4x))))))) <-> p(ap(c_2Erelation_2EWF(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EWF__EQ__INDUCTION__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 600 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V2x (mem(V2x,A_27a) -> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> (V3f = ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),f100(A_27b,A_27a,V1M,V0R,V3f)),V0R),V2x) <-> p(ap(ap(ap(ap(c_2Erelation_2Eapprox(A_27a,A_27b),V0R),V1M),V2x),V3f))))))))))))))) # label(ax_thm_2Erelation_2Eapprox__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 601 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Etransitive__EQC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 602 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R)) <-> p(ap(c_2Erelation_2Etrichotomous(A_27a),ap(c_2Erelation_2ESTRORD(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Etrichotomous__STRORD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 603 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R)) & p(ap(c_2Erelation_2EStrongOrder(A_27a),V0R)) <-> p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EStrongLinearOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 604 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EWF(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2EWF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 605 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ERTC(A_27a),V0R) & ap(c_2Erelation_2ERTC(A_27a),V0R) = ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ETC__RC__EQNS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 606 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (p(ap(ap(V1R,V3y),V2x)) -> p(ap(V0P,V3y))))) & p(ap(ap(c_2Erelation_2EWFP(A_27a),V1R),V2x)) -> p(ap(V0P,V2x))))) -> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Erelation_2EWFP(A_27a),V1R),V4x)) -> p(ap(V0P,V4x)))))))))))) # label(conj_thm_2Erelation_2EWFP__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 607 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2Einv(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27b,arr(A_27a,bool)))))))) # label(mem_c_2Erelation_2Einv) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 608 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) -> p(ap(c_2Erelation_2EOrder(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EWeakOrd__Ord) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 609 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <-> V2y = V1x | p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__CASES__TC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 610 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EWF__antisymmetric) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 611 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V1R,V2y),V3z)) -> ap(V0f,V2y) = ap(ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V0f),V1R),V3z),V2y)))))))))))))) # label(conj_thm_2Erelation_2ERESTRICT__LEMMA) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 612 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EIDEM(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2ETC(A_27a))))) # label(conj_thm_2Erelation_2EIDEM__TC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 613 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y)))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V4x),V5y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))))))))))))))) # label(conj_thm_2Erelation_2ERTC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 614 (all A_27a (ne(A_27a) -> (all V0A (mem(V0A,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2Ediag(A_27a),V0A),V1x),V2y)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0A)) & V1x = V2y))))))))) # label(ax_thm_2Erelation_2Ediag__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 615 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERINTER(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27b,bool))))))))) # label(mem_c_2Erelation_2ERINTER) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 616 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Etransitive__RTC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 617 (all A_27b all A_27a all V0R (mem(V0R,arr(A_27b,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2x f97(A_27b,A_27a,V0R,V2x,V1f) = ap(f98(A_27b,A_27a,V0R,V1f),V2x)))))) # label(lameq_f98) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 618 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V5y),V6z)) & p(ap(ap(V1P,V5y),V6z)) -> p(ap(ap(V1P,V4x),V6z))))))))) -> (all V7u (mem(V7u,A_27a) -> (all V8v (mem(V8v,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) -> p(ap(ap(V1P,V7u),V8v)))))))))))))) # label(conj_thm_2Erelation_2ETC__STRONG__INDUCT__LEFT1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 619 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V1x)))))))) # label(conj_thm_2Erelation_2ERTC__REFL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 620 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EPreOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2EPreOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 621 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1Q,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1Q),V2x),V3y)))))))))))))) # label(conj_thm_2Erelation_2ETC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 622 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y)))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V4x),V5y)) -> p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))))))))))))))) # label(conj_thm_2Erelation_2ERC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 623 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EOrder(A_27a),V0R)) <-> p(ap(c_2Erelation_2EStrongOrder(A_27a),ap(c_2Erelation_2ESTRORD(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2ESTRORD__Strong) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 624 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ETC__RTC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 625 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EPreOrder(A_27a),V0R)) <-> p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EPreOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 626 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)),V0R)) <-> p(ap(c_2Erelation_2Esymmetric(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Esymmetric__inv__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 627 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1R_27 (mem(V1R_27,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1R_27,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V1R_27),V2x),V3y)))))))))))))) # label(conj_thm_2Erelation_2EEQC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 628 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__SINGLE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 629 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) -> V0R = ap(c_2Erelation_2ESC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2Esymmetric__SC__identity) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 630 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERDOM__DELETE(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27a,arr(A_27b,bool))))))))) # label(mem_c_2Erelation_2ERDOM__DELETE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 631 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> ((all V1x (mem(V1x,A_27z) -> V1x = ap(V0f,ap(V0f,V1x)))) <-> p(ap(c_2Erelation_2EINVOL(A_27z),V0f))))))) # label(conj_thm_2Erelation_2EINVOL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 632 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> ((all V3P (mem(V3P,arr(A_27a,arr(A_27a,bool))) -> ((all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (all V8z (mem(V8z,A_27a) -> (p(ap(ap(V3P,V6x),V7y)) & p(ap(ap(V3P,V7y),V8z)) -> p(ap(ap(V3P,V6x),V8z))))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V3P,V4x),V5y))))))) -> p(ap(ap(V3P,V1a),V2b))))) <-> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1a),V2b))))))))))) # label(ax_thm_2Erelation_2ETC__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 633 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2Einv__RC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 634 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ERTC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2ERTC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 635 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Etransitive__RC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 636 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V3y),V2x)) -> p(ap(V1P,V3y))))) -> p(ap(V1P,V2x))))) -> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V4x)) -> p(ap(V1P,V4x)))))))))))) # label(conj_thm_2Erelation_2EWFP__INDUCT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 637 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ETC__TRANSITIVE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 638 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EEMPTY__REL(A_27a),arr(A_27a,arr(A_27a,bool))))) # label(mem_c_2Erelation_2EEMPTY__REL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 639 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <-> V2y = V1x | (exists V3u (mem(V3u,A_27a) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3u),V2y)) & p(ap(ap(V0R,V1x),V3u))))))))))))) # label(conj_thm_2Erelation_2ERTC__CASES1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 640 (all A_27a (ne(A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R1)) -> p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R1),V1R2)))) & (p(ap(c_2Erelation_2Eantisymmetric(A_27a),V1R2)) -> p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R1),V1R2)))))))))) # label(conj_thm_2Erelation_2Eantisymmetric__RINTER) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 641 (all A_27z (ne(A_27z) -> mem(c_2Erelation_2EINVOL(A_27z),arr(arr(A_27z,A_27z),bool)))) # label(mem_c_2Erelation_2EINVOL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 642 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2EEQC__R) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 643 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EStrongOrder(A_27a),V0R)) -> ap(c_2Erelation_2ESTRORD(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = V0R))))) # label(conj_thm_2Erelation_2ESTRORD__RC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 644 (all A_27z (ne(A_27z) -> mem(c_2Erelation_2EIDEM(A_27z),arr(arr(A_27z,A_27z),bool)))) # label(mem_c_2Erelation_2EIDEM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 645 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2EEQC(A_27a),V0R) = ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) & ap(c_2Erelation_2EEQC(A_27a),V0R) = ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)) & ap(c_2Erelation_2EEQC(A_27a),V0R) = ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2EEQC__MOVES__IN) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 646 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> ap(V1f,V2x) = ap(V1f,V3y)))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V4x),V5y)) -> ap(V1f,V4x) = ap(V1f,V5y))))))))))))))) # label(conj_thm_2Erelation_2ERTC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 647 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2u (mem(V2u,A_27a) -> (all V3v (mem(V3v,A_27b) -> (p(ap(ap(V0R,V2u),V3v)) & V1x != V2u <-> p(ap(ap(ap(ap(c_2Erelation_2ERDOM__DELETE(A_27a,A_27b),V0R),V1x),V2u),V3v))))))))))))))) # label(ax_thm_2Erelation_2ERDOM__DELETE__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 648 (all A_27g (ne(A_27g) -> (all A_27h (ne(A_27h) -> (all A_27k (ne(A_27k) -> (all V0R1 (mem(V0R1,arr(A_27h,arr(A_27k,bool))) -> (all V1R2 (mem(V1R2,arr(A_27g,arr(A_27h,bool))) -> (all V2x (mem(V2x,A_27g) -> (all V3z (mem(V3z,A_27k) -> (p(ap(ap(ap(ap(c_2Erelation_2EO(A_27g,A_27h,A_27k),V0R1),V1R2),V2x),V3z)) <-> (exists V4y (p(ap(ap(V1R2,V2x),V4y)) & p(ap(ap(V0R1,V4y),V3z)) & mem(V4y,A_27h)))))))))))))))))) # label(ax_thm_2Erelation_2EO__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 649 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),ap(ap(c_2Erelation_2ERRESTRICT(A_27a,A_27b),V1R),V2s)))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V1R))) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s))))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM__RRESTRICT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 650 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) & p(ap(ap(V0R,V2x),V3y)) <-> p(ap(ap(ap(ap(c_2Erelation_2ERRESTRICT(A_27a,A_27b),V0R),V1s),V2x),V3y))))))))))))))) # label(ax_thm_2Erelation_2ERRESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 651 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V0f),V1R),V2x) = f99(A_27b,A_27a,V0f,V2x,V1R))))))))))) # label(ax_thm_2Erelation_2ERESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 652 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> ap(c_2Erelation_2Einv(A_27b,A_27a),ap(c_2Erelation_2Einv(A_27a,A_27b),V0R)) = V0R)))))) # label(conj_thm_2Erelation_2Einv__inv) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 653 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) <-> p(ap(c_2Erelation_2Esymmetric(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Esymmetric__RC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 654 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> (p(ap(c_2Erelation_2EINVOL(A_27z),V0f)) -> (all V1a (mem(V1a,A_27z) -> (all V2b (mem(V2b,A_27z) -> (ap(V0f,V2b) = V1a <-> V2b = ap(V0f,V1a))))))))))) # label(conj_thm_2Erelation_2EINVOL__ONE__ENO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 655 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ediamond(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) <-> p(ap(c_2Erelation_2Ercdiamond(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Ercdiamond__diamond) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 656 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),bool)))))))) # label(mem_c_2Erelation_2EINDUCTIVE__INVARIANT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 657 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERESTRICT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,A_27b))))))))) # label(mem_c_2Erelation_2ERESTRICT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 658 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V0R,V2y),V3z)) & p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(V0R,V1x),V3z))))))))) <-> p(ap(c_2Erelation_2Etransitive(A_27a),V0R))))))) # label(ax_thm_2Erelation_2Etransitive__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 659 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y)))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))))))))))))))) # label(conj_thm_2Erelation_2ETC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 660 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(V0P,V2x)) & p(ap(ap(V1R,V2x),V3y)) -> p(ap(V0P,V3y))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V0P,V4x)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1R),V4x),V5y)) -> p(ap(V0P,V5y)))))))))))))) # label(conj_thm_2Erelation_2ETC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 661 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ESN(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2ESN) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 662 (all A_27a all A_27b all V2x (mem(V2x,A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V3f ap(f101(A_27a,A_27b,V2x,V0R,V1M),V3f) = ap(ap(ap(ap(c_2Erelation_2Eapprox(A_27a,A_27b),V0R),V1M),V2x),V3f)))))))) # label(lameq_f101) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 663 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27b,bool))) -> (all V2M (mem(V2M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V3D (mem(V3D,arr(A_27a,bool)) -> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V0R),V3D),V1P),V2M)) & p(ap(V3D,V4x)) & p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> p(ap(ap(V1P,V4x),ap(ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V2M),V4x)))))))))))))))))) # label(conj_thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__WFREC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 664 (all A_27b all A_27a all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V3f ap(f103(A_27b,A_27a,V1M,V0R),V3f) = f102(A_27b,A_27a,V1M,V0R,V3f)))))) # label(lameq_f103) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 665 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Ediamond(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Ediamond) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 666 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27b) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V2y),V1x)) <-> p(ap(ap(ap(c_2Erelation_2Einv(A_27a,A_27b),V0R),V1x),V2y))))))))))))) # label(ax_thm_2Erelation_2Einv__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 667 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R)) <-> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> p(ap(ap(V0R,V1a),V2b)) | p(ap(ap(V0R,V2b),V1a)) | V1a = V2b))))))))) # label(ax_thm_2Erelation_2Etrichotomous) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 668 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERUNIV(A_27a,A_27b),arr(A_27a,arr(A_27b,bool))))))) # label(mem_c_2Erelation_2ERUNIV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 669 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> p(ap(ap(V0R,V1x),V1x)))) <-> p(ap(c_2Erelation_2Ereflexive(A_27a),V0R))))))) # label(ax_thm_2Erelation_2Ereflexive__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 670 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> ($F <-> p(ap(ap(c_2Erelation_2EEMPTY__REL(A_27a),V0x),V1y))))))))) # label(ax_thm_2Erelation_2EEMPTY__REL__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.72 671 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27b,bool))) -> (all V2M (mem(V2M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (p(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V0R),V1P),V2M)) & p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (all V3x (mem(V3x,A_27a) -> p(ap(ap(V1P,V3x),ap(ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V2M),V3x)))))))))))))))) # label(conj_thm_2Erelation_2EINDUCTIVE__INVARIANT__WFREC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 672 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2ESN(A_27a),V0R)) <-> p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))))) # label(ax_thm_2Erelation_2ESN__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 673 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) -> V0R = ap(c_2Erelation_2ETC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2Etransitive__TC__identity) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 674 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27b,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(ap(ap(c_2Erelation_2Einv__image(A_27a,A_27b),V0R),V1f),V2x),V3y)) <-> p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y)))))))))))))))) # label(conj_thm_2Erelation_2Einv__image__thm) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 675 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Eirreflexive(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Eirreflexive) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 676 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V2y),V1x)) <-> p(ap(ap(V0R,V1x),V2y))))))) <-> p(ap(c_2Erelation_2Esymmetric(A_27a),V0R))))))) # label(ax_thm_2Erelation_2Esymmetric__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 677 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y))))))) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3x),V4y)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4y),V5z)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3x),V5z))))))))))))) # label(conj_thm_2Erelation_2ETC__RULES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 678 (all A_27g (ne(A_27g) -> (all V0Z (mem(V0Z,arr(A_27g,arr(A_27g,bool))) -> (p(ap(c_2Erelation_2EWeakOrder(A_27g),V0Z)) <-> p(ap(c_2Erelation_2Ereflexive(A_27g),V0Z)) & p(ap(c_2Erelation_2Etransitive(A_27g),V0Z)) & p(ap(c_2Erelation_2Eantisymmetric(A_27g),V0Z))))))) # label(ax_thm_2Erelation_2EWeakOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 679 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1B (mem(V1B,arr(A_27a,bool)) -> ((exists V2w (p(ap(V1B,V2w)) & mem(V2w,A_27a))) -> (exists V3min (mem(V3min,A_27a) & p(ap(V1B,V3min)) & (all V4b (mem(V4b,A_27a) -> (p(ap(ap(V0R,V4b),V3min)) -> -p(ap(V1B,V4b)))))))))) <-> p(ap(c_2Erelation_2EWF(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EWF__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 680 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2y),V3z)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V3z)))))))))))))) # label(conj_thm_2Erelation_2ERTC__RTC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 681 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2EWFREC(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),arr(A_27a,A_27b)))))))) # label(mem_c_2Erelation_2EWFREC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 682 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etotal(A_27a),V0R)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> p(ap(ap(V0R,V1x),V2y)) | p(ap(ap(V0R,V2y),V1x))))))))))) # label(ax_thm_2Erelation_2Etotal__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 683 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) -> p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Esymmetric__TC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 684 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V2x (mem(V2x,A_27a) -> ap(ap(ap(c_2Erelation_2Ethe__fun(A_27a,A_27b),V0R),V1M),V2x) = ap(c_2Emin_2E_40(arr(A_27a,A_27b)),f101(A_27a,A_27b,V2x,V0R,V1M)))))))))))) # label(ax_thm_2Erelation_2Ethe__fun__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 685 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWCR(A_27a),V0R)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) & p(ap(ap(V0R,V1x),V3z)) -> (exists V4u (mem(V4u,A_27a) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2y),V4u)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3z),V4u)))))))))))))))) # label(ax_thm_2Erelation_2EWCR__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 686 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2R3 (mem(V2R3,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V1R2),V2R3)) = ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),V1R2)),V2R3))))))))))) # label(conj_thm_2Erelation_2ERINTER__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 687 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> V0R = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) & ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2ESC(A_27a),V0R) & ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) & ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R)) = ap(c_2Erelation_2ERTC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) & ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R) & ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))) # label(conj_thm_2Erelation_2Einv__MOVES__OUT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 688 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(V1P,V5y),V6z)) & p(ap(ap(V1P,V4x),V5y)) -> p(ap(ap(V1P,V4x),V6z))))))))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) -> (all V7u (mem(V7u,A_27a) -> (all V8v (mem(V8v,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) -> p(ap(ap(V1P,V7u),V8v)))))))))))))) # label(conj_thm_2Erelation_2ETC__INDUCT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 689 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2z (mem(V2z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) -> p(ap(ap(V0R,V1x),V2z)) | (exists V3y (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3y),V2z)) & p(ap(ap(V0R,V1x),V3y)) & mem(V3y,A_27a)))))))))))) # label(conj_thm_2Erelation_2ETC__CASES1__E) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 690 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ediamond(A_27a),V0R)) -> p(ap(c_2Erelation_2ECR(A_27a),V0R))) & (p(ap(c_2Erelation_2Ercdiamond(A_27a),V0R)) -> p(ap(c_2Erelation_2ECR(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Eestablish__CR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 691 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1Q,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V1Q),V2x),V3y)))))))))))))) # label(conj_thm_2Erelation_2ERC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 692 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EWCR(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2EWCR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 693 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Ereflexive__RTC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 694 (all A_27g (ne(A_27g) -> (all V0Z (mem(V0Z,arr(A_27g,arr(A_27g,bool))) -> (p(ap(c_2Erelation_2EStrongOrder(A_27g),V0Z)) <-> p(ap(c_2Erelation_2Eirreflexive(A_27g),V0Z)) & p(ap(c_2Erelation_2Etransitive(A_27g),V0Z))))))) # label(ax_thm_2Erelation_2EStrongOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 695 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1y (mem(V1y,A_27b) -> (p(ap(ap(c_2Erelation_2ERRANGE(A_27a,A_27b),V0R),V1y)) <-> (exists V2x (p(ap(ap(V0R,V2x),V1y)) & mem(V2x,A_27a)))))))))))) # label(ax_thm_2Erelation_2ERRANGE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 696 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V2y),V1x)) | p(ap(ap(V0R,V1x),V2y)) <-> p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V1x),V2y))))))))))) # label(ax_thm_2Erelation_2ESC__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 697 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERRESTRICT(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,bool),arr(A_27a,arr(A_27b,bool))))))))) # label(mem_c_2Erelation_2ERRESTRICT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 698 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1Q,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V1Q),V2x),V3y)))))))))))))) # label(conj_thm_2Erelation_2ESC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 699 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Ereflexive__EQC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 700 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERCOMPL(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27b,bool)))))))) # label(mem_c_2Erelation_2ERCOMPL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 701 (all A_27b all A_27a all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V2f ap(c_2Ebool_2E_21(A_27a),f105(A_27b,A_27a,V0R,V1M,V2f)) = ap(f106(A_27b,A_27a,V1M,V0R),V2f)))))) # label(lameq_f106) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 702 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eantisymmetric(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R))) <-> p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Eantisymmetric__inv) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 703 (all A_27b all A_27a all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> (all V4y ap(f100(A_27b,A_27a,V1M,V0R,V3f),V4y) = ap(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V3f),V0R),V4y)),V4y)))))))) # label(lameq_f100) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 704 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> p(ap(c_2Erelation_2Eantisymmetric(arr(A_27a,arr(A_27b,bool))),c_2Erelation_2ERSUBSET(A_27a,A_27b))))))) # label(conj_thm_2Erelation_2ERSUBSET__antisymmetric) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 705 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2EStrongLinearOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2EStrongLinearOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 706 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V3y),V2x)) -> p(ap(V1P,V3y))))) -> p(ap(V1P,V2x))))) -> (all V4x (mem(V4x,A_27a) -> p(ap(V1P,V4x)))))))))))) # label(conj_thm_2Erelation_2EWF__INDUCTION__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 707 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ESC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2ESC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 708 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Eequivalence(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EEQC__EQUIVALENCE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 709 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2z (mem(V2z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) -> p(ap(ap(V0R,V1x),V2z)) | (exists V3y (p(ap(ap(V0R,V3y),V2z)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V3y)) & mem(V3y,A_27a)))))))))))) # label(conj_thm_2Erelation_2ETC__CASES2__E) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 710 (all A_27g (ne(A_27g) -> mem(c_2Erelation_2EOrder(A_27g),arr(arr(A_27g,arr(A_27g,bool)),bool)))) # label(mem_c_2Erelation_2EOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 711 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EIDEM(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2ESC(A_27a))))) # label(conj_thm_2Erelation_2EIDEM__SC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 712 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) <-> p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Esymmetric__inv) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 713 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2S1 (mem(V2S1,arr(A_27c,arr(A_27a,bool))) -> (all V3S2 (mem(V3S2,arr(A_27c,arr(A_27a,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27c,A_27a),V2S1),V3S2)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0R1),V1R2)) -> p(ap(ap(c_2Erelation_2ERSUBSET(A_27c,A_27b),ap(ap(c_2Erelation_2EO(A_27c,A_27a,A_27b),V0R1),V2S1)),ap(ap(c_2Erelation_2EO(A_27c,A_27a,A_27b),V1R2),V3S2)))))))))))))))))) # label(conj_thm_2Erelation_2EO__MONO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 714 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) & p(ap(ap(V0R,V2y),V1x)) -> V1x = V2y)))))))))) # label(ax_thm_2Erelation_2Eantisymmetric__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 715 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0M (mem(V0M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V1R),V0M) = V2f -> (p(ap(c_2Erelation_2EWF(A_27a),V1R)) -> (all V3x (mem(V3x,A_27a) -> ap(V2f,V3x) = ap(ap(V0M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V2f),V1R),V3x)),V3x))))))))))))))) # label(conj_thm_2Erelation_2EWFREC__COROLLARY) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 716 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ERTC(A_27a),V0R) = ap(c_2Erelation_2ERTC(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ERTC__IDEM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 717 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Ercdiamond(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Ercdiamond) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 718 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2z (mem(V2z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) <-> p(ap(ap(V0R,V1x),V2z)) | (exists V3y (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3y),V2z)) & p(ap(ap(V0R,V1x),V3y)) & mem(V3y,A_27a)))))))))))) # label(conj_thm_2Erelation_2ETC__CASES1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 719 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Ediag(A_27a),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2Ediag) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 720 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> (-p(ap(ap(V0R,V1x),V2y)) <-> p(ap(ap(ap(c_2Erelation_2ERCOMPL(A_27a,A_27b),V0R),V1x),V2y))))))))))))) # label(ax_thm_2Erelation_2ERCOMPL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 721 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0R1),V1R2)) <-> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(ap(V0R1,V2x),V3y)) -> p(ap(ap(V1R2,V2x),V3y)))))))))))))))) # label(ax_thm_2Erelation_2ERSUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 722 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27b,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (p(ap(c_2Erelation_2EWF(A_27b),V0R)) -> p(ap(c_2Erelation_2EWF(A_27a),ap(ap(c_2Erelation_2Einv__image(A_27a,A_27b),V0R),V1f)))))))))))) # label(conj_thm_2Erelation_2EWF__inv__image) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 723 (all A_27b all A_27a all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> (all V4v ap(f102(A_27b,A_27a,V1M,V0R,V3f),V4v) = ap(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V3f),V0R),V4v)),V4v)))))))) # label(lameq_f102) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 724 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0R1),V1R2)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V1R2),V0R1)) -> V1R2 = V0R1))))))))) # label(conj_thm_2Erelation_2ERSUBSET__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 725 (all A_27a (ne(A_27a) -> c_2Emin_2E_3D(A_27a) = ap(c_2Erelation_2Einv(A_27a,A_27a),c_2Emin_2E_3D(A_27a)))) # label(conj_thm_2Erelation_2Einv__Id) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 726 (all A_27b all A_27a all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V2x ap(f104(A_27b,A_27a,V1M,V0R),V2x) = ap(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),ap(ap(ap(c_2Erelation_2Ethe__fun(A_27a,A_27b),ap(c_2Erelation_2ETC(A_27a),V0R)),f103(A_27b,A_27a,V1M,V0R)),V2x)),V0R),V2x)),V2x)))))) # label(lameq_f104) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 727 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),V0R),c_2Erelation_2EEMPTY__REL(A_27a))) <-> c_2Erelation_2EEMPTY__REL(A_27a) = V0R) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),c_2Erelation_2EEMPTY__REL(A_27a)),V0R)))))) # label(conj_thm_2Erelation_2EREMPTY__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 728 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V0R,V1x),V3z)) & p(ap(ap(V0R,V1x),V2y)) -> (exists V4u (mem(V4u,A_27a) & p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V3z),V4u)) & p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V2y),V4u))))))))))) <-> p(ap(c_2Erelation_2Ercdiamond(A_27a),V0R))))))) # label(ax_thm_2Erelation_2Ercdiamond__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 729 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EIDEM(arr(A_27a,arr(A_27a,bool))),c_2Erelation_2ESTRORD(A_27a))))) # label(conj_thm_2Erelation_2EIDEM__STRORD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 730 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)) & ap(c_2Erelation_2ERC(A_27a),V0R) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) & ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ERC__MOVES__OUT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 731 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V2x (mem(V2x,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V3y ap(f99(A_27b,A_27a,V0f,V2x,V1R),V3y) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(V1R,V3y),V2x)),ap(V0f,V3y)),c_2Ebool_2EARB(A_27b))))))))) # label(lameq_f99) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 732 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> (p(ap(c_2Erelation_2EINVOL(A_27z),V0f)) -> (all V1a (mem(V1a,A_27z) -> (all V2b (mem(V2b,A_27z) -> (V1a = V2b <-> ap(V0f,V2b) = ap(V0f,V1a))))))))))) # label(conj_thm_2Erelation_2EINVOL__ONE__ONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 733 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2ESC(A_27a),V0R) & ap(c_2Erelation_2ESC(A_27a),V0R) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2Einv__SC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 734 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y)))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V4x),V5y)) -> p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),ap(V1f,V4x)),ap(V1f,V5y))))))))))))))) # label(conj_thm_2Erelation_2ESC__lifts__monotonicities) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 735 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> ((all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V3y),V2x)) -> p(ap(V1P,V3y))))) -> p(ap(V1P,V2x))))) -> (all V4x (mem(V4x,A_27a) -> p(ap(V1P,V4x))))))) -> p(ap(c_2Erelation_2EWF(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EINDUCTION__WF__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 736 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> ((all V3P (mem(V3P,arr(A_27a,arr(A_27a,bool))) -> ((all V4x (mem(V4x,A_27a) -> p(ap(ap(V3P,V4x),V4x)))) & (all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (all V7z (mem(V7z,A_27a) -> (p(ap(ap(V0R,V5x),V6y)) & p(ap(ap(V3P,V6y),V7z)) -> p(ap(ap(V3P,V5x),V7z))))))))) -> p(ap(ap(V3P,V1a),V2b))))) <-> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1a),V2b))))))))))) # label(ax_thm_2Erelation_2ERTC__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 737 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ECR(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2ECR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 738 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0R1 (mem(V0R1,arr(A_27c,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27d,arr(A_27c,bool))) -> (all V2R3 (mem(V2R3,arr(A_27a,arr(A_27d,bool))) -> ap(ap(c_2Erelation_2EO(A_27a,A_27c,A_27b),V0R1),ap(ap(c_2Erelation_2EO(A_27a,A_27d,A_27c),V1R2),V2R3)) = ap(ap(c_2Erelation_2EO(A_27a,A_27d,A_27b),ap(ap(c_2Erelation_2EO(A_27d,A_27c,A_27b),V0R1),V1R2)),V2R3))))))))))))))) # label(conj_thm_2Erelation_2EO__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 739 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> ((all V3Q (mem(V3Q,arr(A_27a,bool)) -> ((all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(V0R,V4y),V5z)) & p(ap(V3Q,V4y)) -> p(ap(V3Q,V5z))))))) & p(ap(V3Q,V1a)) -> p(ap(V3Q,V2b))))) <-> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1a),V2b))))))))))) # label(conj_thm_2Erelation_2ERTC__ALT__RIGHT__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 740 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> -p(ap(ap(V0R,V1x),V1x)))) <-> p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R))))))) # label(ax_thm_2Erelation_2Eirreflexive__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 741 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(V0R,V5y),V6z)) & p(ap(ap(V1P,V4x),V5y)) -> p(ap(ap(V1P,V4x),V6z))))))))) -> (all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7x),V8y)) -> p(ap(ap(V1P,V7x),V8y)))))))))))))) # label(conj_thm_2Erelation_2ETC__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 742 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1x)) <-> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V2y),V1x)) -> p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V2y)))))))))))) # label(conj_thm_2Erelation_2EWFP__CASES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 743 (all A_27a (ne(A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eirreflexive(A_27a),V1R2)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),V0R1),V1R2)) -> p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R1))))))))) # label(conj_thm_2Erelation_2Eirreflexive__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 744 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> ((all V1x (mem(V1x,A_27z) -> ap(V0f,V1x) = ap(V0f,ap(V0f,V1x)))) <-> p(ap(c_2Erelation_2EIDEM(A_27z),V0f))))))) # label(conj_thm_2Erelation_2EIDEM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 745 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) <-> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Etransitive__inv) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 746 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWeakOrder(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))) <-> p(ap(c_2Erelation_2EOrder(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ERC__Weak) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 747 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> V0R = ap(ap(c_2Erelation_2EO(A_27a,A_27b,A_27b),c_2Emin_2E_3D(A_27b)),V0R))))))) # label(conj_thm_2Erelation_2EId__O) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 748 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ediamond(A_27a),V0R)) <-> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) & p(ap(ap(V0R,V1x),V3z)) -> (exists V4u (p(ap(ap(V0R,V2y),V4u)) & p(ap(ap(V0R,V3z),V4u)) & mem(V4u,A_27a))))))))))))))) # label(ax_thm_2Erelation_2Ediamond__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 749 (all A_27a (ne(A_27a) -> p(ap(c_2Erelation_2EWF(A_27a),c_2Erelation_2EEMPTY__REL(A_27a))))) # label(conj_thm_2Erelation_2EWF__EMPTY__REL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 750 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eequivalence(A_27a),V0R)) <-> p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) & p(ap(c_2Erelation_2Ereflexive(A_27a),V0R))))))) # label(ax_thm_2Erelation_2Eequivalence__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 751 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ESTRORD(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2ESTRORD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 752 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2D (mem(V2D,arr(A_27a,bool)) -> (all V3P (mem(V3P,arr(A_27a,arr(A_27b,bool))) -> (all V4M (mem(V4M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V5x (mem(V5x,A_27a) -> (p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V1R),V2D),V3P),V4M)) & p(ap(V2D,V5x)) & p(ap(c_2Erelation_2EWF(A_27a),V1R)) & V0f = ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V1R),V4M) -> p(ap(ap(V3P,V5x),ap(V0f,V5x)))))))))))))))))))) # label(conj_thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__ON__WFREC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 753 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) -> (all V1y (mem(V1y,A_27a) -> (all V2z (mem(V2z,A_27a) -> (V2z = V1y <-> p(ap(ap(V0R,V1y),V2z)) & p(ap(ap(V0R,V2z),V1y)))))))))))) # label(conj_thm_2Erelation_2EWeakOrder__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 754 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) <-> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Ereflexive__inv) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 755 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y)) | p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__TC__RC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 756 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Ereflexive(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Ereflexive) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 757 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2P (mem(V2P,arr(A_27a,arr(A_27b,bool))) -> (all V3M (mem(V3M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V4x (mem(V4x,A_27a) -> (p(ap(c_2Erelation_2EWF(A_27a),V1R)) & p(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V1R),V2P),V3M)) & V0f = ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V1R),V3M) -> p(ap(ap(V2P,V4x),ap(V0f,V4x)))))))))))))))))) # label(conj_thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__WFREC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 758 (all A_27a (ne(A_27a) -> (all V0b (mem(V0b,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2Q (mem(V2Q,arr(A_27a,bool)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V2Q,V5y)) & p(ap(ap(V1R,V4x),V5y)) -> p(ap(V2Q,V4x))))))) & (all V3x (mem(V3x,A_27a) -> (p(ap(ap(V1R,V3x),V0b)) -> p(ap(V2Q,V3x))))) -> (all V6a (mem(V6a,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V1R),V6a),V0b)) -> p(ap(V2Q,V6a)))))))))))))) # label(conj_thm_2Erelation_2ETC__INDUCT__ALT__LEFT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 759 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2b (mem(V2b,A_27a) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(V1Q,V4y)) & p(ap(ap(V0R,V3x),V4y)) -> p(ap(V1Q,V3x))))))) & p(ap(V1Q,V2b)) -> (all V5x (mem(V5x,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V5x),V2b)) -> p(ap(V1Q,V5x)))))))))))))) # label(conj_thm_2Erelation_2ERTC__ALT__INDUCT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 760 (all A_27b all A_27a all V0R (mem(V0R,arr(A_27b,arr(A_27b,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V3y ap(f97(A_27b,A_27a,V0R,V2x,V1f),V3y) = ap(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y))))))))) # label(lameq_f97) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 761 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27a) -> ((exists V2y (p(ap(ap(V0R,V1x),V2y)) & mem(V2y,A_27b))) <-> p(ap(ap(c_2Erelation_2ERDOM(A_27a,A_27b),V0R),V1x))))))))))) # label(ax_thm_2Erelation_2ERDOM__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 762 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ediamond(A_27a),V0R)) -> p(ap(c_2Erelation_2Ediamond(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Ediamond__RC__diamond) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 763 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EWF__irreflexive) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 764 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2Eapprox(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),arr(A_27a,arr(arr(A_27a,A_27b),bool))))))))) # label(mem_c_2Erelation_2Eapprox) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 765 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (p(ap(c_2Erelation_2Etotal(A_27a),V0R)) -> p(ap(c_2Erelation_2Etotal(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f)))))))))))) # label(conj_thm_2Erelation_2Etotal__inv__image) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 766 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) <-> (all V1x (mem(V1x,A_27a) -> p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1x))))))))) # label(conj_thm_2Erelation_2EWF__EQ__WFP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 767 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> ap(V1f,V2x) = ap(V1f,V3y)))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V4x),V5y)) -> ap(V1f,V5y) = ap(V1f,V4x))))))))))))))) # label(conj_thm_2Erelation_2ERC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 768 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Etotal(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Etotal) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 769 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Eantisymmetric(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Eantisymmetric) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 770 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1R1 (mem(V1R1,arr(A_27a,arr(A_27b,bool))) -> (all V2R2 (mem(V2R2,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V1R1))) | p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V2R2))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V1R1),V2R2))))))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM__RUNION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 771 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ERC__REFLEXIVE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 772 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2Ethe__fun(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(arr(A_27a,A_27b),arr(A_27a,A_27b)),arr(A_27a,arr(A_27a,A_27b))))))))) # label(mem_c_2Erelation_2Ethe__fun) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 773 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> ($T <-> p(ap(ap(c_2Erelation_2ERUNIV(A_27a,A_27b),V0x),V1y))))))))))) # label(ax_thm_2Erelation_2ERUNIV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 774 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> ap(V1f,V3y) = ap(V1f,V2x)))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) -> ap(V1f,V4x) = ap(V1f,V5y))))))))))))))) # label(conj_thm_2Erelation_2ETC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 775 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(ap(ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),V1R2),V2x),V3y)) <-> p(ap(ap(V1R2,V2x),V3y)) | p(ap(ap(V0R1,V2x),V3y))))))))))))))) # label(ax_thm_2Erelation_2ERUNION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 776 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V1x)))))))) # label(conj_thm_2Erelation_2EEQC__REFL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 777 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2z (mem(V2z,A_27a) -> ((exists V3y (mem(V3y,A_27a) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3y),V2z)) & p(ap(ap(V0R,V1x),V3y)))) <-> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z))))))))))) # label(conj_thm_2Erelation_2EEXTEND__RTC__TC__EQN) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 778 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> ((all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V2y),V1x)) -> p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V2y))))) -> p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1x))))))))) # label(conj_thm_2Erelation_2EWFP__RULES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 779 (all A_27b all A_27a all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> (all V3x ap(f105(A_27b,A_27a,V0R,V1M,V2f),V3x) = ap(ap(c_2Emin_2E_3D(A_27b),ap(V2f,V3x)),ap(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V2f),V0R),V3x)),V3x))))))))) # label(lameq_f105) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 780 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> p(ap(ap(V1P,V2x),V2x)))) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(V1P,V3x),V4y)) & p(ap(ap(V0R,V4y),V5z)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3x),V4y)) -> p(ap(ap(V1P,V3x),V5z))))))))) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) -> p(ap(ap(V1P,V6x),V7y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__STRONG__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 781 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERUNION(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,arr(A_27b,bool))))))))) # label(mem_c_2Erelation_2ERUNION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 782 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) -> p(ap(c_2Erelation_2Ereflexive(A_27b),ap(ap(c_2Erelation_2Einv__image(A_27b,A_27a),V0R),V1f)))))))))))) # label(conj_thm_2Erelation_2Ereflexive__inv__image) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 783 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 784 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ETC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 785 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) -> ap(c_2Erelation_2ERC(A_27a),V0R) = V0R))))) # label(conj_thm_2Erelation_2Ereflexive__RC__identity) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 786 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> (V0f = ap(ap(c_2Ecombin_2Eo(A_27z,A_27z,A_27z),V0f),V0f) <-> p(ap(c_2Erelation_2EIDEM(A_27z),V0f))))))) # label(ax_thm_2Erelation_2EIDEM__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 787 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> p(ap(ap(V1P,V2x),V2x)))) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(V1P,V4y),V5z)) & p(ap(ap(V0R,V3x),V4y)) -> p(ap(ap(V1P,V3x),V5z))))))))) -> (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V6x),V7y)) -> p(ap(ap(V1P,V6x),V7y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__INDUCT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 788 (all A_27g (ne(A_27g) -> mem(c_2Erelation_2EStrongOrder(A_27g),arr(arr(A_27g,arr(A_27g,bool)),bool)))) # label(mem_c_2Erelation_2EStrongOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 789 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V2y)) & p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V2y),V3z)) -> p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V1x),V3z))))))))))))) # label(conj_thm_2Erelation_2EEQC__TRANS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 790 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V1R,V2x),V3y)) & p(ap(V0P,V2x)) -> p(ap(V0P,V3y))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V0P,V4x)) & p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V1R),V4x),V5y)) -> p(ap(V0P,V5y)))))))))))))) # label(conj_thm_2Erelation_2ERC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 791 (all A_27a (ne(A_27a) -> (all V0A (mem(V0A,arr(A_27a,bool)) -> ap(c_2Erelation_2Ediag(A_27a),V0A) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2Ediag(A_27a),V0A)))))) # label(conj_thm_2Erelation_2Einv__diag) # label(axiom) # label(non_clause). [assumption]. 3.15/3.73 792 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V5y),V6z)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) & p(ap(ap(V1P,V5y),V6z)) & p(ap(ap(V1P,V4x),V5y)) -> p(ap(ap(V1P,V4x),V6z))))))))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) -> (all V7u (mem(V7u,A_27a) -> (all V8v (mem(V8v,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7u),V8v)) -> p(ap(ap(V1P,V7u),V8v)))))))))))))) # label(conj_thm_2Erelation_2ETC__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 793 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2ERSUBSET(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,arr(A_27b,bool)),bool))))))) # label(mem_c_2Erelation_2ERSUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 794 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (all V9z (mem(V9z,A_27a) -> (p(ap(ap(V1P,V7x),V8y)) & p(ap(ap(V1P,V8y),V9z)) -> p(ap(ap(V1P,V7x),V9z))))))))) & (all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (p(ap(ap(V1P,V5x),V6y)) -> p(ap(ap(V1P,V6y),V5x))))))) & (all V4x (mem(V4x,A_27a) -> p(ap(ap(V1P,V4x),V4x)))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) -> (all V10x (mem(V10x,A_27a) -> (all V11y (mem(V11y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V10x),V11y)) -> p(ap(ap(V1P,V10x),V11y)))))))))))))) # label(conj_thm_2Erelation_2EEQC__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 795 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> ((exists V2y (mem(V2y,A_27b) & p(ap(ap(V1R,V0x),V2y)))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V1R)))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 796 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1Q,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V1Q),V2x),V3y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 797 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) -> p(ap(c_2Erelation_2Ereflexive(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Ereflexive__TC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 798 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (all V9z (mem(V9z,A_27a) -> (p(ap(ap(V1P,V7x),V8y)) & p(ap(ap(V1P,V8y),V9z)) & p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V8y),V9z)) & p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V7x),V8y)) -> p(ap(ap(V1P,V7x),V9z))))))))) & (all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V5x),V6y)) & p(ap(ap(V1P,V5x),V6y)) -> p(ap(ap(V1P,V6y),V5x))))))) & (all V4x (mem(V4x,A_27a) -> p(ap(ap(V1P,V4x),V4x)))) & (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) -> (all V10x (mem(V10x,A_27a) -> (all V11y (mem(V11y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V10x),V11y)) -> p(ap(ap(V1P,V10x),V11y)))))))))))))) # label(conj_thm_2Erelation_2ESTRONG__EQC__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 799 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ESC__SYMMETRIC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 800 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2ESN(A_27a),V0R)) & p(ap(c_2Erelation_2EWCR(A_27a),V0R)) -> p(ap(c_2Erelation_2ECR(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ENewmans__lemma) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 801 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ELinearOrder(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2ELinearOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 802 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Esymmetric(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Esymmetric) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 803 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27b,arr(A_27b,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ap(ap(c_2Erelation_2Einv__image(A_27a,A_27b),V0R),V1f) = f98(A_27b,A_27a,V0R,V1f))))))))) # label(ax_thm_2Erelation_2Einv__image__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 804 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERC(A_27a),V0R))))) # label(conj_thm_2Erelation_2ERC__IDEM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 805 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(ap(ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),V1R2),V2x),V3y)) <-> p(ap(ap(V1R2,V2x),V3y)) & p(ap(ap(V0R1,V2x),V3y))))))))))))))) # label(ax_thm_2Erelation_2ERINTER) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 806 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ERC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2ERC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 807 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1P (mem(V1P,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> p(ap(ap(V1P,V2x),V3y))))))) & (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (all V6z (mem(V6z,A_27a) -> (p(ap(ap(V1P,V5y),V6z)) & p(ap(ap(V0R,V4x),V5y)) -> p(ap(ap(V1P,V4x),V6z))))))))) -> (all V7x (mem(V7x,A_27a) -> (all V8y (mem(V8y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V7x),V8y)) -> p(ap(ap(V1P,V7x),V8y)))))))))))))) # label(conj_thm_2Erelation_2ETC__INDUCT__LEFT1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 808 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(ap(c_2Erelation_2ERUNION(A_27a,A_27a),V0R),c_2Emin_2E_3D(A_27a)) = ap(c_2Erelation_2ERC(A_27a),V0R))))) # label(conj_thm_2Erelation_2ERC__OR__Id) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 809 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R)) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) -> p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Eirrefl__trans__implies__antisym) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 810 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ediamond(A_27a),V0R)) -> p(ap(c_2Erelation_2Ediamond(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Ediamond__TC__diamond) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 811 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(V0P,V2x)) & p(ap(ap(V1R,V2x),V3y)) -> p(ap(V0P,V3y))))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V0P,V4x)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V1R),V4x),V5y)) -> p(ap(V0P,V5y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 812 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eequivalence(A_27a),V0R)) -> V0R = ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))) # label(conj_thm_2Erelation_2Eequivalence__inv__identity) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 813 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27b,bool))) -> (all V2k (mem(V2k,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V1R))) & V0x != V2k <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),ap(ap(c_2Erelation_2ERDOM__DELETE(A_27a,A_27b),V1R),V2k))))))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM__DELETE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 814 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Etrichotomous(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Etrichotomous) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 815 (all A_27g (ne(A_27g) -> (all A_27h (ne(A_27h) -> (all A_27k (ne(A_27k) -> mem(c_2Erelation_2EO(A_27g,A_27h,A_27k),arr(arr(A_27h,arr(A_27k,bool)),arr(arr(A_27g,arr(A_27h,bool)),arr(A_27g,arr(A_27k,bool))))))))))) # label(mem_c_2Erelation_2EO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 816 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> (c_2Ecombin_2EI(A_27z) = ap(ap(c_2Ecombin_2Eo(A_27z,A_27z,A_27z),V0f),V0f) <-> p(ap(c_2Erelation_2EINVOL(A_27z),V0f))))))) # label(ax_thm_2Erelation_2EINVOL__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 817 (all A_27g (ne(A_27g) -> mem(c_2Erelation_2EWeakOrder(A_27g),arr(arr(A_27g,arr(A_27g,bool)),bool)))) # label(mem_c_2Erelation_2EWeakOrder) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 818 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27a),V0R)) <-> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),c_2Emin_2E_3D(A_27a)),V0R))))))) # label(conj_thm_2Erelation_2Ereflexive__Id__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 819 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2ETC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Erelation_2ETC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 820 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERC__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 821 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Erelation_2Enf(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(A_27a,bool))))))) # label(mem_c_2Erelation_2Enf) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 822 (all A_27a (ne(A_27a) -> mem(c_2Erelation_2Eequivalence(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Erelation_2Eequivalence) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 823 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27b,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V1R2),V0R1) = ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V0R1),V1R2))))))))) # label(conj_thm_2Erelation_2ERINTER__COMM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 824 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2EEQC(A_27a),V0R) = ap(c_2Erelation_2EEQC(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2EEQC__IDEM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 825 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (all V3z (mem(V3z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2y),V3z)) & p(ap(ap(V0R,V1x),V2y)) -> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V3z))))))))))))) # label(conj_thm_2Erelation_2EEXTEND__RTC__TC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 826 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ESC(A_27a),V0R) = ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ESC__IDEM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 827 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) & (all V1a (mem(V1a,A_27a) -> (all V2b (mem(V2b,A_27a) -> p(ap(ap(V0R,V1a),V2b)) | p(ap(ap(V0R,V2b),V1a)))))) <-> p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EWeakLinearOrder__dichotomy) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 828 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Eirreflexive(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R))) <-> p(ap(c_2Erelation_2Eirreflexive(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Eirreflexive__inv) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 829 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1M (mem(V1M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V1M)),V0R),V2x)),V2x) = ap(ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V1M),V2x)))))))))))) # label(conj_thm_2Erelation_2EWFREC__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 830 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> p(ap(c_2Erelation_2Esymmetric(A_27a),ap(c_2Erelation_2EEQC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Esymmetric__EQC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 831 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(V0R,V1x),V2y)) <-> ap(V0R,V1x) = ap(V0R,V2y)))))) <-> p(ap(c_2Erelation_2Eequivalence(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EALT__equivalence) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 832 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V0R,V2x),V3y)) -> ap(V1f,V2x) = ap(V1f,V3y)))))) -> (all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ESC(A_27a),V0R),V4x),V5y)) -> ap(V1f,V5y) = ap(V1f,V4x))))))))))))))) # label(conj_thm_2Erelation_2ESC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 833 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1D (mem(V1D,arr(A_27a,bool)) -> (all V2P (mem(V2P,arr(A_27a,arr(A_27b,bool))) -> (all V3M (mem(V3M,arr(arr(A_27a,A_27b),arr(A_27a,A_27b))) -> (p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V0R),V1D),V2P),V3M)) <-> (all V4f (mem(V4f,arr(A_27a,A_27b)) -> (all V5x (mem(V5x,A_27a) -> ((all V6y (mem(V6y,A_27a) -> (p(ap(V1D,V6y)) -> (p(ap(ap(V0R,V6y),V5x)) -> p(ap(ap(V2P,V6y),ap(V4f,V6y))))))) & p(ap(V1D,V5x)) -> p(ap(ap(V2P,V5x),ap(ap(V3M,V4f),V5x))))))))))))))))))))) # label(ax_thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 834 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2Einv__TC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 835 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V2x (mem(V2x,A_27a) -> (all V3v (mem(V3v,A_27b) -> (all V4f (mem(V4f,arr(A_27a,A_27b)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),ap(c_2Eoption_2ESOME(A_27a),V2x)),V3v),V4f) = ap(V4f,V2x))))))) & (all V0v (mem(V0v,A_27b) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> V0v = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),c_2Eoption_2ENONE(A_27a)),V0v),V1f))))))))) # label(ax_thm_2Eoption_2Eoption__case__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.75 836 (all A_27a (ne(A_27a) -> (all V1r (mem(V1r,ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone)) -> (V1r = ap(c_2Eoption_2Eoption__REP(A_27a),ap(c_2Eoption_2Eoption__ABS(A_27a),V1r)) <-> p(ap(k(ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone),c_2Ebool_2ET),V1r))))) & (all V0a (mem(V0a,ty_2Eoption_2Eoption(A_27a)) -> ap(c_2Eoption_2Eoption__ABS(A_27a),ap(c_2Eoption_2Eoption__REP(A_27a),V0a)) = V0a)))) # label(ax_thm_2Eoption_2Eoption__REP__ABS__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 837 (all A_27a (ne(A_27a) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> V0opt = c_2Eoption_2ENONE(A_27a) | (exists V1x (V0opt = ap(c_2Eoption_2ESOME(A_27a),V1x) & mem(V1x,A_27a))))))) # label(conj_thm_2Eoption_2Eoption__CASES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 838 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0m1 (mem(V0m1,ty_2Eoption_2Eoption(A_27b)) -> (all V1m2 (mem(V1m2,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(c_2Eoption_2EOPTION__BIND(A_27a,A_27b),V0m1),ap(c_2Ecombin_2EK(ty_2Eoption_2Eoption(A_27a),A_27b),V1m2)) = ap(ap(c_2Eoption_2EOPTION__IGNORE__BIND(A_27a,A_27b),V0m1),V1m2))))))))) # label(ax_thm_2Eoption_2EOPTION__IGNORE__BIND__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 839 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__NONE(A_27a),V0x)) <-> c_2Eoption_2ENONE(A_27a) = V0x))))) # label(conj_thm_2Eoption_2EIS__NONE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 840 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2Esome(A_27a),arr(arr(A_27a,bool),ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2Esome) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 841 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Eoption_2Eoption(A_27a)) -> (all V1f (mem(V1f,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> (all V2y (mem(V2y,A_27b) -> ((exists V4x (ap(V1f,V4x) = ap(c_2Eoption_2ESOME(A_27b),V2y) & ap(c_2Eoption_2ESOME(A_27a),V4x) = V0p & mem(V4x,A_27a))) <-> ap(ap(c_2Eoption_2EOPTION__BIND(A_27b,A_27a),V0p),V1f) = ap(c_2Eoption_2ESOME(A_27b),V2y)) & (V0p = c_2Eoption_2ENONE(A_27a) | (exists V3x (c_2Eoption_2ENONE(A_27b) = ap(V1f,V3x) & V0p = ap(c_2Eoption_2ESOME(A_27a),V3x) & mem(V3x,A_27a))) <-> ap(ap(c_2Eoption_2EOPTION__BIND(A_27b,A_27a),V0p),V1f) = c_2Eoption_2ENONE(A_27b)))))))))))) # label(conj_thm_2Eoption_2EOPTION__BIND__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 842 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0g (mem(V0g,arr(A_27b,ty_2Eoption_2Eoption(A_27a))) -> (all V1f (mem(V1f,arr(A_27c,ty_2Eoption_2Eoption(A_27b))) -> (all V2m (mem(V2m,A_27c) -> ap(ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27a,A_27b,A_27c),V0g),V1f),V2m) = ap(ap(c_2Eoption_2EOPTION__BIND(A_27a,A_27b),ap(V1f,V2m)),V0g))))))))))))) # label(ax_thm_2Eoption_2EOPTION__MCOMP__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 843 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0x1 (mem(V0x1,ty_2Eoption_2Eoption(A_27a)) -> (all V1x2 (mem(V1x2,ty_2Eoption_2Eoption(A_27a)) -> (all V2y1 (mem(V2y1,ty_2Eoption_2Eoption(A_27b)) -> (all V3y2 (mem(V3y2,ty_2Eoption_2Eoption(A_27b)) -> (all V4f1 (mem(V4f1,arr(A_27a,arr(A_27b,A_27c))) -> (all V5f2 (mem(V5f2,arr(A_27a,arr(A_27b,A_27c))) -> (V2y1 = V3y2 & (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27b) -> (ap(c_2Eoption_2ESOME(A_27b),V7y) = V3y2 & ap(c_2Eoption_2ESOME(A_27a),V6x) = V1x2 -> ap(ap(V5f2,V6x),V7y) = ap(ap(V4f1,V6x),V7y)))))) & V0x1 = V1x2 -> ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27c,A_27a,A_27b),V5f2),V1x2),V3y2) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27c,A_27a,A_27b),V4f1),V0x1),V2y1)))))))))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP2__cong) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 844 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1P_27 (mem(V1P_27,arr(A_27a,bool)) -> (all V2opt (mem(V2opt,ty_2Eoption_2Eoption(A_27a)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> p(ap(V1P_27,V3x))))) -> (p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V0P),V2opt)) -> p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V1P_27),V2opt)))))))))))) # label(conj_thm_2Eoption_2EOPTION__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 845 (all A0 (ne(A0) -> ne(ty_2Eoption_2Eoption(A0)))) # label(ne_ty_2Eoption_2Eoption) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 846 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2Eoption__CASE(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27a),arr(A_27b,arr(arr(A_27a,A_27b),A_27b)))))))) # label(mem_c_2Eoption_2Eoption__CASE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 847 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0m (mem(V0m,ty_2Eoption_2Eoption(A_27a)) -> (all V1v (mem(V1v,A_27c) -> ap(ap(c_2Eoption_2EOPTION__IGNORE__BIND(A_27a,A_27c),ap(c_2Eoption_2ESOME(A_27c),V1v)),V0m) = V0m & ap(ap(c_2Eoption_2EOPTION__IGNORE__BIND(A_27a,A_27b),c_2Eoption_2ENONE(A_27b)),V0m) = c_2Eoption_2ENONE(A_27a))))))))))) # label(conj_thm_2Eoption_2EOPTION__IGNORE__BIND__thm) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 848 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),ap(c_2Eoption_2ESOME(A_27a),V1x)) = ap(c_2Eoption_2ESOME(A_27b),ap(V0f,V1x)))))) & (all V2f (mem(V2f,arr(A_27a,A_27b)) -> c_2Eoption_2ENONE(A_27b) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V2f),c_2Eoption_2ENONE(A_27a)))))))) # label(ax_thm_2Eoption_2EOPTION__MAP__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 849 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,ty_2Eoption_2Eoption(arr(A_27b,A_27c))) -> (all V1g (mem(V1g,ty_2Eoption_2Eoption(arr(A_27a,A_27b))) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(c_2Eoption_2EOPTION__APPLY(A_27c,A_27a),ap(ap(c_2Eoption_2EOPTION__APPLY(arr(A_27a,A_27c),arr(A_27a,A_27b)),ap(ap(c_2Eoption_2EOPTION__APPLY(arr(arr(A_27a,A_27b),arr(A_27a,A_27c)),arr(A_27b,A_27c)),ap(c_2Eoption_2ESOME(arr(arr(A_27b,A_27c),arr(arr(A_27a,A_27b),arr(A_27a,A_27c)))),c_2Ecombin_2Eo(A_27a,A_27c,A_27b))),V0f)),V1g)),V2x) = ap(ap(c_2Eoption_2EOPTION__APPLY(A_27c,A_27b),V0f),ap(ap(c_2Eoption_2EOPTION__APPLY(A_27b,A_27a),V1g),V2x)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__APPLY__o) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 850 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2x ap(V0P,V2x) = ap(f108(A_27a,V0P),V2x)))) # label(lameq_f108) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 851 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(c_2Ebool_2E_3F(A_27a),f49(A_27a,V0P))),ap(c_2Eoption_2ESOME(A_27a),ap(c_2Emin_2E_40(A_27a),f108(A_27a,V0P)))),c_2Eoption_2ENONE(A_27a)) = ap(c_2Eoption_2Esome(A_27a),V0P))))) # label(ax_thm_2Eoption_2Esome__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 852 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(ty_2Eoption_2Eoption(A_27a))) -> (all V1y (mem(V1y,A_27a) -> (ap(c_2Eoption_2EOPTION__JOIN(A_27a),V0x) = ap(c_2Eoption_2ESOME(A_27a),V1y) <-> V0x = ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V1y))))))))) # label(conj_thm_2Eoption_2EOPTION__JOIN__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 853 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2ESOME(A_27a),arr(A_27a,ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2ESOME) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 854 (all A_27b all A_27a all V1x (mem(V1x,A_27a) -> (all V2f ap(f107(A_27b,A_27a,V1x),V2f) = ap(V2f,V1x)))) # label(lameq_f107) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 855 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Eoption_2ESOME(A_27a),V0x) != c_2Eoption_2ENONE(A_27a))))) # label(conj_thm_2Eoption_2ENOT__NONE__SOME) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 856 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0g (mem(V0g,arr(A_27c,ty_2Eoption_2Eoption(A_27d))) -> (all V1f (mem(V1f,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27d,A_27c,A_27c),V0g),c_2Eoption_2ESOME(A_27c)) = V0g & V1f = ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27b,A_27b,A_27a),c_2Eoption_2ESOME(A_27b)),V1f))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MCOMP__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 857 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTION__IGNORE__BIND(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27b),arr(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27a)))))))) # label(mem_c_2Eoption_2EOPTION__IGNORE__BIND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 858 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTION__APPLY(A_27a,A_27b),arr(ty_2Eoption_2Eoption(arr(A_27b,A_27a)),arr(ty_2Eoption_2Eoption(A_27b),ty_2Eoption_2Eoption(A_27a)))))))) # label(mem_c_2Eoption_2EOPTION__APPLY) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 859 (all A_27a (ne(A_27a) -> ap(c_2Eoption_2EOPTION__JOIN(A_27a),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a))) = c_2Eoption_2ENONE(A_27a) & (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> ap(c_2Eoption_2EOPTION__JOIN(A_27a),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(A_27a)),V0x)) = V0x)))) # label(ax_thm_2Eoption_2EOPTION__JOIN__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 860 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> (all V2y (mem(V2y,ty_2Eoption_2Eoption(A_27b)) -> ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27c,A_27a,A_27b),V0f),V1x),V2y) = ap(ap(c_2Eoption_2EOPTION__APPLY(A_27c,A_27b),ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,arr(A_27b,A_27c)),V0f),V1x)),V2y))))))))))))) # label(conj_thm_2Eoption_2EOPTION__APPLY__MAP2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 861 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> (((all V3x (mem(V3x,A_27a) -> -p(ap(V0P,V3x)))) -> p(ap(V1Q,c_2Eoption_2ENONE(A_27a)))) & (all V2x (mem(V2x,A_27a) -> (p(ap(V0P,V2x)) -> p(ap(V1Q,ap(c_2Eoption_2ESOME(A_27a),V2x)))))) -> p(ap(V1Q,ap(c_2Eoption_2Esome(A_27a),V0P)))))))))) # label(conj_thm_2Eoption_2Esome__intro) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 862 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> ((all V1a (mem(V1a,A_27a) -> p(ap(V0P,ap(c_2Eoption_2ESOME(A_27a),V1a))))) & p(ap(V0P,c_2Eoption_2ENONE(A_27a))) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> p(ap(V0P,V2x))))))))) # label(conj_thm_2Eoption_2Eoption__Induct) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 863 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27c,A_27a))) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27b)) -> (all V2y (mem(V2y,ty_2Eoption_2Eoption(A_27c)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Eoption_2EIS__SOME(A_27b),V1x)),ap(c_2Eoption_2EIS__SOME(A_27c),V2y))),ap(c_2Eoption_2ESOME(A_27a),ap(ap(V0f,ap(c_2Eoption_2ETHE(A_27b),V1x)),ap(c_2Eoption_2ETHE(A_27c),V2y)))),c_2Eoption_2ENONE(A_27a)) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),V1x),V2y))))))))))))) # label(ax_thm_2Eoption_2EOPTION__MAP2__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 864 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27c,A_27b)) -> (all V1g (mem(V1g,arr(A_27a,A_27c)) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27c),V0f),V1g)),V2x) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27c,A_27b),V0f),ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27c),V1g),V2x)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__COMPOSE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 865 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,A_27a)) -> (all V1x (mem(V1x,A_27b) -> ap(ap(c_2Eoption_2EOPTION__APPLY(A_27a,A_27b),ap(c_2Eoption_2ESOME(arr(A_27b,A_27a)),V0f)),ap(c_2Eoption_2ESOME(A_27b),V1x)) = ap(c_2Eoption_2ESOME(A_27a),ap(V0f,V1x)))))))))) # label(conj_thm_2Eoption_2ESOME__SOME__APPLY) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 866 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,ty_2Eoption_2Eoption(arr(A_27a,A_27b))) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2Eoption_2EOPTION__APPLY(A_27b,A_27a),V0f),ap(c_2Eoption_2ESOME(A_27a),V1x)) = ap(ap(c_2Eoption_2EOPTION__APPLY(A_27b,arr(A_27a,A_27b)),ap(c_2Eoption_2ESOME(arr(arr(A_27a,A_27b),A_27b)),f107(A_27b,A_27a,V1x))),V0f))))))))) # label(conj_thm_2Eoption_2ESOME__APPLY__PERMUTE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 867 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,A_27a)) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27b)) -> (c_2Eoption_2ENONE(A_27a) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V0f),V1x) <-> V1x = c_2Eoption_2ENONE(A_27b)) & (V1x = c_2Eoption_2ENONE(A_27b) <-> ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V0f),V1x) = c_2Eoption_2ENONE(A_27a)))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__EQ__NONE__both__ways) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 868 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V1x (mem(V1x,A_27b) -> (all V2f (mem(V2f,arr(A_27b,ty_2Eoption_2Eoption(A_27a))) -> ap(V2f,V1x) = ap(ap(c_2Eoption_2EOPTION__BIND(A_27a,A_27b),ap(c_2Eoption_2ESOME(A_27b),V1x)),V2f))))) & (all V0f (mem(V0f,arr(A_27b,ty_2Eoption_2Eoption(A_27a))) -> ap(ap(c_2Eoption_2EOPTION__BIND(A_27a,A_27b),c_2Eoption_2ENONE(A_27b)),V0f) = c_2Eoption_2ENONE(A_27a))))))) # label(ax_thm_2Eoption_2EOPTION__BIND__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 869 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1X (mem(V1X,ty_2Eoption_2Eoption(A_27a)) -> (all V2x (mem(V2x,A_27a) -> (c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),V1X),c_2Eoption_2ENONE(A_27a)) <-> (p(V0P) -> p(ap(c_2Eoption_2EIS__NONE(A_27a),V1X)))) & ((p(ap(c_2Eoption_2EIS__SOME(A_27a),V1X)) -> p(V0P)) <-> c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),V1X)) & (p(V0P) & V1X = ap(c_2Eoption_2ESOME(A_27a),V2x) <-> ap(c_2Eoption_2ESOME(A_27a),V2x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),V1X),c_2Eoption_2ENONE(A_27a))) & (ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),V1X) = ap(c_2Eoption_2ESOME(A_27a),V2x) <-> ap(c_2Eoption_2ESOME(A_27a),V2x) = V1X & -p(V0P)))))))))) # label(conj_thm_2Eoption_2EIF__NONE__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 870 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27b)) -> c_2Eoption_2ENONE(A_27a) = ap(ap(c_2Eoption_2EOPTION__APPLY(A_27a,A_27b),c_2Eoption_2ENONE(arr(A_27b,A_27a))),V0x))) & (all V1f (mem(V1f,arr(A_27b,A_27a)) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27b)) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27b,A_27a),V1f),V2x) = ap(ap(c_2Eoption_2EOPTION__APPLY(A_27a,A_27b),ap(c_2Eoption_2ESOME(arr(A_27b,A_27a)),V1f)),V2x))))))))) # label(ax_thm_2Eoption_2EOPTION__APPLY__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 871 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTION__BIND(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27b),arr(arr(A_27b,ty_2Eoption_2Eoption(A_27a)),ty_2Eoption_2Eoption(A_27a)))))))) # label(mem_c_2Eoption_2EOPTION__BIND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 872 (all A_27a all V0y (mem(V0y,A_27a) -> (all V2x ap(ap(c_2Emin_2E_3D(A_27a),V0y),V2x) = ap(f110(A_27a,V0y),V2x)))) # label(lameq_f110) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 873 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Eoption_2ESOME(A_27a),V0x) != c_2Eoption_2ENONE(A_27a))))) # label(conj_thm_2Eoption_2ENOT__SOME__NONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 874 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EIS__SOME(A_27a),arr(ty_2Eoption_2Eoption(A_27a),bool)))) # label(mem_c_2Eoption_2EIS__SOME) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 875 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> (p(ap(V0P,c_2Eoption_2ENONE(A_27a))) & (all V1a (mem(V1a,A_27a) -> p(ap(V0P,ap(c_2Eoption_2ESOME(A_27a),V1a))))) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> p(ap(V0P,V2x))))))))) # label(conj_thm_2Eoption_2Eoption__induction) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 876 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0v_27 (mem(V0v_27,A_27b) -> (all V1f_27 (mem(V1f_27,arr(A_27a,A_27b)) -> (all V2M (mem(V2M,ty_2Eoption_2Eoption(A_27a)) -> (all V3M_27 (mem(V3M_27,ty_2Eoption_2Eoption(A_27a)) -> (all V4v (mem(V4v,A_27b) -> (all V5f (mem(V5f,arr(A_27a,A_27b)) -> (V2M = V3M_27 & (c_2Eoption_2ENONE(A_27a) = V3M_27 -> V4v = V0v_27) & (all V6x (mem(V6x,A_27a) -> (V3M_27 = ap(c_2Eoption_2ESOME(A_27a),V6x) -> ap(V1f_27,V6x) = ap(V5f,V6x)))) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V3M_27),V0v_27),V1f_27) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V2M),V4v),V5f)))))))))))))))))) # label(conj_thm_2Eoption_2Eoption__case__cong) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 877 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27b)),V1x),c_2Eoption_2ENONE(A_27b)),ap(ap(c_2Ecombin_2Eo(A_27a,ty_2Eoption_2Eoption(A_27b),A_27b),c_2Eoption_2ESOME(A_27b)),V0f)) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),V1x))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__CASE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 878 (all A_27a (ne(A_27a) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> (all V1opt_27 (mem(V1opt_27,ty_2Eoption_2Eoption(A_27a)) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (all V3P_27 (mem(V3P_27,arr(A_27a,bool)) -> (V1opt_27 = V0opt & (all V4x (mem(V4x,A_27a) -> (V1opt_27 = ap(c_2Eoption_2ESOME(A_27a),V4x) -> (p(ap(V3P_27,V4x)) <-> p(ap(V2P,V4x)))))) -> (p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V3P_27),V1opt_27)) <-> p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V2P),V0opt)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 879 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> (all V1e (mem(V1e,A_27b) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V0x),V1e),V2f) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(c_2Eoption_2EIS__SOME(A_27a),V0x)),ap(V2f,ap(c_2Eoption_2ETHE(A_27a),V0x))),V1e))))))))))) # label(conj_thm_2Eoption_2Eoption__case__compute) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 880 (all A_27a (ne(A_27a) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> c_2Eoption_2ENONE(A_27a) = V0opt | (exists V1x (V0opt = ap(c_2Eoption_2ESOME(A_27a),V1x) & mem(V1x,A_27a))))))) # label(conj_thm_2Eoption_2Eoption__nchotomy) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 881 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27d,ty_2Eoption_2Eoption(A_27c))) -> (all V1g (mem(V1g,arr(A_27b,ty_2Eoption_2Eoption(A_27d))) -> (all V2h (mem(V2h,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27c,A_27b,A_27a),ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27c,A_27d,A_27b),V0f),V1g)),V2h) = ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27c,A_27d,A_27a),V0f),ap(ap(c_2Eoption_2EOPTION__MCOMP(A_27d,A_27b,A_27a),V1g),V2h)))))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MCOMP__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 882 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> (all V1g (mem(V1g,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> (p(ap(c_2Eoption_2EIS__SOME(A_27b),ap(ap(c_2Eoption_2EOPTION__BIND(A_27b,A_27a),V0x),V1g))) -> p(ap(c_2Eoption_2EIS__SOME(A_27a),V0x))))))))))) # label(conj_thm_2Eoption_2EIS__SOME__BIND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 883 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0o1 (mem(V0o1,ty_2Eoption_2Eoption(A_27a)) -> (all V1o2 (mem(V1o2,ty_2Eoption_2Eoption(A_27a)) -> (all V2f1 (mem(V2f1,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> (all V3f2 (mem(V3f2,arr(A_27a,ty_2Eoption_2Eoption(A_27b))) -> ((all V4x (mem(V4x,A_27a) -> (V1o2 = ap(c_2Eoption_2ESOME(A_27a),V4x) -> ap(V2f1,V4x) = ap(V3f2,V4x)))) & V0o1 = V1o2 -> ap(ap(c_2Eoption_2EOPTION__BIND(A_27b,A_27a),V1o2),V3f2) = ap(ap(c_2Eoption_2EOPTION__BIND(A_27b,A_27a),V0o1),V2f1)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__BIND__cong) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 884 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> (all V1nc (mem(V1nc,A_27b) -> (all V2sc (mem(V2sc,arr(A_27a,A_27b)) -> (all V3v (mem(V3v,A_27b) -> (V3v = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V0opt),V1nc),V2sc) <-> (exists V4x (V0opt = ap(c_2Eoption_2ESOME(A_27a),V4x) & ap(V2sc,V4x) = V3v & mem(V4x,A_27a))) | V1nc = V3v & V0opt = c_2Eoption_2ENONE(A_27a)))))))))))))) # label(conj_thm_2Eoption_2Eoption__case__eq) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 885 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2Eoption__REP(A_27a),arr(ty_2Eoption_2Eoption(A_27a),ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone))))) # label(mem_c_2Eoption_2Eoption__REP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 886 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,arr(A_27b,bool))) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> (all V3y (mem(V3y,ty_2Eoption_2Eoption(A_27b)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27b) -> (p(ap(ap(V0P,V4x),V5y)) -> p(ap(ap(V1Q,V4x),V5y))))))) -> (p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27b),V0P),V2x),V3y)) -> p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27b),V1Q),V2x),V3y)))))))))))))))) # label(conj_thm_2Eoption_2EOPTREL__MONO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 887 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2Eoption__ABS(A_27a),arr(ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone),ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2Eoption__ABS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 888 (all A_27a (ne(A_27a) -> (all V0Q (mem(V0Q,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(V0Q,ap(c_2Eoption_2Esome(A_27a),V1P))) -> (exists V2x (p(ap(V1P,V2x)) & p(ap(V0Q,ap(c_2Eoption_2ESOME(A_27a),V2x))) & mem(V2x,A_27a))) | (all V3x (mem(V3x,A_27a) -> -p(ap(V1P,V3x)))) & p(ap(V0Q,c_2Eoption_2ENONE(A_27a)))))))))) # label(conj_thm_2Eoption_2Esome__elim) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 889 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($F <-> p(ap(c_2Eoption_2EIS__NONE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V0x)))))) & (p(ap(c_2Eoption_2EIS__NONE(A_27a),c_2Eoption_2ENONE(A_27a))) <-> $T))) # label(ax_thm_2Eoption_2EIS__NONE__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 890 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1o1 (mem(V1o1,ty_2Eoption_2Eoption(A_27a)) -> (all V2o2 (mem(V2o2,ty_2Eoption_2Eoption(A_27b)) -> (ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27c,A_27a,A_27b),V0f),V1o1),V2o2) = c_2Eoption_2ENONE(A_27c) <-> c_2Eoption_2ENONE(A_27b) = V2o2 | c_2Eoption_2ENONE(A_27a) = V1o1))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP2__NONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 891 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EOPTION__CHOICE(A_27a),arr(ty_2Eoption_2Eoption(A_27a),arr(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27a)))))) # label(mem_c_2Eoption_2EOPTION__CHOICE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 892 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EOPTION__JOIN(A_27a),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption(A_27a)),ty_2Eoption_2Eoption(A_27a))))) # label(mem_c_2Eoption_2EOPTION__JOIN) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 893 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0opt1 (mem(V0opt1,ty_2Eoption_2Eoption(A_27a)) -> (all V1opt2 (mem(V1opt2,ty_2Eoption_2Eoption(A_27a)) -> (all V2f1 (mem(V2f1,arr(A_27a,A_27b)) -> (all V3f2 (mem(V3f2,arr(A_27a,A_27b)) -> (V0opt1 = V1opt2 & (all V4x (mem(V4x,A_27a) -> (V1opt2 = ap(c_2Eoption_2ESOME(A_27a),V4x) -> ap(V3f2,V4x) = ap(V2f1,V4x)))) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V2f1),V0opt1) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V3f2),V1opt2)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 894 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (-p(V0P) <-> c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),ap(c_2Eoption_2ESOME(A_27a),V1x)),c_2Eoption_2ENONE(A_27a))) & (c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V1x)) <-> p(V0P)) & (V1x = V2y & p(V0P) <-> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),ap(c_2Eoption_2ESOME(A_27a),V1x)),c_2Eoption_2ENONE(A_27a)) = ap(c_2Eoption_2ESOME(A_27a),V2y)) & (V2y = V1x & -p(V0P) <-> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),V0P),c_2Eoption_2ENONE(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V1x)) = ap(c_2Eoption_2ESOME(A_27a),V2y)))))))))) # label(conj_thm_2Eoption_2EIF__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 895 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> (p(ap(V0P,c_2Eoption_2ENONE(A_27a))) | (exists V2x (p(ap(V0P,ap(c_2Eoption_2ESOME(A_27a),V2x))) & mem(V2x,A_27a))) <-> (exists V1opt (p(ap(V0P,V1opt)) & mem(V1opt,ty_2Eoption_2Eoption(A_27a))))))))) # label(conj_thm_2Eoption_2EEXISTS__OPTION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 896 (all A_27a (ne(A_27a) -> (all V0m2 (mem(V0m2,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(c_2Eoption_2EOPTION__CHOICE(A_27a),c_2Eoption_2ENONE(A_27a)),V0m2) = V0m2)) & (all V1x (mem(V1x,A_27a) -> (all V2m2 (mem(V2m2,ty_2Eoption_2Eoption(A_27a)) -> ap(c_2Eoption_2ESOME(A_27a),V1x) = ap(ap(c_2Eoption_2EOPTION__CHOICE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V1x)),V2m2))))))) # label(ax_thm_2Eoption_2EOPTION__CHOICE__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 897 (all A_27a (ne(A_27a) -> (exists V0rep (mem(V0rep,arr(ty_2Eoption_2Eoption(A_27a),ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone))) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone),ty_2Eoption_2Eoption(A_27a)),k(ty_2Esum_2Esum(A_27a,ty_2Eone_2Eone),c_2Ebool_2ET)),V0rep)))))) # label(ax_thm_2Eoption_2Eoption__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 898 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Eoption_2ETHE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V0x)) = V0x)))) # label(ax_thm_2Eoption_2ETHE__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 899 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> ((all V2x (mem(V2x,A_27a) -> p(ap(V0P,ap(c_2Eoption_2ESOME(A_27a),V2x))))) & p(ap(V0P,c_2Eoption_2ENONE(A_27a))) <-> (all V1opt (mem(V1opt,ty_2Eoption_2Eoption(A_27a)) -> p(ap(V0P,V1opt))))))))) # label(conj_thm_2Eoption_2EFORALL__OPTION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 900 (all A_27a (ne(A_27a) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> ((exists V1x (mem(V1x,A_27a) & ap(c_2Eoption_2ESOME(A_27a),V1x) = V0opt)) <-> p(ap(c_2Eoption_2EIS__SOME(A_27a),V0opt))))))) # label(conj_thm_2Eoption_2EIS__SOME__EXISTS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 901 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> (c_2Eoption_2ENONE(A_27a) = V1x <-> c_2Eoption_2ENONE(A_27b) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),V1x)))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 902 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Eoption_2Eoption__ABS(A_27a),ap(c_2Esum_2EINL(A_27a,ty_2Eone_2Eone),V0x)) = ap(c_2Eoption_2ESOME(A_27a),V0x))))) # label(ax_thm_2Eoption_2ESOME__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 903 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0m1 (mem(V0m1,ty_2Eoption_2Eoption(A_27a)) -> (all V1m2 (mem(V1m2,ty_2Eoption_2Eoption(A_27b)) -> (all V2y (mem(V2y,A_27b) -> (ap(c_2Eoption_2ESOME(A_27b),V2y) = ap(ap(c_2Eoption_2EOPTION__IGNORE__BIND(A_27b,A_27a),V0m1),V1m2) <-> (exists V3x (V1m2 = ap(c_2Eoption_2ESOME(A_27b),V2y) & V0m1 = ap(c_2Eoption_2ESOME(A_27a),V3x) & mem(V3x,A_27a)))) & (V1m2 = c_2Eoption_2ENONE(A_27b) | c_2Eoption_2ENONE(A_27a) = V0m1 <-> c_2Eoption_2ENONE(A_27b) = ap(ap(c_2Eoption_2EOPTION__IGNORE__BIND(A_27b,A_27a),V0m1),V1m2)))))))))))) # label(conj_thm_2Eoption_2EOPTION__IGNORE__BIND__EQUALS__OPTION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 904 (all V0b (mem(V0b,bool) -> (c_2Eoption_2ENONE(ty_2Eone_2Eone) = ap(c_2Eoption_2EOPTION__GUARD,V0b) <-> -p(V0b)) & (ap(c_2Eoption_2EOPTION__GUARD,V0b) = ap(c_2Eoption_2ESOME(ty_2Eone_2Eone),c_2Eone_2Eone) <-> p(V0b)))) # label(conj_thm_2Eoption_2EOPTION__GUARD__EQ__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 905 (all A_27a all V0y (mem(V0y,A_27a) -> (all V1x ap(f109(A_27a,V0y),V1x) = ap(ap(c_2Emin_2E_3D(A_27a),V1x),V0y)))) # label(lameq_f109) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 906 (all V0b (mem(V0b,bool) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(ty_2Eone_2Eone)),V0b),ap(c_2Eoption_2ESOME(ty_2Eone_2Eone),c_2Eone_2Eone)),c_2Eoption_2ENONE(ty_2Eone_2Eone)) = ap(c_2Eoption_2EOPTION__GUARD,V0b))) # label(conj_thm_2Eoption_2EOPTION__GUARD__COND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 907 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTREL(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),arr(ty_2Eoption_2Eoption(A_27a),arr(ty_2Eoption_2Eoption(A_27b),bool)))))))) # label(mem_c_2Eoption_2EOPTREL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 908 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EOPTION__ALL(A_27a),arr(arr(A_27a,bool),arr(ty_2Eoption_2Eoption(A_27a),bool))))) # label(mem_c_2Eoption_2EOPTION__ALL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 909 (all A_27a (ne(A_27a) -> (all V0m1 (mem(V0m1,ty_2Eoption_2Eoption(A_27a)) -> V0m1 = ap(ap(c_2Eoption_2EOPTION__CHOICE(A_27a),V0m1),c_2Eoption_2ENONE(A_27a)))))) # label(conj_thm_2Eoption_2EOPTION__CHOICE__NONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 910 (all A_27a (ne(A_27a) -> (all V0m1 (mem(V0m1,ty_2Eoption_2Eoption(A_27a)) -> (all V1m2 (mem(V1m2,ty_2Eoption_2Eoption(A_27a)) -> (ap(ap(c_2Eoption_2EOPTION__CHOICE(A_27a),V0m1),V1m2) = c_2Eoption_2ENONE(A_27a) <-> c_2Eoption_2ENONE(A_27a) = V1m2 & V0m1 = c_2Eoption_2ENONE(A_27a)))))))) # label(conj_thm_2Eoption_2EOPTION__CHOICE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 911 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(ty_2Eoption_2Eoption(A_27a),ty_2Eoption_2Eoption(A_27b)))))))) # label(mem_c_2Eoption_2EOPTION__MAP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 912 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> (all V2y (mem(V2y,A_27b) -> ((exists V3z (mem(V3z,A_27a) & ap(V0f,V3z) = V2y & V1x = ap(c_2Eoption_2ESOME(A_27a),V3z))) <-> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),V1x) = ap(c_2Eoption_2ESOME(A_27b),V2y)))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 913 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V1y) = ap(c_2Eoption_2ESOME(A_27a),V0x) <-> V0x = V1y))))))) # label(conj_thm_2Eoption_2ESOME__11) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 914 (all A_27a (ne(A_27a) -> c_2Eoption_2ENONE(A_27a) = ap(c_2Eoption_2Eoption__ABS(A_27a),ap(c_2Esum_2EINR(A_27a,ty_2Eone_2Eone),c_2Eone_2Eone)))) # label(ax_thm_2Eoption_2ENONE__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 915 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27b) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (all V2e (mem(V2e,ty_2Eoption_2Eoption(A_27a)) -> (all V8x (mem(V8x,A_27a) -> ($T <-> p(ap(c_2Eoption_2EIS__SOME(A_27a),ap(c_2Eoption_2ESOME(A_27a),V8x)))))) & ($F <-> p(ap(c_2Eoption_2EIS__SOME(A_27a),c_2Eoption_2ENONE(A_27a)))) & (all V10x (mem(V10x,ty_2Eoption_2Eoption(A_27a)) -> (-p(ap(c_2Eoption_2EIS__SOME(A_27a),V10x)) <-> c_2Eoption_2ENONE(A_27a) = V10x))) & (all V11x (mem(V11x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V11x)) -> ap(c_2Eoption_2ESOME(A_27a),ap(c_2Eoption_2ETHE(A_27a),V11x)) = V11x))) & (all V12x (mem(V12x,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V12x),c_2Eoption_2ENONE(A_27a)),c_2Eoption_2ESOME(A_27a)) = V12x)) & (all V13x (mem(V13x,ty_2Eoption_2Eoption(A_27a)) -> V13x = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V13x),V13x),c_2Eoption_2ESOME(A_27a)))) & (all V14x (mem(V14x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__NONE(A_27a),V14x)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V14x),V0e),V1f) = V0e))) & (all V17v (mem(V17v,A_27b) -> (all V18f (mem(V18f,arr(A_27a,A_27b)) -> V17v = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),c_2Eoption_2ENONE(A_27a)),V17v),V18f))))) & (all V22f (mem(V22f,arr(A_27a,A_27b)) -> (all V23x (mem(V23x,A_27a) -> ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V22f),ap(c_2Eoption_2ESOME(A_27a),V23x)) = ap(c_2Eoption_2ESOME(A_27b),ap(V22f,V23x)))))) & (all V25x (mem(V25x,ty_2Eoption_2Eoption(A_27a)) -> ap(c_2Eoption_2EOPTION__JOIN(A_27a),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(A_27a)),V25x)) = V25x)) & ap(c_2Eoption_2EOPTION__JOIN(A_27a),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a))) = c_2Eoption_2ENONE(A_27a) & (all V24f (mem(V24f,arr(A_27a,A_27b)) -> c_2Eoption_2ENONE(A_27b) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V24f),c_2Eoption_2ENONE(A_27a)))) & (all V19x (mem(V19x,A_27a) -> (all V20v (mem(V20v,A_27b) -> (all V21f (mem(V21f,arr(A_27a,A_27b)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),ap(c_2Eoption_2ESOME(A_27a),V19x)),V20v),V21f) = ap(V21f,V19x))))))) & (all V16x (mem(V16x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V16x)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V16x),V2e),c_2Eoption_2ESOME(A_27a)) = V16x))) & (all V15x (mem(V15x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V15x)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V15x),V0e),V1f) = ap(V1f,ap(c_2Eoption_2ETHE(A_27a),V15x))))) & (all V9x (mem(V9x,ty_2Eoption_2Eoption(A_27a)) -> (V9x = c_2Eoption_2ENONE(A_27a) <-> p(ap(c_2Eoption_2EIS__NONE(A_27a),V9x))))) & (all V7x (mem(V7x,A_27a) -> ap(c_2Eoption_2ESOME(A_27a),V7x) != c_2Eoption_2ENONE(A_27a))) & (all V6x (mem(V6x,A_27a) -> c_2Eoption_2ENONE(A_27a) != ap(c_2Eoption_2ESOME(A_27a),V6x))) & (all V5x (mem(V5x,A_27a) -> V5x = ap(c_2Eoption_2ETHE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V5x)))) & (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V3x) = ap(c_2Eoption_2ESOME(A_27a),V4y) <-> V3x = V4y))))))))))))))) # label(conj_thm_2Eoption_2Eoption__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 916 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Eoption_2EOPTION__MCOMP(A_27a,A_27b,A_27c),arr(arr(A_27b,ty_2Eoption_2Eoption(A_27a)),arr(arr(A_27c,ty_2Eoption_2Eoption(A_27b)),arr(A_27c,ty_2Eoption_2Eoption(A_27a))))))))))) # label(mem_c_2Eoption_2EOPTION__MCOMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 917 (all A_27a (ne(A_27a) -> c_2Eoption_2ENONE(A_27a) = ap(c_2Eoption_2Esome(A_27a),k(A_27a,c_2Ebool_2EF)))) # label(conj_thm_2Eoption_2Esome__F) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 918 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V0x),V0x),c_2Eoption_2ESOME(A_27a)) = V0x)))) # label(conj_thm_2Eoption_2Eoption__case__SOME__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 919 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> V0x = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V0x),c_2Eoption_2ENONE(A_27a)),c_2Eoption_2ESOME(A_27a)))))) # label(conj_thm_2Eoption_2Eoption__case__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 920 (all A_27a (ne(A_27a) -> (all V0y (mem(V0y,A_27a) -> ap(c_2Eoption_2ESOME(A_27a),V0y) = ap(c_2Eoption_2Esome(A_27a),f110(A_27a,V0y)) & ap(c_2Eoption_2ESOME(A_27a),V0y) = ap(c_2Eoption_2Esome(A_27a),f109(A_27a,V0y)))))) # label(conj_thm_2Eoption_2Esome__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 921 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0e (mem(V0e,A_27b) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> (exists V2fn ((all V3x (mem(V3x,A_27a) -> ap(V2fn,ap(c_2Eoption_2ESOME(A_27a),V3x)) = ap(V1f,V3x))) & V0e = ap(V2fn,c_2Eoption_2ENONE(A_27a)) & mem(V2fn,arr(ty_2Eoption_2Eoption(A_27a),A_27b)))))))))))) # label(conj_thm_2Eoption_2Eoption__Axiom) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 922 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eoption_2Eoption(A_27a)) -> (-p(ap(c_2Eoption_2EIS__SOME(A_27a),V0x)) <-> V0x = c_2Eoption_2ENONE(A_27a)))))) # label(conj_thm_2Eoption_2ENOT__IS__SOME__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 923 (all A_27a (ne(A_27a) -> ($F <-> p(ap(c_2Eoption_2EIS__SOME(A_27a),c_2Eoption_2ENONE(A_27a)))) & (all V0x (mem(V0x,A_27a) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),ap(c_2Eoption_2ESOME(A_27a),V0x))) <-> $T))))) # label(ax_thm_2Eoption_2EIS__SOME__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 924 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0option (mem(V0option,arr(ty_2Eoption_2Eoption(A_27a),arr(arr(A_27a,ty_2Eoption_2Eoption(A_27a)),A_27b))) -> p(ap(c_2Ebool_2EDATATYPE(A_27b),ap(ap(V0option,c_2Eoption_2ENONE(A_27a)),c_2Eoption_2ESOME(A_27a)))))))))) # label(conj_thm_2Eoption_2Edatatype__option) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 925 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> (all V2y (mem(V2y,ty_2Eoption_2Eoption(A_27b)) -> (p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27b),V0R),V1x),V2y)) <-> (exists V3x0 ((exists V4y0 (ap(c_2Eoption_2ESOME(A_27b),V4y0) = V2y & p(ap(ap(V0R,V3x0),V4y0)) & ap(c_2Eoption_2ESOME(A_27a),V3x0) = V1x & mem(V4y0,A_27b))) & mem(V3x0,A_27a))) | c_2Eoption_2ENONE(A_27a) = V1x & V2y = c_2Eoption_2ENONE(A_27b)))))))))))) # label(ax_thm_2Eoption_2EOPTREL__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 926 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27c,A_27a))) -> (all V1x (mem(V1x,A_27b) -> (all V2y (mem(V2y,A_27c) -> ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),ap(c_2Eoption_2ESOME(A_27b),V1x)),ap(c_2Eoption_2ESOME(A_27c),V2y)) = ap(c_2Eoption_2ESOME(A_27a),ap(ap(V0f,V1x),V2y)) & c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),c_2Eoption_2ENONE(A_27b)),c_2Eoption_2ENONE(A_27c)) & c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),c_2Eoption_2ENONE(A_27b)),ap(c_2Eoption_2ESOME(A_27c),V2y)) & c_2Eoption_2ENONE(A_27a) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),ap(c_2Eoption_2ESOME(A_27b),V1x)),c_2Eoption_2ENONE(A_27c)))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP2__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 927 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1o1 (mem(V1o1,ty_2Eoption_2Eoption(A_27a)) -> (all V2o2 (mem(V2o2,ty_2Eoption_2Eoption(A_27b)) -> (all V3v (mem(V3v,A_27c) -> ((exists V4x1 ((exists V5x2 (V1o1 = ap(c_2Eoption_2ESOME(A_27a),V4x1) & V3v = ap(ap(V0f,V4x1),V5x2) & ap(c_2Eoption_2ESOME(A_27b),V5x2) = V2o2 & mem(V5x2,A_27b))) & mem(V4x1,A_27a))) <-> ap(c_2Eoption_2ESOME(A_27c),V3v) = ap(ap(ap(c_2Eoption_2EOPTION__MAP2(A_27c,A_27a,A_27b),V0f),V1o1),V2o2)))))))))))))))) # label(conj_thm_2Eoption_2EOPTION__MAP2__SOME) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 928 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),arr(arr(A_27b,arr(A_27c,A_27a)),arr(ty_2Eoption_2Eoption(A_27b),arr(ty_2Eoption_2Eoption(A_27c),ty_2Eoption_2Eoption(A_27a))))))))))) # label(mem_c_2Eoption_2EOPTION__MAP2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 929 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> p(ap(ap(V0R,V1x),V1x)))) -> (all V2x (mem(V2x,ty_2Eoption_2Eoption(A_27a)) -> p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27a),V0R),V2x),V2x))))))))) # label(conj_thm_2Eoption_2EOPTREL__refl) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 930 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2ENONE(A_27a),ty_2Eoption_2Eoption(A_27a)))) # label(mem_c_2Eoption_2ENONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 931 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,ty_2Eoption_2Eoption(A_27a)) -> (p(ap(c_2Eoption_2EIS__SOME(A_27a),V1x)) <-> p(ap(c_2Eoption_2EIS__SOME(A_27b),ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),V1x)))))))))))) # label(conj_thm_2Eoption_2EIS__SOME__MAP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 932 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2EIS__NONE(A_27a),arr(ty_2Eoption_2Eoption(A_27a),bool)))) # label(mem_c_2Eoption_2EIS__NONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 933 (all A_27a (ne(A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(V1P,V2x)) <-> p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V1P),ap(c_2Eoption_2ESOME(A_27a),V2x)))))))) & (all V0P (mem(V0P,arr(A_27a,bool)) -> ($T <-> p(ap(ap(c_2Eoption_2EOPTION__ALL(A_27a),V0P),c_2Eoption_2ENONE(A_27a)))))))) # label(ax_thm_2Eoption_2EOPTION__ALL__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 934 (all A_27a (ne(A_27a) -> mem(c_2Eoption_2ETHE(A_27a),arr(ty_2Eoption_2Eoption(A_27a),A_27a)))) # label(mem_c_2Eoption_2ETHE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 935 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0x (mem(V0x,A_27b) -> (all V1y (mem(V1y,A_27c) -> (all V2f (mem(V2f,arr(A_27b,arr(A_27c,A_27a))) -> ap(ap(V2f,V0x),V1y) = ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),ap(ap(c_2Epair_2E_2C(A_27b,A_27c),V0x),V1y)),V2f))))))))))))) # label(conj_thm_2Epair_2Epair__case__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 936 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> ap(V0f,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)) = ap(ap(ap(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),V0f),V1x),V2y))))))))))))) # label(ax_thm_2Epair_2ECURRY__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 937 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2EREP__prod(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(A_27a,arr(A_27b,bool)))))))) # label(mem_c_2Epair_2EREP__prod) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 938 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f_27 (mem(V0f_27,arr(A_27b,arr(A_27c,A_27a))) -> (all V1M (mem(V1M,ty_2Epair_2Eprod(A_27b,A_27c)) -> (all V2M_27 (mem(V2M_27,ty_2Epair_2Eprod(A_27b,A_27c)) -> (all V3f (mem(V3f,arr(A_27b,arr(A_27c,A_27a))) -> ((all V4x (mem(V4x,A_27b) -> (all V5y (mem(V5y,A_27c) -> (ap(ap(c_2Epair_2E_2C(A_27b,A_27c),V4x),V5y) = V2M_27 -> ap(ap(V0f_27,V4x),V5y) = ap(ap(V3f,V4x),V5y)))))) & V2M_27 = V1M -> ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),V1M),V3f) = ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),V2M_27),V0f_27)))))))))))))))) # label(conj_thm_2Epair_2Epair__case__cong) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 939 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Epair_2Eprod(A_27a,A_27b)) -> (exists V1q ((exists V2r (mem(V2r,A_27b) & ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1q),V2r) = V0x)) & mem(V1q,A_27a))))))))) # label(conj_thm_2Epair_2EABS__PAIR__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 940 (all A_27b all A_27a all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (all V4a f111(A_27a,A_27b,V4a,V2x,V3y) = ap(f112(A_27b,A_27a,V2x,V3y),V4a)))))) # label(lameq_f112) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 941 (all A_27b all A_27a all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V2s ap(f144(A_27b,A_27a,V0R1,V1R2),V2s) = f143(A_27a,A_27b,V2s,V0R1,V1R2)))))) # label(lameq_f144) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 942 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f_27 (mem(V0f_27,arr(A_27a,arr(A_27b,A_27c))) -> (all V1f (mem(V1f,arr(A_27a,arr(A_27b,A_27c))) -> (all V2M_27 (mem(V2M_27,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V3M (mem(V3M,ty_2Epair_2Eprod(A_27a,A_27b)) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27b) -> (V2M_27 = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4x),V5y) -> ap(ap(V0f_27,V4x),V5y) = ap(ap(V1f,V4x),V5y)))))) & V2M_27 = V3M -> ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f_27),V2M_27) = ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V1f),V3M)))))))))))))))) # label(conj_thm_2Epair_2EUNCURRY__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 943 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Epair_2Eprod(A_27a,A_27b)) -> (exists V1q ((exists V2r (mem(V2r,A_27b) & ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1q),V2r) = V0x)) & mem(V1q,A_27a))))))))) # label(conj_thm_2Epair_2Epair__CASES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 944 (all A_27b all A_27a all V1p ap(f115(A_27b,A_27a),V1p) = ap(c_2Ebool_2E_3F(A_27a),f114(A_27b,A_27a,V1p))) # label(lameq_f115) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 945 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27c,A_27d)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27c) -> ap(ap(ap(c_2Epair_2E_23_23(A_27a,A_27c,A_27b,A_27d),V0f),V1g),ap(ap(c_2Epair_2E_2C(A_27a,A_27c),V2x),V3y)) = ap(ap(c_2Epair_2E_2C(A_27b,A_27d),ap(V0f,V2x)),ap(V1g,V3y)))))))))))))))))) # label(conj_thm_2Epair_2EPAIR__MAP__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 946 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (p(ap(c_2Ebool_2E_21(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f129(A_27b,A_27a,V0P)))) <-> (all V2x (mem(V2x,A_27a) -> p(ap(c_2Ebool_2E_21(A_27b),ap(V0P,V2x)))))))))))) # label(conj_thm_2Epair_2EELIM__PFORALL__EVAL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 947 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1v (mem(V1v,ty_2Epair_2Eprod(A_27a,A_27b)) -> ap(ap(V0f,ap(c_2Epair_2EFST(A_27a,A_27b),V1v)),ap(c_2Epair_2ESND(A_27a,A_27b),V1v)) = ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f),V1v))))))))))) # label(ax_thm_2Epair_2EUNCURRY) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 948 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,ty_2Epair_2Eprod(A_27b,A_27a)) -> ap(c_2Epair_2ESWAP(A_27a,A_27b),V0a) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(c_2Epair_2ESND(A_27b,A_27a),V0a)),ap(c_2Epair_2EFST(A_27b,A_27a),V0a)))))))) # label(ax_thm_2Epair_2ESWAP__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 949 (all A_27a all A_27c all A_27b all V2p1 (mem(V2p1,A_27a) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (all V3p2 ap(f125(A_27a,A_27c,A_27b,V2p1,V0P),V3p2) = ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2p1),V3p2))))))) # label(lameq_f125) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 950 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1x ap(f129(A_27b,A_27a,V0P),V1x) = ap(V0P,V1x)))) # label(lameq_f129) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 951 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27d,A_27c)) -> (all V1g (mem(V1g,arr(A_27a,arr(A_27b,A_27d))) -> ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27b,A_27c),arr(A_27b,A_27d)),ap(c_2Ecombin_2Eo(A_27b,A_27c,A_27d),V0f)),V1g)) = ap(ap(c_2Ecombin_2Eo(ty_2Epair_2Eprod(A_27a,A_27b),A_27c,A_27d),V0f),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27d),V1g)))))))))))))) # label(conj_thm_2Epair_2Eo__UNCURRY__R) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 952 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (p(ap(c_2Ebool_2E_3F(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f128(A_27b,A_27a,V0P)))) <-> (exists V1x (mem(V1x,A_27a) & (exists V2y (mem(V2y,A_27b) & p(ap(ap(V0P,V1x),V2y))))))))))))) # label(conj_thm_2Epair_2EPEXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 953 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> ap(c_2Epair_2ESND(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)) = V1y)))))))) # label(conj_thm_2Epair_2ESND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 954 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> ((exists V2p__1 ((exists V3p__2 (p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2p__1),V3p__2))) & mem(V3p__2,A_27b))) & mem(V2p__1,A_27a))) <-> (exists V1p (mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b)) & p(ap(V0P,V1p))))))))))) # label(conj_thm_2Epair_2EEXISTS__PROD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 955 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (all V1g (mem(V1g,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (ap(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),V1g) = ap(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),V0f) <-> V0f = V1g))))))))))) # label(conj_thm_2Epair_2ECURRY__ONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 956 (all A_27c all A_27a all A_27b all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (all V1p ap(f124(A_27c,A_27a,A_27b,V0P),V1p) = ap(V0P,V1p)))) # label(lameq_f124) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 957 (all A_27a all A_27b all V2x (mem(V2x,A_27a) -> (all V1p (mem(V1p,arr(A_27a,arr(A_27b,bool))) -> (all V3y ap(f113(A_27a,A_27b,V2x,V1p),V3y) = ap(ap(c_2Emin_2E_3D(arr(A_27a,arr(A_27b,bool))),V1p),f112(A_27b,A_27a,V2x,V3y))))))) # label(lameq_f113) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 958 (all A_27a all A_27b all V2s (mem(V2s,A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V3t ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f142(A_27b,A_27a,V3t,V1R2,V0R1,V2s)) = ap(f143(A_27a,A_27b,V2s,V0R1,V1R2),V3t)))))))) # label(lameq_f143) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 959 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,bool))) -> (p(ap(c_2Ebool_2E_21(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V0f))) <-> p(ap(c_2Ebool_2E_21(A_27a),ap(ap(c_2Ecombin_2Eo(A_27a,bool,arr(A_27b,bool)),c_2Ebool_2E_21(A_27b)),V0f)))))))))) # label(conj_thm_2Epair_2EFORALL__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 960 (all A_27b all A_27c all A_27a all V2p (mem(V2p,ty_2Epair_2Eprod(arr(A_27a,A_27b),arr(A_27a,A_27c))) -> (all V3a ap(f139(A_27b,A_27c,A_27a,V2p),V3a) = ap(ap(c_2Epair_2E_2C(A_27b,A_27c),ap(ap(c_2Epair_2EFST(arr(A_27a,A_27b),arr(A_27a,A_27c)),V2p),V3a)),ap(ap(c_2Epair_2ESND(arr(A_27a,A_27b),arr(A_27a,A_27c)),V2p),V3a))))) # label(lameq_f139) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 961 (all A_27c all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x ap(f123(A_27c,A_27a,A_27b,V0f),V1x) = ap(ap(V0f,ap(c_2Epair_2EFST(A_27a,A_27b),V1x)),ap(c_2Epair_2ESND(A_27a,A_27b),V1x))))) # label(lameq_f123) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 962 (all A_27b all A_27a all V2p ap(c_2Ebool_2E_3F(A_27a),f119(A_27b,A_27a,V2p)) = ap(f120(A_27b,A_27a),V2p)) # label(lameq_f120) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 963 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1g (mem(V1g,arr(A_27a,arr(A_27b,A_27c))) -> (ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V1g) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f) <-> V1g = V0f))))))))))) # label(conj_thm_2Epair_2EUNCURRY__ONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 964 (all A_27a all A_27b all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V2s (mem(V2s,A_27a) -> (all V3t ap(f147(A_27a,A_27b,V1R2,V0R1,V2s),V3t) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f146(A_27b,A_27a,V2s,V0R1,V3t,V1R2))))))))) # label(lameq_f147) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 965 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27c)),bool)) -> (p(ap(c_2Ebool_2E_3F_21(ty_2Epair_2Eprod(arr(A_27a,A_27b),arr(A_27a,A_27c))),f140(A_27b,A_27c,A_27a,V0P))) <-> p(ap(c_2Ebool_2E_3F_21(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27c))),f138(A_27c,A_27b,A_27a,V0P)))))))))))) # label(conj_thm_2Epair_2EPAIR__FUN__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 966 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2Etotal(A_27a),V0R1)) & p(ap(c_2Erelation_2Etotal(A_27b),V1R2)) -> p(ap(c_2Erelation_2Etotal(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2)))))))))))) # label(conj_thm_2Epair_2Etotal__LEX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 967 (all A_27b all A_27a all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27b) -> (all V5a f116(A_27a,A_27b,V5a,V3x,V4y) = ap(f117(A_27b,A_27a,V3x,V4y),V5a)))))) # label(lameq_f117) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 968 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0P (mem(V0P,arr(A_27c,A_27d)) -> (all V1M (mem(V1M,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V2N (mem(V2N,arr(A_27a,arr(A_27b,A_27c))) -> ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a,A_27b),A_27d),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27d),f133(A_27b,A_27c,A_27d,A_27a,V2N,V0P))),V1M) = ap(V0P,ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),f131(A_27b,A_27c,A_27a,V2N))),V1M)))))))))))))))) # label(conj_thm_2Epair_2ELET2__RAND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 969 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (exists V1fn ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> ap(ap(V0f,V2x),V3y) = ap(V1fn,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)))))) & mem(V1fn,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)))))))))))) # label(conj_thm_2Epair_2Epair__Axiom) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 970 (all A_27b all A_27a all V2s (mem(V2s,A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V3t (mem(V3t,A_27b) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V4u f145(A_27a,A_27b,V2s,V0R1,V4u,V3t,V1R2) = ap(f146(A_27b,A_27a,V2s,V0R1,V3t,V1R2),V4u)))))))))) # label(lameq_f146) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 971 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (p(ap(c_2Ebool_2E_3F(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f129(A_27b,A_27a,V0P)))) <-> (exists V2x (p(ap(c_2Ebool_2E_3F(A_27b),ap(V0P,V2x))) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Epair_2EELIM__PEXISTS__EVAL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 972 (all A_27a2 all A_27b all A_27c all A_27a1 all V1N (mem(V1N,arr(A_27a1,arr(A_27a2,arr(A_27b,A_27c)))) -> (all V3x ap(f135(A_27a2,A_27b,A_27c,A_27a1,V1N),V3x) = f134(A_27c,A_27b,A_27a1,A_27a2,V3x,V1N)))) # label(lameq_f135) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 973 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2ESND(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27b)))))) # label(mem_c_2Epair_2ESND) # label(axiom) # label(non_clause). [assumption]. 3.15/3.76 974 (all A_27b all A_27a1 all A_27c all A_27a2 all V1N (mem(V1N,arr(A_27a1,arr(A_27a2,arr(A_27b,A_27c)))) -> (all V5x (mem(V5x,A_27a1) -> (all V2b (mem(V2b,A_27b) -> (all V6y ap(ap(ap(V1N,V5x),V6y),V2b) = ap(f136(A_27b,A_27a1,A_27c,A_27a2,V1N,V5x,V2b),V6y)))))))) # label(lameq_f136) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 975 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2EFST(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27a)))))) # label(mem_c_2Epair_2EFST) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 976 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> f123(A_27c,A_27a,A_27b,V0f) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f))))))))) # label(conj_thm_2Epair_2EELIM__UNCURRY) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 977 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2a (mem(V2a,A_27a) -> (all V3b (mem(V3b,A_27b) -> (V0x = V2a & V3b = V1y <-> ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)))))))))))))) # label(conj_thm_2Epair_2ECLOSED__PAIR__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 978 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2ELEX(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27b,arr(A_27b,bool)),arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))))))))) # label(mem_c_2Epair_2ELEX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 979 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2Ereflexive(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2))) <-> p(ap(c_2Erelation_2Ereflexive(A_27a),V0R1)) | p(ap(c_2Erelation_2Ereflexive(A_27b),V1R2))))))))))) # label(conj_thm_2Epair_2Ereflexive__LEX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 980 (all A0 (ne(A0) -> (all A1 (ne(A1) -> ne(ty_2Epair_2Eprod(A0,A1)))))) # label(ne_ty_2Epair_2Eprod) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 981 (all A_27d all A_27c all A_27a all A_27b all V2N (mem(V2N,arr(A_27a,arr(A_27b,A_27c))) -> (all V5x (mem(V5x,A_27a) -> (all V0P (mem(V0P,arr(A_27c,A_27d)) -> (all V6y ap(f132(A_27d,A_27c,A_27a,A_27b,V2N,V5x,V0P),V6y) = ap(V0P,ap(ap(V2N,V5x),V6y))))))))) # label(lameq_f132) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 982 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27b,A_27c)) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27c,A_27a))) -> (all V2v (mem(V2v,A_27a) -> (V2v = ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),V0p),V1f) <-> (exists V3x (mem(V3x,A_27b) & (exists V4y (mem(V4y,A_27c) & ap(ap(c_2Epair_2E_2C(A_27b,A_27c),V3x),V4y) = V0p & V2v = ap(ap(V1f,V3x),V4y)))))))))))))))))) # label(conj_thm_2Epair_2Epair__case__eq) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 983 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V2a (mem(V2a,A_27a) -> (all V3b (mem(V3b,A_27b) -> (all V4c (mem(V4c,A_27a) -> (all V5d (mem(V5d,A_27b) -> (p(ap(ap(V0R1,V2a),V4c)) | p(ap(ap(V1R2,V3b),V5d)) & V2a = V4c <-> p(ap(ap(ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4c),V5d)))))))))))))))))))) # label(conj_thm_2Epair_2ELEX__DEF__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 984 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2ESWAP(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27b,A_27a),ty_2Epair_2Eprod(A_27a,A_27b))))))) # label(mem_c_2Epair_2ESWAP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 985 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1p_27 (mem(V1p_27,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (all V3P_27 (mem(V3P_27,arr(A_27a,bool)) -> (all V4Q (mem(V4Q,arr(A_27b,bool)) -> (all V5Q_27 (mem(V5Q_27,arr(A_27b,bool)) -> (V1p_27 = V0p & (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27b) -> (V1p_27 = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V6x),V7y) -> (p(ap(V3P_27,V6x)) <-> p(ap(V2P,V6x)))))))) & (all V8x (mem(V8x,A_27a) -> (all V9y (mem(V9y,A_27b) -> (V1p_27 = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V8x),V9y) -> (p(ap(V4Q,V9y)) <-> p(ap(V5Q_27,V9y)))))))) -> (p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V2P),V4Q),V0p)) <-> p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V3P_27),V5Q_27),V1p_27)))))))))))))))))))) # label(conj_thm_2Epair_2EPROD__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 986 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),arr(arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c),arr(A_27a,arr(A_27b,A_27c)))))))))) # label(mem_c_2Epair_2ECURRY) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 987 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> ap(c_2Epair_2EUNCURRY(A_27a,A_27b,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f144(A_27b,A_27a,V0R1,V1R2)) = ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2))))))))) # label(ax_thm_2Epair_2ELEX__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 988 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27b,A_27a)) -> (all V1y (mem(V1y,A_27a) -> ((exists V2x (mem(V2x,A_27b) & V0p = ap(ap(c_2Epair_2E_2C(A_27b,A_27a),V2x),V1y))) <-> ap(c_2Epair_2ESND(A_27b,A_27a),V0p) = V1y))))))))) # label(conj_thm_2Epair_2ESND__EQ__EQUIV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 989 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2a (mem(V2a,A_27a) -> (all V3b (mem(V3b,A_27b) -> (ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2a),V3b) <-> V2a = V0x & V3b = V1y))))))))))))) # label(conj_thm_2Epair_2EPAIR__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 990 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> V0x = ap(c_2Epair_2EFST(A_27a,A_27b),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)))))))))) # label(conj_thm_2Epair_2EFST) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 991 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,ty_2Epair_2Eprod(A_27a,A_27b)) -> ap(c_2Epair_2EABS__prod(A_27a,A_27b),ap(c_2Epair_2EREP__prod(A_27a,A_27b),V0a)) = V0a)) & (all V1r (mem(V1r,arr(A_27a,arr(A_27b,bool))) -> (ap(c_2Epair_2EREP__prod(A_27a,A_27b),ap(c_2Epair_2EABS__prod(A_27a,A_27b),V1r)) = V1r <-> p(ap(f120(A_27b,A_27a),V1r))))))))) # label(ax_thm_2Epair_2EABS__REP__prod) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 992 (all A_27c all A_27b all A_27a1 all A_27a2 all V3x (mem(V3x,A_27a1) -> (all V1N (mem(V1N,arr(A_27a1,arr(A_27a2,arr(A_27b,A_27c)))) -> (all V4y ap(f134(A_27c,A_27b,A_27a1,A_27a2,V3x,V1N),V4y) = ap(ap(V1N,V3x),V4y)))))) # label(lameq_f134) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 993 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) & p(ap(c_2Erelation_2EWF(A_27b),V1Q)) -> p(ap(c_2Erelation_2EWF(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R),V1Q)))))))))))) # label(conj_thm_2Epair_2EWF__LEX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 994 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> V0f = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),ap(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),V0f)))))))))) # label(conj_thm_2Epair_2EUNCURRY__CURRY__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 995 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27b,A_27c)) -> (all V1f (mem(V1f,arr(A_27b,arr(A_27c,A_27a))) -> ap(ap(V1f,ap(c_2Epair_2EFST(A_27b,A_27c),V0p)),ap(c_2Epair_2ESND(A_27b,A_27c),V0p)) = ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),V0p),V1f))))))))))) # label(ax_thm_2Epair_2Epair__CASE__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 996 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0pair (mem(V0pair,arr(arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b))),A_27c)) -> p(ap(c_2Ebool_2EDATATYPE(A_27c),ap(V0pair,c_2Epair_2E_2C(A_27a,A_27b)))))))))))) # label(conj_thm_2Epair_2Edatatype__pair) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 997 (all A_27a all A_27b all V2a (mem(V2a,A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V3b ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V2a),V0x)),ap(ap(c_2Emin_2E_3D(A_27b),V3b),V1y)) = ap(f121(A_27a,A_27b,V2a,V0x,V1y),V3b)))))))) # label(lameq_f121) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 998 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> V0f = ap(c_2Epair_2ECURRY(A_27a,A_27b,A_27c),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f)))))))))) # label(conj_thm_2Epair_2ECURRY__UNCURRY__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 999 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,ty_2Epair_2Eprod(A_27a,A_27b)) -> ap(ap(c_2Epair_2E_2C(A_27a,A_27b),ap(c_2Epair_2EFST(A_27a,A_27b),V0x)),ap(c_2Epair_2ESND(A_27a,A_27b),V0x)) = V0x)))))) # label(ax_thm_2Epair_2EPAIR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 1000 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1f (mem(V1f,arr(A_27a,A_27c)) -> (all V2g (mem(V2g,arr(A_27b,A_27d)) -> ap(V2g,ap(c_2Epair_2ESND(A_27a,A_27b),V0p)) = ap(c_2Epair_2ESND(A_27c,A_27d),ap(ap(ap(c_2Epair_2E_23_23(A_27a,A_27b,A_27c,A_27d),V1f),V2g),V0p)))))))))))))))) # label(conj_thm_2Epair_2ESND__PAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 1001 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27b),V1R2)) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R1)) -> p(ap(c_2Erelation_2Etransitive(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2)))))))))))) # label(conj_thm_2Epair_2Etransitive__LEX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 1002 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27a,arr(A_27a,bool))) -> (all V2R3 (mem(V2R3,arr(A_27b,arr(A_27b,bool))) -> (all V3R4 (mem(V3R4,arr(A_27b,arr(A_27b,bool))) -> (all V4x (mem(V4x,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V5y (mem(V5y,ty_2Epair_2Eprod(A_27a,A_27b)) -> ((all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (p(ap(ap(V0R1,V6x),V7y)) -> p(ap(ap(V1R2,V6x),V7y))))))) & (all V8x (mem(V8x,A_27b) -> (all V9y (mem(V9y,A_27b) -> (p(ap(ap(V2R3,V8x),V9y)) -> p(ap(ap(V3R4,V8x),V9y))))))) -> (p(ap(ap(ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V2R3),V4x),V5y)) -> p(ap(ap(ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V1R2),V3R4),V4x),V5y)))))))))))))))))))) # label(conj_thm_2Epair_2ELEX__MONO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 1003 (all A_27a2 all A_27c all A_27b all A_27a1 all V1N (mem(V1N,arr(A_27a1,arr(A_27a2,arr(A_27b,A_27c)))) -> (all V2b (mem(V2b,A_27b) -> (all V5x ap(f137(A_27a2,A_27c,A_27b,A_27a1,V1N,V2b),V5x) = f136(A_27b,A_27a1,A_27c,A_27a2,V1N,V5x,V2b)))))) # label(lameq_f137) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 1004 (all A_27b all A_27a all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V2s ap(f148(A_27b,A_27a,V1R2,V0R1),V2s) = f147(A_27a,A_27b,V1R2,V0R1,V2s)))))) # label(lameq_f148) # label(axiom) # label(non_clause). [assumption]. 3.15/3.77 1005 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (p(ap(V1Q,V3y)) & p(ap(V0P,V2x)) <-> p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V0P),V1Q),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V3y)))))))))))))))) # label(conj_thm_2Epair_2EPROD__ALL__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1006 (all A_27a all A_27b all V2s (mem(V2s,A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V4u (mem(V4u,A_27a) -> (all V3t (mem(V3t,A_27b) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V5v ap(ap(c_2Ebool_2E_2F_5C,ap(ap(V0R1,V2s),V4u)),ap(ap(V1R2,V3t),V5v)) = ap(f145(A_27a,A_27b,V2s,V0R1,V4u,V3t,V1R2),V5v)))))))))))) # label(lameq_f145) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1007 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> ((all V1p (mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b)) -> p(ap(V0P,V1p)))) <-> (all V2p__1 (mem(V2p__1,A_27a) -> (all V3p__2 (mem(V3p__2,A_27b) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2p__1),V3p__2)))))))))))))) # label(conj_thm_2Epair_2EFORALL__PROD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1008 (all A_27a all A_27b all V4a (mem(V4a,A_27a) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27b) -> (all V5b ap(f111(A_27a,A_27b,V4a,V2x,V3y),V5b) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V4a),V2x)),ap(ap(c_2Emin_2E_3D(A_27b),V5b),V3y))))))))) # label(lameq_f111) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1009 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> mem(c_2Epair_2E_23_23(A_27a,A_27b,A_27c,A_27d),arr(arr(A_27a,A_27c),arr(arr(A_27b,A_27d),arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27c,A_27d))))))))))))) # label(mem_c_2Epair_2E_23_23) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1010 (all A_27a all A_27b all V3x (mem(V3x,A_27a) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V4y ap(ap(V0P,V3x),V4y) = ap(f127(A_27a,A_27b,V3x,V0P),V4y)))))) # label(lameq_f127) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1011 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)) = ap(ap(V0f,V1x),V2y))))))))))))) # label(conj_thm_2Epair_2EUNCURRY__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1012 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> (ap(c_2Epair_2EFST(A_27a,A_27b),V0p) = V1x <-> (exists V2y (ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y) = V0p & mem(V2y,A_27b)))))))))))) # label(conj_thm_2Epair_2EFST__EQ__EQUIV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1013 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),arr(arr(A_27a,arr(A_27b,A_27c)),arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c))))))))) # label(mem_c_2Epair_2EUNCURRY) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1014 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V2v1 (mem(V2v1,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V3v2 (mem(V3v2,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V4R1_27 (mem(V4R1_27,arr(A_27a,arr(A_27a,bool))) -> (all V5R2_27 (mem(V5R2_27,arr(A_27b,arr(A_27b,bool))) -> (all V6v1_27 (mem(V6v1_27,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V7v2_27 (mem(V7v2_27,ty_2Epair_2Eprod(A_27a,A_27b)) -> (V6v1_27 = V2v1 & (all V12a (mem(V12a,A_27a) -> (all V13b (mem(V13b,A_27b) -> (all V14c (mem(V14c,A_27a) -> (all V15d (mem(V15d,A_27b) -> (V12a = V14c & ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V14c),V15d) = V7v2_27 & ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V12a),V13b) = V6v1_27 -> (p(ap(ap(V1R2,V13b),V15d)) <-> p(ap(ap(V5R2_27,V13b),V15d)))))))))))) & (all V8a (mem(V8a,A_27a) -> (all V9b (mem(V9b,A_27b) -> (all V10c (mem(V10c,A_27a) -> (all V11d (mem(V11d,A_27b) -> (ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V8a),V9b) = V6v1_27 & V7v2_27 = ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V10c),V11d) -> (p(ap(ap(V4R1_27,V8a),V10c)) <-> p(ap(ap(V0R1,V8a),V10c)))))))))))) & V3v2 = V7v2_27 -> (p(ap(ap(ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2),V2v1),V3v2)) <-> p(ap(ap(ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V4R1_27),V5R2_27),V6v1_27),V7v2_27)))))))))))))))))))))))) # label(conj_thm_2Epair_2ELEX__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1015 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1q (mem(V1q,ty_2Epair_2Eprod(A_27a,A_27b)) -> (ap(c_2Epair_2EFST(A_27a,A_27b),V1q) = ap(c_2Epair_2EFST(A_27a,A_27b),V0p) & ap(c_2Epair_2ESND(A_27a,A_27b),V0p) = ap(c_2Epair_2ESND(A_27a,A_27b),V1q) <-> V0p = V1q))))))))) # label(conj_thm_2Epair_2EPAIR__FST__SND__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1016 (all A_27b all A_27c all A_27a all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> (all V2p1 ap(f126(A_27b,A_27c,A_27a,V0P),V2p1) = f125(A_27a,A_27c,A_27b,V2p1,V0P)))) # label(lameq_f126) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1017 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2ERPROD(A_27a,A_27b),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27b,arr(A_27b,bool)),arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool))))))))) # label(mem_c_2Epair_2ERPROD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1018 (all A_27b all A_27a all V1p (mem(V1p,arr(A_27a,arr(A_27b,bool))) -> (all V2x ap(f114(A_27b,A_27a,V1p),V2x) = ap(c_2Ebool_2E_3F(A_27b),f113(A_27a,A_27b,V2x,V1p))))) # label(lameq_f114) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1019 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2EWF(A_27a),V0R)) & p(ap(c_2Erelation_2EWF(A_27b),V1Q)) -> p(ap(c_2Erelation_2EWF(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ERPROD(A_27a,A_27b),V0R),V1Q)))))))))))) # label(conj_thm_2Epair_2EWF__RPROD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1020 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1P_27 (mem(V1P_27,arr(A_27a,bool)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (all V3Q_27 (mem(V3Q_27,arr(A_27b,bool)) -> (all V4p (mem(V4p,ty_2Epair_2Eprod(A_27a,A_27b)) -> ((all V6y (mem(V6y,A_27b) -> (p(ap(V2Q,V6y)) -> p(ap(V3Q_27,V6y))))) & (all V5x (mem(V5x,A_27a) -> (p(ap(V0P,V5x)) -> p(ap(V1P_27,V5x))))) -> (p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V0P),V2Q),V4p)) -> p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V1P_27),V3Q_27),V4p)))))))))))))))))) # label(conj_thm_2Epair_2EPROD__ALL__MONO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1021 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2EABS__prod(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,bool)),ty_2Epair_2Eprod(A_27a,A_27b))))))) # label(mem_c_2Epair_2EABS__prod) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1022 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))))))) # label(mem_c_2Epair_2E_2C) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1023 (all A_27c all A_27a all A_27b all V3x (mem(V3x,A_27a) -> (all V2N (mem(V2N,arr(A_27a,arr(A_27b,A_27c))) -> (all V4y ap(ap(V2N,V3x),V4y) = ap(f130(A_27c,A_27a,A_27b,V3x,V2N),V4y)))))) # label(lameq_f130) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1024 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),A_27c)) -> ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),f126(A_27b,A_27c,A_27a,V0P)) = f124(A_27c,A_27a,A_27b,V0P))))))))) # label(conj_thm_2Epair_2ELAMBDA__PROD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1025 (all A_27b all A_27c all A_27a all V2N (mem(V2N,arr(A_27a,arr(A_27b,A_27c))) -> (all V3x f130(A_27c,A_27a,A_27b,V3x,V2N) = ap(f131(A_27b,A_27c,A_27a,V2N),V3x)))) # label(lameq_f131) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1026 (all A_27a1 (ne(A_27a1) -> (all A_27a2 (ne(A_27a2) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0M (mem(V0M,ty_2Epair_2Eprod(A_27a1,A_27a2)) -> (all V1N (mem(V1N,arr(A_27a1,arr(A_27a2,arr(A_27b,A_27c)))) -> (all V2b (mem(V2b,A_27b) -> ap(ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a1,A_27a2),arr(A_27b,A_27c)),ap(c_2Epair_2EUNCURRY(A_27a1,A_27a2,arr(A_27b,A_27c)),f135(A_27a2,A_27b,A_27c,A_27a1,V1N))),V0M),V2b) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(A_27a1,A_27a2),A_27c),ap(c_2Epair_2EUNCURRY(A_27a1,A_27a2,A_27c),f137(A_27a2,A_27c,A_27b,A_27a1,V1N,V2b))),V0M))))))))))))))) # label(conj_thm_2Epair_2ELET2__RATOR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1027 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> mem(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),arr(ty_2Epair_2Eprod(A_27b,A_27c),arr(arr(A_27b,arr(A_27c,A_27a)),A_27a))))))))) # label(mem_c_2Epair_2Epair__CASE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1028 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> ap(ap(c_2Epair_2ERPROD(A_27a,A_27b),V0R1),V1R2) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f148(A_27b,A_27a,V1R2,V0R1)))))))))) # label(ax_thm_2Epair_2ERPROD__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1029 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (exists V0rep (mem(V0rep,arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(A_27a,arr(A_27b,bool)))) & p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(arr(A_27a,arr(A_27b,bool)),ty_2Epair_2Eprod(A_27a,A_27b)),f115(A_27b,A_27a)),V0rep)))))))) # label(ax_thm_2Epair_2Eprod__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1030 (all A_27b all A_27c all A_27d all A_27a all V2N (mem(V2N,arr(A_27a,arr(A_27b,A_27c))) -> (all V0P (mem(V0P,arr(A_27c,A_27d)) -> (all V5x f132(A_27d,A_27c,A_27a,A_27b,V2N,V5x,V0P) = ap(f133(A_27b,A_27c,A_27d,A_27a,V2N,V0P),V5x)))))) # label(lameq_f133) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1031 (all A_27b all A_27a all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2a ap(f122(A_27b,A_27a,V0x,V1y),V2a) = f121(A_27a,A_27b,V2a,V0x,V1y)))))) # label(lameq_f122) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1032 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,arr(A_27d,A_27c)))) -> (all V1x (mem(V1x,A_27d) -> ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),ap(ap(c_2Ecombin_2EC(A_27a,A_27d,arr(A_27b,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27d,arr(A_27b,A_27c)),arr(A_27b,arr(A_27d,A_27c))),c_2Ecombin_2EC(A_27b,A_27d,A_27c)),V0f)),V1x)) = ap(ap(c_2Ecombin_2EC(ty_2Epair_2Eprod(A_27a,A_27b),A_27d,A_27c),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,arr(A_27d,A_27c)),V0f)),V1x))))))))))))) # label(conj_thm_2Epair_2EC__UNCURRY__L) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1033 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (all V1f (mem(V1f,arr(A_27a,A_27c)) -> (all V2g (mem(V2g,arr(A_27b,A_27d)) -> ap(V1f,ap(c_2Epair_2EFST(A_27a,A_27b),V0p)) = ap(c_2Epair_2EFST(A_27c,A_27d),ap(ap(ap(c_2Epair_2E_23_23(A_27a,A_27b,A_27c,A_27d),V1f),V2g),V0p)))))))))))))))) # label(conj_thm_2Epair_2EFST__PAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1034 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0x (mem(V0x,A_27b) -> (all V1y (mem(V1y,A_27c) -> (all V2f (mem(V2f,arr(A_27b,arr(A_27c,A_27a))) -> ap(ap(V2f,V0x),V1y) = ap(ap(c_2Epair_2Epair__CASE(A_27a,A_27b,A_27c),ap(ap(c_2Epair_2E_2C(A_27b,A_27c),V0x),V1y)),V2f))))))))))))) # label(conj_thm_2Epair_2Epair__case__thm) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1035 (all A_27b all A_27a all V3t (mem(V3t,A_27b) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V2s (mem(V2s,A_27a) -> (all V4u ap(f142(A_27b,A_27a,V3t,V1R2,V0R1,V2s),V4u) = f141(A_27a,A_27b,V3t,V1R2,V4u,V0R1,V2s)))))))))) # label(lameq_f142) # label(axiom) # label(non_clause). [assumption]. 3.15/3.78 1036 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((exists V1p (mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b)) & p(ap(ap(V0P,ap(c_2Epair_2EFST(A_27a,A_27b),V1p)),ap(c_2Epair_2ESND(A_27a,A_27b),V1p))))) <-> (exists V2p1 ((exists V3p2 (p(ap(ap(V0P,V2p1),V3p2)) & mem(V3p2,A_27b))) & mem(V2p1,A_27a)))))))))) # label(conj_thm_2Epair_2EELIM__PEXISTS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1037 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(A_27a,A_27b),arr(A_27d,A_27c))) -> (all V1g (mem(V1g,arr(A_27a,arr(A_27b,A_27d))) -> ap(ap(c_2Ecombin_2ES(ty_2Epair_2Eprod(A_27a,A_27b),A_27d,A_27c),V0f),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27d),V1g)) = ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),ap(ap(c_2Ecombin_2ES(A_27a,arr(A_27b,A_27d),arr(A_27b,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27a,arr(arr(A_27b,A_27d),arr(A_27b,A_27c)),arr(A_27b,arr(A_27d,A_27c))),c_2Ecombin_2ES(A_27b,A_27d,A_27c)),ap(ap(c_2Ecombin_2Eo(A_27a,arr(A_27b,arr(A_27d,A_27c)),arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b))),ap(c_2Ecombin_2Eo(A_27b,arr(A_27d,A_27c),ty_2Epair_2Eprod(A_27a,A_27b)),V0f)),c_2Epair_2E_2C(A_27a,A_27b)))),V1g)))))))))))))) # label(conj_thm_2Epair_2ES__UNCURRY__R) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1038 (all A_27c all A_27b all A_27a all V0P (mem(V0P,arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27c)),bool)) -> (all V1f ap(f138(A_27c,A_27b,A_27a,V0P),V1f) = ap(V0P,V1f)))) # label(lameq_f138) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1039 (all A_27b all A_27c all A_27a all V0P (mem(V0P,arr(arr(A_27a,ty_2Epair_2Eprod(A_27b,A_27c)),bool)) -> (all V2p ap(f140(A_27b,A_27c,A_27a,V0P),V2p) = ap(V0P,f139(A_27b,A_27c,A_27a,V2p))))) # label(lameq_f140) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1040 (all A_27b all A_27a all V2p (mem(V2p,arr(A_27a,arr(A_27b,bool))) -> (all V3x ap(f119(A_27b,A_27a,V2p),V3x) = ap(c_2Ebool_2E_3F(A_27b),f118(A_27a,A_27b,V3x,V2p))))) # label(lameq_f119) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1041 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y) = ap(c_2Epair_2EABS__prod(A_27a,A_27b),f122(A_27b,A_27a,V0x,V1y)))))))))) # label(ax_thm_2Epair_2ECOMMA__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1042 (all A_27a all A_27b all V3t (mem(V3t,A_27b) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (all V4u (mem(V4u,A_27a) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V2s (mem(V2s,A_27a) -> (all V5v ap(ap(c_2Ebool_2E_5C_2F,ap(ap(V0R1,V2s),V4u)),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V2s),V4u)),ap(ap(V1R2,V3t),V5v))) = ap(f141(A_27a,A_27b,V3t,V1R2,V4u,V0R1,V2s),V5v)))))))))))) # label(lameq_f141) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1043 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V3x f127(A_27a,A_27b,V3x,V0P) = ap(f128(A_27b,A_27a,V0P),V3x)))) # label(lameq_f128) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1044 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2p (mem(V2p,ty_2Epair_2Eprod(A_27a,A_27b)) -> (p(ap(ap(ap(c_2Epair_2EPROD__ALL(A_27a,A_27b),V0P),V1Q),V2p)) <-> p(ap(V0P,ap(c_2Epair_2EFST(A_27a,A_27b),V2p))) & p(ap(V1Q,ap(c_2Epair_2ESND(A_27a,A_27b),V2p)))))))))))))) # label(ax_thm_2Epair_2EPROD__ALL__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1045 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)) -> ((all V1p__1 (mem(V1p__1,A_27a) -> (all V2p__2 (mem(V2p__2,A_27b) -> p(ap(V0P,ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1p__1),V2p__2))))))) -> (all V3p (mem(V3p,ty_2Epair_2Eprod(A_27a,A_27b)) -> p(ap(V0P,V3p))))))))))) # label(conj_thm_2Epair_2Epair__induction) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1046 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27b,A_27c))) -> (all V1v (mem(V1v,ty_2Epair_2Eprod(A_27a,A_27b)) -> ap(ap(c_2Epair_2EUNCURRY(A_27a,A_27b,A_27c),V0f),V1v) = ap(ap(V0f,ap(c_2Epair_2EFST(A_27a,A_27b),V1v)),ap(c_2Epair_2ESND(A_27a,A_27b),V1v)))))))))))) # label(conj_thm_2Epair_2EUNCURRY__VAR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1047 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epair_2EPROD__ALL(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)))))))) # label(mem_c_2Epair_2EPROD__ALL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1048 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R1 (mem(V0R1,arr(A_27a,arr(A_27a,bool))) -> (all V1R2 (mem(V1R2,arr(A_27b,arr(A_27b,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R1)) & p(ap(c_2Erelation_2Esymmetric(A_27b),V1R2)) -> p(ap(c_2Erelation_2Esymmetric(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2ELEX(A_27a,A_27b),V0R1),V1R2)))))))))))) # label(conj_thm_2Epair_2Esymmetric__LEX) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1049 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((all V1p (mem(V1p,ty_2Epair_2Eprod(A_27a,A_27b)) -> p(ap(ap(V0P,ap(c_2Epair_2EFST(A_27a,A_27b),V1p)),ap(c_2Epair_2ESND(A_27a,A_27b),V1p))))) <-> (all V2p1 (mem(V2p1,A_27a) -> (all V3p2 (mem(V3p2,A_27b) -> p(ap(ap(V0P,V2p1),V3p2))))))))))))) # label(conj_thm_2Epair_2EELIM__PFORALL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1050 (all A_27a all A_27b all V5a (mem(V5a,A_27a) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27b) -> (all V6b ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V5a),V3x)),ap(ap(c_2Emin_2E_3D(A_27b),V6b),V4y)) = ap(f116(A_27a,A_27b,V5a,V3x,V4y),V6b)))))))) # label(lameq_f116) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1051 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27d)) -> (all V2p (mem(V2p,ty_2Epair_2Eprod(A_27a,A_27b)) -> ap(ap(ap(c_2Epair_2E_23_23(A_27a,A_27b,A_27c,A_27d),V0f),V1g),V2p) = ap(ap(c_2Epair_2E_2C(A_27c,A_27d),ap(V0f,ap(c_2Epair_2EFST(A_27a,A_27b),V2p))),ap(V1g,ap(c_2Epair_2ESND(A_27a,A_27b),V2p))))))))))))))))) # label(ax_thm_2Epair_2EPAIR__MAP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1052 (all A_27a all A_27b all V3x (mem(V3x,A_27a) -> (all V2p (mem(V2p,arr(A_27a,arr(A_27b,bool))) -> (all V4y ap(ap(c_2Emin_2E_3D(arr(A_27a,arr(A_27b,bool))),V2p),f117(A_27b,A_27a,V3x,V4y)) = ap(f118(A_27a,A_27b,V3x,V2p),V4y)))))) # label(lameq_f118) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1053 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> p(ap(ap(V0P,V1x),V2y)))))) <-> p(ap(c_2Ebool_2E_21(ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),f128(A_27b,A_27a,V0P))))))))))) # label(conj_thm_2Epair_2EPFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1054 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = V1n | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Eprim__rec_2ELESS__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1055 (all A_27a all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V5x f156(A_27a,V5x,V0f) = ap(f157(A_27a,V0f),V5x)))) # label(lameq_f157) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1056 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2EPRIM__REC(A_27a),arr(A_27a,arr(arr(A_27a,arr(ty_2Enum_2Enum,A_27a)),arr(ty_2Enum_2Enum,A_27a)))))) # label(mem_c_2Eprim__rec_2EPRIM__REC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1057 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V1n))) -> V1n = V0m | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Eprim__rec_2ELESS__LEMMA1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1058 (all A_27a all V0e (mem(V0e,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V2fn1 ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),ap(V2fn1,c_2Enum_2E0)),V0e)),ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f164(A_27a,V1f,V2fn1))) = ap(f165(A_27a,V0e,V1f),V2fn1)))))) # label(lameq_f165) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1059 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2Ewellfounded(A_27a),arr(arr(A_27a,arr(A_27a,bool)),bool)))) # label(mem_c_2Eprim__rec_2Ewellfounded) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1060 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),arr(arr(ty_2Enum_2Enum,A_27a),arr(A_27a,arr(arr(A_27a,A_27a),arr(ty_2Enum_2Enum,bool))))))) # label(mem_c_2Eprim__rec_2ESIMP__REC__REL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1061 (all A_27a all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V2fn1 (mem(V2fn1,arr(ty_2Enum_2Enum,A_27a)) -> (all V3n ap(ap(c_2Emin_2E_3D(A_27a),ap(V2fn1,ap(c_2Enum_2ESUC,V3n))),ap(ap(V1f,ap(V2fn1,V3n)),V3n)) = ap(f164(A_27a,V1f,V2fn1),V3n)))))) # label(lameq_f164) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1062 (all A_27a (ne(A_27a) -> ap(c_2Erelation_2Einv__image(A_27a,ty_2Enum_2Enum),c_2Eprim__rec_2E_3C) = c_2Eprim__rec_2Emeasure(A_27a))) # label(ax_thm_2Eprim__rec_2Emeasure__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1063 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(ap(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),V0x),V1f),c_2Enum_2E0),V2n) = V0x)) & (all V3m (mem(V3m,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(ap(ap(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),V0x),V1f),ap(c_2Enum_2ESUC,V3m)),V4n) = ap(ap(V1f,ap(ap(ap(ap(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),V0x),V1f),V3m),ap(c_2Eprim__rec_2EPRE,V4n))),V4n))))))))))) # label(conj_thm_2Eprim__rec_2EPRIM__REC__EQN) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1064 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2g1 (mem(V2g1,arr(ty_2Enum_2Enum,A_27a)) -> (all V3g2 (mem(V3g2,arr(ty_2Enum_2Enum,A_27a)) -> (all V4m1 (mem(V4m1,ty_2Enum_2Enum) -> (all V5m2 (mem(V5m2,ty_2Enum_2Enum) -> (p(ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V2g1),V0x),V1f),V4m1)) & p(ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V3g2),V0x),V1f),V5m2)) -> (all V6n (mem(V6n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V6n),V5m2)) & p(ap(ap(c_2Eprim__rec_2E_3C,V6n),V4m1)) -> ap(V2g1,V6n) = ap(V3g2,V6n))))))))))))))))))) # label(conj_thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1065 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Enum_2ESUC,V0m) = V1n -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Eprim__rec_2EEQ__LESS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1066 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2ESIMP__REC(A_27a),arr(A_27a,arr(arr(A_27a,A_27a),arr(ty_2Enum_2Enum,A_27a)))))) # label(mem_c_2Eprim__rec_2ESIMP__REC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1067 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (exists V2fn ((all V3n (mem(V3n,ty_2Enum_2Enum) -> ap(ap(V1f,V3n),ap(V2fn,V3n)) = ap(V2fn,ap(c_2Enum_2ESUC,V3n)))) & ap(V2fn,c_2Enum_2E0) = V0e & mem(V2fn,arr(ty_2Enum_2Enum,A_27a)))))))))) # label(conj_thm_2Eprim__rec_2Enum__Axiom) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1068 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (exists V3fun (mem(V3fun,arr(ty_2Enum_2Enum,A_27a)) & p(ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V3fun),V0x),V1f),V2n)))))))))))) # label(conj_thm_2Eprim__rec_2ESIMP__REC__EXISTS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1069 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Eprim__rec_2Ewellfounded(A_27a),V0R)) <-> -(exists V1f ((all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(V0R,ap(V1f,ap(c_2Enum_2ESUC,V2n))),ap(V1f,V2n))))) & mem(V1f,arr(ty_2Enum_2Enum,A_27a))))))))) # label(ax_thm_2Eprim__rec_2Ewellfounded__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1070 (all A_27a (ne(A_27a) -> (all V0fun (mem(V0fun,arr(ty_2Enum_2Enum,A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V0fun),V1x),V2f),V3n)) <-> (all V4m (mem(V4m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V4m),V3n)) -> ap(V2f,ap(V0fun,V4m)) = ap(V0fun,ap(c_2Enum_2ESUC,V4m))))) & ap(V0fun,c_2Enum_2E0) = V1x))))))))))) # label(ax_thm_2Eprim__rec_2ESIMP__REC__REL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1071 (all A_27a all V3x (mem(V3x,A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V4y ap(f154(A_27a,V3x,V0f),V4y) = ap(ap(c_2Emin_2E_3D(A_27a),V4y),ap(V0f,V3x))))))) # label(lameq_f154) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1072 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Eprim__rec_2ELESS__SUC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1073 (all V0m (mem(V0m,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,V0m)))) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V0m))))) # label(conj_thm_2Eprim__rec_2ELESS__SUC__SUC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1074 (all V0n (mem(V0n,ty_2Enum_2Enum) -> -p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V0n)))) # label(conj_thm_2Eprim__rec_2ELESS__REFL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1075 (all A_27a all V5x (mem(V5x,A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V6y ap(ap(c_2Emin_2E_3D(A_27a),V6y),ap(V0f,V5x)) = ap(f156(A_27a,V5x,V0f),V6y)))))) # label(lameq_f156) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1076 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,V0n) != V0n)) # label(conj_thm_2Eprim__rec_2ESUC__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1077 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),arr(A_27a,arr(arr(A_27a,arr(ty_2Enum_2Enum,A_27a)),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,A_27a))))))) # label(mem_c_2Eprim__rec_2EPRIM__REC__FUN) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1078 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Eprim__rec_2ESUC__LESS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1079 (all A_27a all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V0x (mem(V0x,A_27a) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3y (mem(V3y,A_27a) -> (all V4g ap(f160(A_27a,V1f,V0x,V2n,V3y),V4g) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V4g),V0x),V1f),ap(c_2Enum_2ESUC,V2n))),ap(ap(c_2Emin_2E_3D(A_27a),V3y),ap(V4g,V2n)))))))))))) # label(lameq_f160) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1080 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V1n))) -> (V0m != V1n -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)))))))) # label(conj_thm_2Eprim__rec_2ELESS__SUC__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1081 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> ap(ap(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),V0x),V1f) = ap(ap(c_2Eprim__rec_2ESIMP__REC(arr(ty_2Enum_2Enum,A_27a)),k(ty_2Enum_2Enum,V0x)),f163(A_27a,V1f)))))))) # label(ax_thm_2Eprim__rec_2EPRIM__REC__FUN) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1082 (all V4x f152(V4x) = ap(f153,V4x)) # label(lameq_f153) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1083 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Eprim__rec_2ELESS__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1084 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> ap(ap(ap(c_2Eprim__rec_2EPRIM__REC(A_27a),V0x),V1f),V2m) = ap(ap(ap(ap(c_2Eprim__rec_2EPRIM__REC__FUN(A_27a),V0x),V1f),V2m),ap(c_2Eprim__rec_2EPRE,V2m)))))))))) # label(ax_thm_2Eprim__rec_2EPRIM__REC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1085 (all V0n (mem(V0n,ty_2Enum_2Enum) -> -p(ap(ap(c_2Eprim__rec_2E_3C,V0n),c_2Enum_2E0)))) # label(conj_thm_2Eprim__rec_2ENOT__LESS__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1086 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(c_2Ebool_2E_3F_21(A_27a),f161(A_27a,V2n,V0x,V1f))))))))))) # label(conj_thm_2Eprim__rec_2ESIMP__REC__REL__UNIQUE__RESULT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1087 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y ap(f158(V0x),V1y) = ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1y),ap(c_2Enum_2ESUC,V0x))))) # label(lameq_f158) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1088 (all A_27a all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V3y ap(c_2Ebool_2E_3F(arr(ty_2Enum_2Enum,A_27a)),f160(A_27a,V1f,V0x,V2n,V3y)) = ap(f161(A_27a,V2n,V0x,V1f),V3y)))))))) # label(lameq_f161) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1089 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Eprim__rec_2Ewellfounded(A_27a),V0R)) <-> p(ap(c_2Erelation_2EWF(A_27a),V0R))))))) # label(conj_thm_2Eprim__rec_2EWF__IFF__WELLFOUNDED) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1090 (all V2x f150(V2x) = ap(f151,V2x)) # label(lameq_f151) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1091 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n ap(f149(V0m),V1n) = ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0m),ap(c_2Enum_2ESUC,V1n))))) # label(lameq_f149) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1092 (all A_27a all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V3x ap(f155(A_27a,V0f),V3x) = f154(A_27a,V3x,V0f)))) # label(lameq_f155) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1093 (all A_27a (ne(A_27a) -> mem(c_2Eprim__rec_2Emeasure(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Eprim__rec_2Emeasure) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1094 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = V1n -> -p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Eprim__rec_2ENOT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1095 (all V0x f158(V0x) = ap(f159,V0x)) # label(lameq_f159) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1096 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n))) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Eprim__rec_2ELESS__MONO__REV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1097 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> p(ap(c_2Ebool_2E_3F_21(arr(ty_2Enum_2Enum,A_27a)),f165(A_27a,V0e,V1f))))))))) # label(conj_thm_2Eprim__rec_2Enum__Axiom__old) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1098 (all A_27a all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V3fun (mem(V3fun,arr(ty_2Enum_2Enum,A_27a)) -> (all V4n ap(ap(V1f,ap(V3fun,ap(c_2Eprim__rec_2EPRE,V4n))),V4n) = ap(f162(A_27a,V1f,V3fun),V4n)))))) # label(lameq_f162) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1099 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V1x)),ap(V0f,V2y))) <-> p(ap(ap(ap(c_2Eprim__rec_2Emeasure(A_27a),V0f),V1x),V2y))))))))))) # label(conj_thm_2Eprim__rec_2Emeasure__thm) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1100 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) | V1n = V0m -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Eprim__rec_2ELESS__LEMMA2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1101 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f_27 (mem(V1f_27,arr(A_27a,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (exists V3g (mem(V3g,arr(ty_2Enum_2Enum,A_27a)) & p(ap(ap(ap(ap(c_2Eprim__rec_2ESIMP__REC__REL(A_27a),V3g),V0x),V1f_27),ap(c_2Enum_2ESUC,V2n))) & ap(ap(ap(c_2Eprim__rec_2ESIMP__REC(A_27a),V0x),V1f_27),V2n) = ap(V3g,V2n))))))))))) # label(ax_thm_2Eprim__rec_2ESIMP__REC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1102 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> ap(ap(ap(c_2Eprim__rec_2EPRIM__REC(A_27a),V0x),V1f),c_2Enum_2E0) = V0x & (all V2m (mem(V2m,ty_2Enum_2Enum) -> ap(ap(V1f,ap(ap(ap(c_2Eprim__rec_2EPRIM__REC(A_27a),V0x),V1f),V2m)),V2m) = ap(ap(ap(c_2Eprim__rec_2EPRIM__REC(A_27a),V0x),V1f),ap(c_2Enum_2ESUC,V2m)))))))))) # label(conj_thm_2Eprim__rec_2EPRIM__REC__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1103 (all A_27a (ne(A_27a) -> (all V0m (mem(V0m,arr(A_27a,ty_2Enum_2Enum)) -> p(ap(c_2Erelation_2EWF(A_27a),ap(c_2Eprim__rec_2Emeasure(A_27a),V0m))))))) # label(conj_thm_2Eprim__rec_2EWF__measure) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1104 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Enum_2ESUC,V0n))))) # label(conj_thm_2Eprim__rec_2ELESS__SUC__REFL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1105 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(c_2Eprim__rec_2EPRE,V0m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0m),c_2Enum_2E0)),c_2Enum_2E0),ap(c_2Emin_2E_40(ty_2Enum_2Enum),f149(V0m))))) # label(ax_thm_2Eprim__rec_2EPRE__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1106 (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3y ap(f150(V2x),V3y) = ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3y),ap(c_2Enum_2ESUC,V2x))))) # label(lameq_f150) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1107 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Enum_2ESUC,V0n))))) # label(conj_thm_2Eprim__rec_2ELESS__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1108 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> V1n != V0m))))) # label(conj_thm_2Eprim__rec_2ELESS__NOT__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1109 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2a (mem(V2a,A_27a) -> (p(ap(V0P,V2a)) & (all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> (exists V4y (mem(V4y,A_27a) & p(ap(V0P,V4y)) & p(ap(ap(V1R,V3x),V4y))))))) -> (exists V5f (mem(V5f,arr(ty_2Enum_2Enum,A_27a)) & (all V6n (mem(V6n,ty_2Enum_2Enum) -> p(ap(V0P,ap(V5f,V6n))) & p(ap(ap(V1R,ap(V5f,V6n)),ap(V5f,ap(c_2Enum_2ESUC,V6n)))))) & V2a = ap(V5f,c_2Enum_2E0)))))))))))) # label(conj_thm_2Eprim__rec_2EDC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1110 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> ap(ap(ap(c_2Eprim__rec_2ESIMP__REC(A_27a),V0x),V1f),ap(c_2Enum_2ESUC,V2m)) = ap(V1f,ap(ap(ap(c_2Eprim__rec_2ESIMP__REC(A_27a),V0x),V1f),V2m)))) & ap(ap(ap(c_2Eprim__rec_2ESIMP__REC(A_27a),V0x),V1f),c_2Enum_2E0) = V0x)))))) # label(conj_thm_2Eprim__rec_2ESIMP__REC__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1111 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(c_2Eprim__rec_2EPRE,ap(c_2Enum_2ESUC,V0m)) = V0m)) # label(conj_thm_2Eprim__rec_2EPRE_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1112 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Enum_2ESUC,V1n) = ap(c_2Enum_2ESUC,V0m) <-> V0m = V1n))))) # label(conj_thm_2Eprim__rec_2EINV__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.79 1113 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Eprim__rec_2ELESS__MONO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1114 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ((exists V2P (mem(V2P,arr(ty_2Enum_2Enum,bool)) & -p(ap(V2P,V1n)) & p(ap(V2P,V0m)) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(V2P,ap(c_2Enum_2ESUC,V3n))) -> p(ap(V2P,V3n))))))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(ax_thm_2Eprim__rec_2ELESS__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1115 (all V4x (mem(V4x,ty_2Enum_2Enum) -> (all V5y ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V5y),ap(c_2Enum_2ESUC,V4x)) = ap(f152(V4x),V5y)))) # label(lameq_f152) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1116 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Erelation_2ETC(ty_2Enum_2Enum),f151),V0m),ap(c_2Enum_2ESUC,V1n))) <-> p(ap(ap(ap(c_2Erelation_2ERTC(ty_2Enum_2Enum),f153),V0m),V1n))))))) # label(conj_thm_2Eprim__rec_2ETC__IM__RTC__SUC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1117 (all A_27a all V1f (mem(V1f,arr(A_27a,arr(ty_2Enum_2Enum,A_27a))) -> (all V3fun f162(A_27a,V1f,V3fun) = ap(f163(A_27a,V1f),V3fun)))) # label(lameq_f163) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1118 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1m (mem(V1m,A_27a) -> (all V2n (mem(V2n,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),f157(A_27a,V0f)),V1m),V2n)) <-> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),f155(A_27a,V0f)),ap(V0f,V1m)),V2n))))))))))) # label(conj_thm_2Eprim__rec_2ERTC__IM__TC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1119 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Eglb(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Eposet_2Eglb) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1120 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1c (mem(V1c,arr(A_27a,bool)) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) -> (exists V2x (p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),V0p),V1c),V2x)) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Eposet_2Ecomplete__down) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1121 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Edown__continuous(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),bool))))) # label(mem_c_2Eposet_2Edown__continuous) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1122 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Eup__continuous(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),bool))))) # label(mem_c_2Eposet_2Eup__continuous) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1123 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> ((all V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V0s,V4x)) & p(ap(ap(V1r,V4x),V5y)) & p(ap(ap(V1r,V5y),V4x)) & p(ap(V0s,V5y)) -> V4x = V5y))))) & (all V6x (mem(V6x,A_27a) -> (all V7y (mem(V7y,A_27a) -> (all V8z (mem(V8z,A_27a) -> (p(ap(V0s,V6x)) & p(ap(V0s,V8z)) & p(ap(ap(V1r,V7y),V8z)) & p(ap(ap(V1r,V6x),V7y)) & p(ap(V0s,V7y)) -> p(ap(ap(V1r,V6x),V8z))))))))) & (all V3x (mem(V3x,A_27a) -> (p(ap(V0s,V3x)) -> p(ap(ap(V1r,V3x),V3x))))) & (exists V2x (p(ap(V0s,V2x)) & mem(V2x,A_27a))) <-> p(ap(c_2Eposet_2Eposet(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)))))))))) # label(ax_thm_2Eposet_2Eposet__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1124 (all A_27b all A_27a all V4g (mem(V4g,arr(A_27a,A_27b)) -> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> (all V2r (mem(V2r,arr(A_27b,arr(A_27b,bool))) -> (all V0t (mem(V0t,arr(A_27a,bool)) -> (all V5x ap(f167(A_27b,A_27a,V4g,V3f,V2r,V0t),V5x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(V0t,V5x)),ap(ap(V2r,ap(V3f,V5x)),ap(V4g,V5x)))))))))))) # label(lameq_f167) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1125 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(V0s,V4y)) & p(ap(ap(V1r,V3x),V4y)) & p(ap(V0s,V3x)) -> p(ap(ap(V1r,ap(V2f,V3x)),ap(V2f,V4y)))))))) <-> p(ap(ap(c_2Eposet_2Emonotonic(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2f))))))))))) # label(ax_thm_2Eposet_2Emonotonic__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1126 (all A_27b all A_27a all V0t (mem(V0t,arr(A_27a,bool)) -> (all V2r (mem(V2r,arr(A_27b,arr(A_27b,bool))) -> (all V3f f168(A_27b,A_27a,V0t,V2r,V3f) = ap(f169(A_27b,A_27a,V0t,V2r),V3f)))))) # label(lameq_f169) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1127 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eposet_2Efunction(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(arr(A_27a,A_27b),bool)))))))) # label(mem_c_2Eposet_2Efunction) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1128 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (p(ap(ap(c_2Eposet_2Eup__continuous(A_27a),V0p),V1f)) & p(ap(ap(c_2Eposet_2Edown__continuous(A_27a),V0p),V1f)) <-> p(ap(ap(c_2Eposet_2Econtinuous(A_27a),V0p),V1f))))))))) # label(ax_thm_2Eposet_2Econtinuous__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1129 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Emonotonic(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),bool))))) # label(mem_c_2Eposet_2Emonotonic) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1130 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Ebottom(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(A_27a,bool))))) # label(mem_c_2Eposet_2Ebottom) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1131 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Egfp(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),arr(A_27a,bool)))))) # label(mem_c_2Eposet_2Egfp) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1132 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2p (mem(V2p,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Elub(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2p),V3x)) <-> (all V4y (mem(V4y,A_27a) -> (p(ap(V2p,V4y)) & p(ap(V0s,V4y)) -> p(ap(ap(V1r,V4y),V3x))))) & (all V5z (mem(V5z,A_27a) -> ((all V6y (mem(V6y,A_27a) -> (p(ap(V2p,V6y)) & p(ap(V0s,V6y)) -> p(ap(ap(V1r,V6y),V5z))))) & p(ap(V0s,V5z)) -> p(ap(ap(V1r,V3x),V5z))))) & p(ap(V0s,V3x))))))))))))) # label(ax_thm_2Eposet_2Elub__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1133 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0t (mem(V0t,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27b,bool)) -> (all V2r (mem(V2r,arr(A_27b,arr(A_27b,bool))) -> ap(ap(c_2Epair_2E_2C(arr(arr(A_27a,A_27b),bool),arr(arr(A_27a,A_27b),arr(arr(A_27a,A_27b),bool))),ap(ap(c_2Eposet_2Efunction(A_27a,A_27b),V0t),V1s)),f169(A_27b,A_27a,V0t,V2r)) = ap(ap(c_2Eposet_2Epointwise__lift(A_27a,A_27b),V0t),ap(ap(c_2Epair_2E_2C(arr(A_27b,bool),arr(A_27b,arr(A_27b,bool))),V1s),V2r)))))))))))) # label(ax_thm_2Eposet_2Epointwise__lift__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1134 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) & p(ap(c_2Eposet_2Eposet(A_27a),V0p)) -> (exists V1x (p(ap(ap(c_2Eposet_2Etop(A_27a),V0p),V1x)) & mem(V1x,A_27a)))))))) # label(conj_thm_2Eposet_2Ecomplete__top) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1135 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Eposet_2Ebottom(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2x)) <-> (all V3y (mem(V3y,A_27a) -> (p(ap(V0s,V3y)) -> p(ap(ap(V1r,V2x),V3y))))) & p(ap(V0s,V2x))))))))))) # label(ax_thm_2Eposet_2Ebottom__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1136 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (p(ap(c_2Eposet_2Eposet(A_27a),V0p)) & p(ap(ap(c_2Eposet_2Emonotonic(A_27a),V0p),V1f)) & p(ap(ap(ap(c_2Eposet_2Efunction(A_27a,A_27a),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),V1f)) & p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) -> (exists V3x (mem(V3x,A_27a) & p(ap(ap(ap(c_2Eposet_2Egfp(A_27a),V0p),V1f),V3x)))) & (exists V2x (mem(V2x,A_27a) & p(ap(ap(ap(c_2Eposet_2Elfp(A_27a),V0p),V1f),V2x))))))))))) # label(conj_thm_2Eposet_2Eknaster__tarski) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1137 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2x (mem(V2x,A_27a) -> (all V3x_27 (mem(V3x_27,A_27a) -> (p(ap(c_2Eposet_2Eposet(A_27a),V0p)) & p(ap(ap(ap(c_2Eposet_2Egfp(A_27a),V0p),V1f),V3x_27)) & p(ap(ap(ap(c_2Eposet_2Egfp(A_27a),V0p),V1f),V2x)) -> V2x = V3x_27))))))))))) # label(conj_thm_2Eposet_2Egfp__unique) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1138 (all A_27b all A_27a all V0t (mem(V0t,arr(A_27a,bool)) -> (all V2r (mem(V2r,arr(A_27b,arr(A_27b,bool))) -> (all V3f (mem(V3f,arr(A_27a,A_27b)) -> (all V4g ap(c_2Ebool_2E_21(A_27a),f167(A_27b,A_27a,V4g,V3f,V2r,V0t)) = ap(f168(A_27b,A_27a,V0t,V2r,V3f),V4g)))))))) # label(lameq_f168) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1139 (all A_27a all V0s (mem(V0s,arr(A_27a,bool)) -> (all V2p (mem(V2p,arr(A_27a,bool)) -> (all V4j ap(f166(A_27a,V0s,V2p),V4j) = ap(ap(c_2Ebool_2E_2F_5C,ap(V0s,V4j)),ap(V2p,V4j))))))) # label(lameq_f166) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1140 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (all V4z (mem(V4z,A_27a) -> (p(ap(c_2Eposet_2Eposet(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r))) & p(ap(V0s,V2x)) & p(ap(ap(V1r,V2x),V3y)) & p(ap(ap(V1r,V3y),V4z)) & p(ap(V0s,V4z)) & p(ap(V0s,V3y)) -> p(ap(ap(V1r,V2x),V4z))))))))))))))) # label(conj_thm_2Eposet_2Eposet__trans) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1141 (all A_27a all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3c (mem(V3c,arr(A_27a,bool)) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V5y ap(f171(A_27a,V2f,V3c,V0s),V5y) = ap(c_2Ebool_2E_3F(A_27a),f170(A_27a,V0s,V3c,V2f,V5y))))))))) # label(lameq_f171) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1142 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Ecarrier(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(A_27a,bool))))) # label(mem_c_2Eposet_2Ecarrier) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1143 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (p(ap(c_2Eposet_2Eposet(A_27a),V0p)) & p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) & p(ap(ap(c_2Eposet_2Emonotonic(A_27a),V0p),V1f)) & p(ap(ap(ap(c_2Eposet_2Efunction(A_27a,A_27a),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),V1f)) -> (exists V2x (mem(V2x,A_27a) & p(ap(ap(ap(c_2Eposet_2Elfp(A_27a),V0p),V1f),V2x))))))))))) # label(conj_thm_2Eposet_2Eknaster__tarski__lfp) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1144 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Eposet_2Etop(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2x)) <-> p(ap(V0s,V2x)) & (all V3y (mem(V3y,A_27a) -> (p(ap(V0s,V3y)) -> p(ap(ap(V1r,V3y),V2x)))))))))))))) # label(ax_thm_2Eposet_2Etop__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1145 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,arr(A_27a,bool)) -> (all V1b (mem(V1b,arr(A_27b,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(V0a,V3x)) -> p(ap(V1b,ap(V2f,V3x)))))) <-> p(ap(ap(ap(c_2Eposet_2Efunction(A_27a,A_27b),V0a),V1b),V2f))))))))))))) # label(ax_thm_2Eposet_2Efunction__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1146 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Etop(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(A_27a,bool))))) # label(mem_c_2Eposet_2Etop) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1147 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (p(ap(c_2Eposet_2Eposet(A_27a),V0p)) & p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) -> (exists V1x (p(ap(ap(c_2Eposet_2Ebottom(A_27a),V0p),V1x)) & mem(V1x,A_27a)))))))) # label(conj_thm_2Eposet_2Ecomplete__bottom) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1148 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2p (mem(V2p,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(V0s,V3x)) & (all V4y (mem(V4y,A_27a) -> (p(ap(V0s,V4y)) & p(ap(V2p,V4y)) -> p(ap(ap(V1r,V3x),V4y))))) & (all V5z (mem(V5z,A_27a) -> (p(ap(V0s,V5z)) & (all V6y (mem(V6y,A_27a) -> (p(ap(V2p,V6y)) & p(ap(V0s,V6y)) -> p(ap(ap(V1r,V5z),V6y))))) -> p(ap(ap(V1r,V5z),V3x))))) <-> p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2p),V3x))))))))))))) # label(ax_thm_2Eposet_2Eglb__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1149 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) & p(ap(ap(ap(c_2Eposet_2Efunction(A_27a,A_27a),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),ap(c_2Eposet_2Ecarrier(A_27a),V0p)),V1f)) & p(ap(ap(c_2Eposet_2Emonotonic(A_27a),V0p),V1f)) & p(ap(c_2Eposet_2Eposet(A_27a),V0p)) -> (exists V2x (mem(V2x,A_27a) & p(ap(ap(ap(c_2Eposet_2Egfp(A_27a),V0p),V1f),V2x))))))))))) # label(conj_thm_2Eposet_2Eknaster__tarski__gfp) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1150 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (p(ap(c_2Eposet_2Eposet(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r))) & p(ap(V0s,V2x)) -> p(ap(ap(V1r,V2x),V2x))))))))))) # label(conj_thm_2Eposet_2Eposet__refl) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1151 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Erelation(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Eposet_2Erelation) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1152 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2c (mem(V2c,arr(A_27a,bool)) -> (p(ap(ap(c_2Eposet_2Echain(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2c)) <-> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(V0s,V3x)) & p(ap(V0s,V4y)) & p(ap(V2c,V3x)) & p(ap(V2c,V4y)) -> p(ap(ap(V1r,V3x),V4y)) | p(ap(ap(V1r,V4y),V3x)))))))))))))))) # label(ax_thm_2Eposet_2Echain__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1153 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1c (mem(V1c,arr(A_27a,bool)) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) -> (exists V2x (mem(V2x,A_27a) & p(ap(ap(ap(c_2Eposet_2Elub(A_27a),V0p),V1c),V2x))))))))))) # label(conj_thm_2Eposet_2Ecomplete__up) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1154 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3x (mem(V3x,A_27a) -> (ap(V2f,V3x) = V3x & (all V4y (mem(V4y,A_27a) -> (p(ap(V0s,V4y)) & p(ap(ap(V1r,V4y),ap(V2f,V4y))) -> p(ap(ap(V1r,V4y),V3x))))) & p(ap(V0s,V3x)) <-> p(ap(ap(ap(c_2Eposet_2Egfp(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2f),V3x))))))))))))) # label(ax_thm_2Eposet_2Egfp__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1155 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Econtinuous(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),bool))))) # label(mem_c_2Eposet_2Econtinuous) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1156 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2x (mem(V2x,A_27a) -> (all V3x_27 (mem(V3x_27,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Elfp(A_27a),V0p),V1f),V3x_27)) & p(ap(ap(ap(c_2Eposet_2Elfp(A_27a),V0p),V1f),V2x)) & p(ap(c_2Eposet_2Eposet(A_27a),V0p)) -> V2x = V3x_27))))))))))) # label(conj_thm_2Eposet_2Elfp__unique) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1157 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2p (mem(V2p,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2p),V3x)) <-> p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),f166(A_27a,V0s,V2p)),V3x))))))))))))) # label(conj_thm_2Eposet_2Eglb__pred) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1158 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Echain(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Eposet_2Echain) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1159 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Eposet_2Ecarrier(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)) = V0s)))))) # label(ax_thm_2Eposet_2Ecarrier__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1160 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (p(ap(ap(c_2Eposet_2Edown__continuous(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2f)) <-> (all V3c (mem(V3c,arr(A_27a,bool)) -> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V3c),V4x)) & p(ap(ap(c_2Eposet_2Echain(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V3c)) -> p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),f171(A_27a,V2f,V3c,V0s)),ap(V2f,V4x))))))))))))))))) # label(ax_thm_2Eposet_2Edown__continuous__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1161 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> ((all V3c (mem(V3c,arr(A_27a,bool)) -> (all V4x (mem(V4x,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Elub(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V3c),V4x)) & p(ap(ap(c_2Eposet_2Echain(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V3c)) -> p(ap(ap(ap(c_2Eposet_2Elub(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),f171(A_27a,V2f,V3c,V0s)),ap(V2f,V4x)))))))) <-> p(ap(ap(c_2Eposet_2Eup__continuous(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2f))))))))))) # label(ax_thm_2Eposet_2Eup__continuous__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1162 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Elfp(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,A_27a),arr(A_27a,bool)))))) # label(mem_c_2Eposet_2Elfp) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1163 (all A_27a (ne(A_27a) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> ((all V1c (mem(V1c,arr(A_27a,bool)) -> (exists V3x (p(ap(ap(ap(c_2Eposet_2Eglb(A_27a),V0p),V1c),V3x)) & mem(V3x,A_27a))) & (exists V2x (p(ap(ap(ap(c_2Eposet_2Elub(A_27a),V0p),V1c),V2x)) & mem(V2x,A_27a))))) <-> p(ap(c_2Eposet_2Ecomplete(A_27a),V0p))))))) # label(ax_thm_2Eposet_2Ecomplete__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1164 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Ecomplete(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),bool)))) # label(mem_c_2Eposet_2Ecomplete) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1165 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Eposet(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),bool)))) # label(mem_c_2Eposet_2Eposet) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1166 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2p (mem(V2p,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Elub(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),f166(A_27a,V0s,V2p)),V3x)) <-> p(ap(ap(ap(c_2Eposet_2Elub(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2p),V3x))))))))))))) # label(conj_thm_2Eposet_2Elub__pred) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1167 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> V1r = ap(c_2Eposet_2Erelation(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)))))))) # label(ax_thm_2Eposet_2Erelation__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1168 (all A_27a (ne(A_27a) -> mem(c_2Eposet_2Elub(A_27a),arr(ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Eposet_2Elub) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1169 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0p (mem(V0p,ty_2Epair_2Eprod(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))) -> (all V1t (mem(V1t,arr(A_27b,bool)) -> (p(ap(c_2Eposet_2Ecomplete(A_27a),V0p)) -> p(ap(c_2Eposet_2Ecomplete(arr(A_27b,A_27a)),ap(ap(c_2Eposet_2Epointwise__lift(A_27b,A_27a),V1t),V0p)))))))))))) # label(conj_thm_2Eposet_2Ecomplete__pointwise) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1170 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eposet_2Epointwise__lift(A_27a,A_27b),arr(arr(A_27a,bool),arr(ty_2Epair_2Eprod(arr(A_27b,bool),arr(A_27b,arr(A_27b,bool))),ty_2Epair_2Eprod(arr(arr(A_27a,A_27b),bool),arr(arr(A_27a,A_27b),arr(arr(A_27a,A_27b),bool)))))))))) # label(mem_c_2Eposet_2Epointwise__lift) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1171 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(ap(c_2Eposet_2Elfp(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r)),V2f),V3x)) <-> p(ap(V0s,V3x)) & (all V4y (mem(V4y,A_27a) -> (p(ap(V0s,V4y)) & p(ap(ap(V1r,ap(V2f,V4y)),V4y)) -> p(ap(ap(V1r,V3x),V4y))))) & V3x = ap(V2f,V3x)))))))))))) # label(ax_thm_2Eposet_2Elfp__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1172 (all A_27a all V0s (mem(V0s,arr(A_27a,bool)) -> (all V3c (mem(V3c,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V5y (mem(V5y,A_27a) -> (all V6z ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2E_2F_5C,ap(V0s,V6z)),ap(V3c,V6z))),ap(ap(c_2Emin_2E_3D(A_27a),V5y),ap(V2f,V6z))) = ap(f170(A_27a,V0s,V3c,V2f,V5y),V6z)))))))))) # label(lameq_f170) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1173 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Eposet_2Eposet(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r))) -> (exists V2x (p(ap(V0s,V2x)) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Eposet_2Eposet__nonempty) # label(axiom) # label(non_clause). [assumption]. 3.15/3.80 1174 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1r (mem(V1r,arr(A_27a,arr(A_27a,bool))) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(c_2Eposet_2Eposet(A_27a),ap(ap(c_2Epair_2E_2C(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))),V0s),V1r))) & p(ap(V0s,V2x)) & p(ap(ap(V1r,V3y),V2x)) & p(ap(ap(V1r,V2x),V3y)) & p(ap(V0s,V3y)) -> V3y = V2x))))))))))) # label(conj_thm_2Eposet_2Eposet__antisym) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1175 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n))) <-> p(ap(c_2Earithmetic_2EODD,V1n)) & p(ap(c_2Earithmetic_2EODD,V0m))))))) # label(conj_thm_2Earithmetic_2EODD__MULT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1176 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n))))) # label(conj_thm_2Earithmetic_2EONE__MOD__IFF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1177 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1178 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (-p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m))))))) # label(conj_thm_2Earithmetic_2ENOT__LESS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1179 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> ((all V3q (mem(V3q,ty_2Enum_2Enum) -> (all V4r (mem(V4r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2n)) & V1m = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V2n)),V4r) -> p(ap(V0P,V3q))))))) <-> p(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,V1m),V2n))))))))))) # label(conj_thm_2Earithmetic_2EDIV__P__UNIV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1180 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = c_2Enum_2E0 <-> c_2Enum_2E0 = V0m & V1n = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EADD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1181 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V0m),V2p))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p))))))))) # label(conj_thm_2Earithmetic_2ELE__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1182 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n)))))))))) # label(conj_thm_2Earithmetic_2ELT__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1183 (all V0m (mem(V0m,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V0m) & ap(ap(c_2Earithmetic_2E_2D,V0m),c_2Enum_2E0) = V0m)) # label(conj_thm_2Earithmetic_2ESUB__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1184 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V0n),V1m) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V1m)))))) # label(conj_thm_2Earithmetic_2ESUB__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1185 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (-p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),V0m))))))) # label(conj_thm_2Earithmetic_2ENOT__LEQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1186 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (c_2Enum_2E0 != V0n <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))))) # label(conj_thm_2Earithmetic_2ENOT__ZERO__LT__ZERO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1187 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n))) <-> p(ap(c_2Earithmetic_2EEVEN,V1n)) | p(ap(c_2Earithmetic_2EEVEN,V0m))))))) # label(conj_thm_2Earithmetic_2EEVEN__MULT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1188 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EDIV2,V0n) = ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))) # label(ax_thm_2Earithmetic_2EDIV2__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1189 (all V0n (mem(V0n,ty_2Enum_2Enum) -> V0n = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),c_2Enum_2E0) & V0n = ap(ap(c_2Earithmetic_2EABS__DIFF,c_2Enum_2E0),V0n))) # label(conj_thm_2Earithmetic_2EABS__DIFF__ZERO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1190 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__ADD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1191 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V1n)),ap(V0f,ap(c_2Enum_2ESUC,V1n)))))) -> p(ap(c_2Ebool_2EONE__ONE(ty_2Enum_2Enum,ty_2Enum_2Enum),V0f))))) # label(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__ONE__ONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1192 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V1m)) & p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V0n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V2p),ap(ap(c_2Earithmetic_2EMIN,V1m),V0n)))) & (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMIN,V1m),V0n)),V2p)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V2p)) | p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V2p))))))))) # label(conj_thm_2Earithmetic_2EMIN__LT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1193 (all V0z (mem(V0z,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Earithmetic_2EEXP,V1x),V2y)),V0z) = ap(ap(c_2Earithmetic_2EEXP,V1x),ap(ap(c_2Earithmetic_2E_2A,V2y),V0z)))))))) # label(conj_thm_2Earithmetic_2EEXP__EXP__MULT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1194 (all V0n1 (mem(V0n1,ty_2Enum_2Enum) -> (all V1n2 (mem(V1n2,ty_2Enum_2Enum) -> (all V2m1 (mem(V2m1,ty_2Enum_2Enum) -> (all V3m2 (mem(V3m2,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,ap(ap(c_2Earithmetic_2E_2B,V0n1),V1n2)),ap(ap(c_2Earithmetic_2E_2B,V2m1),V3m2))),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EABS__DIFF,V0n1),V2m1)),ap(ap(c_2Earithmetic_2EABS__DIFF,V1n2),V3m2)))))))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__SUMS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1195 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V1n),V0m) = ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))))) # label(conj_thm_2Earithmetic_2EADD__SYM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1196 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = V0m | V1n = c_2Enum_2E0 <-> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMIN,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2EMIN__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1197 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),ap(ap(c_2Earithmetic_2E_2D,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) # label(conj_thm_2Earithmetic_2ESUB__LESS__OR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1198 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((exists V4x ((all V5y (mem(V5y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,V5y),V4x)) -> -p(ap(V0P,V5y))))) & p(ap(V0P,V4x)) & mem(V4x,ty_2Enum_2Enum))) <-> (exists V2x ((all V3y (mem(V3y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,V3y),V2x)) -> -p(ap(V0P,V3y))))) & mem(V2x,ty_2Enum_2Enum))) & (exists V1x (p(ap(V0P,V1x)) & mem(V1x,ty_2Enum_2Enum)))))) # label(conj_thm_2Earithmetic_2EEXISTS__GREATEST) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1199 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> ((all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V1n)) -> p(ap(V0P,V2m))))) -> p(ap(V0P,V1n))))) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(V0P,V3n))))))) # label(conj_thm_2Earithmetic_2ECOMPLETE__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1200 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2A,V0x),V1y))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1y)) | p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0x)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1y))))))) # label(conj_thm_2Earithmetic_2EONE__LT__MULT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1201 (all A_27a (ne(A_27a) -> (all V0v_27 (mem(V0v_27,A_27a) -> (all V1f_27 (mem(V1f_27,arr(ty_2Enum_2Enum,A_27a)) -> (all V2M (mem(V2M,ty_2Enum_2Enum) -> (all V3M_27 (mem(V3M_27,ty_2Enum_2Enum) -> (all V4v (mem(V4v,A_27a) -> (all V5f (mem(V5f,arr(ty_2Enum_2Enum,A_27a)) -> ((V3M_27 = c_2Enum_2E0 -> V4v = V0v_27) & (all V6n (mem(V6n,ty_2Enum_2Enum) -> (V3M_27 = ap(c_2Enum_2ESUC,V6n) -> ap(V1f_27,V6n) = ap(V5f,V6n)))) & V2M = V3M_27 -> ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V3M_27),V0v_27),V1f_27) = ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V2M),V4v),V5f)))))))))))))))) # label(conj_thm_2Earithmetic_2Enum__case__cong) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1202 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1m),V3x),V4y)) & p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V2n),V4y),V5z)) -> p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)),V3x),V5z))))))))))))))))) # label(conj_thm_2Earithmetic_2ENRC__ADD__I) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1203 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)),ap(ap(c_2Earithmetic_2E_2D,V1m),V0n)),ap(ap(c_2Earithmetic_2E_2D,V0n),V1m)))))) # label(ax_thm_2Earithmetic_2EABS__DIFF__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1204 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) <-> ap(c_2Enum_2ESUC,ap(c_2Eprim__rec_2EPRE,V0m)) = V0m))) # label(conj_thm_2Earithmetic_2ESUC__PRE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1205 (all V0m (mem(V0m,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V0m)))) # label(conj_thm_2Earithmetic_2ELESS__EQ__REFL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1206 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (V0a = c_2Enum_2E0 <-> ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n))) = c_2Enum_2E0))))))) # label(conj_thm_2Earithmetic_2Efindq__eq__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1207 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V2p))))))) # label(conj_thm_2Earithmetic_2EMULT__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1208 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Eprim__rec_2EPRE,V1m)),ap(c_2Eprim__rec_2EPRE,V0n))))))))) # label(conj_thm_2Earithmetic_2EINV__PRE__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1209 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (all V3p (mem(V3p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (ap(ap(c_2Earithmetic_2EMOD,V2b),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1a),V0n) <-> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2b),V3p)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1a),V3p)),V0n))))))))))) # label(conj_thm_2Earithmetic_2EADD__MOD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1210 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))) # label(conj_thm_2Earithmetic_2EEVEN__DOUBLE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1211 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0n),V1q)),V2m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,V2m),ap(ap(c_2Earithmetic_2E_2A,V0n),V1q))),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2m),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__SUB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1212 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0p)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1q))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0p)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1q)))))))) # label(conj_thm_2Earithmetic_2EDOUBLE__LT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1213 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Eprim__rec_2EPRE,V0m)),ap(c_2Eprim__rec_2EPRE,V1n))))))))) # label(conj_thm_2Earithmetic_2EINV__PRE__LESS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1214 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,V0m),c_2Enum_2E0)) & p(ap(ap(c_2Earithmetic_2E_3E,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3E,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__GREATER) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1215 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,V1m),ap(c_2Enum_2ESUC,V2n)) = ap(ap(c_2Earithmetic_2E_2A,V1m),ap(ap(c_2Earithmetic_2EEXP,V1m),V2n)))))) # label(ax_thm_2Earithmetic_2EEXP_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1216 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EEXP,V0m),c_2Enum_2E0))) # label(ax_thm_2Earithmetic_2EEXP_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1217 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> (V0m = V1n <-> ap(c_2Eprim__rec_2EPRE,V1n) = ap(c_2Eprim__rec_2EPRE,V0m))))))) # label(conj_thm_2Earithmetic_2EINV__PRE__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1218 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V1n),V0m)),ap(ap(c_2Earithmetic_2E_2D,V2p),V0m))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p))))))))) # label(conj_thm_2Earithmetic_2ELT__SUB__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1219 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p))))))))) # label(conj_thm_2Earithmetic_2ELESS__LESS__EQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1220 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> ((exists V3n (mem(V3n,ty_2Enum_2Enum) & p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V3n),V1x),V2y)))) <-> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Earithmetic_2ERTC__eq__NRC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1221 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2A,V1k),V0n)),V0n) = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EMOD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1222 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1n),V2x),V3y)) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2x),V3y))))))))))))) # label(conj_thm_2Earithmetic_2ENRC__RTC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1223 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EABS__DIFF,V1m),V0n) = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__SYM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1224 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p))))))))) # label(conj_thm_2Earithmetic_2ELESS__TRANS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1225 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2i (mem(V2i,ty_2Enum_2Enum) -> (all V3j (mem(V3j,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2i)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V3j)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V2i),V3j)))))))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__MULT2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1226 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1c (mem(V1c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1c)) -> ((exists V3n (mem(V3n,ty_2Enum_2Enum) & p(ap(V0P,V3n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) | p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <-> (exists V2n (mem(V2n,ty_2Enum_2Enum) & p(ap(ap(c_2Eprim__rec_2E_3C,V2n),V1c)) & p(ap(V0P,V2n)))))))))) # label(conj_thm_2Earithmetic_2EBOUNDED__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1227 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) & ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)) & V0m = ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0) & ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0m) = V0m)))) # label(conj_thm_2Earithmetic_2EADD__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1228 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V1x),ap(ap(c_2Earithmetic_2EDIV,V2r),V0n)) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V1x),V0n)),V2r)),V0n)))))))) # label(conj_thm_2Earithmetic_2EADD__DIV__ADD__DIV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1229 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Eprim__rec_2E_3C,V1m),V2n)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0a),V1m)),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f185(V0a,V1m,V2n)),ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n)))))) = ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n))))))))) # label(conj_thm_2Earithmetic_2EDIVMOD__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1230 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,ap(c_2Enum_2ESUC,V0n))) <-> -p(ap(c_2Earithmetic_2EODD,V0n))))) # label(ax_thm_2Earithmetic_2EODD_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1231 $F <-> p(ap(c_2Earithmetic_2EODD,c_2Enum_2E0)) # label(ax_thm_2Earithmetic_2EODD_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1232 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (exists V1m ((V0n = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,c_2Enum_2E0))),V1m) | V0n = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,c_2Enum_2E0))),V1m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) & mem(V1m,ty_2Enum_2Enum))))) # label(conj_thm_2Earithmetic_2EODD__OR__EVEN) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1233 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ((exists V1m (mem(V1m,ty_2Enum_2Enum) & V0n = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)))) <-> p(ap(c_2Earithmetic_2EODD,V0n))))) # label(conj_thm_2Earithmetic_2EODD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1234 (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) -> (all V4q ap(f180(V1a,V2m,V3n,V0f),V4q) = ap(V0f,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2B,V1a),V4q)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2D,V2m),ap(ap(c_2Earithmetic_2E_2A,V3n),V4q))),V3n)))))))))))) # label(lameq_f180) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1235 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n != ap(c_2Enum_2ESUC,V0m) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__SUC__EQ__COR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1236 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Eprim__rec_2EPRE,V0m)),ap(c_2Eprim__rec_2EPRE,V1n)))))))) # label(conj_thm_2Earithmetic_2EPRE__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1237 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,A_27a) -> (all V4z (mem(V4z,A_27a) -> (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)),V3x),V4z)) -> (exists V5y (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1m),V3x),V5y)) & p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V2n),V5y),V4z)) & mem(V5y,A_27a)))))))))))))))) # label(conj_thm_2Earithmetic_2ENRC__ADD__E) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1238 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x),V2y)) <-> p(ap(ap(V0R,V1x),V2y))))))))))) # label(conj_thm_2Earithmetic_2ENRC__1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1239 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Earithmetic_2EFACT,V0n))))) # label(conj_thm_2Earithmetic_2EFACT__LESS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1240 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMAX,V1m),V0n)),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2p)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V2p))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V1m)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V0n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),ap(ap(c_2Earithmetic_2EMAX,V1m),V0n)))))))))) # label(conj_thm_2Earithmetic_2EMAX__LE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1241 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EDIV,V0n),V0n) & c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V0n),V0n)))) # label(conj_thm_2Earithmetic_2EDIVMOD__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1242 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n = V0m <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2EEQ__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1243 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(c_2Enum_2ESUC,V1x)),ap(c_2Enum_2ESUC,V2y)))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__SUC__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1244 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2e (mem(V2e,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),V2e)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EEXP,V1x),V2e)),V0n)))))))) # label(conj_thm_2Earithmetic_2EEXP__MOD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1245 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2p),V0m)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n)) = ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2ELEFT__ADD__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1246 (all V0z (mem(V0z,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V1x),V0z)),ap(ap(c_2Earithmetic_2EEXP,V2y),V0z)) = ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Earithmetic_2E_2A,V1x),V2y)),V0z))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__MULT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1247 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1j (mem(V1j,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1j),V2k)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V1j),V0n)),ap(ap(c_2Earithmetic_2EMOD,V2k),V0n))),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__PLUS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1248 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0x))) & V1y = ap(ap(c_2Earithmetic_2EDIV,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0x))) <-> ap(c_2Earithmetic_2ENUMERAL,V2z) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0x))),V1y)) & (c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0x))) & V1y = ap(ap(c_2Earithmetic_2EDIV,ap(c_2Earithmetic_2ENUMERAL,V2z)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0x))) <-> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0x))),V1y) = ap(c_2Earithmetic_2ENUMERAL,V2z)))))))) # label(conj_thm_2Earithmetic_2ENUMERAL__MULT__EQ__DIV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1249 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)))))))) # label(conj_thm_2Earithmetic_2ELESS__ADD__SUC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1250 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V3d ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1m),V3d)),V0a),ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V3d)))) = ap(f179(V0a,V1m),V3d)))))) # label(lameq_f179) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1251 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),c_2Enum_2E0),V1x) = V1x)))))) # label(conj_thm_2Earithmetic_2EFUNPOW__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1252 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (-(p(ap(c_2Earithmetic_2EODD,V0m)) <-> p(ap(c_2Earithmetic_2EODD,V1n))) <-> p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EODD__ADD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1253 (all V0n (mem(V0n,ty_2Enum_2Enum) -> -(p(ap(c_2Earithmetic_2EODD,V0n)) & p(ap(c_2Earithmetic_2EEVEN,V0n))))) # label(conj_thm_2Earithmetic_2EEVEN__AND__ODD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1254 (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) -> (all V3n ap(f181(V2m,V1a,V0f),V3n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V3n),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0)),ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Eprim__rec_2E_3C,V2m),V3n)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1a),V2m)),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f180(V1a,V2m,V3n,V0f)),ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n))))))))))))) # label(lameq_f181) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1255 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> (ap(c_2Enum_2ESUC,V0m) = V1n <-> ap(c_2Eprim__rec_2EPRE,V1n) = V0m)))))) # label(conj_thm_2Earithmetic_2EPRE__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1256 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),ap(ap(c_2Earithmetic_2EEXP,V1x),V0n)))))))) # label(conj_thm_2Earithmetic_2EX__LE__X__EXP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1257 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT1,V0n) = ap(ap(c_2Earithmetic_2E_2B,V0n),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Enum_2ESUC,c_2Enum_2E0))))) # label(ax_thm_2Earithmetic_2EBIT1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1258 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n != ap(c_2Enum_2ESUC,V0m) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__NOT__SUC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1259 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x)))),V0n) = ap(ap(c_2Earithmetic_2EEXP,V0n),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) & ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x))) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1x)))),V0n)))))) # label(conj_thm_2Earithmetic_2EEXP__SUB__NUMERAL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1260 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V1n)),ap(V0f,ap(c_2Enum_2ESUC,V1n)))))) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (exists V3n (mem(V3n,ty_2Enum_2Enum) & p(ap(ap(c_2Eprim__rec_2E_3C,V2b),ap(V0f,V3n)))))))))) # label(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__UNBOUNDED) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1261 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V2r),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V1q),V0n)),V2r)),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__TIMES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1262 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = V0m -> c_2Enum_2E0 = V1n))))) # label(conj_thm_2Earithmetic_2EADD__INV__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1263 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m),V0p)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0p)) -> (V2m = V1n <-> ap(ap(c_2Earithmetic_2E_2D,V0p),V2m) = ap(ap(c_2Earithmetic_2E_2D,V0p),V1n))))))))) # label(conj_thm_2Earithmetic_2ESUB__CANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1264 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V1x)))))) # label(conj_thm_2Earithmetic_2EMODEQ__REFL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1265 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1c (mem(V1c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1c)) -> ((all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),V1c)) -> p(ap(V0P,V2n))))) <-> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3n),ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) -> p(ap(V0P,V3n))))) & p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1c),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) # label(conj_thm_2Earithmetic_2EBOUNDED__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1266 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> -p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Enum_2ESUC,V0m)))))))) # label(conj_thm_2Earithmetic_2ELESS__SUC__NOT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1267 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> ((exists V3q (p(ap(ap(c_2Eprim__rec_2E_3C,V2r),V0n)) & ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V0n)),V2r) = V1k & mem(V3q,ty_2Enum_2Enum))) -> V2r = ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1268 (all V0z (mem(V0z,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V2x),V1y)),ap(ap(c_2Earithmetic_2E_2D,V2x),V0z))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2x),V1y)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V0z),V1y))))))))) # label(conj_thm_2Earithmetic_2ELE__SUB__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1269 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2D,V0m),V1n) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ESUB__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1270 (all V0k (mem(V0k,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V0k),ap(c_2Enum_2ESUC,c_2Enum_2E0)))) # label(conj_thm_2Earithmetic_2EMOD__ONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1271 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1p)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1p),ap(ap(c_2Earithmetic_2E_2B,V0m),V2n))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V1p),V0m)),V2n)))))))))) # label(conj_thm_2Earithmetic_2ESUB__LESS__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1272 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (V2p = V1n | c_2Enum_2E0 = V0m <-> ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)))))))) # label(conj_thm_2Earithmetic_2EEQ__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1273 (all V0a (mem(V0a,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0a)),V0a) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) # label(conj_thm_2Earithmetic_2ESUC__SUB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1274 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EZERO__LESS__MULT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1275 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2k),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)))) <-> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),V2k) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),V2k)),V0n))))))))) # label(conj_thm_2Earithmetic_2EMOD__LIFT__PLUS__IFF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1276 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1y),ap(ap(c_2Earithmetic_2E_2A,V0x),V2z))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V1y),V2z)),V0x)))))))))) # label(conj_thm_2Earithmetic_2EDIV__LT__X) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1277 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT2,V0n) = ap(ap(c_2Earithmetic_2E_2B,V0n),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,c_2Enum_2E0)))))) # label(ax_thm_2Earithmetic_2EBIT2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1278 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p))))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1279 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V2n),V0p)),ap(ap(c_2Earithmetic_2EEXP,V2n),V1q)) = ap(ap(c_2Earithmetic_2EEXP,V2n),ap(ap(c_2Earithmetic_2E_2B,V0p),V1q)))))))) # label(conj_thm_2Earithmetic_2EEXP__ADD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1280 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1e0 (mem(V1e0,ty_2Enum_2Enum) -> (all V2e1 (mem(V2e1,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1e0),V2e1)) -> ap(ap(c_2Earithmetic_2EMOD,V2e1),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1e0),V0n))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__INTRO__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1281 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1y)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1y)) <-> ap(ap(c_2Earithmetic_2EMOD,V0x),V1y) = V0x)))))) # label(conj_thm_2Earithmetic_2EX__MOD__Y__EQ__X) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1282 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1y)),V1y))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__TRIANGLE__lem) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1283 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EABS__DIFF,ap(ap(c_2Earithmetic_2E_2B,V0n),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1m),V2p)) = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__ADD__SAME) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1284 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V0m),V1n)),V1n))))))) # label(conj_thm_2Earithmetic_2EMOD__LESS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1285 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V1n)),V0m))))) # label(conj_thm_2Earithmetic_2ESUC__ADD__SYM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1286 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0n),V1q)),V2m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EDIV,V2m),V0n)),V1q) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V2m),ap(ap(c_2Earithmetic_2E_2A,V0n),V1q))),V0n)))))))) # label(conj_thm_2Earithmetic_2EDIV__SUB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1287 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2b)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V2b),V1m)),ap(ap(c_2Earithmetic_2EEXP,V2b),V0n)))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1288 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1zc (mem(V1zc,A_27a) -> (all V2sc (mem(V2sc,arr(ty_2Enum_2Enum,A_27a)) -> (all V3v (mem(V3v,A_27a) -> (V1zc = V3v & V0n = c_2Enum_2E0 | (exists V4x (mem(V4x,ty_2Enum_2Enum) & V0n = ap(c_2Enum_2ESUC,V4x) & ap(V2sc,V4x) = V3v)) <-> V3v = ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V0n),V1zc),V2sc)))))))))))) # label(conj_thm_2Earithmetic_2Enum__case__eq) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1289 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) <-> -p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ENOT__LESS__EQUAL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1290 (all V0n (mem(V0n,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMIN,c_2Enum_2E0),V0n) & c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMIN,V0n),c_2Enum_2E0))) # label(conj_thm_2Earithmetic_2EMIN__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1291 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V1x),ap(ap(c_2Earithmetic_2EEXP,V0b),V1x)))))))) # label(conj_thm_2Earithmetic_2EX__LT__EXP__X) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1292 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1k),V0n)) -> V1k = ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)))))) # label(conj_thm_2Earithmetic_2ELESS__MOD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1293 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (p(ap(V0P,c_2Enum_2E0)) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(V0P,ap(c_2Enum_2ESUC,V2n))))) <-> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(V0P,V1n))))))) # label(conj_thm_2Earithmetic_2EFORALL__NUM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1294 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2A,V2n),ap(c_2Enum_2ESUC,V0p)) = ap(ap(c_2Earithmetic_2E_2A,V1m),ap(c_2Enum_2ESUC,V0p)) <-> V1m = V2n))))))) # label(conj_thm_2Earithmetic_2EMULT__SUC__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1295 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (p(ap(V0P,c_2Enum_2E0)) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(V0P,V2n)) -> p(ap(V0P,ap(c_2Enum_2ESUC,V2n)))))) <-> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(V0P,V1n))))))) # label(conj_thm_2Earithmetic_2EFORALL__NUM__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1296 (all V0c (mem(V0c,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V0c),V0c) = c_2Enum_2E0)) # label(conj_thm_2Earithmetic_2ESUB__EQUAL__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1297 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V0m)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V1i))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1i))))))))) # label(conj_thm_2Earithmetic_2ELESS__MULT__MONO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1298 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(V0P,V2n)) & p(ap(V0P,V1m)) -> p(ap(V0P,ap(ap(c_2Earithmetic_2EMIN,V1m),V2n))) & p(ap(V0P,ap(ap(c_2Earithmetic_2EMAX,V1m),V2n)))))))))) # label(conj_thm_2Earithmetic_2EMIN__MAX__PRED) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1299 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMAX,V0m),V1n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)),V1n),V0m))))) # label(ax_thm_2Earithmetic_2EMAX__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1300 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2E_2B,V1y),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),V1y))))))) # label(conj_thm_2Earithmetic_2ELE__LT1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1301 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1y)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0x)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2EEXP,V0x),V1y)))))))) # label(conj_thm_2Earithmetic_2EONE__LT__EXP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1302 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELT__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1303 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> -(p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Enum_2ESUC,V0m))) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1304 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (-p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) <-> V0n = c_2Enum_2E0))) # label(conj_thm_2Earithmetic_2ENOT__LT__ZERO__EQ__ZERO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1305 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EFACT,ap(c_2Enum_2ESUC,V0n)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0n)),ap(c_2Earithmetic_2EFACT,V0n)))) # label(ax_thm_2Earithmetic_2EFACT_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1306 (all V0n (mem(V0n,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V0n))) # label(conj_thm_2Earithmetic_2EABS__DIFF__EQS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1307 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)),V0m),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__SUB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1308 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1309 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2A,V1q),V0n)),V0n) = V1q))))) # label(conj_thm_2Earithmetic_2EMULT__DIV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1310 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EMOD,V2p),V0n) = c_2Enum_2E0 | c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V1m),V0n) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EDIV,V1m),V0n)),ap(ap(c_2Earithmetic_2EDIV,V2p),V0n)) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,V1m),V2p)),V0n))))))))) # label(conj_thm_2Earithmetic_2EADD__DIV__RWT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1311 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)),V0m),V1n) = ap(ap(c_2Earithmetic_2EMIN,V0m),V1n))))) # label(ax_thm_2Earithmetic_2EMIN__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1312 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1n)),V0m))))))) # label(conj_thm_2Earithmetic_2EZERO__LESS__EXP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1313 (all V5m (mem(V5m,ty_2Enum_2Enum) -> (all V3f (mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) -> (all V4a (mem(V4a,ty_2Enum_2Enum) -> (all V6n ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V6n),c_2Enum_2E0)),V4a),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f174(V3f,V5m,V4a)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V6n))) = ap(f175(V5m,V3f,V4a),V6n)))))))) # label(lameq_f175) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1314 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__CASES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1315 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) -> (exists V2p (mem(V2p,ty_2Enum_2Enum) & V0m = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V2p)),V1n)))))))) # label(conj_thm_2Earithmetic_2ELESS__STRONG__ADD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1316 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) <-> (exists V2p (ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = V1n & mem(V2p,ty_2Enum_2Enum)))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__EXISTS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1317 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> ((exists V4z (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1n),V2x),V4z)) & p(ap(ap(V0R,V4z),V3y)) & mem(V4z,A_27a))) <-> p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(c_2Enum_2ESUC,V1n)),V2x),V3y))))))))))))) # label(conj_thm_2Earithmetic_2ENRC__SUC__RECURSE__LEFT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1318 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (p(ap(c_2Ebool_2EONE__ONE(ty_2Enum_2Enum,ty_2Enum_2Enum),V0f)) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (exists V2n (p(ap(ap(c_2Eprim__rec_2E_3C,V1b),ap(V0f,V2n))) & mem(V2n,ty_2Enum_2Enum)))))))) # label(conj_thm_2Earithmetic_2EONE__ONE__UNBOUNDED) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1319 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(c_2Earithmetic_2EEVEN,V0m)) -> p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2EEXP,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EEVEN__EXP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1320 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (V0m = V1n <-> ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))) # label(conj_thm_2Earithmetic_2EEQ__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1321 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1c (mem(V1c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1c),V0b)) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V2a),ap(ap(c_2Earithmetic_2E_2D,V0b),V1c)) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V2a),V1c)),V0b)))))))) # label(conj_thm_2Earithmetic_2ESUB__SUB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1322 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EEVEN,V0n)) <-> (exists V1m (mem(V1m,ty_2Enum_2Enum) & ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m) = V0n))))) # label(conj_thm_2Earithmetic_2EEVEN__EXISTS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1323 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,V0m) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EADD1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1324 (all V0n (mem(V0n,ty_2Enum_2Enum) -> -p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),c_2Enum_2E0)))) # label(conj_thm_2Earithmetic_2ENOT__SUC__LESS__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1325 (all A_27a (ne(A_27a) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3v (mem(V3v,A_27a) -> (all V4f (mem(V4f,arr(ty_2Enum_2Enum,A_27a)) -> ap(V4f,V2n) = ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),ap(c_2Enum_2ESUC,V2n)),V3v),V4f))))))) & (all V0v (mem(V0v,A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),c_2Enum_2E0),V0v),V1f) = V0v)))))) # label(ax_thm_2Earithmetic_2Enum__case__def) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1326 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),V1n)) <-> V0m = V1n | p(ap(ap(c_2Earithmetic_2E_3E,V0m),V1n))))))) # label(ax_thm_2Earithmetic_2EGREATER__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1327 (all V1m f172(V1m) = ap(f173,V1m)) # label(lameq_f173) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1328 (all A_27a (ne(A_27a) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4x (mem(V4x,A_27a) -> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V2f),ap(c_2Enum_2ESUC,V3n)),V4x) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V2f),V3n),ap(V2f,V4x)))))))) & (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),c_2Enum_2E0),V1x) = V1x)))))) # label(ax_thm_2Earithmetic_2EFUNPOW) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1329 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1330 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2Enat__elim____magic,V0n) = V0n)) # label(ax_thm_2Earithmetic_2Enat__elim____magic) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1331 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1z (mem(V1z,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1z)),ap(ap(c_2Earithmetic_2E_2B,V0x),V1z))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__LE__SUM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1332 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) <-> -p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ENOT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1333 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)))))))))) # label(conj_thm_2Earithmetic_2EADD__MONO__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1334 (all V0k (mem(V0k,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> (exists V2r (mem(V2r,ty_2Enum_2Enum) & (exists V3q (V0k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V1n)),V2r) & p(ap(ap(c_2Eprim__rec_2E_3C,V2r),V1n)) & mem(V3q,ty_2Enum_2Enum)))))))))) # label(conj_thm_2Earithmetic_2EDA) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1335 (all V0m (mem(V0m,ty_2Enum_2Enum) -> V0m = ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EMULT__RIGHT__1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1336 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V3z (mem(V3z,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V2y),V3z)) & p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V3z))))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1337 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EMULT__INCREASES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1338 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EDIV,V1y),V2z)),V0x)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V1y),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2z))))))))))) # label(conj_thm_2Earithmetic_2EDIV__LE__X) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1339 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) | p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),V2p))))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1340 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,V0x) = V0x)) # label(ax_thm_2Earithmetic_2ENUMERAL__DEF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1341 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0p),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0p),V2m)) -> (V1n = V2m <-> ap(ap(c_2Earithmetic_2E_2D,V1n),V0p) = ap(ap(c_2Earithmetic_2E_2D,V2m),V0p))))))))) # label(conj_thm_2Earithmetic_2ECANCEL__SUB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1342 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),c_2Enum_2E0)) <-> c_2Enum_2E0 = V0n))) # label(conj_thm_2Earithmetic_2ELESS__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1343 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m))) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n)))))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m))) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n)))))) & (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m))) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n)))))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V0n)),ap(c_2Earithmetic_2ENUMERAL,V1m))) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1m))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n)))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__NUMERAL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1344 (all V3f (mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) -> (all V5m (mem(V5m,ty_2Enum_2Enum) -> (all V4a (mem(V4a,ty_2Enum_2Enum) -> (all V7d ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V5m),V7d)),V4a),ap(V3f,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V4a)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V5m),V7d)))) = ap(f174(V3f,V5m,V4a),V7d)))))))) # label(lameq_f174) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1345 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3m (mem(V3m,ty_2Enum_2Enum) -> (V3m = V2n <-> ap(ap(c_2Earithmetic_2E_2A,V3m),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1q)),V0p)) = ap(ap(c_2Earithmetic_2E_2A,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1q)),V0p))))))))))) # label(conj_thm_2Earithmetic_2EMULT__EXP__MONO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1346 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V0n)))) # label(conj_thm_2Earithmetic_2EZERO__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1347 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0x),c_2Enum_2E0)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0) = ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),V0x))) # label(conj_thm_2Earithmetic_2EZERO__EXP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1348 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> -(all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,ap(c_2Enum_2ESUC,V1n))),ap(V0f,V1n))))))) # label(conj_thm_2Earithmetic_2ENOT__STRICTLY__DECREASING) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1349 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V2p)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V2p))))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__LESS__TRANS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1350 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x)) -> (ap(ap(c_2Earithmetic_2EMOD,V2z),V0x) = c_2Enum_2E0 & ap(ap(c_2Earithmetic_2EDIV,V2z),V0x) = V1y <-> ap(ap(c_2Earithmetic_2E_2A,V0x),V1y) = V2z)))))))) # label(conj_thm_2Earithmetic_2EMULT__EQ__DIV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1351 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V0n),c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EMODEQ__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.81 1352 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0y)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMOD,V1x),V0y)),V1x))))))) # label(conj_thm_2Earithmetic_2EMOD__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1353 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (V0n = c_2Enum_2E0 | p(ap(c_2Earithmetic_2EODD,V1m)) <-> p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2EEXP,V1m),V0n)))))))) # label(conj_thm_2Earithmetic_2EODD__EXP__IFF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1354 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,V0n)) -> (exists V2m (mem(V2m,ty_2Enum_2Enum) & V0n = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2m))))) & (p(ap(c_2Earithmetic_2EEVEN,V0n)) -> (exists V1m (mem(V1m,ty_2Enum_2Enum) & V0n = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)))))) # label(conj_thm_2Earithmetic_2EEVEN__ODD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1355 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__ADD__INV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1356 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (V1y = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) & ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = V0x <-> ap(ap(c_2Earithmetic_2E_2A,V0x),V1y) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) # label(conj_thm_2Earithmetic_2EMULT__EQ__1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1357 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V0m),V2p))) <-> c_2Enum_2E0 = V0m | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p))))))))) # label(conj_thm_2Earithmetic_2ELE__MULT__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1358 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V2a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V0n)))),V0n)),ap(ap(c_2Earithmetic_2E_2A,V2a),V1m)))))))))) # label(conj_thm_2Earithmetic_2Efindq__divisor) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1359 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V0n),V1x)),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)))))) # label(conj_thm_2Earithmetic_2EADD__MODULUS__RIGHT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1360 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,A_27a) -> (all V4z (mem(V4z,A_27a) -> ((exists V5y (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V1m),V3x),V5y)) & p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V2n),V5y),V4z)) & mem(V5y,A_27a))) <-> p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)),V3x),V4z))))))))))))))) # label(conj_thm_2Earithmetic_2ENRC__ADD__EQN) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1361 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3E_3D,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__GREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1362 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2EOR__LESS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1363 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,V1a),V0n)),ap(ap(c_2Earithmetic_2EEXP,V2b),V0n))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V1a),V2b)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n))))))))) # label(conj_thm_2Earithmetic_2EEXP__EXP__LT__MONO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1364 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ((p(ap(c_2Earithmetic_2EEVEN,V0m)) <-> p(ap(c_2Earithmetic_2EEVEN,V1n))) <-> p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EEVEN__ADD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1365 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n = ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) <-> c_2Enum_2E0 = V1n | V0m = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) # label(conj_thm_2Earithmetic_2EMULT__EQ__ID) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1366 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,V1m))),V0n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,V1m))),ap(c_2Enum_2ESUC,V0n)))))))) # label(conj_thm_2Earithmetic_2ELESS__EXP__SUC__MONO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1367 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n))) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__REV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1368 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),V2y)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EDIV,V1x),V0n)),ap(ap(c_2Earithmetic_2EDIV,V2y),V0n)))))))))) # label(conj_thm_2Earithmetic_2EDIV__LE__MONOTONE) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1369 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)))))))) # label(conj_thm_2Earithmetic_2ERIGHT__SUB__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1370 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (-p(ap(ap(c_2Earithmetic_2E_3E,V0m),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ENOT__GREATER) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1371 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1a),V2b))) <-> (all V3d (mem(V3d,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2B,V2b),V3d) = V1a -> p(ap(V0P,V3d))) & (V2b = ap(ap(c_2Earithmetic_2E_2B,V1a),V3d) -> p(ap(V0P,c_2Enum_2E0)))))))))))) # label(conj_thm_2Earithmetic_2ESUB__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1372 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),V0a),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f179(V0a,V1m)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2n))))))))) # label(conj_thm_2Earithmetic_2Efindq__thm) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1373 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V1n),V0m))))) # label(conj_thm_2Earithmetic_2EADD__COMM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1374 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p))))))) # label(conj_thm_2Earithmetic_2ERIGHT__ADD__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1375 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2A,V1n),V0m) = ap(ap(c_2Earithmetic_2E_2A,V2p),V0m) <-> V0m = c_2Enum_2E0 | V1n = V2p))))))) # label(conj_thm_2Earithmetic_2EEQ__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1376 (all V0m1 (mem(V0m1,ty_2Enum_2Enum) -> (all V1m2 (mem(V1m2,ty_2Enum_2Enum) -> (V0m1 = V1m2 <-> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,c_2Enum_2E0),V0m1),V1m2))))))) # label(conj_thm_2Earithmetic_2EMODEQ__0__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1377 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0p)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1q)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2A,V0p),V1q)))))))) # label(conj_thm_2Earithmetic_2EONE__LT__MULT__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1378 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n ap(ap(c_2Earithmetic_2E_2D,V1m),V2n) = ap(f172(V1m),V2n)))) # label(lameq_f172) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1379 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((exists V1n (p(ap(V0P,V1n)) & mem(V1n,ty_2Enum_2Enum))) -> (exists V2n (mem(V2n,ty_2Enum_2Enum) & p(ap(V0P,V2n)) & (all V3m (mem(V3m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3m),V2n)) -> -p(ap(V0P,V3m)))))))))) # label(conj_thm_2Earithmetic_2EWOP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1380 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))) # label(conj_thm_2Earithmetic_2EADD__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1381 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2B,V1n),V2p) = ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) <-> V0m = V1n))))))) # label(conj_thm_2Earithmetic_2EEQ__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1382 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELT__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1383 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2ELESS__CASES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1384 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,A_27a) -> ap(V0f,ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),V1n),V2x)) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Enum_2ESUC,V1n)),V2x))))))))) # label(conj_thm_2Earithmetic_2EFUNPOW__SUC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1385 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2A,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__MULT) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1386 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Eprim__rec_2Emeasure(A_27a),V0f))))))) # label(conj_thm_2Earithmetic_2Etransitive__measure) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1387 (all A_27a (ne(A_27a) -> mem(c_2Earithmetic_2ENRC(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(ty_2Enum_2Enum,arr(A_27a,arr(A_27a,bool))))))) # label(mem_c_2Earithmetic_2ENRC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1388 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EEVEN,ap(c_2Enum_2ESUC,V0n))) <-> -p(ap(c_2Earithmetic_2EEVEN,V0n))))) # label(ax_thm_2Earithmetic_2EEVEN_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1389 $T <-> p(ap(c_2Earithmetic_2EEVEN,c_2Enum_2E0)) # label(ax_thm_2Earithmetic_2EEVEN_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1390 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EEVEN,V0n)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EMOD__2) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1391 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = V0b | p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n)) | p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1m)) & c_2Enum_2E0 = V0b | V2n = c_2Enum_2E0 & V0b = c_2Enum_2E0 <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0b),V1m)),ap(ap(c_2Earithmetic_2EEXP,V0b),V2n)))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__LE__IFF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1392 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V0n) = c_2Enum_2E0)) # label(ax_thm_2Earithmetic_2EMULT_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1393 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V1m)),V2n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V1m),V2n)),V2n))))) # label(ax_thm_2Earithmetic_2EMULT_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1394 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((exists V1n (p(ap(V0P,V1n)) & mem(V1n,ty_2Enum_2Enum))) <-> (exists V2m (mem(V2m,ty_2Enum_2Enum) & p(ap(V0P,ap(c_2Enum_2ESUC,V2m))))) | p(ap(V0P,c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EEXISTS__NUM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1395 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2b)),V0m)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2b)),V1n)))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__LEQ__MONO__SUC__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1396 (all V0q (mem(V0q,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,V0q),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0q)) # label(conj_thm_2Earithmetic_2EDIV__1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1397 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),ap(ap(c_2Earithmetic_2EDIV,V1y),V2z))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0x),V2z)),V1y)))))))))) # label(conj_thm_2Earithmetic_2EX__LE__DIV) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1398 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ((exists V2d (V1k = ap(ap(c_2Earithmetic_2E_2A,V2d),V0n) & mem(V2d,ty_2Enum_2Enum))) <-> ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) = c_2Enum_2E0)))))) # label(conj_thm_2Earithmetic_2EMOD__EQ__0__DIVISOR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1399 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EABS__DIFF,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V1m)) = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__SUC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1400 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3E,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__GREATER) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1401 (all A_27a (ne(A_27a) -> (all V3R (mem(V3R,arr(A_27a,arr(A_27a,bool))) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (all V5x (mem(V5x,A_27a) -> (all V6y (mem(V6y,A_27a) -> (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V3R),ap(c_2Enum_2ESUC,V4n)),V5x),V6y)) <-> (exists V7z (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V3R),V4n),V7z),V6y)) & p(ap(ap(V3R,V5x),V7z)) & mem(V7z,A_27a)))))))))))) & (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V1x = V2y <-> p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),c_2Enum_2E0),V1x),V2y))))))))))) # label(ax_thm_2Earithmetic_2ENRC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1402 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) -> (ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = V2p <-> V0m = ap(ap(c_2Earithmetic_2E_2D,V2p),V1n))))))))) # label(conj_thm_2Earithmetic_2EADD__EQ__SUB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1403 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = V1n <-> ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = V0m))))) # label(conj_thm_2Earithmetic_2EADD__INV__0__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1404 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = V1n | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(ax_thm_2Earithmetic_2ELESS__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1405 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (-p(ap(c_2Earithmetic_2EODD,V0n)) <-> p(ap(c_2Earithmetic_2EEVEN,V0n))))) # label(conj_thm_2Earithmetic_2EEVEN__ODD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1406 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) -> V1m = V0n))))) # label(conj_thm_2Earithmetic_2ELESS__EQUAL__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1407 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (-p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) & V0m != V1n -> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m))))))) # label(conj_thm_2Earithmetic_2ELESS__CASES__IMP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1408 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EONE__MOD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1409 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0r),V1n)) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EDIV,V0r),V1n)))))) # label(conj_thm_2Earithmetic_2ELESS__DIV__EQ__ZERO) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1410 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V1n)),ap(V0f,ap(c_2Enum_2ESUC,V1n)))))) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V3n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(V0f,V2m)),ap(V0f,V3n))))))))))) # label(conj_thm_2Earithmetic_2ESTRICTLY__INCREASING__TC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1411 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),c_2Enum_2E0),V1x),V2y)) <-> V2y = V1x))))))))) # label(conj_thm_2Earithmetic_2ENRC__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1412 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__OR) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1413 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),V2m),ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),V3n),V1x)) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(ap(c_2Earithmetic_2E_2B,V2m),V3n)),V1x))))))))))) # label(conj_thm_2Earithmetic_2EFUNPOW__ADD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1414 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),V1n)))) = ap(ap(c_2Earithmetic_2EDIV,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2EDIVMOD__CALC_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1415 (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V3n)) -> ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Enum_2E0),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),V3n)))) = ap(ap(c_2Earithmetic_2EMOD,V2m),V3n)))))) # label(conj_thm_2Earithmetic_2EDIVMOD__CALC_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1416 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> V1k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EDIV,V1k),V0n)),V0n)),ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)),V0n))))))) # label(ax_thm_2Earithmetic_2EDIVISION) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1417 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Eprim__rec_2EPRE,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Eprim__rec_2EPRE,V0m)),V1n))))) # label(conj_thm_2Earithmetic_2EPRE__SUB) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1418 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) & ap(ap(c_2Earithmetic_2EEXP,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0n)) # label(conj_thm_2Earithmetic_2EEXP__1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1419 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EDIV,V1k),V0n)),V1k))))))) # label(conj_thm_2Earithmetic_2EDIV__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1420 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__MONO__ADD__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1421 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(V0P,ap(c_2Enum_2ESUC,V1n)),V1n)))) <-> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> p(ap(ap(V0P,V2n),ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) # label(conj_thm_2Earithmetic_2ESUC__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1422 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> ((all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(V0R,ap(V1f,V2n)),ap(V1f,ap(c_2Enum_2ESUC,V2n)))))) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R)) -> (all V3m (mem(V3m,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3m),V4n)) -> p(ap(ap(V0R,ap(V1f,V3m)),ap(V1f,V4n))))))))))))))) # label(conj_thm_2Earithmetic_2Etransitive__monotone) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1423 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1k),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2EMOD,V2x),V0n)))) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V2x),V0n)),V1k) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2x),V1k)),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__LIFT__PLUS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1424 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) <-> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = V0m & V1n = c_2Enum_2E0 | V1n = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) & c_2Enum_2E0 = V0m))))) # label(conj_thm_2Earithmetic_2EADD__EQ__1) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1425 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2D,V0n),V1m))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n))))))) # label(conj_thm_2Earithmetic_2ESUB__LESS__0) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1426 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> (exists V2p (ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) = V1n & mem(V2p,ty_2Enum_2Enum)))))))) # label(conj_thm_2Earithmetic_2ELESS__EQUAL__ADD) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1427 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> V1n = V0m | p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) | p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)))))) # label(conj_thm_2Earithmetic_2ELESS__LESS__CASES) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1428 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2q)) -> ((exists V3k ((exists V4r (ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3k),V2q)),V4r) = V1p & p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2q)) & p(ap(V0P,V4r)) & mem(V4r,ty_2Enum_2Enum))) & mem(V3k,ty_2Enum_2Enum))) <-> p(ap(V0P,ap(ap(c_2Earithmetic_2EMOD,V1p),V2q))))))))))) # label(conj_thm_2Earithmetic_2EMOD__P) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1429 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & p(ap(c_2Earithmetic_2EEVEN,V1m)) <-> p(ap(c_2Earithmetic_2EEVEN,ap(ap(c_2Earithmetic_2EEXP,V1m),V0n)))))))) # label(conj_thm_2Earithmetic_2EEVEN__EXP__IFF) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1430 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),V0n)),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)))))) # label(conj_thm_2Earithmetic_2EADD__MODULUS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1431 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3x (mem(V3x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2n),V3x)),V2n) = ap(ap(c_2Earithmetic_2EMOD,V3x),V2n)))))) # label(conj_thm_2Earithmetic_2EADD__MODULUS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1432 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x0 (mem(V1x0,ty_2Enum_2Enum) -> (all V2x1 (mem(V2x1,ty_2Enum_2Enum) -> (all V3y0 (mem(V3y0,ty_2Enum_2Enum) -> (all V4y1 (mem(V4y1,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x0),V2x1)) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V3y0),V4y1)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2E_2A,V1x0),V3y0)),ap(ap(c_2Earithmetic_2E_2A,V2x1),V4y1))))))))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__MULT__CONG) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1433 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (V0m = ap(ap(c_2Earithmetic_2E_2D,V1n),V2p) <-> V1n = ap(ap(c_2Earithmetic_2E_2B,V0m),V2p) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),c_2Enum_2E0))))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__EQ) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1434 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)),ap(c_2Enum_2ESUC,c_2Enum_2E0)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0m)),V1n)))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__SUC) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1435 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EEXP,V0x),V1y))) <-> c_2Enum_2E0 = V1y | p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x))))))) # label(conj_thm_2Earithmetic_2EZERO__LT__EXP) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1436 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) -> (exists V2p (mem(V2p,ty_2Enum_2Enum) & V0m = ap(ap(c_2Earithmetic_2E_2B,V2p),V1n)))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__ADD__EXISTS) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1437 (all V0z (mem(V0z,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V2x),V1y)),ap(ap(c_2Earithmetic_2E_2D,V2x),V0z))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0z),V2x)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0z),V1y))))))))) # label(conj_thm_2Earithmetic_2ELT__SUB__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1438 (all V3f ap(f178,V3f) = ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Enum_2Enum),f177(V3f))) # label(lameq_f178) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1439 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(V0P,ap(c_2Eprim__rec_2EPRE,V1n))) <-> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (V1n = c_2Enum_2E0 -> p(ap(V0P,c_2Enum_2E0))) & (V1n = ap(c_2Enum_2ESUC,V2m) -> p(ap(V0P,V2m)))))))))) # label(conj_thm_2Earithmetic_2EPRE__ELIM__THM) # label(axiom) # label(non_clause). [assumption]. 3.15/3.82 1440 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V1n),V0m)),ap(ap(c_2Earithmetic_2E_2B,V2p),V0m))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p))))))))) # label(conj_thm_2Earithmetic_2ELE__ADD__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1441 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V1n) = V0m))))) # label(conj_thm_2Earithmetic_2ESUB__ADD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1442 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2z)),V1y)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2EDIV,V1y),V2z))))))))))) # label(conj_thm_2Earithmetic_2EX__LT__DIV) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1443 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p))))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1444 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,V1x),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),V0n)),V0n)))))) # label(conj_thm_2Earithmetic_2EADD__MODULUS__LEFT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1445 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1c (mem(V1c,ty_2Enum_2Enum) -> V0a = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0a),V1c)),V1c))))) # label(conj_thm_2Earithmetic_2EADD__SUB) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1446 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V1k),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EMOD,V1k),V0n)),V0n)))))) # label(conj_thm_2Earithmetic_2EMOD__MOD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1447 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V3e (mem(V3e,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2EEXP,V1x),V3e)),ap(ap(c_2Earithmetic_2EEXP,V2y),V3e)))))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__EXP__CONG) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1448 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),V1x))))))) # label(conj_thm_2Earithmetic_2EMODEQ__MOD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1449 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2q)) -> ((exists V3k ((exists V4r (mem(V4r,ty_2Enum_2Enum) & p(ap(V0P,V3k)) & p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2q)) & V1p = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3k),V2q)),V4r))) & mem(V3k,ty_2Enum_2Enum))) <-> p(ap(V0P,ap(ap(c_2Earithmetic_2EDIV,V1p),V2q))))))))))) # label(conj_thm_2Earithmetic_2EDIV__P) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1450 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMIN,V0m),V1n)),ap(ap(c_2Earithmetic_2EMAX,V0m),V1n))) <-> V1n != V0m))))) # label(conj_thm_2Earithmetic_2EMIN__MAX__LT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1451 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Enum_2ESUC,V1m)))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__IMP__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1452 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) <-> V1n = c_2Enum_2E0 | V0m = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EMULT__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1453 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,A_27a) -> (all V1g (mem(V1g,arr(ty_2Enum_2Enum,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Earithmetic_2Enum__CASE(A_27a),V2n),V0f),V1g) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),V0f),ap(V1g,ap(c_2Eprim__rec_2EPRE,V2n))))))))))) # label(conj_thm_2Earithmetic_2Enum__case__compute) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1454 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(ap(c_2Earithmetic_2E_2B,V1m),V2p)))))))))) # label(conj_thm_2Earithmetic_2ELESS__IMP__LESS__ADD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1455 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1j (mem(V1j,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EMOD,V1j),V0n)),ap(ap(c_2Earithmetic_2EMOD,V2k),V0n))),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2A,V1j),V2k)),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__TIMES2) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1456 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2q)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2A,V0n),V1p)),ap(ap(c_2Earithmetic_2E_2A,V0n),V2q)) = ap(ap(c_2Earithmetic_2E_2A,V0n),ap(ap(c_2Earithmetic_2EMOD,V1p),V2q))))))))) # label(conj_thm_2Earithmetic_2EMOD__COMMON__FACTOR) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1457 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0m))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0m))))))))) # label(conj_thm_2Earithmetic_2EEXP2__LT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1458 (all A_27a (ne(A_27a) -> mem(c_2Earithmetic_2EFUNPOW(A_27a),arr(arr(A_27a,A_27a),arr(ty_2Enum_2Enum,arr(A_27a,A_27a)))))) # label(mem_c_2Earithmetic_2EFUNPOW) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1459 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1q)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2r),V0n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,V1q),V0n)),V2r)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,V0n),V2r)),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__TIMES__SUB) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1460 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EDIV,c_2Enum_2E0),V0n)))) # label(conj_thm_2Earithmetic_2EZERO__DIV) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1461 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m) <-> V1m = V0n))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1462 (all V0m (mem(V0m,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2A,V0m),c_2Enum_2E0))) # label(conj_thm_2Earithmetic_2EMULT__0) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1463 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V2y),V1x)) <-> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x),V2y))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__SYM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1464 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1d (mem(V1d,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1d)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V0n),V1d)),V0n))))))) # label(conj_thm_2Earithmetic_2EDIV__LESS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1465 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V1n),V0m) = ap(ap(c_2Earithmetic_2E_2A,V0m),V1n))))) # label(conj_thm_2Earithmetic_2EMULT__COMM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1466 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (all V3q (mem(V3q,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V3q)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2B,V2p),V3q)))))))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__LESS__EQ__MONO) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1467 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1z (mem(V1z,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),ap(ap(c_2Earithmetic_2E_2B,V2y),V1z))),ap(ap(c_2Earithmetic_2E_2B,V2y),ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1z)))))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__PLUS__LE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1468 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) | (exists V2p (mem(V2p,ty_2Enum_2Enum) & V0n = ap(ap(c_2Earithmetic_2E_2B,V2p),V1m))))))) # label(conj_thm_2Earithmetic_2ELESS__OR__EQ__ADD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1469 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,V0n) != c_2Enum_2E0)) # label(conj_thm_2Earithmetic_2ESUC__NOT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1470 (all V0n (mem(V0n,ty_2Enum_2Enum) -> V0n = ap(ap(c_2Earithmetic_2EMAX,V0n),c_2Enum_2E0) & V0n = ap(ap(c_2Earithmetic_2EMAX,c_2Enum_2E0),V0n))) # label(conj_thm_2Earithmetic_2EMAX__0) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1471 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (V1n = V2p <-> ap(ap(c_2Earithmetic_2E_2B,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)))))))) # label(conj_thm_2Earithmetic_2EEQ__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1472 (all V3f (mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) -> (all V4a ap(f177(V3f),V4a) = ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Enum_2Enum,ty_2Enum_2Enum),f176(V3f,V4a))))) # label(lameq_f177) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1473 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (exists V2m (mem(V2m,ty_2Enum_2Enum) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),ap(ap(c_2Earithmetic_2EEXP,V0b),V2m)))))))))) # label(conj_thm_2Earithmetic_2EEXP__ALWAYS__BIG__ENOUGH) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1474 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)),V2p),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__ADD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1475 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMIN,V0m),ap(ap(c_2Earithmetic_2EMIN,V1n),V2p)) = ap(ap(c_2Earithmetic_2EMIN,ap(ap(c_2Earithmetic_2EMIN,V0m),V1n)),V2p))))))) # label(conj_thm_2Earithmetic_2EMIN__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1476 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> -(p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1477 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> -p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))),V0m)))))) # label(conj_thm_2Earithmetic_2ENOT__SUC__ADD__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1478 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (-p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),V1m)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n))))))) # label(conj_thm_2Earithmetic_2ENOT__SUC__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1479 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) | p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m))))))) # label(conj_thm_2Earithmetic_2EZERO__LESS__ADD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1480 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V1n)),V0m) != c_2Enum_2E0)))) # label(conj_thm_2Earithmetic_2ENOT__EXP__0) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1481 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V1n),V0m)),ap(ap(c_2Earithmetic_2E_2D,V2p),V0m))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p))))))))) # label(conj_thm_2Earithmetic_2ELE__SUB__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1482 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p) = ap(ap(c_2Earithmetic_2E_2D,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p)))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__SUB) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1483 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,V0b),V2m)),ap(ap(c_2Earithmetic_2EEXP,V0b),V1n))))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__LT__MONO) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1484 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0n),V0n) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))) # label(conj_thm_2Earithmetic_2ETIMES2) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1485 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1m)) & V0n = c_2Enum_2E0 <-> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EEXP,V0n),V1m)))))) # label(conj_thm_2Earithmetic_2EEXP__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1486 (all V0k (mem(V0k,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V0k),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2EMOD__1) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1487 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMAX,V0m),ap(ap(c_2Earithmetic_2EMAX,V1n),V2p)) = ap(ap(c_2Earithmetic_2EMAX,ap(ap(c_2Earithmetic_2EMAX,V0m),V1n)),V2p))))))) # label(conj_thm_2Earithmetic_2EMAX__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1488 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (p(ap(c_2Ebool_2EONE__ONE(ty_2Enum_2Enum,ty_2Enum_2Enum),V0f)) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (exists V2a (mem(V2a,ty_2Enum_2Enum) & (all V3x (mem(V3x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V0f,V3x)),V1b)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V3x),V2a)))))))))))) # label(conj_thm_2Earithmetic_2EONE__ONE__INV__IMAGE__BOUNDED) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1489 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(c_2Earithmetic_2EEVEN,V0n)) | p(ap(c_2Earithmetic_2EODD,V0n)))) # label(conj_thm_2Earithmetic_2EEVEN__OR__ODD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1490 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> ap(ap(c_2Earithmetic_2EMOD,V0m),V1n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V1n)))))) # label(conj_thm_2Earithmetic_2ESUB__MOD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1491 (all V0q (mem(V0q,ty_2Enum_2Enum) -> V0q = ap(ap(c_2Earithmetic_2EDIV,V0q),ap(c_2Enum_2ESUC,c_2Enum_2E0)))) # label(conj_thm_2Earithmetic_2EDIV__ONE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1492 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (V1m = c_2Enum_2E0 | ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = V0n <-> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EEXP,V0n),V1m)))))) # label(conj_thm_2Earithmetic_2EEXP__EQ__1) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1493 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> ((all V3q (mem(V3q,ty_2Enum_2Enum) -> (all V4r (mem(V4r,ty_2Enum_2Enum) -> (V1m = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V2n)),V4r) & p(ap(ap(c_2Eprim__rec_2E_3C,V4r),V2n)) -> p(ap(V0P,V4r))))))) <-> p(ap(V0P,ap(ap(c_2Earithmetic_2EMOD,V1m),V2n))))))))))) # label(conj_thm_2Earithmetic_2EMOD__P__UNIV) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1494 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1n)),V0m)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0m)),V1n)) <-> V1n != V0m))))) # label(conj_thm_2Earithmetic_2ENOT__NUM__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1495 (all V3f (mem(V3f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Enum_2Enum)) -> (all V4a (mem(V4a,ty_2Enum_2Enum) -> (all V5m ap(f176(V3f,V4a),V5m) = f175(V5m,V3f,V4a)))))) # label(lameq_f176) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1496 (all V0f ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f183(V0f)) = ap(f184,V0f)) # label(lameq_f184) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1497 (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) -> (all V1a ap(c_2Epair_2EUNCURRY(ty_2Enum_2Enum,ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f182(V1a,V0f)) = ap(f183(V0f),V1a)))) # label(lameq_f183) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1498 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V2p)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V1n),V2p))) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2p))))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__LESS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1499 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1q (mem(V1q,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1q),V0p)) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EEXP,V2n),V0p)),ap(ap(c_2Earithmetic_2EEXP,V2n),V1q)) = ap(ap(c_2Earithmetic_2EEXP,V2n),ap(ap(c_2Earithmetic_2E_2D,V0p),V1q))))))))) # label(conj_thm_2Earithmetic_2EEXP__SUB) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1500 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMIN,V0n),V0n) = V0n)) # label(conj_thm_2Earithmetic_2EMIN__IDEM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1501 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMIN,V1m),V0n)),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2p)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V2p))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),ap(ap(c_2Earithmetic_2EMIN,V1m),V0n))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V1m)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),V0n))))))))) # label(conj_thm_2Earithmetic_2EMIN__LE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1502 (all A_27a (ne(A_27a) -> (all V0num (mem(V0num,arr(ty_2Enum_2Enum,arr(arr(ty_2Enum_2Enum,ty_2Enum_2Enum),A_27a))) -> p(ap(c_2Ebool_2EDATATYPE(A_27a),ap(ap(V0num,c_2Enum_2E0),c_2Enum_2ESUC))))))) # label(conj_thm_2Earithmetic_2Edatatype__num) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1503 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (ap(ap(c_2Earithmetic_2EMOD,V1a),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2b),V0n) <-> ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V2b)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V1a)),V0n))))))))) # label(conj_thm_2Earithmetic_2ESUC__MOD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1504 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2ELESS__MULT2) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1505 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) | c_2Enum_2E0 = V0m <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V0m)))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n))) <-> V0m = c_2Enum_2E0 | p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))))))) # label(conj_thm_2Earithmetic_2ELE__MULT__CANCEL__LBARE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1506 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0y)) -> (ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V1x)),V0y) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EMOD,V1x),V0y)) <-> ap(c_2Enum_2ESUC,V1x) != ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EDIV,V1x),V0y))),V0y))))))) # label(conj_thm_2Earithmetic_2EMOD__SUC__IFF) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1507 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V1m)) | p(ap(ap(c_2Eprim__rec_2E_3C,V2p),V0n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V2p),ap(ap(c_2Earithmetic_2EMAX,V1m),V0n)))) & (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMAX,V1m),V0n)),V2p)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V2p)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V2p))))))))) # label(conj_thm_2Earithmetic_2EMAX__LT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1508 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,V0n),V1m)),V0n)))))) # label(conj_thm_2Earithmetic_2ESUB__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1509 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,V0n) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0n))) # label(conj_thm_2Earithmetic_2ESUC__ONE__ADD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1510 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Enum_2ESUC,V1m)))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__IFF__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1511 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ((all V3y (mem(V3y,ty_2Enum_2Enum) -> (p(ap(V0P,ap(ap(c_2Earithmetic_2E_2B,V3y),V2n))) -> p(ap(V0P,V3y))))) & p(ap(V0P,V1x)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> p(ap(V0P,ap(ap(c_2Earithmetic_2EMOD,V1x),V2n)))))))))) # label(conj_thm_2Earithmetic_2EMOD__ELIM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1512 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1x) = ap(V0f,V1x))))))) # label(conj_thm_2Earithmetic_2EFUNPOW__1) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1513 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EABS__DIFF,V1m),V0n) = ap(ap(c_2Earithmetic_2EABS__DIFF,V0n),V1m))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__COMM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1514 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (V0m = ap(ap(c_2Earithmetic_2E_2B,V1n),V2p) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2p),c_2Enum_2E0)) <-> ap(ap(c_2Earithmetic_2E_2D,V0m),V1n) = V2p))))))) # label(conj_thm_2Earithmetic_2ESUB__RIGHT__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1515 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2EEXP,V1b),V0x))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1b)) | V0x = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EX__LT__EXP__X__IFF) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1516 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0m)),ap(c_2Enum_2ESUC,V1n))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1517 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = c_2Enum_2E0 | c_2Enum_2E0 = V1n <-> V0m = ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2ESUB__EQ__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1518 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (exists V1n (V0m = ap(c_2Enum_2ESUC,V1n) & mem(V1n,ty_2Enum_2Enum))) | c_2Enum_2E0 = V0m)) # label(conj_thm_2Earithmetic_2Enum__CASES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1519 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (V1n = V2m <-> ap(ap(c_2Earithmetic_2EEXP,V0b),V2m) = ap(ap(c_2Earithmetic_2EEXP,V0b),V1n))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1520 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMIN,V1n),V0m) = ap(ap(c_2Earithmetic_2EMIN,V0m),V1n))))) # label(conj_thm_2Earithmetic_2EMIN__COMM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1521 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2k)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EMOD,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V2k))),V1n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,V0m),V1n)),V2k)))))))) # label(conj_thm_2Earithmetic_2EDIV__MOD__MOD__DIV) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1522 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V2p)),V0m),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)),V2p)))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__ADD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1523 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p)))))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__LESS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1524 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),V2c)) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V0a),V1b)),V2c))))))) # label(conj_thm_2Earithmetic_2ESUB__PLUS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1525 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V0m) = c_2Enum_2E0)) # label(ax_thm_2Earithmetic_2ESUB_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1526 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1m),V2n)),c_2Enum_2E0),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2D,V1m),V2n))) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V1m)),V2n))))) # label(ax_thm_2Earithmetic_2ESUB_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1527 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V1m))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__MONO) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1528 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,V0m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m))))))) # label(ax_thm_2Earithmetic_2EGREATER__DEF) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1529 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V1n = c_2Enum_2E0 | p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V0m)) <-> V0m = c_2Enum_2E0 | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) # label(conj_thm_2Earithmetic_2ELE__MULT__CANCEL__RBARE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1530 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2z)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1y),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0x)),V2z))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0x),V2z)),V1y)) <-> V0x = ap(ap(c_2Earithmetic_2EDIV,V1y),V2z))))))))) # label(conj_thm_2Earithmetic_2EDIV__EQ__X) # label(axiom) # label(non_clause). [assumption]. 3.72/3.82 1531 (all V0m (mem(V0m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Eprim__rec_2EPRE,V0m))) # label(conj_thm_2Earithmetic_2EPRE__SUB1) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1532 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3q ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Earithmetic_2E_2B,V0a),V3q)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2D,V1m),ap(ap(c_2Earithmetic_2E_2A,V2n),V3q))),V2n))) = ap(f185(V0a,V1m,V2n),V3q)))))))) # label(lameq_f185) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1533 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2ELESS__IMP__LESS__OR__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1534 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (c_2Enum_2E0 != V1n -> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2ELESS__ADD__NONZERO) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1535 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)),V0m))))))) # label(conj_thm_2Earithmetic_2ESUB__LESS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1536 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> (exists V2k (mem(V2k,ty_2Enum_2Enum) & V0m = ap(ap(c_2Earithmetic_2E_2D,V1n),V2k)))))))) # label(conj_thm_2Earithmetic_2ELESS__EQUAL__DIFF) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1537 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2p)),V0m)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2p)),V1n))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))))) # label(conj_thm_2Earithmetic_2EMULT__LESS__EQ__SUC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1538 (all V0m (mem(V0m,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(c_2Enum_2ESUC,V0m))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__SUC__REFL) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1539 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) <-> p(ap(ap(c_2Earithmetic_2E_3E_3D,V0n),V1m))))))) # label(conj_thm_2Earithmetic_2EGREATER__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1540 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMAX,V0m),V1n) = ap(ap(c_2Earithmetic_2EMAX,V1n),V0m))))) # label(conj_thm_2Earithmetic_2EMAX__COMM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1541 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Earithmetic_2E_2D,V1n),V2p))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V0m),V2p)),V1n)) | p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),c_2Enum_2E0))))))))) # label(conj_thm_2Earithmetic_2ESUB__LEFT__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1542 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1r (mem(V1r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1r),V0n)) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> V2q = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2q),V0n)),V1r)),V0n)))))))) # label(conj_thm_2Earithmetic_2EDIV__MULT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1543 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1z (mem(V1z,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),ap(c_2Enum_2ESUC,V1z))),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1z)))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__SUC__LE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1544 (all V0m (mem(V0m,ty_2Enum_2Enum) -> V0m = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0m)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Earithmetic_2ESUC__SUB1) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1545 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1r (mem(V1r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1r),V0n)) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> V1r = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2q),V0n)),V1r)),V0n)))))))) # label(conj_thm_2Earithmetic_2EMOD__MULT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1546 (all V0m (mem(V0m,ty_2Enum_2Enum) -> V0m = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m))) # label(conj_thm_2Earithmetic_2EMULT__LEFT__1) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1547 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m1 (mem(V1m1,ty_2Enum_2Enum) -> (all V2m2 (mem(V2m2,ty_2Enum_2Enum) -> ((exists V3a (mem(V3a,ty_2Enum_2Enum) & (exists V4b (ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3a),V0n)),V1m1) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V4b),V0n)),V2m2) & mem(V4b,ty_2Enum_2Enum))))) <-> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1m1),V2m2))))))))) # label(ax_thm_2Earithmetic_2EMODEQ__DEF) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1548 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) -> (exists V3n (mem(V3n,ty_2Enum_2Enum) & p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),V3n),V1x),V2y))))))))))))) # label(conj_thm_2Earithmetic_2ERTC__NRC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1549 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> -(p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m))))))) # label(conj_thm_2Earithmetic_2ELESS__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1550 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m1 (mem(V1m1,ty_2Enum_2Enum) -> (all V2m2 (mem(V2m2,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1m1),V2m2)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & ap(ap(c_2Earithmetic_2EMOD,V1m1),V0n) = ap(ap(c_2Earithmetic_2EMOD,V2m2),V0n) | V1m1 = V2m2 & c_2Enum_2E0 = V0n))))))) # label(conj_thm_2Earithmetic_2EMODEQ__THM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1551 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0b),V2m)),ap(ap(c_2Earithmetic_2EEXP,V0b),V1n))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2m),V1n)))))))))) # label(conj_thm_2Earithmetic_2EEXP__BASE__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1552 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2EMOD,c_2Enum_2E0),V0n) = c_2Enum_2E0))) # label(conj_thm_2Earithmetic_2EZERO__MOD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1553 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (V1n = c_2Enum_2E0 | p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V2p)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n)))))))))) # label(conj_thm_2Earithmetic_2ELE__MULT__RCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1554 (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V0f (mem(V0f,arr(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum))) -> (all V2m ap(f182(V1a,V0f),V2m) = f181(V2m,V1a,V0f)))))) # label(lameq_f182) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1555 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1b),V0a)) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),V2c))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0a),V1b)),V2c)))))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__SUB__LESS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1556 (all V0m (mem(V0m,ty_2Enum_2Enum) -> V0m = ap(ap(c_2Earithmetic_2E_2B,V0m),c_2Enum_2E0))) # label(conj_thm_2Earithmetic_2EADD__0) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1557 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (V0n = c_2Enum_2E0 | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1a),V2b)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V1a),V0n)),ap(ap(c_2Earithmetic_2EEXP,V2b),V0n)))))))))) # label(conj_thm_2Earithmetic_2EEXP__EXP__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1558 (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0c),V1b)) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,V2a),V1b)),V0c) = ap(ap(c_2Earithmetic_2E_2B,V2a),ap(ap(c_2Earithmetic_2E_2D,V1b),V0c))))))))) # label(conj_thm_2Earithmetic_2ELESS__EQ__ADD__SUB) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1559 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,V0n)) <-> -p(ap(c_2Earithmetic_2EEVEN,V0n))))) # label(conj_thm_2Earithmetic_2EODD__EVEN) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1560 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,A_27a))) -> (all V1g (mem(V1g,arr(ty_2Enum_2Enum,A_27a)) -> ((all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(V0f,V2n),ap(c_2Enum_2ESUC,V2n)) = ap(V1g,ap(c_2Enum_2ESUC,V2n)))) <-> (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(V0f,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))) = ap(V1g,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V4n))))) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> ap(ap(V0f,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n))) = ap(V1g,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3n)))))))))))) # label(conj_thm_2Earithmetic_2ESUC__ELIM__NUMERALS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1561 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2A,V1n),V0m)))) & (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2ELT__MULT__CANCEL__LBARE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1562 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V0n)) != ap(ap(c_2Earithmetic_2E_2B,V1m),V1m))))) # label(conj_thm_2Earithmetic_2ENOT__ODD__EQ__EVEN) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1563 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (V0n = c_2Enum_2E0 <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2ELE_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1564 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),ap(c_2Enum_2ESUC,V2n))) <-> ap(c_2Enum_2ESUC,V2n) = V1m | p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V2n))))))) # label(conj_thm_2Earithmetic_2ELE_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1565 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,V2p),V0m)),ap(ap(c_2Earithmetic_2E_2A,V2p),V1n)) = ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Earithmetic_2E_2D,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2ELEFT__SUB__DISTRIB) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1566 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> ((exists V3n (mem(V3n,ty_2Enum_2Enum) & p(ap(ap(ap(ap(c_2Earithmetic_2ENRC(A_27a),V0R),ap(c_2Enum_2ESUC,V3n)),V1x),V2y)))) <-> p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Earithmetic_2ETC__eq__NRC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1567 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EMOD,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0 <-> p(ap(c_2Earithmetic_2EEVEN,V0x))))) # label(conj_thm_2Earithmetic_2EEVEN__MOD2) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1568 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMAX,V0m),V1n) <-> c_2Enum_2E0 = V1n & V0m = c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EMAX__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1569 (all V0n (mem(V0n,ty_2Enum_2Enum) -> V0n = ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0n))) # label(ax_thm_2Earithmetic_2EADD_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1570 (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V1m),V2n)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V1m)),V2n))))) # label(ax_thm_2Earithmetic_2EADD_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1571 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> p(ap(c_2Earithmetic_2EODD,ap(ap(c_2Earithmetic_2EEXP,V0m),V1n)))))))) # label(conj_thm_2Earithmetic_2EODD__EXP) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1572 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2A,V1n),V0m))))) # label(conj_thm_2Earithmetic_2EMULT__SYM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1573 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> (all V2q (mem(V2q,ty_2Enum_2Enum) -> ((exists V3r (mem(V3r,ty_2Enum_2Enum) & p(ap(ap(c_2Eprim__rec_2E_3C,V3r),V0n)) & V1k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2q),V0n)),V3r))) -> V2q = ap(ap(c_2Earithmetic_2EDIV,V1k),V0n)))))))) # label(conj_thm_2Earithmetic_2EDIV__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1574 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2B,V2a),ap(ap(c_2Earithmetic_2EDIV,V0m),V1n))),ap(ap(c_2Earithmetic_2EMOD,V0m),V1n)) = ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V2a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),V1n)))))))))) # label(conj_thm_2Earithmetic_2EDIVMOD__CORRECT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1575 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EDIV,V1x),V0y))),V0y) != ap(c_2Enum_2ESUC,V1x) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0y)) -> ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2EMOD,V1x),V0y)) = ap(ap(c_2Earithmetic_2EMOD,ap(c_2Enum_2ESUC,V1x)),V0y)))))) # label(conj_thm_2Earithmetic_2EMOD__SUC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1576 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2z (mem(V2z,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V2z)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EABS__DIFF,V0x),V1y)),ap(ap(c_2Earithmetic_2EABS__DIFF,V1y),V2z)))))))))) # label(conj_thm_2Earithmetic_2EABS__DIFF__TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1577 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2i (mem(V2i,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2i),ap(ap(c_2Earithmetic_2E_2D,V0n),V1m))) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V2i),V1m)),V0n))))))))) # label(conj_thm_2Earithmetic_2ELESS__SUB__ADD__LESS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1578 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m1 (mem(V1m1,ty_2Enum_2Enum) -> (all V2m2 (mem(V2m2,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (ap(ap(c_2Earithmetic_2EMOD,V2m2),V0n) = ap(ap(c_2Earithmetic_2EMOD,V1m1),V0n) <-> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1m1),V2m2)))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__NONZERO__MODEQUALITY) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1579 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMIN,V0m),V1n)),ap(ap(c_2Earithmetic_2EMAX,V0m),V1n))))))) # label(conj_thm_2Earithmetic_2EMIN__MAX__LE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1580 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) -> (exists V2p (ap(ap(c_2Earithmetic_2E_2B,V1n),ap(ap(c_2Earithmetic_2E_2B,V2p),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = V0m & mem(V2p,ty_2Enum_2Enum)))))))) # label(conj_thm_2Earithmetic_2ELESS__ADD__1) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1581 (all V0m (mem(V0m,ty_2Enum_2Enum) -> V0m = c_2Enum_2E0 | p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)))) # label(conj_thm_2Earithmetic_2ELESS__0__CASES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1582 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2D,V0p),V1m)),ap(c_2Enum_2ESUC,V0p))))))) # label(conj_thm_2Earithmetic_2ESUB__LESS__SUC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1583 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V0m) = c_2Enum_2E0 & ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0m & ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) & ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V0m)),V1n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n) & V0m = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m) & c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2A,V0m),c_2Enum_2E0))))) # label(conj_thm_2Earithmetic_2EMULT__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1584 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2EADD__SUC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1585 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMAX,V0n),V0n) = V0n)) # label(conj_thm_2Earithmetic_2EMAX__IDEM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1586 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)) -> (exists V2p (mem(V2p,ty_2Enum_2Enum) & V0m = ap(ap(c_2Earithmetic_2E_2B,V2p),V1n)))))))) # label(conj_thm_2Earithmetic_2ELESS__ADD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1587 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V2p),V0m)),ap(ap(c_2Earithmetic_2E_2B,V2p),V1n)))))))))) # label(conj_thm_2Earithmetic_2ELT__ADD__LCANCEL) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1588 (all V0b1 (mem(V0b1,ty_2Enum_2Enum) -> (all V1b2 (mem(V1b2,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EEXP,V0b1),V2x) = ap(ap(c_2Earithmetic_2EEXP,V1b2),V2x) <-> V0b1 = V1b2 | V2x = c_2Enum_2E0))))))) # label(conj_thm_2Earithmetic_2EEXP__EXP__INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1589 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V0m) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enum_2ESUC,V2n)),V1i) <-> V0m = V1i))))))) # label(conj_thm_2Earithmetic_2EMULT__MONO__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1590 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x0 (mem(V1x0,ty_2Enum_2Enum) -> (all V2x1 (mem(V2x1,ty_2Enum_2Enum) -> (all V3y0 (mem(V3y0,ty_2Enum_2Enum) -> (all V4y1 (mem(V4y1,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V1x0),V2x1)) -> (p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),V3y0),V4y1)) -> p(ap(ap(ap(c_2Earithmetic_2EMODEQ,V0n),ap(ap(c_2Earithmetic_2E_2B,V1x0),V3y0)),ap(ap(c_2Earithmetic_2E_2B,V2x1),V4y1))))))))))))))) # label(conj_thm_2Earithmetic_2EMODEQ__PLUS__CONG) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1591 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0m),ap(c_2Enum_2ESUC,V1n)) = ap(ap(c_2Earithmetic_2E_2B,V0m),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)))))) # label(conj_thm_2Earithmetic_2EMULT__SUC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1592 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V2x),V1n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EMOD,V2x),ap(ap(c_2Earithmetic_2E_2A,V1n),V0m))),V1n)))))))) # label(conj_thm_2Earithmetic_2EMOD__MULT__MOD) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1593 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(c_2Earithmetic_2EODD,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)))))) # label(conj_thm_2Earithmetic_2EODD__DOUBLE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1594 (all A_27a (ne(A_27a) -> mem(c_2Earithmetic_2Enum__CASE(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,arr(arr(ty_2Enum_2Enum,A_27a),A_27a)))))) # label(mem_c_2Earithmetic_2Enum__CASE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1595 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V1n)) <-> V0m = c_2Enum_2E0 & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n))) & (V1n = c_2Enum_2E0 & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),V0m))))))) # label(conj_thm_2Earithmetic_2ELT__MULT__CANCEL__RBARE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1596 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,V2x),ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EDIV,V2x),V0m)),V1n)))))))) # label(conj_thm_2Earithmetic_2EDIV__DIV__DIV__MULT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1597 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EMIN,V0m),V1n) = ap(ap(c_2Earithmetic_2EMAX,V0m),V1n) <-> V1n = V0m))))) # label(conj_thm_2Earithmetic_2EMIN__MAX__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1598 (all A_27a (ne(A_27a) -> mem(c_2Ewhile_2EOWHILE(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,A_27a),arr(A_27a,ty_2Eoption_2Eoption(A_27a))))))) # label(mem_c_2Ewhile_2EOWHILE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1599 (all V0p (mem(V0p,arr(ty_2Enum_2Enum,bool)) -> ((exists V1n (p(ap(V0p,V1n)) & mem(V1n,ty_2Enum_2Enum))) -> p(ap(V0p,ap(c_2Ewhile_2ELEAST,V0p))) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Ewhile_2ELEAST,V0p))) -> -p(ap(V0p,V2n)))))))) # label(conj_thm_2Ewhile_2ELEAST__EXISTS__IMP) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1600 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ap(c_2Ewhile_2EOLEAST,V0P) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(ty_2Enum_2Enum)),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f190(V0P))),ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),ap(c_2Ewhile_2ELEAST,f191(V0P)))),c_2Eoption_2ENONE(ty_2Enum_2Enum)))) # label(ax_thm_2Ewhile_2EOLEAST__def) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1601 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(c_2Ewhile_2EOLEAST,f189(V0x)) = ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V0x) & ap(c_2Ewhile_2EOLEAST,k(ty_2Enum_2Enum,c_2Ebool_2EF)) = c_2Eoption_2ENONE(ty_2Enum_2Enum) & ap(c_2Ewhile_2EOLEAST,k(ty_2Enum_2Enum,c_2Ebool_2ET)) = ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),c_2Enum_2E0) & ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V0x) = ap(c_2Ewhile_2EOLEAST,f188(V0x)))) # label(conj_thm_2Ewhile_2EOLEAST__EQNS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1602 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ap(c_2Ewhile_2ELEAST,V0P) = ap(ap(ap(c_2Ewhile_2EWHILE(ty_2Enum_2Enum),ap(ap(c_2Ecombin_2Eo(ty_2Enum_2Enum,bool,bool),c_2Ebool_2E_7E),V0P)),c_2Enum_2ESUC),c_2Enum_2E0))) # label(ax_thm_2Ewhile_2ELEAST__DEF) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1603 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1g (mem(V1g,arr(A_27a,A_27a)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(ap(c_2Ewhile_2EWHILE(A_27a),V0P),V1g),V2x) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(V0P,V2x)),ap(ap(ap(c_2Ewhile_2EWHILE(A_27a),V0P),V1g),ap(V1g,V2x))),V2x))))))))) # label(ax_thm_2Ewhile_2EWHILE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1604 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V2n ap(f191(V0P),V2n) = ap(V0P,V2n)))) # label(lameq_f191) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1605 (all A_27a all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> (all V3n ap(c_2Ebool_2E_7E,ap(V0G,ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V1f),V3n),V2s))) = ap(f192(A_27a,V0G,V1f,V2s),V3n)))))))) # label(lameq_f192) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1606 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> -p(ap(V0P,V1n)))) <-> ap(c_2Ewhile_2EOLEAST,V0P) = c_2Eoption_2ENONE(ty_2Enum_2Enum)))) # label(conj_thm_2Ewhile_2EOLEAST__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1607 (all V0p (mem(V0p,arr(ty_2Enum_2Enum,bool)) -> (p(ap(V0p,ap(c_2Ewhile_2ELEAST,V0p))) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(c_2Ewhile_2ELEAST,V0p))) -> -p(ap(V0p,V2n))))) <-> (exists V1n (p(ap(V0p,V1n)) & mem(V1n,ty_2Enum_2Enum)))))) # label(conj_thm_2Ewhile_2ELEAST__EXISTS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1608 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ewhile_2EHOARE__SPEC(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool)))))))) # label(mem_c_2Ewhile_2EHOARE__SPEC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1609 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1n ap(V0P,V1n) = ap(f190(V0P),V1n)))) # label(lameq_f190) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1610 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),V0x) = ap(f188(V0x),V1n)))) # label(lameq_f188) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1611 (all A_27a (ne(A_27a) -> (all V0B (mem(V0B,arr(A_27a,bool)) -> (all V1C (mem(V1C,arr(A_27a,A_27a)) -> (all V2R (mem(V2R,arr(A_27a,arr(A_27a,bool))) -> ((all V3s (mem(V3s,A_27a) -> (p(ap(V0B,V3s)) -> p(ap(ap(V2R,ap(V1C,V3s)),V3s))))) & p(ap(c_2Erelation_2EWF(A_27a),V2R)) -> (all V4P (mem(V4P,arr(A_27a,bool)) -> ((all V5s (mem(V5s,A_27a) -> ((p(ap(V0B,V5s)) -> p(ap(V4P,ap(V1C,V5s)))) -> p(ap(V4P,V5s))))) -> (all V6v (mem(V6v,A_27a) -> p(ap(V4P,V6v)))))))))))))))) # label(conj_thm_2Ewhile_2EWHILE__INDUCTION) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1612 (all A_27a (ne(A_27a) -> mem(c_2Ewhile_2EWHILE(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,A_27a),arr(A_27a,A_27a)))))) # label(mem_c_2Ewhile_2EWHILE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1613 (all A_27a (ne(A_27a) -> (all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> (ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),V2s) = c_2Eoption_2ENONE(A_27a) <-> (all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(V0G,ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V1f),V3n),V2s)))))))))))))) # label(conj_thm_2Ewhile_2EOWHILE__EQ__NONE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1614 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(V0P,V1x)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ewhile_2ELEAST,V0P)),V1x)) & p(ap(V0P,ap(c_2Ewhile_2ELEAST,V0P)))))))) # label(conj_thm_2Ewhile_2EFULL__LEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1615 (all A_27a (ne(A_27a) -> (all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> (all V3s_27 (mem(V3s_27,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V3s_27) = ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),V2s) -> V3s_27 = ap(ap(ap(c_2Ewhile_2EWHILE(A_27a),V0G),V1f),V2s)))))))))))) # label(conj_thm_2Ewhile_2EOWHILE__WHILE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1616 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1m),ap(c_2Ewhile_2ELEAST,V0P))) -> -p(ap(V0P,V1m))))))) # label(conj_thm_2Ewhile_2ELESS__LEAST) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1617 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2B (mem(V2B,arr(A_27a,bool)) -> (all V5s ap(f186(A_27a,V0P,V2B),V5s) = ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V5s)),ap(V2B,V5s))))))) # label(lameq_f186) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1618 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1R (mem(V1R,arr(A_27a,arr(A_27a,bool))) -> (all V2B (mem(V2B,arr(A_27a,bool)) -> (all V3C (mem(V3C,arr(A_27a,A_27a)) -> ((all V4s (mem(V4s,A_27a) -> (p(ap(V2B,V4s)) -> p(ap(ap(V1R,ap(V3C,V4s)),V4s))))) & p(ap(c_2Erelation_2EWF(A_27a),V1R)) -> (p(ap(ap(ap(c_2Ewhile_2EHOARE__SPEC(A_27a,A_27a),f186(A_27a,V0P,V2B)),V3C),V0P)) -> p(ap(ap(ap(c_2Ewhile_2EHOARE__SPEC(A_27a,A_27a),V0P),ap(ap(c_2Ewhile_2EWHILE(A_27a),V2B),V3C)),f187(A_27a,V0P,V2B))))))))))))))) # label(conj_thm_2Ewhile_2EWHILE__RULE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1619 (all V0Q (mem(V0Q,arr(ty_2Enum_2Enum,bool)) -> (all V1P (mem(V1P,arr(ty_2Enum_2Enum,bool)) -> ((all V3n (mem(V3n,ty_2Enum_2Enum) -> ((all V4m (mem(V4m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V4m),V3n)) -> -p(ap(V1P,V4m))))) & p(ap(V1P,V3n)) -> p(ap(V0Q,V3n))))) & (exists V2n (p(ap(V1P,V2n)) & mem(V2n,ty_2Enum_2Enum))) -> p(ap(V0Q,ap(c_2Ewhile_2ELEAST,V1P)))))))) # label(conj_thm_2Ewhile_2ELEAST__ELIM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1620 (all A_27a (ne(A_27a) -> (all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),V2s) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(V0G,V2s)),ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),ap(V1f,V2s))),ap(c_2Eoption_2ESOME(A_27a),V2s)))))))))) # label(conj_thm_2Ewhile_2EOWHILE__THM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1621 (all A_27a all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> (all V4n ap(c_2Ebool_2E_7E,ap(V0G,ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V1f),V4n),V2s))) = ap(f193(A_27a,V0G,V1f,V2s),V4n)))))))) # label(lameq_f193) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1622 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1g (mem(V1g,arr(A_27a,A_27a)) -> (exists V2f (mem(V2f,arr(A_27a,A_27a)) & (all V3x (mem(V3x,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(V0P,V3x)),V3x),ap(V2f,ap(V1g,V3x))) = ap(V2f,V3x))))))))))) # label(conj_thm_2Ewhile_2EITERATION) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1623 (all A_27a (ne(A_27a) -> (all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Eoption_2Eoption(A_27a)),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f192(A_27a,V0G,V1f,V2s))),ap(c_2Eoption_2ESOME(A_27a),ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V1f),ap(c_2Ewhile_2ELEAST,f193(A_27a,V0G,V1f,V2s))),V2s))),c_2Eoption_2ENONE(A_27a)) = ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),V2s))))))))) # label(ax_thm_2Ewhile_2EOWHILE__def) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1624 (all V0x (mem(V0x,ty_2Enum_2Enum) -> V0x = ap(c_2Ewhile_2ELEAST,f188(V0x)) & V0x = ap(c_2Ewhile_2ELEAST,f189(V0x)))) # label(conj_thm_2Ewhile_2ELEAST__EQ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1625 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V1n) = ap(c_2Ewhile_2EOLEAST,V0P) <-> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V1n)) -> -p(ap(V0P,V2m))))) & p(ap(V0P,V1n))))))) # label(conj_thm_2Ewhile_2EOLEAST__EQ__SOME) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1626 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27a,bool))) -> (all V1G (mem(V1G,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> ((all V3s (mem(V3s,A_27a) -> (-p(ap(V1G,V3s)) -> p(ap(ap(V0P,V3s),V3s))))) & (all V4s1 (mem(V4s1,A_27a) -> (all V5s2 (mem(V5s2,A_27a) -> (p(ap(ap(V0P,ap(V2f,V4s1)),V5s2)) & p(ap(V1G,V4s1)) -> p(ap(ap(V0P,V4s1),V5s2))))))) -> (all V6s1 (mem(V6s1,A_27a) -> (all V7s2 (mem(V7s2,A_27a) -> (ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V1G),V2f),V6s1) = ap(c_2Eoption_2ESOME(A_27a),V7s2) -> p(ap(ap(V0P,V6s1),V7s2)))))))))))))))) # label(conj_thm_2Ewhile_2EOWHILE__IND) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1627 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(V0P,V1x)) -> p(ap(V0P,ap(c_2Ewhile_2ELEAST,V0P)))))))) # label(conj_thm_2Ewhile_2ELEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1628 (all A_27a (ne(A_27a) -> (all V0G (mem(V0G,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,A_27a)) -> (all V2s (mem(V2s,A_27a) -> (all V3s_27 (mem(V3s_27,A_27a) -> (ap(c_2Eoption_2ESOME(A_27a),V3s_27) = ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V0G),V1f),V2s) -> -p(ap(V0G,V3s_27))))))))))))) # label(conj_thm_2Ewhile_2EOWHILE__ENDCOND) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1629 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (all V1Q (mem(V1Q,arr(ty_2Eoption_2Eoption(ty_2Enum_2Enum),bool)) -> (((all V2n (mem(V2n,ty_2Enum_2Enum) -> -p(ap(V0P,V2n)))) -> p(ap(V1Q,c_2Eoption_2ENONE(ty_2Enum_2Enum)))) & (all V3n (mem(V3n,ty_2Enum_2Enum) -> ((all V4m (mem(V4m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V4m),V3n)) -> -p(ap(V0P,V4m))))) & p(ap(V0P,V3n)) -> p(ap(V1Q,ap(c_2Eoption_2ESOME(ty_2Enum_2Enum),V3n)))))) -> p(ap(V1Q,ap(c_2Ewhile_2EOLEAST,V0P)))))))) # label(conj_thm_2Ewhile_2EOLEAST__INTRO) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1630 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1C (mem(V1C,arr(A_27a,A_27b)) -> (all V2Q (mem(V2Q,arr(A_27b,bool)) -> (p(ap(ap(ap(c_2Ewhile_2EHOARE__SPEC(A_27a,A_27b),V0P),V1C),V2Q)) <-> (all V3s (mem(V3s,A_27a) -> (p(ap(V0P,V3s)) -> p(ap(V2Q,ap(V1C,V3s))))))))))))))))) # label(ax_thm_2Ewhile_2EHOARE__SPEC__DEF) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1631 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1G (mem(V1G,arr(A_27a,bool)) -> (all V2f (mem(V2f,arr(A_27a,A_27a)) -> (all V3s (mem(V3s,A_27a) -> ((all V4x (mem(V4x,A_27a) -> (p(ap(V1G,V4x)) & p(ap(V0P,V4x)) -> p(ap(V0P,ap(V2f,V4x)))))) & p(ap(V0P,V3s)) -> (all V5s_27 (mem(V5s_27,A_27a) -> (ap(ap(ap(c_2Ewhile_2EOWHILE(A_27a),V1G),V2f),V3s) = ap(c_2Eoption_2ESOME(A_27a),V5s_27) -> p(ap(V0P,V5s_27)))))))))))))))) # label(conj_thm_2Ewhile_2EOWHILE__INV__IND) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1632 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V2B (mem(V2B,arr(A_27a,bool)) -> (all V6s ap(f187(A_27a,V0P,V2B),V6s) = ap(ap(c_2Ebool_2E_2F_5C,ap(V0P,V6s)),ap(c_2Ebool_2E_7E,ap(V2B,V6s)))))))) # label(lameq_f187) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1633 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V2n ap(f189(V0x),V2n) = ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0x),V2n)))) # label(lameq_f189) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1634 (all A_27a (ne(A_27a) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4zf (mem(V4zf,A_27a) -> (all V5bf1 (mem(V5bf1,arr(ty_2Enum_2Enum,A_27a)) -> (all V6bf2 (mem(V6bf2,arr(ty_2Enum_2Enum,A_27a)) -> ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(A_27a),ap(c_2Earithmetic_2EBIT1,V3n)),V4zf),V5bf1),V6bf2) = ap(V5bf1,V3n))))))))) & (all V7n (mem(V7n,ty_2Enum_2Enum) -> (all V8zf (mem(V8zf,A_27a) -> (all V9bf1 (mem(V9bf1,arr(ty_2Enum_2Enum,A_27a)) -> (all V10bf2 (mem(V10bf2,arr(ty_2Enum_2Enum,A_27a)) -> ap(V10bf2,V7n) = ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(A_27a),ap(c_2Earithmetic_2EBIT2,V7n)),V8zf),V9bf1),V10bf2))))))))) & (all V0zf (mem(V0zf,A_27a) -> (all V1bf1 (mem(V1bf1,arr(ty_2Enum_2Enum,A_27a)) -> (all V2bf2 (mem(V2bf2,arr(ty_2Enum_2Enum,A_27a)) -> V0zf = ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(A_27a),c_2Earithmetic_2EZERO),V0zf),V1bf1),V2bf2))))))))) # label(ax_thm_2Enumeral_2EiBIT__cases) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1635 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,c_2Earithmetic_2EZERO),V0n) = c_2Earithmetic_2EZERO & ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0n),V1m)),V1m))) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,V0n)),V1m) & ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumeral_2EiDUB,ap(ap(c_2Earithmetic_2E_2A,V0n),V1m))),V1m)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,V0n)),V1m) & ap(ap(c_2Earithmetic_2E_2A,V0n),c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO)))) # label(conj_thm_2Enumeral_2Enumeral__mult) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1636 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT1,V0n)) = ap(c_2Earithmetic_2EBIT2,V0n))) # label(conj_thm_2Enumeral_2Enumeral__suc_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1637 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,V1n)) = ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT2,V1n)))) # label(conj_thm_2Enumeral_2Enumeral__suc_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1638 (all V0x (mem(V0x,ty_2Enum_2Enum) -> V0x = ap(c_2Earithmetic_2EDIV2,ap(c_2Earithmetic_2EBIT1,V0x)))) # label(conj_thm_2Enumeral_2EDIV2__BIT1) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1639 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumeral_2EiiSUC,ap(c_2Earithmetic_2EBIT2,V0n)) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,V0n)) & ap(c_2Enumeral_2EiiSUC,ap(c_2Earithmetic_2EBIT1,V0n)) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,V0n)) & ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO) = ap(c_2Enumeral_2EiiSUC,c_2Earithmetic_2EZERO))) # label(conj_thm_2Enumeral_2Enumeral__iisuc) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1640 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ($T <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Earithmetic_2EZERO),V0n))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),c_2Earithmetic_2EZERO)) <-> $F) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m))) & (-p(ap(ap(c_2Earithmetic_2E_3C_3D,V1m),V0n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m)))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m)))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),V1m))) & ($F <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2EBIT1,V0n)),c_2Earithmetic_2EZERO))))))) # label(conj_thm_2Enumeral_2Enumeral__lte) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1641 (all V0b (mem(V0b,bool) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral_2EiSUB,V0b),c_2Earithmetic_2EZERO),V1x) = c_2Earithmetic_2EZERO)))) # label(ax_thm_2Enumeral_2EiSUB__DEF_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1642 (all V9b (mem(V9b,bool) -> (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V11x (mem(V11x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral_2EiSUB,V9b),ap(c_2Earithmetic_2EBIT2,V10n)),V11x) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V9b),ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(ty_2Enum_2Enum),V11x),ap(c_2Earithmetic_2EBIT2,V10n)),f198(V10n)),f199(V10n))),ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(ty_2Enum_2Enum),V11x),ap(c_2Earithmetic_2EBIT1,V10n)),f200(V10n)),f201(V10n))))))))) # label(ax_thm_2Enumeral_2EiSUB__DEF_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1643 (all V2b (mem(V2b,bool) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4x (mem(V4x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V2b),ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(ty_2Enum_2Enum),V4x),ap(c_2Earithmetic_2EBIT1,V3n)),f194(V3n)),f195(V3n))),ap(ap(ap(ap(c_2Enumeral_2EiBIT__cases(ty_2Enum_2Enum),V4x),ap(c_2Enumeral_2EiDUB,V3n)),f196(V3n)),f197(V3n))) = ap(ap(ap(c_2Enumeral_2EiSUB,V2b),ap(c_2Earithmetic_2EBIT1,V3n)),V4x))))))) # label(ax_thm_2Enumeral_2EiSUB__DEF_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1644 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT1,V0n)),c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V0n))) & ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V0n))),c_2Earithmetic_2EZERO)) & ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) # label(conj_thm_2Enumeral_2ETWO__EXP__THM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1645 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> (p(ap(V0P,c_2Earithmetic_2EZERO)) & (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(V0P,V2n)) -> p(ap(V0P,ap(c_2Earithmetic_2EBIT2,V2n)))))) & (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(V0P,V1n)) -> p(ap(V0P,ap(c_2Earithmetic_2EBIT1,V1n)))))) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(V0P,V3n))))))) # label(conj_thm_2Enumeral_2Ebit__induction) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1646 (all V0n (mem(V0n,ty_2Enum_2Enum) -> c_2Earithmetic_2EZERO = ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT1,V0n)))) # label(ax_thm_2Enumeral_2Eexactlog__def_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1647 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f202),ap(ap(c_2Enumeral_2Eonecount,V1n),c_2Earithmetic_2EZERO)) = ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V1n)))) # label(ax_thm_2Enumeral_2Eexactlog__def_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1648 (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,V2m),ap(c_2Earithmetic_2EBIT2,V3n)) = ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Earithmetic_2EZERO),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2m),ap(c_2Earithmetic_2EBIT2,V3n))))))))) # label(conj_thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1649 (all V4m (mem(V4m,ty_2Enum_2Enum) -> (all V5n (mem(V5n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V4m),ap(c_2Earithmetic_2EBIT1,V5n)) = ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Earithmetic_2EZERO),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V4m),ap(c_2Earithmetic_2EBIT1,V5n))))))))) # label(conj_thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1650 (all V6m (mem(V6m,ty_2Enum_2Enum) -> (all V7n (mem(V7n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V6m),ap(c_2Earithmetic_2EBIT2,V7n)) = ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Earithmetic_2EZERO),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V6m),ap(c_2Earithmetic_2EBIT2,V7n))))))))) # label(conj_thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1651 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,V0m),ap(c_2Earithmetic_2EBIT1,V1n)) = ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),c_2Earithmetic_2EZERO),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0m),ap(c_2Earithmetic_2EBIT1,V1n))))))))) # label(conj_thm_2Enumeral_2EDIVMOD__NUMERAL__CALC_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1652 (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V13m ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V10n),V13m)) = ap(f199(V10n),V13m)))) # label(lameq_f199) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1653 (all V0acc (mem(V0acc,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT2,V1n)),V0acc) = ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT1,V1n)),ap(c_2Earithmetic_2EBIT1,V0acc)) & ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V1n))),ap(c_2Earithmetic_2EBIT1,V0acc)) = ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EBIT1,V1n)),V0acc) & ap(ap(c_2Enumeral_2Etexp__help,c_2Earithmetic_2EZERO),V0acc) = ap(c_2Earithmetic_2EBIT2,V0acc))))) # label(conj_thm_2Enumeral_2Enumeral__texp__help) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1654 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1b (mem(V1b,bool) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3m (mem(V3m,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumeral_2EiSUB,V1b),c_2Earithmetic_2EZERO),V0x) = c_2Earithmetic_2EZERO & V2n = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),c_2Earithmetic_2EZERO) & ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) & ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) & ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) & ap(c_2Earithmetic_2EBIT1,V2n) = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT2,V2n)),c_2Earithmetic_2EZERO) & ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) & ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT1,V3m)) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) & ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) & ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT2,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V2n),V3m)) & ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V2n),V3m)) = ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),ap(c_2Earithmetic_2EBIT1,V2n)),ap(c_2Earithmetic_2EBIT2,V3m)) & ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),ap(c_2Earithmetic_2EBIT1,V2n)),c_2Earithmetic_2EZERO) = ap(c_2Enumeral_2EiDUB,V2n))))))))) # label(conj_thm_2Enumeral_2EiSUB__THM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1655 (all V0n (mem(V0n,ty_2Enum_2Enum) -> V0n = ap(ap(c_2Earithmetic_2E_2B,c_2Enum_2E0),V0n))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1656 (all V1n (mem(V1n,ty_2Enum_2Enum) -> V1n = ap(ap(c_2Earithmetic_2E_2B,V1n),c_2Enum_2E0))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1657 (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,c_2Enum_2E0),V4n) = c_2Enum_2E0)) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1658 (all V6n (mem(V6n,ty_2Enum_2Enum) -> (all V7m (mem(V7m,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2A,V6n),V7m)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,V6n)),ap(c_2Earithmetic_2ENUMERAL,V7m)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1659 (all V9n (mem(V9n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,V9n),c_2Enum_2E0) = V9n)) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1660 (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V11m (mem(V11m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,V10n)),ap(c_2Earithmetic_2ENUMERAL,V11m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2D,V10n),V11m)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1661 (all V12n (mem(V12n,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V12n))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1662 (all V13n (mem(V13n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V13n))) = c_2Enum_2E0)) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1663 (all V18n (mem(V18n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Eprim__rec_2EPRE,V18n)) = ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,V18n)))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1664 (all V21n (mem(V21n,ty_2Enum_2Enum) -> (all V22m (mem(V22m,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,V22m) = ap(c_2Earithmetic_2ENUMERAL,V21n) <-> V22m = V21n))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1665 (all V23n (mem(V23n,ty_2Enum_2Enum) -> ($F <-> p(ap(ap(c_2Eprim__rec_2E_3C,V23n),c_2Enum_2E0))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1666 (all V24n (mem(V24n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V24n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,V24n)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1667 (all V25n (mem(V25n,ty_2Enum_2Enum) -> (all V26m (mem(V26m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V25n),V26m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,V25n)),ap(c_2Earithmetic_2ENUMERAL,V26m)))))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1668 (all V27n (mem(V27n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,c_2Enum_2E0),V27n)) <-> $F))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1669 (all V29n (mem(V29n,ty_2Enum_2Enum) -> (all V30m (mem(V30m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V29n)),ap(c_2Earithmetic_2ENUMERAL,V30m))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V30m),V29n))))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1670 (all V31n (mem(V31n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,c_2Enum_2E0),V31n)) <-> $T))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1671 (all V32n (mem(V32n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V32n),c_2Earithmetic_2EZERO)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V32n)),c_2Enum_2E0))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1672 (all V35n (mem(V35n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E_3D,V35n),c_2Enum_2E0)) <-> $T))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1673 (all V37n (mem(V37n,ty_2Enum_2Enum) -> (all V38m (mem(V38m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E_3D,ap(c_2Earithmetic_2ENUMERAL,V37n)),ap(c_2Earithmetic_2ENUMERAL,V38m))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V38m),V37n))))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1674 (all V39n (mem(V39n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,V39n)) <-> p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2ENUMERAL,V39n)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1675 (all V40n (mem(V40n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2ENUMERAL,V40n))) <-> p(ap(c_2Earithmetic_2EEVEN,V40n))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1676 (all V36n (mem(V36n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3E_3D,c_2Enum_2E0),V36n)) <-> V36n = c_2Enum_2E0))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1677 (all V33n (mem(V33n,ty_2Enum_2Enum) -> (all V34m (mem(V34m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V33n),V34m)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,V33n)),ap(c_2Earithmetic_2ENUMERAL,V34m)))))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1678 (all V28n (mem(V28n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),V28n)) <-> p(ap(ap(c_2Earithmetic_2E_3E,ap(c_2Earithmetic_2ENUMERAL,V28n)),c_2Enum_2E0))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1679 (all V20n (mem(V20n,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,V20n) = c_2Enum_2E0 <-> c_2Earithmetic_2EZERO = V20n))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1680 (all V19n (mem(V19n,ty_2Enum_2Enum) -> (c_2Earithmetic_2EZERO = V19n <-> c_2Enum_2E0 = ap(c_2Earithmetic_2ENUMERAL,V19n)))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1681 (all V17n (mem(V17n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,V17n)) = ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2ENUMERAL,V17n)))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1682 (all V15n (mem(V15n,ty_2Enum_2Enum) -> (all V16m (mem(V16m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,V15n)),ap(c_2Earithmetic_2ENUMERAL,V16m)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2EEXP,V15n),V16m)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1683 (all V14n (mem(V14n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EEXP,V14n),c_2Enum_2E0))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1684 (all V8n (mem(V8n,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2D,c_2Enum_2E0),V8n))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1685 (all V5n (mem(V5n,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2E_2A,V5n),c_2Enum_2E0))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1686 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3m (mem(V3m,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V2n),V3m))) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,V2n)),ap(c_2Earithmetic_2ENUMERAL,V3m)))))) # label(conj_thm_2Enumeral_2Enumeral__distrib_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1687 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V6m ap(f195(V3n),V6m) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V3n),V6m))))) # label(lameq_f195) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1688 (all A_27a (ne(A_27a) -> mem(c_2Enumeral_2EiBIT__cases(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,arr(arr(ty_2Enum_2Enum,A_27a),arr(arr(ty_2Enum_2Enum,A_27a),A_27a))))))) # label(mem_c_2Enumeral_2EiBIT__cases) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1689 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> c_2Earithmetic_2EZERO = ap(ap(c_2Enumeral_2Einternal__mult,c_2Earithmetic_2EZERO),V0n) & ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT2,V0n)),V1m) = ap(c_2Enumeral_2EiDUB,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Enumeral_2Einternal__mult,V0n),V1m)),V1m))) & ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumeral_2EiDUB,ap(ap(c_2Enumeral_2Einternal__mult,V0n),V1m))),V1m)) = ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT1,V0n)),V1m) & ap(ap(c_2Enumeral_2Einternal__mult,V0n),c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO)))) # label(conj_thm_2Enumeral_2Einternal__mult__characterisation) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1690 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EDIV2,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Earithmetic_2ENUMERAL,V0n))) # label(conj_thm_2Enumeral_2Enumeral__div2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1691 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Enum_2ESUC,V1n)) = ap(c_2Earithmetic_2EDIV2,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))))) # label(conj_thm_2Enumeral_2Enumeral__div2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1692 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(c_2Enumeral_2EiDUB,V0x) = ap(ap(c_2Earithmetic_2E_2B,V0x),V0x))) # label(ax_thm_2Enumeral_2EiDUB) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1693 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V5m ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V3n),V5m)) = ap(f194(V3n),V5m)))) # label(lameq_f194) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1694 (all A_27a (ne(A_27a) -> (all V0zf (mem(V0zf,A_27a) -> (all V1b1f (mem(V1b1f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V2b2f (mem(V2b2f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (exists V3f (V0zf = ap(V3f,c_2Earithmetic_2EZERO) & (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(V1b1f,V4n),ap(V3f,V4n)) = ap(V3f,ap(c_2Earithmetic_2EBIT1,V4n)))) & (all V5n (mem(V5n,ty_2Enum_2Enum) -> ap(V3f,ap(c_2Earithmetic_2EBIT2,V5n)) = ap(ap(V2b2f,V5n),ap(V3f,V5n)))) & mem(V3f,arr(ty_2Enum_2Enum,A_27a)))))))))))) # label(conj_thm_2Enumeral_2Ebit__initiality) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1695 (all V2x ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2x),c_2Earithmetic_2EZERO)),c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT1,V2x)) = ap(f202,V2x)) # label(lameq_f202) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1696 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (ap(c_2Enumeral_2Eexactlog,V0n) = ap(c_2Earithmetic_2EBIT1,V1m) -> V0n = ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2B,V1m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) # label(conj_thm_2Enumeral_2Eexactlog__characterisation) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1697 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(ap(c_2Enumeral_2Etexp__help,V0n),c_2Enum_2E0))) # label(conj_thm_2Enumeral_2Etexp__help0) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1698 (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V3n ap(f203(V1x,V2y),V3n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EODD,V3n)),ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EDIV2,V3n)),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V1x)))),ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT1,V1x)),ap(c_2Earithmetic_2EBIT2,V2y)))))))) # label(lameq_f203) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1699 (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V14m ap(f200(V10n),V14m) = ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V10n),V14m))))) # label(lameq_f200) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1700 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Earithmetic_2EFACT,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))))) = ap(c_2Earithmetic_2EFACT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))))) # label(conj_thm_2Enumeral_2Enumeral__fact_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1701 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))),ap(c_2Earithmetic_2EFACT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n)))) = ap(c_2Earithmetic_2EFACT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))))) # label(conj_thm_2Enumeral_2Enumeral__fact_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1702 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> c_2Earithmetic_2EZERO = ap(ap(c_2Earithmetic_2E_2A,V0n),c_2Earithmetic_2EZERO) & ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,V1x)),ap(c_2Earithmetic_2EBIT1,V2y)) = ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT1,V1x)),ap(c_2Earithmetic_2EBIT1,V2y)) & ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f206(V1x,V2y)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V1x))) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,V1x)),ap(c_2Earithmetic_2EBIT2,V2y)) & ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT2,V1x)),ap(c_2Earithmetic_2EBIT1,V2y)) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f204(V1x,V2y)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V1x))) & ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2EBIT1,V1x)),ap(c_2Earithmetic_2EBIT2,V2y)) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f203(V1x,V2y)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V2y))) & c_2Earithmetic_2EZERO = ap(ap(c_2Earithmetic_2E_2A,c_2Earithmetic_2EZERO),V0n))))))) # label(conj_thm_2Enumeral_2Eenumeral__mult) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1703 (all V0n (mem(V0n,ty_2Enum_2Enum) -> -p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2EBIT2,V0n))) & p(ap(c_2Earithmetic_2EODD,ap(c_2Earithmetic_2EBIT1,V0n))) & -p(ap(c_2Earithmetic_2EODD,c_2Earithmetic_2EZERO)) & -p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2EBIT1,V0n))) & p(ap(c_2Earithmetic_2EEVEN,ap(c_2Earithmetic_2EBIT2,V0n))) & p(ap(c_2Earithmetic_2EEVEN,c_2Earithmetic_2EZERO)))) # label(conj_thm_2Enumeral_2Enumeral__evenodd) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1704 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0x),V0x) = ap(c_2Enumeral_2EiSQR,V0x))) # label(ax_thm_2Enumeral_2EiSQR) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1705 (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V5m (mem(V5m,ty_2Enum_2Enum) -> (all V6n ap(f205(V1x,V2y,V5m),V6n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EODD,V5m)),ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EDIV2,V5m)),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT2,V2y)))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EODD,V6n)),ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EDIV2,V6n)),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT2,V1x)))),ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT2,V1x)),ap(c_2Earithmetic_2EBIT2,V2y))))))))))) # label(lameq_f205) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1706 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Etexp__help,V0n),V1a) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2E_2B,V1a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) # label(conj_thm_2Enumeral_2Etexp__help__thm) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1707 (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V4m ap(f204(V1x,V2y),V4m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(c_2Earithmetic_2EODD,V4m)),ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Earithmetic_2EDIV2,V4m)),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V2y)))),ap(ap(c_2Enumeral_2Einternal__mult,ap(c_2Earithmetic_2EBIT2,V1x)),ap(c_2Earithmetic_2EBIT1,V2y)))))))) # label(lameq_f204) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1708 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT2,ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,V0n))))) # label(conj_thm_2Enumeral_2Enumeral__pre_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1709 (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT1,V2n) = ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT2,V2n)))) # label(conj_thm_2Enumeral_2Enumeral__pre_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1710 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V1n)) = ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,V1n))))) # label(conj_thm_2Enumeral_2Enumeral__pre_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1711 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,A_27a)) -> (all V1x (mem(V1x,A_27a) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> V1x = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),c_2Enum_2E0),V1x) & ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),V1x) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Eprim__rec_2EPRE,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n)))),ap(V0f,V1x)) & ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V2n))),V1x) = ap(ap(ap(c_2Earithmetic_2EFUNPOW(A_27a),V0f),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V2n))),ap(V0f,V1x)))))))))) # label(conj_thm_2Enumeral_2Enumeral__funpow) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1712 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMAX,ap(c_2Earithmetic_2ENUMERAL,V0x)),ap(c_2Earithmetic_2ENUMERAL,V1y)) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0x),V1y)),V1y),V0x)) & ap(ap(c_2Earithmetic_2EMAX,V0x),c_2Enum_2E0) = V0x & ap(ap(c_2Earithmetic_2EMAX,c_2Enum_2E0),V0x) = V0x)))) # label(conj_thm_2Enumeral_2Enumeral__MAX) # label(axiom) # label(non_clause). [assumption]. 3.72/3.83 1713 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ($T <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT1,V0n)))) & (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m)))) & (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m)))) & (-p(ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m)))) & (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m)))) & (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),c_2Earithmetic_2EZERO)) <-> $F) & ($T <-> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Earithmetic_2EZERO),ap(c_2Earithmetic_2EBIT2,V0n)))))))) # label(conj_thm_2Enumeral_2Enumeral__lt) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1714 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V1n),ap(c_2Enumeral_2EiSQR,ap(ap(c_2Earithmetic_2EEXP,V1n),V2m))) = ap(ap(c_2Earithmetic_2EEXP,V1n),ap(c_2Earithmetic_2EBIT1,V2m)))))) # label(conj_thm_2Enumeral_2Enumeral__exp_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1715 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4m (mem(V4m,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,V3n),ap(c_2Earithmetic_2EBIT2,V4m)) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Enumeral_2EiSQR,V3n)),ap(c_2Enumeral_2EiSQR,ap(ap(c_2Earithmetic_2EEXP,V3n),V4m))))))) # label(conj_thm_2Enumeral_2Enumeral__exp_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1716 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO) = ap(ap(c_2Earithmetic_2EEXP,V0n),c_2Earithmetic_2EZERO))) # label(conj_thm_2Enumeral_2Enumeral__exp_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1717 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> V0n = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) & ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) & ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) & ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = ap(c_2Enum_2ESUC,V0n) & ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = ap(c_2Enum_2ESUC,V0n) & ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) & ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) & ap(c_2Enumeral_2EiiSUC,V0n) = ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) & ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),c_2Earithmetic_2EZERO)) = ap(c_2Enumeral_2EiiSUC,V0n) & ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) & ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) = ap(c_2Earithmetic_2EBIT1,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) & ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) & ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiiSUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) & ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) & ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT1,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) & ap(c_2Earithmetic_2EBIT2,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT2,V1m))) & ap(c_2Earithmetic_2EBIT1,ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2B,V0n),V1m))) = ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2EBIT2,V0n)),ap(c_2Earithmetic_2EBIT1,V1m))) & ap(c_2Enumeral_2EiZ,ap(ap(c_2Earithmetic_2E_2B,c_2Earithmetic_2EZERO),V0n)) = V0n)))) # label(conj_thm_2Enumeral_2Enumeral__add) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1718 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> ap(c_2Earithmetic_2EDIVMOD,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),V0a),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Eprim__rec_2E_3C,V1m),V2n)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0a),V1m)),ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f185(V0a,V1m,V2n)),ap(c_2Earithmetic_2Efindq,ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V1m),V2n)))))))))))) # label(conj_thm_2Enumeral_2Edivmod__POS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1719 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V8m ap(c_2Enumeral_2EiDUB,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V3n),V8m)) = ap(f197(V3n),V8m)))) # label(lameq_f197) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1720 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enum_2ESUC,ap(c_2Enum_2ESUC,V0n)) = ap(c_2Enumeral_2EiiSUC,V0n))) # label(ax_thm_2Enumeral_2EiiSUC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1721 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V7m ap(f196(V3n),V7m) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V3n),V7m))))) # label(lameq_f196) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1722 (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V12m ap(f198(V10n),V12m) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V10n),V12m))))) # label(lameq_f198) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1723 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMIN,c_2Enum_2E0),V0x) = c_2Enum_2E0 & ap(ap(c_2Earithmetic_2EMIN,V0x),c_2Enum_2E0) = c_2Enum_2E0 & ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V0x),V1y)),V0x),V1y)) = ap(ap(c_2Earithmetic_2EMIN,ap(c_2Earithmetic_2ENUMERAL,V0x)),ap(c_2Earithmetic_2ENUMERAL,V1y)))))) # label(conj_thm_2Enumeral_2Enumeral__MIN) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1724 (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V5m ap(f206(V1x,V2y),V5m) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f205(V1x,V2y,V5m)),ap(c_2Enumeral_2Eexactlog,ap(c_2Earithmetic_2EBIT2,V2y)))))))) # label(lameq_f206) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1725 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Enumeral_2Eonecount,V0n),V1a))) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Enumeral_2Eonecount,V0n),V1a)),V1a))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = V0n))))) # label(conj_thm_2Enumeral_2Eonecount__characterisation) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1726 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ($F <-> ap(c_2Earithmetic_2EBIT1,V0n) = c_2Earithmetic_2EZERO) & ($F <-> ap(c_2Earithmetic_2EBIT1,V0n) = c_2Earithmetic_2EZERO) & (c_2Earithmetic_2EZERO = ap(c_2Earithmetic_2EBIT2,V0n) <-> $F) & (V0n = V1m <-> ap(c_2Earithmetic_2EBIT2,V0n) = ap(c_2Earithmetic_2EBIT2,V1m)) & (V0n = V1m <-> ap(c_2Earithmetic_2EBIT1,V0n) = ap(c_2Earithmetic_2EBIT1,V1m)) & ($F <-> ap(c_2Earithmetic_2EBIT2,V0n) = ap(c_2Earithmetic_2EBIT1,V1m)) & ($F <-> ap(c_2Earithmetic_2EBIT1,V0n) = ap(c_2Earithmetic_2EBIT2,V1m)) & (c_2Earithmetic_2EZERO = ap(c_2Earithmetic_2EBIT2,V0n) <-> $F))))) # label(conj_thm_2Enumeral_2Enumeral__eq) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1727 (all V0x (mem(V0x,ty_2Enum_2Enum) -> V0x = ap(c_2Enumeral_2EiZ,V0x))) # label(ax_thm_2Enumeral_2EiZ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1728 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT1,V0n)) = ap(c_2Earithmetic_2EBIT2,ap(c_2Enumeral_2EiDUB,V0n)) & ap(c_2Enumeral_2EiDUB,c_2Earithmetic_2EZERO) = c_2Earithmetic_2EZERO & ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V0n)) = ap(c_2Enumeral_2EiDUB,ap(c_2Earithmetic_2EBIT2,V0n)))) # label(conj_thm_2Enumeral_2EiDUB__removal) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1729 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2acc (mem(V2acc,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Etexp__help,ap(c_2Enum_2ESUC,V1n)),V2acc) = ap(ap(c_2Enumeral_2Etexp__help,V1n),ap(c_2Earithmetic_2EBIT1,V2acc)))))) # label(ax_thm_2Enumeral_2Etexp__help__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1730 (all V0acc (mem(V0acc,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Etexp__help,c_2Enum_2E0),V0acc) = ap(c_2Earithmetic_2EBIT2,V0acc))) # label(ax_thm_2Enumeral_2Etexp__help__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1731 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Eonecount,c_2Earithmetic_2EZERO),V0x) = V0x)) # label(ax_thm_2Enumeral_2Eonecount__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1732 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4x (mem(V4x,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Eonecount,ap(c_2Earithmetic_2EBIT2,V3n)),V4x) = c_2Earithmetic_2EZERO)))) # label(ax_thm_2Enumeral_2Eonecount__def_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1733 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Enumeral_2Eonecount,V1n),ap(c_2Enum_2ESUC,V2x)) = ap(ap(c_2Enumeral_2Eonecount,ap(c_2Earithmetic_2EBIT1,V1n)),V2x))))) # label(ax_thm_2Enumeral_2Eonecount__def_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1734 (all V10n (mem(V10n,ty_2Enum_2Enum) -> (all V15m ap(f201(V10n),V15m) = ap(c_2Earithmetic_2EBIT1,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2EF),V10n),V15m))))) # label(lameq_f201) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1735 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1m),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(ap(ap(c_2Enumeral_2EiSUB,c_2Ebool_2ET),V0n),V1m))),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(ap(c_2Earithmetic_2E_2D,V0n),V1m)))))) # label(conj_thm_2Enumeral_2Enumeral__sub) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1736 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(c_2Edivides_2Edivides,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)))) # label(conj_thm_2Edivides_2EONE__DIVIDES__ALL) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1737 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0m),V1n)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Edivides_2EPRIMES,V0m)),ap(c_2Edivides_2EPRIMES,V1n)))))))) # label(conj_thm_2Edivides_2ELT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1738 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (V0x = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) <-> p(ap(ap(c_2Edivides_2Edivides,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) # label(conj_thm_2Edivides_2EDIVIDES__ONE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1739 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) -> p(ap(ap(c_2Edivides_2Edivides,V0m),ap(c_2Earithmetic_2EFACT,V1n)))))))) # label(conj_thm_2Edivides_2ELEQ__DIVIDES__FACT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1740 (all V0p (mem(V0p,ty_2Enum_2Enum) -> ((exists V1i (mem(V1i,ty_2Enum_2Enum) & V0p = ap(c_2Edivides_2EPRIMES,V1i))) <-> p(ap(c_2Edivides_2Eprime,V0p))))) # label(conj_thm_2Edivides_2EPRIME__INDEX) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1741 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1b),V0a)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b)) -> -p(ap(ap(c_2Edivides_2Edivides,V0a),V1b))))))) # label(conj_thm_2Edivides_2ENOT__LT__DIVIDES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1742 (all V0a (mem(V0a,ty_2Enum_2Enum) -> ((all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V1b),V0a)) -> V1b = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) | V1b = V0a))) & ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != V0a <-> p(ap(c_2Edivides_2Eprime,V0a))))) # label(ax_thm_2Edivides_2Eprime__def) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1743 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) & p(ap(ap(c_2Edivides_2Edivides,V0a),V2c)) -> p(ap(ap(c_2Edivides_2Edivides,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),V2c)))))))))) # label(conj_thm_2Edivides_2EDIVIDES__ADD__1) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1744 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> -(p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Edivides_2EPRIMES,V0n)),V1p)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1p),ap(c_2Edivides_2EPRIMES,ap(c_2Enum_2ESUC,V0n)))) & p(ap(c_2Edivides_2Eprime,V1p))))))) # label(conj_thm_2Edivides_2EPRIMES__NO__GAP) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1745 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(c_2Edivides_2EPRIMES,V0n))))) # label(conj_thm_2Edivides_2EZERO__LT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1746 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0b)) -> p(ap(ap(c_2Edivides_2Edivides,V0b),ap(c_2Earithmetic_2EFACT,V0b)))))) # label(conj_thm_2Edivides_2EDIVIDES__FACT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1747 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0p))))) # label(conj_thm_2Edivides_2EONE__LT__PRIME) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1748 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(c_2Edivides_2Edivides,V0a),V0a)))) # label(conj_thm_2Edivides_2EDIVIDES__REFL) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1749 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) <-> (exists V2q (mem(V2q,ty_2Enum_2Enum) & ap(ap(c_2Earithmetic_2E_2A,V2q),V0a) = V1b))))))) # label(ax_thm_2Edivides_2Edivides__def) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1750 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (V0n != ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) -> (exists V1p (p(ap(ap(c_2Edivides_2Edivides,V1p),V0n)) & p(ap(c_2Edivides_2Eprime,V1p)) & mem(V1p,ty_2Enum_2Enum)))))) # label(conj_thm_2Edivides_2EPRIME__FACTOR) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1751 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1p ap(f207(V0n),V1p) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Edivides_2Eprime,V1p)),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Edivides_2EPRIMES,V0n)),V1p))))) # label(lameq_f207) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1752 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0a),c_2Enum_2E0)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1b),c_2Enum_2E0)),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),c_2Ebool_2ET),ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1b),c_2Enum_2E0)),c_2Ebool_2ET),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EMOD,V1b),V0a)),c_2Enum_2E0)))))))))) # label(conj_thm_2Edivides_2Ecompute__divides) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1753 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) & p(ap(ap(c_2Edivides_2Edivides,V1b),V2c)) -> p(ap(ap(c_2Edivides_2Edivides,V0a),V2c))))))))) # label(conj_thm_2Edivides_2EDIVIDES__TRANS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1754 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b)) & p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b))))))) # label(conj_thm_2Edivides_2EDIVIDES__LE) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1755 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V1n)) & p(ap(ap(c_2Edivides_2Edivides,V0m),V1n)) & p(ap(c_2Edivides_2Eprime,V0m)) -> V1n = V0m))))) # label(conj_thm_2Edivides_2Eprime__divides__only__self) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1756 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (V0m = c_2Enum_2E0 <-> p(ap(ap(c_2Edivides_2Edivides,c_2Enum_2E0),V0m))))) # label(conj_thm_2Edivides_2EZERO__DIVIDES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1757 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0m),V1n)) -> V1n = c_2Enum_2E0 | p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n))))))) # label(conj_thm_2Edivides_2EDIVIDES__LEQ__OR__ZERO) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1758 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (exists V1i (mem(V1i,ty_2Enum_2Enum) & (all V2j (mem(V2j,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2j),V1i)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Edivides_2EPRIMES,V2j)),V0n))))) & p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Edivides_2EPRIMES,V1i))))))) # label(conj_thm_2Edivides_2ENEXT__LARGER__PRIME) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1759 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(c_2Edivides_2Edivides,V0a),c_2Enum_2E0)))) # label(conj_thm_2Edivides_2EALL__DIVIDES__0) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1760 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(c_2Edivides_2Eprime,ap(c_2Edivides_2EPRIMES,V0n))))) # label(conj_thm_2Edivides_2EprimePRIMES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1761 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) -> p(ap(ap(c_2Edivides_2Edivides,V0a),ap(ap(c_2Earithmetic_2E_2A,V1b),V2c)))))))))) # label(conj_thm_2Edivides_2EDIVIDES__MULT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1762 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) -> (exists V1i (mem(V1i,ty_2Enum_2Enum) & V0p = ap(c_2Edivides_2EPRIMES,V1i)))))) # label(conj_thm_2Edivides_2EPRIMES__ONTO) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1763 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) & p(ap(ap(c_2Edivides_2Edivides,V1b),V0a)) -> V0a = V1b))))) # label(conj_thm_2Edivides_2EDIVIDES__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1764 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),V2c))) & p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) -> p(ap(ap(c_2Edivides_2Edivides,V0a),V2c))))))))) # label(conj_thm_2Edivides_2EDIVIDES__ADD__2) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1765 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(c_2Edivides_2EPRIMES,V0m) = ap(c_2Edivides_2EPRIMES,V1n) -> V1n = V0m))))) # label(conj_thm_2Edivides_2EPRIMES__11) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1766 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = V0n | c_2Enum_2E0 = V1m <-> p(ap(ap(c_2Edivides_2Edivides,ap(ap(c_2Earithmetic_2E_2A,V0n),V1m)),V1m))))))) # label(conj_thm_2Edivides_2EDIVIDES__MULT__LEFT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1767 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Ewhile_2ELEAST,f207(V0n)) = ap(c_2Edivides_2EPRIMES,ap(c_2Enum_2ESUC,V0n)))) # label(ax_thm_2Edivides_2EPRIMES__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1768 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Edivides_2EPRIMES,V0n))))) # label(conj_thm_2Edivides_2EINDEX__LESS__PRIMES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1769 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0a),V2c)) & p(ap(ap(c_2Edivides_2Edivides,V0a),V1b)) -> p(ap(ap(c_2Edivides_2Edivides,V0a),ap(ap(c_2Earithmetic_2E_2D,V1b),V2c)))))))))) # label(conj_thm_2Edivides_2EDIVIDES__SUB) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1770 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0p))))) # label(conj_thm_2Edivides_2EPRIME__POS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1771 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (exists V1p (mem(V1p,ty_2Enum_2Enum) & p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1p)) & p(ap(c_2Edivides_2Eprime,V1p)))))) # label(conj_thm_2Edivides_2EEUCLID) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1772 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Edivides_2EPRIMES,V0n)),ap(c_2Edivides_2EPRIMES,ap(c_2Enum_2ESUC,V0n)))))) # label(conj_thm_2Edivides_2EINFINITE__PRIMES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1773 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (exists V1i (mem(V1i,ty_2Enum_2Enum) & p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Edivides_2EPRIMES,V1i))))))) # label(conj_thm_2Edivides_2EEUCLID__PRIMES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1774 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Edivides_2EPRIMES,V0n))))) # label(conj_thm_2Edivides_2EONE__LT__PRIMES) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1775 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EINJA(A_27a),arr(A_27a,arr(ty_2Enum_2Enum,arr(A_27a,bool)))))) # label(mem_c_2Eind__type_2EINJA) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1776 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Eind__type_2EFCONS(A_27a),V0a),V1f),V2n) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2n),c_2Enum_2E0)),V0a),ap(V1f,ap(ap(c_2Earithmetic_2E_2D,V2n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))))) # label(conj_thm_2Eind__type_2EFCONS__DEST) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1777 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EBOTTOM(A_27a),ty_2Eind__type_2Erecspace(A_27a)))) # label(mem_c_2Eind__type_2EBOTTOM) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1778 (all A_27a (ne(A_27a) -> (all V0n1 (mem(V0n1,ty_2Enum_2Enum) -> (all V1n2 (mem(V1n2,ty_2Enum_2Enum) -> (ap(c_2Eind__type_2EINJN(A_27a),V0n1) = ap(c_2Eind__type_2EINJN(A_27a),V1n2) <-> V0n1 = V1n2))))))) # label(conj_thm_2Eind__type_2EINJN__INJ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1779 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1i (mem(V1i,A_27a) -> (all V2r (mem(V2r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> c_2Eind__type_2EBOTTOM(A_27a) != ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V0c),V1i),V2r))))))))) # label(conj_thm_2Eind__type_2ECONSTR__BOT) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1780 (all A0 (ne(A0) -> ne(ty_2Eind__type_2Erecspace(A0)))) # label(ne_ty_2Eind__type_2Erecspace) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1781 (all A_27a all A_27b all V4r (mem(V4r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> (all V1f (mem(V1f,arr(ty_2Eind__type_2Erecspace(A_27a),A_27b)) -> (all V5n ap(V1f,ap(V4r,V5n)) = ap(f221(A_27a,A_27b,V4r,V1f),V5n)))))) # label(lameq_f221) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1782 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0Fn (mem(V0Fn,arr(ty_2Enum_2Enum,arr(A_27a,arr(arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a)),arr(arr(ty_2Enum_2Enum,A_27b),A_27b))))) -> (exists V1f (mem(V1f,arr(ty_2Eind__type_2Erecspace(A_27a),A_27b)) & (all V2c (mem(V2c,ty_2Enum_2Enum) -> (all V3i (mem(V3i,A_27a) -> (all V4r (mem(V4r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> ap(ap(ap(ap(V0Fn,V2c),V3i),V4r),f221(A_27a,A_27b,V4r,V1f)) = ap(V1f,ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V2c),V3i),V4r)))))))))))))))) # label(conj_thm_2Eind__type_2ECONSTR__REC) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1783 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> f210(A_27a,V0f) = ap(c_2Eind__type_2EINJF(A_27a),V0f))))) # label(ax_thm_2Eind__type_2EINJF) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1784 (all A_27a (ne(A_27a) -> (all V2a (mem(V2a,A_27a) -> (all V3f (mem(V3f,arr(ty_2Enum_2Enum,A_27a)) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Eind__type_2EFCONS(A_27a),V2a),V3f),ap(c_2Enum_2ESUC,V4n)) = ap(V3f,V4n))))))) & (all V0a (mem(V0a,A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,A_27a)) -> ap(ap(ap(c_2Eind__type_2EFCONS(A_27a),V0a),V1f),c_2Enum_2E0) = V0a)))))) # label(ax_thm_2Eind__type_2EFCONS) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1785 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> (all V1n ap(ap(V0f,ap(c_2Eind__type_2ENUMFST,V1n)),ap(c_2Eind__type_2ENUMSND,V1n)) = ap(f210(A_27a,V0f),V1n)))) # label(lameq_f210) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1786 (all V0b1 (mem(V0b1,bool) -> (all V1x1 (mem(V1x1,ty_2Enum_2Enum) -> (all V2b2 (mem(V2b2,bool) -> (all V3x2 (mem(V3x2,ty_2Enum_2Enum) -> (V1x1 = V3x2 & (p(V2b2) <-> p(V0b1)) <-> ap(ap(c_2Eind__type_2ENUMSUM,V2b2),V3x2) = ap(ap(c_2Eind__type_2ENUMSUM,V0b1),V1x1)))))))))) # label(conj_thm_2Eind__type_2ENUMSUM__INJ) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1787 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2Emk__rec(A_27a),arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),ty_2Eind__type_2Erecspace(A_27a))))) # label(mem_c_2Eind__type_2Emk__rec) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1788 (all A_27a all V0a0 ap(c_2Ebool_2E_21(arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)),f218(A_27a,V0a0)) = ap(f219(A_27a),V0a0)) # label(lameq_f219) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1789 (all A_27a all V0f1 (mem(V0f1,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V1f2 (mem(V1f2,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V3a ap(ap(ap(c_2Ebool_2ECOND(bool),ap(c_2Eind__type_2ENUMLEFT,V2n)),ap(ap(V0f1,ap(c_2Eind__type_2ENUMRIGHT,V2n)),V3a)),ap(ap(V1f2,ap(c_2Eind__type_2ENUMRIGHT,V2n)),V3a)) = ap(f211(A_27a,V0f1,V2n,V1f2),V3a)))))))) # label(lameq_f211) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1790 (all A_27a all V1ZRECSPACE_27 (mem(V1ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (all V2a0 (mem(V2a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V3c (mem(V3c,ty_2Enum_2Enum) -> (all V4i ap(f215(A_27a,V1ZRECSPACE_27,V2a0,V3c),V4i) = ap(c_2Ebool_2E_3F(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))),f214(A_27a,V3c,V4i,V2a0,V1ZRECSPACE_27))))))))) # label(lameq_f215) # label(axiom) # label(non_clause). [assumption]. 3.72/3.84 1791 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EFCONS(A_27a),arr(A_27a,arr(arr(ty_2Enum_2Enum,A_27a),arr(ty_2Enum_2Enum,A_27a)))))) # label(mem_c_2Eind__type_2EFCONS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1792 (all V0x (mem(V0x,bool) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> V1y = ap(c_2Eind__type_2ENUMRIGHT,ap(ap(c_2Eind__type_2ENUMSUM,V0x),V1y)) & (p(ap(c_2Eind__type_2ENUMLEFT,ap(ap(c_2Eind__type_2ENUMSUM,V0x),V1y))) <-> p(V0x)))))) # label(ax_thm_2Eind__type_2ENUMSUM__DEST) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1793 (all A_27a (ne(A_27a) -> c_2Eind__type_2EZRECSPACE(A_27a) = f219(A_27a))) # label(ax_thm_2Eind__type_2EZRECSPACE__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1794 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> ap(ap(c_2Eind__type_2ENUMPAIR,V0x),V1y) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1y)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))) # label(ax_thm_2Eind__type_2ENUMPAIR) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1795 (all A_27a (ne(A_27a) -> (all V0a1 (mem(V0a1,A_27a) -> (all V1a2 (mem(V1a2,A_27a) -> (V0a1 = V1a2 <-> ap(c_2Eind__type_2EINJA(A_27a),V0a1) = ap(c_2Eind__type_2EINJA(A_27a),V1a2)))))))) # label(conj_thm_2Eind__type_2EINJA__INJ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1796 (all A_27a all A_27b all A_27c all A_27d all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V3g_27 (mem(V3g_27,arr(A_27d,A_27b)) -> (all V6h f224(A_27b,A_27d,A_27c,A_27a,V6h,V0f,V3g_27) = ap(f225(A_27a,A_27b,A_27c,A_27d,V0f,V3g_27),V6h)))))) # label(lameq_f225) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1797 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EZCONSTR(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,arr(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool))),arr(ty_2Enum_2Enum,arr(A_27a,bool)))))))) # label(mem_c_2Eind__type_2EZCONSTR) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1798 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1i (mem(V1i,A_27a) -> (all V2r (mem(V2r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V0c),V1i),V2r) = ap(c_2Eind__type_2Emk__rec(A_27a),ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V0c),V1i),f220(A_27a,V2r))))))))))) # label(ax_thm_2Eind__type_2ECONSTR) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1799 (all A_27a all V2r (mem(V2r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> (all V3n ap(c_2Eind__type_2Edest__rec(A_27a),ap(V2r,V3n)) = ap(f220(A_27a,V2r),V3n)))) # label(lameq_f220) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1800 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Eind__type_2Erecspace(A_27a),bool)) -> (p(ap(V0P,c_2Eind__type_2EBOTTOM(A_27a))) & (all V1c (mem(V1c,ty_2Enum_2Enum) -> (all V2i (mem(V2i,A_27a) -> (all V3r (mem(V3r,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> ((all V4n (mem(V4n,ty_2Enum_2Enum) -> p(ap(V0P,ap(V3r,V4n))))) -> p(ap(V0P,ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V1c),V2i),V3r)))))))))) -> (all V5x (mem(V5x,ty_2Eind__type_2Erecspace(A_27a)) -> p(ap(V0P,V5x))))))))) # label(conj_thm_2Eind__type_2ECONSTR__IND) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1801 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all A_27d (ne(A_27d) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V1f_27 (mem(V1f_27,arr(A_27c,A_27a)) -> (all V2g (mem(V2g,arr(A_27b,A_27d)) -> (all V3g_27 (mem(V3g_27,arr(A_27d,A_27b)) -> (p(ap(ap(c_2Eind__type_2EISO(A_27a,A_27c),V0f),V1f_27)) & p(ap(ap(c_2Eind__type_2EISO(A_27b,A_27d),V2g),V3g_27)) -> p(ap(ap(c_2Eind__type_2EISO(arr(A_27a,A_27b),arr(A_27c,A_27d)),f223(A_27c,A_27d,A_27a,A_27b,V1f_27,V2g)),f225(A_27a,A_27b,A_27c,A_27d,V0f,V3g_27)))))))))))))))))))) # label(conj_thm_2Eind__type_2EISO__FUN) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1802 (all A_27a (ne(A_27a) -> (all V0f1 (mem(V0f1,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> (all V1f2 (mem(V1f2,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> (ap(c_2Eind__type_2EINJF(A_27a),V1f2) = ap(c_2Eind__type_2EINJF(A_27a),V0f1) <-> V0f1 = V1f2))))))) # label(conj_thm_2Eind__type_2EINJF__INJ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1803 (all A_27a (ne(A_27a) -> (all V0ZRECSPACE_27 (mem(V0ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (p(ap(V0ZRECSPACE_27,c_2Eind__type_2EZBOT(A_27a))) & (all V1c (mem(V1c,ty_2Enum_2Enum) -> (all V2i (mem(V2i,A_27a) -> (all V3r (mem(V3r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> ((all V4n (mem(V4n,ty_2Enum_2Enum) -> p(ap(V0ZRECSPACE_27,ap(V3r,V4n))))) -> p(ap(V0ZRECSPACE_27,ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V1c),V2i),V3r)))))))))) -> (all V5a0 (mem(V5a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V5a0)) -> p(ap(V0ZRECSPACE_27,V5a0)))))))))) # label(conj_thm_2Eind__type_2EZRECSPACE__ind) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1804 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EZRECSPACE(A_27a),arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)))) # label(mem_c_2Eind__type_2EZRECSPACE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1805 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27b,A_27a)) -> (p(ap(ap(c_2Eind__type_2EISO(A_27a,A_27b),V0f),V1g)) -> (all V8a (mem(V8a,A_27a) -> (all V9b (mem(V9b,A_27b) -> (ap(V0f,V8a) = V9b <-> V8a = ap(V1g,V9b)))))) & (all V5P (mem(V5P,arr(A_27a,bool)) -> ((exists V6x (mem(V6x,A_27a) & p(ap(V5P,V6x)))) <-> (exists V7x (mem(V7x,A_27b) & p(ap(V5P,ap(V1g,V7x)))))))) & (all V2P (mem(V2P,arr(A_27a,bool)) -> ((all V4x (mem(V4x,A_27b) -> p(ap(V2P,ap(V1g,V4x))))) <-> (all V3x (mem(V3x,A_27a) -> p(ap(V2P,V3x)))))))))))))))) # label(conj_thm_2Eind__type_2EISO__USAGE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1806 (all A_27a (ne(A_27a) -> (all V1r (mem(V1r,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V1r)) <-> ap(c_2Eind__type_2Edest__rec(A_27a),ap(c_2Eind__type_2Emk__rec(A_27a),V1r)) = V1r))) & (all V0a (mem(V0a,ty_2Eind__type_2Erecspace(A_27a)) -> V0a = ap(c_2Eind__type_2Emk__rec(A_27a),ap(c_2Eind__type_2Edest__rec(A_27a),V0a)))))) # label(ax_thm_2Eind__type_2Erecspace__repfns) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1807 (all A_27a all V0f1 (mem(V0f1,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1f2 (mem(V1f2,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V2n f211(A_27a,V0f1,V2n,V1f2) = ap(f212(A_27a,V0f1,V1f2),V2n)))))) # label(lameq_f212) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1808 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EINJP(A_27a),arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),arr(ty_2Enum_2Enum,arr(A_27a,bool))))))) # label(mem_c_2Eind__type_2EINJP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1809 (all A_27a (ne(A_27a) -> (all V0c1 (mem(V0c1,ty_2Enum_2Enum) -> (all V1i1 (mem(V1i1,A_27a) -> (all V2r1 (mem(V2r1,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> (all V3c2 (mem(V3c2,ty_2Enum_2Enum) -> (all V4i2 (mem(V4i2,A_27a) -> (all V5r2 (mem(V5r2,arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a))) -> (ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V3c2),V4i2),V5r2) = ap(ap(ap(c_2Eind__type_2ECONSTR(A_27a),V0c1),V1i1),V2r1) <-> V1i1 = V4i2 & V5r2 = V2r1 & V3c2 = V0c1))))))))))))))) # label(conj_thm_2Eind__type_2ECONSTR__INJ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1810 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1y (mem(V1y,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (ap(c_2Eind__type_2Emk__rec(A_27a),V1y) = ap(c_2Eind__type_2Emk__rec(A_27a),V0x) -> (p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V1y)) & p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V0x)) -> V1y = V0x)))))))) # label(conj_thm_2Eind__type_2EMK__REC__INJ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1811 (all A_27d all A_27b all A_27a all A_27c all V4h (mem(V4h,arr(A_27a,A_27b)) -> (all V1f_27 (mem(V1f_27,arr(A_27c,A_27a)) -> (all V2g (mem(V2g,arr(A_27b,A_27d)) -> (all V5a_27 ap(V2g,ap(V4h,ap(V1f_27,V5a_27))) = ap(f222(A_27d,A_27b,A_27a,A_27c,V4h,V1f_27,V2g),V5a_27)))))))) # label(lameq_f222) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1812 (all A_27a all V3c (mem(V3c,ty_2Enum_2Enum) -> (all V4i (mem(V4i,A_27a) -> (all V2a0 (mem(V2a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1ZRECSPACE_27 (mem(V1ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (all V5r ap(f214(A_27a,V3c,V4i,V2a0,V1ZRECSPACE_27),V5r) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(arr(ty_2Enum_2Enum,arr(A_27a,bool))),V2a0),ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V3c),V4i),V5r))),ap(c_2Ebool_2E_21(ty_2Enum_2Enum),f213(A_27a,V5r,V1ZRECSPACE_27)))))))))))) # label(lameq_f214) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1813 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EZBOT(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,bool))))) # label(mem_c_2Eind__type_2EZBOT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1814 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2ECONSTR(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,arr(arr(ty_2Enum_2Enum,ty_2Eind__type_2Erecspace(A_27a)),ty_2Eind__type_2Erecspace(A_27a))))))) # label(mem_c_2Eind__type_2ECONSTR) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1815 (all V0x1 (mem(V0x1,ty_2Enum_2Enum) -> (all V1y1 (mem(V1y1,ty_2Enum_2Enum) -> (all V2x2 (mem(V2x2,ty_2Enum_2Enum) -> (all V3y2 (mem(V3y2,ty_2Enum_2Enum) -> (ap(ap(c_2Eind__type_2ENUMPAIR,V0x1),V1y1) = ap(ap(c_2Eind__type_2ENUMPAIR,V2x2),V3y2) -> V2x2 = V0x1))))))))) # label(conj_thm_2Eind__type_2ENUMPAIR__INJ__LEMMA) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1816 (all A_27a all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n k(A_27a,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),V0m)) = ap(f208(A_27a,V0m),V1n)))) # label(lameq_f208) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1817 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1i (mem(V1i,A_27a) -> (all V2r (mem(V2r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V0c),V1i),V2r) = ap(ap(c_2Eind__type_2EINJP(A_27a),ap(c_2Eind__type_2EINJN(A_27a),ap(c_2Enum_2ESUC,V0c))),ap(ap(c_2Eind__type_2EINJP(A_27a),ap(c_2Eind__type_2EINJA(A_27a),V1i)),ap(c_2Eind__type_2EINJF(A_27a),V2r))))))))))) # label(ax_thm_2Eind__type_2EZCONSTR) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1818 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,ty_2Eind__type_2Erecspace(A_27a)) -> (all V1y (mem(V1y,ty_2Eind__type_2Erecspace(A_27a)) -> (V1y = V0x <-> ap(c_2Eind__type_2Edest__rec(A_27a),V1y) = ap(c_2Eind__type_2Edest__rec(A_27a),V0x)))))))) # label(conj_thm_2Eind__type_2EDEST__REC__INJ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1819 (all A_27a all V2a0 (mem(V2a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1ZRECSPACE_27 (mem(V1ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (all V3c ap(c_2Ebool_2E_3F(A_27a),f215(A_27a,V1ZRECSPACE_27,V2a0,V3c)) = ap(f216(A_27a,V2a0,V1ZRECSPACE_27),V3c)))))) # label(lameq_f216) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1820 (all A_27a all V1ZRECSPACE_27 (mem(V1ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (all V2a0 ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(arr(ty_2Enum_2Enum,arr(A_27a,bool))),V2a0),c_2Eind__type_2EZBOT(A_27a))),ap(c_2Ebool_2E_3F(ty_2Enum_2Enum),f216(A_27a,V2a0,V1ZRECSPACE_27)))),ap(V1ZRECSPACE_27,V2a0)) = ap(f217(A_27a,V1ZRECSPACE_27),V2a0)))) # label(lameq_f217) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1821 (all A_27b all A_27d all A_27c all A_27a all V6h (mem(V6h,arr(A_27c,A_27d)) -> (all V0f (mem(V0f,arr(A_27a,A_27c)) -> (all V3g_27 (mem(V3g_27,arr(A_27d,A_27b)) -> (all V7a ap(f224(A_27b,A_27d,A_27c,A_27a,V6h,V0f,V3g_27),V7a) = ap(V3g_27,ap(V6h,ap(V0f,V7a)))))))))) # label(lameq_f224) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1822 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> V0x = ap(c_2Eind__type_2ENUMFST,ap(ap(c_2Eind__type_2ENUMPAIR,V0x),V1y)) & V1y = ap(c_2Eind__type_2ENUMSND,ap(ap(c_2Eind__type_2ENUMPAIR,V0x),V1y)))))) # label(ax_thm_2Eind__type_2ENUMPAIR__DEST) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1823 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EINJN(A_27a),arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))))) # label(mem_c_2Eind__type_2EINJN) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1824 (all A_27a (ne(A_27a) -> (exists V0rep (p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(arr(ty_2Enum_2Enum,arr(A_27a,bool)),ty_2Eind__type_2Erecspace(A_27a)),c_2Eind__type_2EZRECSPACE(A_27a)),V0rep)) & mem(V0rep,arr(ty_2Eind__type_2Erecspace(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,bool)))))))) # label(ax_thm_2Eind__type_2Erecspace__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1825 (all V0x1 (mem(V0x1,ty_2Enum_2Enum) -> (all V1y1 (mem(V1y1,ty_2Enum_2Enum) -> (all V2x2 (mem(V2x2,ty_2Enum_2Enum) -> (all V3y2 (mem(V3y2,ty_2Enum_2Enum) -> (ap(ap(c_2Eind__type_2ENUMPAIR,V2x2),V3y2) = ap(ap(c_2Eind__type_2ENUMPAIR,V0x1),V1y1) <-> V3y2 = V1y1 & V0x1 = V2x2))))))))) # label(conj_thm_2Eind__type_2ENUMPAIR__INJ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1826 (all A_27a (ne(A_27a) -> p(ap(ap(c_2Eind__type_2EISO(A_27a,A_27a),i(A_27a)),i(A_27a))))) # label(conj_thm_2Eind__type_2EISO__REFL) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1827 (all A_27a all V0a0 (mem(V0a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1ZRECSPACE_27 ap(f218(A_27a,V0a0),V1ZRECSPACE_27) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(c_2Ebool_2E_21(arr(ty_2Enum_2Enum,arr(A_27a,bool))),f217(A_27a,V1ZRECSPACE_27))),ap(V1ZRECSPACE_27,V0a0))))) # label(lameq_f218) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1828 (all A_27a (ne(A_27a) -> (all V0m (mem(V0m,ty_2Enum_2Enum) -> f208(A_27a,V0m) = ap(c_2Eind__type_2EINJN(A_27a),V0m))))) # label(ax_thm_2Eind__type_2EINJN) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1829 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2Edest__rec(A_27a),arr(ty_2Eind__type_2Erecspace(A_27a),arr(ty_2Enum_2Enum,arr(A_27a,bool)))))) # label(mem_c_2Eind__type_2Edest__rec) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1830 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1i (mem(V1i,A_27a) -> (all V2r (mem(V2r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> ((all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(c_2Eind__type_2EZRECSPACE(A_27a),ap(V2r,V3n))))) -> p(ap(c_2Eind__type_2EZRECSPACE(A_27a),ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V0c),V1i),V2r)))))))))) & p(ap(c_2Eind__type_2EZRECSPACE(A_27a),c_2Eind__type_2EZBOT(A_27a))))) # label(conj_thm_2Eind__type_2EZRECSPACE__rules) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1831 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EINJF(A_27a),arr(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool))),arr(ty_2Enum_2Enum,arr(A_27a,bool)))))) # label(mem_c_2Eind__type_2EINJF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1832 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> k(ty_2Enum_2Enum,f209(A_27a,V0a)) = ap(c_2Eind__type_2EINJA(A_27a),V0a))))) # label(ax_thm_2Eind__type_2EINJA) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1833 (all A_27a (ne(A_27a) -> (all V0a0 (mem(V0a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V0a0)) <-> c_2Eind__type_2EZBOT(A_27a) = V0a0 | (exists V1c ((exists V2i (mem(V2i,A_27a) & (exists V3r (V0a0 = ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V1c),V2i),V3r) & (all V4n (mem(V4n,ty_2Enum_2Enum) -> p(ap(c_2Eind__type_2EZRECSPACE(A_27a),ap(V3r,V4n))))) & mem(V3r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))))))) & mem(V1c,ty_2Enum_2Enum)))))))) # label(conj_thm_2Eind__type_2EZRECSPACE__cases) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1834 (all A_27a (ne(A_27a) -> ap(ap(c_2Eind__type_2EINJP(A_27a),ap(c_2Eind__type_2EINJN(A_27a),c_2Enum_2E0)),ap(c_2Emin_2E_40(arr(ty_2Enum_2Enum,arr(A_27a,bool))),k(arr(ty_2Enum_2Enum,arr(A_27a,bool)),c_2Ebool_2ET))) = c_2Eind__type_2EZBOT(A_27a))) # label(ax_thm_2Eind__type_2EZBOT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1835 (all V0b (mem(V0b,bool) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V0b),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1x)) = ap(ap(c_2Eind__type_2ENUMSUM,V0b),V1x))))) # label(ax_thm_2Eind__type_2ENUMSUM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1836 (all A_27c all A_27d all A_27a all A_27b all V1f_27 (mem(V1f_27,arr(A_27c,A_27a)) -> (all V2g (mem(V2g,arr(A_27b,A_27d)) -> (all V4h ap(f223(A_27c,A_27d,A_27a,A_27b,V1f_27,V2g),V4h) = f222(A_27d,A_27b,A_27a,A_27c,V4h,V1f_27,V2g)))))) # label(lameq_f223) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1837 (all A_27a all V5r (mem(V5r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> (all V1ZRECSPACE_27 (mem(V1ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (all V6n ap(f213(A_27a,V5r,V1ZRECSPACE_27),V6n) = ap(V1ZRECSPACE_27,ap(V5r,V6n))))))) # label(lameq_f213) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1838 (all A_27a (ne(A_27a) -> (all V0f1 (mem(V0f1,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1f1_27 (mem(V1f1_27,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V2f2 (mem(V2f2,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V3f2_27 (mem(V3f2_27,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (ap(ap(c_2Eind__type_2EINJP(A_27a),V1f1_27),V3f2_27) = ap(ap(c_2Eind__type_2EINJP(A_27a),V0f1),V2f2) <-> V1f1_27 = V0f1 & V2f2 = V3f2_27))))))))))) # label(conj_thm_2Eind__type_2EINJP__INJ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1839 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Eind__type_2EFNIL(A_27a),V0n) = c_2Ebool_2EARB(A_27a))))) # label(ax_thm_2Eind__type_2EFNIL) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1840 (all A_27a (ne(A_27a) -> mem(c_2Eind__type_2EFNIL(A_27a),arr(ty_2Enum_2Enum,A_27a)))) # label(mem_c_2Eind__type_2EFNIL) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1841 (all A_27a (ne(A_27a) -> (all V0c (mem(V0c,ty_2Enum_2Enum) -> (all V1i (mem(V1i,A_27a) -> (all V2r (mem(V2r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> c_2Eind__type_2EZBOT(A_27a) != ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V0c),V1i),V2r))))))))) # label(conj_thm_2Eind__type_2EZCONSTR__ZBOT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1842 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Eind__type_2EISO(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,A_27a),bool))))))) # label(mem_c_2Eind__type_2EISO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1843 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1g (mem(V1g,arr(A_27b,A_27a)) -> (p(ap(ap(c_2Eind__type_2EISO(A_27a,A_27b),V0f),V1g)) <-> (all V2x (mem(V2x,A_27b) -> ap(V0f,ap(V1g,V2x)) = V2x)) & (all V3y (mem(V3y,A_27a) -> V3y = ap(V1g,ap(V0f,V3y))))))))))))) # label(ax_thm_2Eind__type_2EISO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1844 (all A_27A (ne(A_27A) -> (all A_27B (ne(A_27B) -> (all A_27C (ne(A_27C) -> (all V0P (mem(V0P,arr(A_27A,arr(A_27B,A_27C))) -> ((all V1x1 (mem(V1x1,A_27A) -> (all V2y1 (mem(V2y1,A_27B) -> (all V3x2 (mem(V3x2,A_27A) -> (all V4y2 (mem(V4y2,A_27B) -> (V1x1 = V3x2 & V2y1 = V4y2 <-> ap(ap(V0P,V3x2),V4y2) = ap(ap(V0P,V1x1),V2y1)))))))))) -> (exists V5X ((exists V6Y ((all V7x (mem(V7x,A_27A) -> (all V8y (mem(V8y,A_27B) -> ap(V5X,ap(ap(V0P,V7x),V8y)) = V7x & V8y = ap(V6Y,ap(ap(V0P,V7x),V8y)))))) & mem(V6Y,arr(A_27C,A_27B)))) & mem(V5X,arr(A_27C,A_27A))))))))))))) # label(conj_thm_2Eind__type_2EINJ__INVERSE2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1845 (all A_27a (ne(A_27a) -> (all V0f1 (mem(V0f1,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1f2 (mem(V1f2,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> ap(ap(c_2Eind__type_2EINJP(A_27a),V0f1),V1f2) = f212(A_27a,V0f1,V1f2))))))) # label(ax_thm_2Eind__type_2EINJP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1846 (all A_27a (ne(A_27a) -> (all V0ZRECSPACE_27 (mem(V0ZRECSPACE_27,arr(arr(ty_2Enum_2Enum,arr(A_27a,bool)),bool)) -> (p(ap(V0ZRECSPACE_27,c_2Eind__type_2EZBOT(A_27a))) & (all V1c (mem(V1c,ty_2Enum_2Enum) -> (all V2i (mem(V2i,A_27a) -> (all V3r (mem(V3r,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,bool)))) -> ((all V4n (mem(V4n,ty_2Enum_2Enum) -> p(ap(c_2Eind__type_2EZRECSPACE(A_27a),ap(V3r,V4n))) & p(ap(V0ZRECSPACE_27,ap(V3r,V4n))))) -> p(ap(V0ZRECSPACE_27,ap(ap(ap(c_2Eind__type_2EZCONSTR(A_27a),V1c),V2i),V3r)))))))))) -> (all V5a0 (mem(V5a0,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (p(ap(c_2Eind__type_2EZRECSPACE(A_27a),V5a0)) -> p(ap(V0ZRECSPACE_27,V5a0)))))))))) # label(conj_thm_2Eind__type_2EZRECSPACE__strongind) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1847 (all A_27a all V0a (mem(V0a,A_27a) -> (all V2b ap(f209(A_27a,V0a),V2b) = ap(ap(c_2Emin_2E_3D(A_27a),V2b),V0a)))) # label(lameq_f209) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1848 (all A_27a (ne(A_27a) -> c_2Eind__type_2EBOTTOM(A_27a) = ap(c_2Eind__type_2Emk__rec(A_27a),c_2Eind__type_2EZBOT(A_27a)))) # label(ax_thm_2Eind__type_2EBOTTOM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1849 (all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2x (mem(V2x,A_27a) -> (all V1g (mem(V1g,arr(A_27b,ty_2Enum_2Enum)) -> (all V3y ap(f226(A_27a,A_27b,V0f,V2x,V1g),V3y) = ap(ap(c_2Earithmetic_2E_2B,ap(V0f,V2x)),ap(V1g,V3y))))))))) # label(lameq_f226) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1850 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EbasicSize_2Epair__size(A_27a,A_27b),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27b,ty_2Enum_2Enum),arr(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Enum_2Enum)))))))) # label(mem_c_2EbasicSize_2Epair__size) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1851 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27b,ty_2Enum_2Enum)) -> ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Enum_2Enum),f227(A_27b,A_27a,V0f,V1g)) = ap(ap(c_2EbasicSize_2Epair__size(A_27a,A_27b),V0f),V1g))))))))) # label(ax_thm_2EbasicSize_2Epair__size__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1852 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> c_2Enum_2E0 = ap(ap(c_2EbasicSize_2Eoption__size(A_27a),V0f),c_2Eoption_2ENONE(A_27a)))) & (all V1f (mem(V1f,arr(A_27a,ty_2Enum_2Enum)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(c_2EbasicSize_2Eoption__size(A_27a),V1f),ap(c_2Eoption_2ESOME(A_27a),V2x)) = ap(c_2Enum_2ESUC,ap(V1f,V2x)))))))) # label(ax_thm_2EbasicSize_2Eoption__size__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1853 (all V0b (mem(V0b,bool) -> ap(c_2EbasicSize_2Ebool__size,V0b) = c_2Enum_2E0)) # label(ax_thm_2EbasicSize_2Ebool__size__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1854 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27b,ty_2Enum_2Enum)) -> (all V2x ap(f227(A_27b,A_27a,V0f,V1g),V2x) = f226(A_27a,A_27b,V0f,V2x,V1g)))))) # label(lameq_f227) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1855 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2EbasicSize_2Esum__size(A_27a,A_27b),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27b,ty_2Enum_2Enum),arr(ty_2Esum_2Esum(A_27a,A_27b),ty_2Enum_2Enum)))))))) # label(mem_c_2EbasicSize_2Esum__size) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1856 (all A_27a (ne(A_27a) -> mem(c_2EbasicSize_2Eoption__size(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(ty_2Eoption_2Eoption(A_27a),ty_2Enum_2Enum))))) # label(mem_c_2EbasicSize_2Eoption__size) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1857 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,ty_2Enum_2Enum)) -> (all V1g (mem(V1g,arr(A_27b,ty_2Enum_2Enum)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(ap(c_2EbasicSize_2Esum__size(A_27a,A_27b),V0f),V1g),ap(c_2Esum_2EINL(A_27a,A_27b),V2x)) = ap(V0f,V2x))))))) & (all V3f (mem(V3f,arr(A_27a,ty_2Enum_2Enum)) -> (all V4g (mem(V4g,arr(A_27b,ty_2Enum_2Enum)) -> (all V5y (mem(V5y,A_27b) -> ap(ap(ap(c_2EbasicSize_2Esum__size(A_27a,A_27b),V3f),V4g),ap(c_2Esum_2EINR(A_27a,A_27b),V5y)) = ap(V4g,V5y))))))))))) # label(ax_thm_2EbasicSize_2Esum__size__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1858 (all V0x (mem(V0x,ty_2Eone_2Eone) -> c_2Enum_2E0 = ap(c_2EbasicSize_2Eone__size,V0x))) # label(ax_thm_2EbasicSize_2Eone__size__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1859 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0r)) -> c_2Enum_2E0 = ap(ap(c_2Elogroot_2EROOT,V0r),c_2Enum_2E0) & ap(ap(c_2Elogroot_2EROOT,V0r),V1n) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f228(V1n,V0r)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Elogroot_2EROOT,V0r),ap(ap(c_2Earithmetic_2EDIV,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0r)))))))))) # label(conj_thm_2Elogroot_2EROOT__COMPUTE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1860 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),c_2Enum_2E0),c_2Enum_2E0) = ap(c_2Elogroot_2ESQRTd,c_2Earithmetic_2EZERO) & ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),c_2Enum_2E0) & ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Elogroot_2EiSQRT0,ap(c_2Enum_2ESUC,V0n)) & ap(c_2Elogroot_2EiSQRT1,ap(c_2Enum_2ESUC,V0n)) = ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,V0n))) & ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,V0n))) = ap(c_2Elogroot_2EiSQRT2,ap(c_2Enum_2ESUC,V0n)) & ap(c_2Elogroot_2EiSQRT0,ap(c_2Enum_2ESUC,V0n)) = ap(c_2Elogroot_2ESQRTd,ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,V0n)))) & ap(c_2Elogroot_2ESQRTd,ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,V0n)))) = ap(c_2Elogroot_2EiSQRT1,ap(c_2Enum_2ESUC,V0n)) & ap(c_2Elogroot_2EiSQRT3,ap(c_2Enum_2ESUC,V0n)) = ap(c_2Elogroot_2ESQRTd,ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT2,V0n)))) & ap(c_2Elogroot_2ESQRTd,ap(c_2Enum_2ESUC,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT2,V0n)))) = ap(c_2Elogroot_2EiSQRT2,ap(c_2Enum_2ESUC,V0n)) & ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT1,ap(c_2Earithmetic_2EBIT1,V0n))) = ap(c_2Elogroot_2EiSQRT3,V0n) & ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Elogroot_2ESQRTd,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) # label(conj_thm_2Elogroot_2Enumeral__sqrt) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1861 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2r)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0a),V2r)),ap(ap(c_2Earithmetic_2EEXP,V1b),V2r))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b)))))))))) # label(conj_thm_2Elogroot_2EEXP__LE__ISO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1862 (all V1p ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f239(V1p)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))) = ap(f240,V1p)) # label(lameq_f240) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1863 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) -> p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,V0a),ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V0a),V1n))))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0a),ap(ap(c_2Elogroot_2ELOG,V0a),V1n))),V1n))))))) # label(ax_thm_2Elogroot_2ELOG) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1864 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0r)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2y)) -> ap(ap(c_2Elogroot_2EROOT,V0r),ap(ap(c_2Earithmetic_2EDIV,V1x),ap(ap(c_2Earithmetic_2EEXP,V2y),V0r))) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Elogroot_2EROOT,V0r),V1x)),V2y)))))))) # label(conj_thm_2Elogroot_2EROOT__DIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1865 (all V1p ap(f236,V1p) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f235(V1p)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))) # label(lameq_f236) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1866 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0r)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Elogroot_2EROOT,V0r),V1n)),V0r)),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2EROOT,V0r),V1n))),V0r)))))))) # label(ax_thm_2Elogroot_2EROOT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1867 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0r)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),V2y)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Elogroot_2EROOT,V0r),V1x)),ap(ap(c_2Elogroot_2EROOT,V0r),V2y))))))))))) # label(conj_thm_2Elogroot_2EROOT__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1868 (all V3c (mem(V3c,ty_2Enum_2Enum) -> (all V2d (mem(V2d,ty_2Enum_2Enum) -> (all V4e ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V4e),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2d),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V3c))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Enum_2ESUC,V2d)),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V4e)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(f233(V3c,V2d),V4e)))))) # label(lameq_f233) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1869 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2b)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1a)) -> ap(ap(c_2Elogroot_2ELOG,V1a),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V1a),ap(c_2Enum_2ESUC,V0n))),V2b)) = ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V1a),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V1a),V0n)),V2b)))))))))) # label(conj_thm_2Elogroot_2ELOG__ADD1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1870 (all V2d (mem(V2d,ty_2Enum_2Enum) -> (all V3c ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f233(V3c,V2d)),ap(ap(c_2Earithmetic_2E_2D,V3c),V2d)) = ap(f234(V2d),V3c)))) # label(lameq_f234) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1871 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1b),ap(ap(c_2Earithmetic_2EEXP,V0a),V2c))) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) -> ap(ap(c_2Elogroot_2ELOG,V0a),ap(ap(c_2Earithmetic_2E_2B,V1b),ap(ap(c_2Earithmetic_2EEXP,V0a),V2c))) = V2c))))))) # label(conj_thm_2Elogroot_2ELOG__ADD) # label(axiom) # label(non_clause). [assumption]. 3.74/3.84 1872 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1x)) -> ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V0b),V1x)) = ap(ap(c_2Elogroot_2ELOG,V0b),ap(ap(c_2Earithmetic_2E_2A,V0b),V1x))))))) # label(conj_thm_2Elogroot_2ELOG__MULT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1873 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2p)),V0r))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V2p),V0r)),V1n)) -> V2p = ap(ap(c_2Elogroot_2EROOT,V0r),V1n)))))))) # label(conj_thm_2Elogroot_2EROOT__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1874 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1x)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) -> ap(ap(c_2Elogroot_2ELOG,V0a),V1x) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Elogroot_2ELOG,V0a),ap(ap(c_2Earithmetic_2EDIV,V1x),V0a)))))))) # label(conj_thm_2Elogroot_2ELOG__DIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1875 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Elogroot_2EiSQRT2,V0n) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f236),ap(c_2Elogroot_2ESQRTd,V0n)))) # label(ax_thm_2Elogroot_2EiSQRT2__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1876 (all V0e (mem(V0e,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0e)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,V0e),V1a)),ap(ap(c_2Earithmetic_2EEXP,V0e),V2b))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,V1a),V2b)))))))))) # label(conj_thm_2Elogroot_2ELT__EXP__ISO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1877 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,V0a),ap(c_2Enum_2ESUC,V2p)))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0a),V2p)),V1n)) -> ap(ap(c_2Elogroot_2ELOG,V0a),V1n) = V2p))))))) # label(conj_thm_2Elogroot_2ELOG__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1878 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V2x ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2x)),V0r))),V2x),ap(c_2Enum_2ESUC,V2x)) = ap(f228(V1n,V0r),V2x)))))) # label(lameq_f228) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1879 (all V1p ap(f230,V1p) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f229(V1p)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))) # label(lameq_f230) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1880 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Elogroot_2EROOT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Elogroot_2EROOT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),ap(ap(c_2Elogroot_2EROOT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)))) = ap(c_2Elogroot_2ESQRTd,V0n))) # label(ax_thm_2Elogroot_2ESQRTd__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1881 (all V1p (mem(V1p,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V2d ap(f231(V1p),V2d) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2d),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,V2d),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) # label(lameq_f231) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1882 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Elogroot_2EiSQRT3,V0n) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f240),ap(c_2Elogroot_2ESQRTd,V0n)))) # label(ax_thm_2Elogroot_2EiSQRT3__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1883 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Elogroot_2ESQRTd,V0n)) = ap(ap(c_2Elogroot_2EROOT,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Earithmetic_2ENUMERAL,V0n)))) # label(conj_thm_2Elogroot_2Enumeral__root2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1884 (all V0e (mem(V0e,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0e)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V0e),V1a)),ap(ap(c_2Earithmetic_2EEXP,V0e),V2b))) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,V1a),V2b)))))))))) # label(conj_thm_2Elogroot_2ELE__EXP__ISO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1885 (all V1p (mem(V1p,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V2d ap(f239(V1p),V2d) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f238(V2d)),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))))))) # label(lameq_f239) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1886 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) -> ap(ap(c_2Elogroot_2ELOG,V0a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = c_2Enum_2E0))) # label(conj_thm_2Elogroot_2ELOG__1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1887 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1x),V0b)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2y)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0b)) -> ap(ap(c_2Elogroot_2ELOG,V0b),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V0b),V2y)),V1x)) = ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V0b),V2y))))))))) # label(conj_thm_2Elogroot_2ELOG__add__digit) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1888 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Elogroot_2ELOG,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Elogroot_2ELOG,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)))) = V0n))) # label(conj_thm_2Elogroot_2ELOG__MOD) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1889 (all V2d (mem(V2d,ty_2Enum_2Enum) -> (all V3c ap(f238(V2d),V3c) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f237(V3c,V2d)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V3c)),V2d))))) # label(lameq_f238) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1890 (all V1p (mem(V1p,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V2d ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V2d),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2d)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(f229(V1p),V2d)))) # label(lameq_f229) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1891 (all V3c (mem(V3c,ty_2Enum_2Enum) -> (all V2d (mem(V2d,ty_2Enum_2Enum) -> (all V4e ap(f237(V3c,V2d),V4e) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V4e),c_2Enum_2E0)),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V2d),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V3c)))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(c_2Enum_2ESUC,V2d)),ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,V4e),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))) # label(lameq_f237) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1892 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) -> ap(ap(c_2Elogroot_2ELOG,V0a),V0a) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Elogroot_2ELOG__BASE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1893 (all V1p (mem(V1p,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V2d ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f234(V2d)),ap(c_2Enum_2ESUC,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))) = ap(f235(V1p),V2d)))) # label(lameq_f235) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1894 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1a)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2b)) -> ap(ap(c_2Elogroot_2ELOG,V1a),ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EEXP,V1a),V0n)),V2b)) = ap(ap(c_2Earithmetic_2E_2B,V0n),ap(ap(c_2Elogroot_2ELOG,V1a),V2b))))))))) # label(conj_thm_2Elogroot_2ELOG__EXP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1895 (all V1p ap(f232,V1p) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f231(V1p)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),V1p)))) # label(lameq_f232) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1896 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Elogroot_2EiSQRT0,V0n) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f230),ap(c_2Elogroot_2ESQRTd,V0n)))) # label(ax_thm_2Elogroot_2EiSQRT0__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1897 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EEXP,V0a),ap(ap(c_2Earithmetic_2E_2A,V1b),V2c)) = ap(ap(c_2Earithmetic_2EEXP,ap(ap(c_2Earithmetic_2EEXP,V0a),V1b)),V2c))))))) # label(conj_thm_2Elogroot_2EEXP__MUL) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1898 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Elogroot_2EiSQRT1,V0n) = ap(ap(c_2Ebool_2ELET(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum),ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),f232),ap(c_2Elogroot_2ESQRTd,V0n)))) # label(ax_thm_2Elogroot_2EiSQRT1__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1899 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1x)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1x),V2y)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Elogroot_2ELOG,V0a),V1x)),ap(ap(c_2Elogroot_2ELOG,V0a),V2y))))))))))) # label(conj_thm_2Elogroot_2ELOG__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1900 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2r)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0a),V1b)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,V0a),V2r)),ap(ap(c_2Earithmetic_2EEXP,V1b),V2r))))))))))) # label(conj_thm_2Elogroot_2EEXP__LT__ISO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1901 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,V1n),V0m)),c_2Enum_2E0),ap(c_2Enum_2ESUC,ap(ap(c_2Elogroot_2ELOG,V0m),ap(ap(c_2Earithmetic_2EDIV,V1n),V0m)))) = ap(ap(c_2Elogroot_2ELOG,V0m),V1n)))))) # label(conj_thm_2Elogroot_2ELOG__RWT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1902 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b)) & p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1b),V0a)) <-> c_2Enum_2E0 = ap(ap(c_2Elogroot_2ELOG,V0a),V1b))))))) # label(conj_thm_2Elogroot_2ELOG__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1903 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2r (mem(V2r,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0a)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1x)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2r)) -> ap(ap(c_2Elogroot_2ELOG,V0a),ap(ap(c_2Elogroot_2EROOT,V2r),V1x)) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Elogroot_2ELOG,V0a),V1x)),V2r)))))))) # label(conj_thm_2Elogroot_2ELOG__ROOT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1904 (exists V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,ty_2Enum_2Enum))) & (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V1a)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V1a),ap(ap(V0f,V1a),V2n))),V2n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(ap(c_2Earithmetic_2EEXP,V1a),ap(c_2Enum_2ESUC,ap(ap(V0f,V1a),V2n)))))))))))) # label(conj_thm_2Elogroot_2ELOG__exists) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1905 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0r)) -> (exists V2rt (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,V2rt),V0r)),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Enum_2ESUC,V2rt)),V0r))) & mem(V2rt,ty_2Enum_2Enum)))))))) # label(conj_thm_2Elogroot_2EROOT__exists) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1906 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (V0n != c_2Enum_2E0 -> (exists V2p (mem(V2p,ty_2Enum_2Enum) & (exists V3q (ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V3q),V1m)),ap(ap(c_2Egcd_2Egcd,V1m),V0n)) = ap(ap(c_2Earithmetic_2E_2A,V2p),V0n) & mem(V3q,ty_2Enum_2Enum)))))))))) # label(conj_thm_2Egcd_2ELINEAR__GCD) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1907 (all V0a (mem(V0a,ty_2Enum_2Enum) -> V0a = ap(ap(c_2Egcd_2Egcd,c_2Enum_2E0),V0a))) # label(conj_thm_2Egcd_2EGCD__0L) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1908 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0m),c_2Enum_2E0)),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1n),c_2Enum_2E0))),c_2Enum_2E0),ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2A,V0m),V1n)),ap(ap(c_2Egcd_2Egcd,V0m),V1n))) = ap(ap(c_2Egcd_2Elcm,V0m),V1n))))) # label(ax_thm_2Egcd_2Elcm__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1909 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (c_2Enum_2E0 != V1m & c_2Enum_2E0 != V0n -> (exists V2p (mem(V2p,ty_2Enum_2Enum) & (exists V3q (V1m = ap(ap(c_2Earithmetic_2E_2A,V3q),ap(ap(c_2Egcd_2Egcd,V0n),V1m)) & ap(ap(c_2Egcd_2Egcd,V2p),V3q) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) & ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Egcd_2Egcd,V0n),V1m)) = V0n & mem(V3q,ty_2Enum_2Enum)))))))))) # label(conj_thm_2Egcd_2EFACTOR__OUT__GCD) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1910 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) -> ap(ap(c_2Egcd_2Egcd,V0p),V1b) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) | p(ap(ap(c_2Edivides_2Edivides,V0p),V1b))))))) # label(conj_thm_2Egcd_2EPRIME__GCD) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1911 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Elcm,V0x),c_2Enum_2E0) = c_2Enum_2E0 & ap(ap(c_2Egcd_2Elcm,c_2Enum_2E0),V0x) = c_2Enum_2E0)) # label(conj_thm_2Egcd_2ELCM__0) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1912 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) & p(ap(ap(c_2Edivides_2Edivides,V0p),ap(ap(c_2Earithmetic_2E_2A,V1a),V2b))) -> p(ap(ap(c_2Edivides_2Edivides,V0p),V2b)) | p(ap(ap(c_2Edivides_2Edivides,V0p),V1a))))))))) # label(conj_thm_2Egcd_2EP__EUCLIDES) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1913 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V0a),c_2Enum_2E0)),V1b),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2EMOD,V1b),V0a)),V0a)) = ap(ap(c_2Egcd_2Egcd,V0a),V1b))))) # label(conj_thm_2Egcd_2EGCD__EFFICIENTLY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1914 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) -> (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2p),ap(ap(c_2Egcd_2Elcm,V0m),V1n))) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V2p)) -> -p(ap(ap(c_2Edivides_2Edivides,V0m),V2p)) | -p(ap(ap(c_2Edivides_2Edivides,V1n),V2p)))))))))) # label(conj_thm_2Egcd_2ELCM__LEAST) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1915 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V1b),ap(ap(c_2Earithmetic_2E_2A,V0a),V2c))) & ap(ap(c_2Egcd_2Egcd,V0a),V1b) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) -> p(ap(ap(c_2Edivides_2Edivides,V1b),V2c))))))))) # label(conj_thm_2Egcd_2EL__EUCLIDES) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1916 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V2k),ap(ap(c_2Egcd_2Egcd,V0m),V1n)) = ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2A,V2k),V0m)),ap(ap(c_2Earithmetic_2E_2A,V2k),V1n)))))))) # label(conj_thm_2Egcd_2EGCD__COMMON__FACTOR) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1917 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),ap(ap(c_2Egcd_2Egcd,V0a),V1b))))))) # label(conj_thm_2Egcd_2EGCD__IS__GCD) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1918 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Egcd_2Eis__gcd,V1b),V0a),V2c)) <-> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V2c))))))))) # label(conj_thm_2Egcd_2EIS__GCD__SYM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1919 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0x) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) & ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Egcd_2Egcd,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Egcd_2EGCD__1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1920 (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V3x (mem(V3x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,V2y),V3x)),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2D,V3x),V2y)),ap(c_2Enum_2ESUC,V2y))),ap(ap(c_2Egcd_2Egcd,ap(c_2Enum_2ESUC,V3x)),ap(ap(c_2Earithmetic_2E_2D,V2y),V3x))) = ap(ap(c_2Egcd_2Egcd,ap(c_2Enum_2ESUC,V3x)),ap(c_2Enum_2ESUC,V2y)))))) # label(conj_thm_2Egcd_2Egcd__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1921 (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Enum_2ESUC,V1x)),c_2Enum_2E0) = ap(c_2Enum_2ESUC,V1x))) # label(conj_thm_2Egcd_2Egcd__def_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1922 (all V0y (mem(V0y,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,c_2Enum_2E0),V0y) = V0y)) # label(conj_thm_2Egcd_2Egcd__def_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1923 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Egcd_2Eis__gcd,ap(ap(c_2Earithmetic_2E_2D,V0a),V1b)),V1b),V2c)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1b),V0a)) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V2c))))))))) # label(conj_thm_2Egcd_2EIS__GCD__MINUS__L) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1924 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2d (mem(V2d,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V2d),V1b)) & p(ap(ap(c_2Edivides_2Edivides,V2d),V0a)) -> p(ap(ap(c_2Edivides_2Edivides,V2d),ap(ap(c_2Egcd_2Egcd,V0a),V1b)))))) & p(ap(ap(c_2Edivides_2Edivides,ap(ap(c_2Egcd_2Egcd,V0a),V1b)),V1b)) & p(ap(ap(c_2Edivides_2Edivides,ap(ap(c_2Egcd_2Egcd,V0a),V1b)),V0a)))))) # label(conj_thm_2Egcd_2EGCD__IS__GREATEST__COMMON__DIVISOR) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1925 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) -> ((all V2x (mem(V2x,ty_2Enum_2Enum) -> p(ap(ap(V0P,ap(c_2Enum_2ESUC,V2x)),c_2Enum_2E0)))) & (all V3x (mem(V3x,ty_2Enum_2Enum) -> (all V4y (mem(V4y,ty_2Enum_2Enum) -> ((-p(ap(ap(c_2Earithmetic_2E_3C_3D,V4y),V3x)) -> p(ap(ap(V0P,ap(c_2Enum_2ESUC,V3x)),ap(ap(c_2Earithmetic_2E_2D,V4y),V3x)))) & (p(ap(ap(c_2Earithmetic_2E_3C_3D,V4y),V3x)) -> p(ap(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V3x),V4y)),ap(c_2Enum_2ESUC,V4y)))) -> p(ap(ap(V0P,ap(c_2Enum_2ESUC,V3x)),ap(c_2Enum_2ESUC,V4y)))))))) & (all V1y (mem(V1y,ty_2Enum_2Enum) -> p(ap(ap(V0P,c_2Enum_2E0),V1y)))) -> (all V5v (mem(V5v,ty_2Enum_2Enum) -> (all V6v1 (mem(V6v1,ty_2Enum_2Enum) -> p(ap(ap(V0P,V5v),V6v1))))))))) # label(conj_thm_2Egcd_2Egcd__ind) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1926 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) -> ((all V5x (mem(V5x,ty_2Enum_2Enum) -> (all V6y (mem(V6y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V5x)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V6y)) & p(ap(ap(V0P,V5x),V6y)) -> p(ap(ap(V0P,V5x),ap(ap(c_2Earithmetic_2E_2B,V5x),V6y)))))))) & (all V4x (mem(V4x,ty_2Enum_2Enum) -> p(ap(ap(V0P,V4x),V4x)))) & (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3y (mem(V3y,ty_2Enum_2Enum) -> (p(ap(ap(V0P,V2x),V3y)) -> p(ap(ap(V0P,V3y),V2x))))))) & (all V1y (mem(V1y,ty_2Enum_2Enum) -> p(ap(ap(V0P,c_2Enum_2E0),V1y)))) -> (all V7m (mem(V7m,ty_2Enum_2Enum) -> (all V8n (mem(V8n,ty_2Enum_2Enum) -> p(ap(ap(V0P,V7m),V8n))))))))) # label(conj_thm_2Egcd_2EGCD__SUCfree__ind) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1927 (all V0p (mem(V0p,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(c_2Edivides_2Eprime,V0p)) -> p(ap(ap(c_2Edivides_2Edivides,V0p),V1b)) | p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0p),V1b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) # label(conj_thm_2Egcd_2EPRIME__IS__GCD) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1928 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(c_2Earithmetic_2EODD,V1n)) & p(ap(c_2Earithmetic_2EEVEN,V0m)) -> ap(ap(c_2Egcd_2Egcd,V0m),V1n) = ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2EDIV,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),V1n)) & (p(ap(c_2Earithmetic_2EEVEN,V1n)) & p(ap(c_2Earithmetic_2EEVEN,V0m)) -> ap(ap(c_2Egcd_2Egcd,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2EDIV,V0m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EDIV,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))) # label(conj_thm_2Egcd_2EBINARY__GCD) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1929 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),c_2Enum_2E0),V0a)))) # label(conj_thm_2Egcd_2EIS__GCD__0R) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1930 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (all V3d (mem(V3d,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V2c)) & p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V3d)) -> V2c = V3d))))))))) # label(conj_thm_2Egcd_2EIS__GCD__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1931 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> (ap(ap(c_2Egcd_2Egcd,V0m),V2k) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) -> ap(ap(c_2Egcd_2Egcd,V0m),ap(ap(c_2Earithmetic_2E_2A,V2k),V1n)) = ap(ap(c_2Egcd_2Egcd,V0m),V1n)))))))) # label(conj_thm_2Egcd_2EGCD__CANCEL__MULT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1932 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> p(ap(ap(c_2Edivides_2Edivides,V0m),ap(ap(c_2Egcd_2Elcm,V0m),V1n))) & (all V2p (mem(V2p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V0m),V2p)) & p(ap(ap(c_2Edivides_2Edivides,V1n),V2p)) -> p(ap(ap(c_2Edivides_2Edivides,ap(ap(c_2Egcd_2Elcm,V0m),V1n)),V2p))))) & p(ap(ap(c_2Edivides_2Edivides,V1n),ap(ap(c_2Egcd_2Elcm,V0m),V1n))))))) # label(conj_thm_2Egcd_2ELCM__IS__LEAST__COMMON__MULTIPLE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1933 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V0a),V1b) = ap(ap(c_2Egcd_2Egcd,V0a),ap(ap(c_2Earithmetic_2E_2B,V0a),V1b)))))) # label(conj_thm_2Egcd_2EGCD__ADD__R__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1934 (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V2a),V3b) = ap(ap(c_2Egcd_2Egcd,V2a),ap(ap(c_2Earithmetic_2E_2B,V3b),V2a)))))) # label(conj_thm_2Egcd_2EGCD__ADD__R__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1935 (all V0a (mem(V0a,ty_2Enum_2Enum) -> V0a = ap(ap(c_2Egcd_2Egcd,V0a),c_2Enum_2E0))) # label(conj_thm_2Egcd_2EGCD__0R) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1936 (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x)) = ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1x))),c_2Enum_2E0))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1937 (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V2x))),c_2Enum_2E0) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V2x)))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1938 (all V3y (mem(V3y,ty_2Enum_2Enum) -> (all V4x (mem(V4x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3y)))),ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4x))),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) = ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V4x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V3y))))))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1939 (all V7y (mem(V7y,ty_2Enum_2Enum) -> (all V8x (mem(V8x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V8x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V7y))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V7y))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V8x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V8x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V7y)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V7y)))),ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V8x))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V7y))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V8x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1940 (all V9y (mem(V9y,ty_2Enum_2Enum) -> (all V10x (mem(V10x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V10x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V9y))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V9y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V10x)))),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V10x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V9y)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V9y)))),ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V10x))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V9y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V10x))))))))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1941 (all V5y (mem(V5y,ty_2Enum_2Enum) -> (all V6x (mem(V6x,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5y))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6x)))),ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6x))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5y)))),ap(ap(c_2Egcd_2Egcd,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V6x))),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V5y))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V6x))))))))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1942 (all V0y (mem(V0y,ty_2Enum_2Enum) -> V0y = ap(ap(c_2Egcd_2Egcd,c_2Enum_2E0),V0y))) # label(conj_thm_2Egcd_2Egcd__def__compute_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1943 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2B,V0a),V1b)),V0a) = ap(ap(c_2Egcd_2Egcd,V0a),V1b))))) # label(conj_thm_2Egcd_2EGCD__ADD__L) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1944 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,c_2Enum_2E0),V0a),V0a)))) # label(conj_thm_2Egcd_2EIS__GCD__0L) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1945 (all V0x (mem(V0x,ty_2Enum_2Enum) -> V0x = ap(ap(c_2Egcd_2Elcm,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),V0x) & V0x = ap(ap(c_2Egcd_2Elcm,V0x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) # label(conj_thm_2Egcd_2ELCM__1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1946 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1n)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0m)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Egcd_2Elcm,V1n),V0m))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),ap(ap(c_2Egcd_2Elcm,V0m),V1n)))))))) # label(conj_thm_2Egcd_2ELCM__LE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1947 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V2c),V0a)) & (all V3d (mem(V3d,ty_2Enum_2Enum) -> (p(ap(ap(c_2Edivides_2Edivides,V3d),V1b)) & p(ap(ap(c_2Edivides_2Edivides,V3d),V0a)) -> p(ap(ap(c_2Edivides_2Edivides,V3d),V2c))))) & p(ap(ap(c_2Edivides_2Edivides,V2c),V1b)) <-> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V2c))))))))) # label(ax_thm_2Egcd_2Eis__gcd__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1948 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V1b),V0a) = ap(ap(c_2Egcd_2Egcd,V0a),V1b))))) # label(conj_thm_2Egcd_2EGCD__SYM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1949 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V0a),V1b) = ap(ap(c_2Egcd_2Egcd,V0a),ap(ap(c_2Earithmetic_2E_2B,V0a),V1b)))))) # label(conj_thm_2Egcd_2EGCD__ADD__R) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1950 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (c_2Enum_2E0 = V1m & V0n = c_2Enum_2E0 <-> c_2Enum_2E0 = ap(ap(c_2Egcd_2Egcd,V0n),V1m)))))) # label(conj_thm_2Egcd_2EGCD__EQ__0) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1951 (all V0a (mem(V0a,ty_2Enum_2Enum) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V0a),V0a)))) # label(conj_thm_2Egcd_2EIS__GCD__REF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1952 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Elcm,V1b),V0a) = ap(ap(c_2Egcd_2Elcm,V0a),V1b))))) # label(conj_thm_2Egcd_2ELCM__COMM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1953 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2c (mem(V2c,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),ap(ap(c_2Earithmetic_2E_2D,V1b),V0a)),V2c)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b)) -> p(ap(ap(ap(c_2Egcd_2Eis__gcd,V0a),V1b),V2c))))))))) # label(conj_thm_2Egcd_2EIS__GCD__MINUS__R) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1954 (all V0a (mem(V0a,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V0a),V0a) = V0a)) # label(conj_thm_2Egcd_2EGCD__REF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1955 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2B,V0a),V1b)),V0a) = ap(ap(c_2Egcd_2Egcd,V0a),V1b))))) # label(conj_thm_2Egcd_2EGCD__ADD__L__THM_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1956 (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> ap(ap(c_2Egcd_2Egcd,V2a),V3b) = ap(ap(c_2Egcd_2Egcd,ap(ap(c_2Earithmetic_2E_2B,V3b),V2a)),V2a))))) # label(conj_thm_2Egcd_2EGCD__ADD__L__THM_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1957 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (ap(c_2Enumpair_2Etri,V0n) = c_2Enum_2E0 <-> c_2Enum_2E0 = V0n) & (c_2Enum_2E0 = ap(c_2Enumpair_2Etri,V0n) <-> c_2Enum_2E0 = V0n))) # label(conj_thm_2Enumpair_2Etri__eq__0) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1958 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Enfst,V0n) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Etri,ap(c_2Enumpair_2Einvtri,V0n))),ap(c_2Enumpair_2Einvtri,V0n))),V0n))) # label(ax_thm_2Enumpair_2Enfst__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1959 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (exists V1x ((exists V2y (mem(V2y,ty_2Enum_2Enum) & ap(ap(c_2Enumpair_2Enpair,V1x),V2y) = V0n)) & mem(V1x,ty_2Enum_2Enum))))) # label(conj_thm_2Enumpair_2Enpair__cases) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1960 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Ensnd,V0n) = ap(ap(c_2Earithmetic_2E_2D,V0n),ap(c_2Enumpair_2Etri,ap(c_2Enumpair_2Einvtri,V0n))))) # label(ax_thm_2Enumpair_2Ensnd__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1961 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V3r ap(f242(V0f,V1n),V3r) = ap(ap(c_2Enumpair_2Encons,ap(V0f,V1n)),V3r)))))) # label(lameq_f242) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1962 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1t (mem(V1t,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Enlen,V1t)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(c_2Enumpair_2Enlen,ap(ap(c_2Enumpair_2Encons,V0h),V1t)) & c_2Enum_2E0 = ap(c_2Enumpair_2Enlen,c_2Enum_2E0))))) # label(conj_thm_2Enumpair_2Enlen__thm) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1963 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (all V6r ap(f245(A_27a,V0f,V4n),V6r) = f244(A_27a,V0f,V4n,V6r)))))) # label(lameq_f245) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1964 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enumpair_2Etri,V0n)),ap(c_2Enumpair_2Etri,V1m)))))))) # label(conj_thm_2Enumpair_2Etri__LT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1965 (all A_27a (ne(A_27a) -> mem(c_2Enumpair_2Enlistrec(A_27a),arr(A_27a,arr(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))),arr(ty_2Enum_2Enum,A_27a)))))) # label(mem_c_2Enumpair_2Enlistrec) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1966 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V1a (mem(V1a,A_27a) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumpair_2Enfoldl(A_27a),V0f),V1a),V2l) = ap(ap(ap(ap(c_2Enumpair_2Enlistrec(arr(A_27a,A_27a)),i(A_27a)),f246(A_27a,V0f)),V2l),V1a))))))))) # label(ax_thm_2Enumpair_2Enfoldl__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1967 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Enumpair_2Einvtri0,V0n),c_2Enum_2E0)) = ap(c_2Enumpair_2Einvtri,V0n))) # label(ax_thm_2Enumpair_2Einvtri__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1968 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (all V6r (mem(V6r,arr(A_27a,A_27a)) -> (all V7a ap(V6r,ap(ap(V0f,V4n),V7a)) = ap(f244(A_27a,V0f,V4n,V6r),V7a)))))))) # label(lameq_f244) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1969 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (all V2h (mem(V2h,ty_2Enum_2Enum) -> (all V3t (mem(V3t,ty_2Enum_2Enum) -> (V1y = V3t & V2h = V0x <-> ap(ap(c_2Enumpair_2Encons,V2h),V3t) = ap(ap(c_2Enumpair_2Encons,V0x),V1y)))))))))) # label(conj_thm_2Enumpair_2Encons__11) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1970 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Etri,ap(c_2Enum_2ESUC,V0n)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enumpair_2Etri,V0n)))) # label(ax_thm_2Enumpair_2Etri__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1971 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> c_2Enum_2E0 != ap(ap(c_2Enumpair_2Encons,V0x),V1y))))) # label(conj_thm_2Enumpair_2Encons__not__nnil) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1972 (all V0n (mem(V0n,ty_2Enum_2Enum) -> V0n = ap(ap(c_2Enumpair_2Enpair,ap(c_2Enumpair_2Enfst,V0n)),ap(c_2Enumpair_2Ensnd,V0n)))) # label(conj_thm_2Enumpair_2Enpair) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1973 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1t (mem(V1t,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Enumpair_2Enpair,V0h),V1t)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(ap(c_2Enumpair_2Encons,V0h),V1t))))) # label(ax_thm_2Enumpair_2Encons__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1974 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0m),V1n)) <-> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Etri,V0m)),ap(c_2Enumpair_2Etri,V1n)))))))) # label(conj_thm_2Enumpair_2Etri__LE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1975 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0y),V1x)) -> ap(c_2Enumpair_2Einvtri,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Etri,V1x)),V0y)) = V1x))))) # label(conj_thm_2Enumpair_2Einvtri__linverse__r) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1976 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V1n ap(f243(V0f),V1n) = k(ty_2Enum_2Enum,f242(V0f,V1n))))) # label(lameq_f243) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1977 (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Etri,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,V1n))),ap(c_2Enumpair_2Etri,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V1n)))))) # label(conj_thm_2Enumpair_2Etri__def__compute_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1978 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Enumpair_2Etri,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) = ap(c_2Enumpair_2Etri,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,V0n))))) # label(conj_thm_2Enumpair_2Etri__def__compute_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1979 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Ensnd,V0n)),V0n)))) # label(conj_thm_2Enumpair_2Ensnd__le) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1980 (all V0l1 (mem(V0l1,ty_2Enum_2Enum) -> (all V1l2 (mem(V1l2,ty_2Enum_2Enum) -> ap(ap(c_2Enumpair_2Enapp,V0l1),V1l2) = ap(ap(ap(c_2Enumpair_2Enlistrec(ty_2Enum_2Enum),V1l2),f248),V0l1))))) # label(ax_thm_2Enumpair_2Enapp__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1981 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2t (mem(V2t,ty_2Enum_2Enum) -> (p(ap(V0P,V2t)) -> p(ap(V0P,ap(ap(c_2Enumpair_2Encons,V1h),V2t)))))))) & p(ap(V0P,c_2Enum_2E0)) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(V0P,V3n))))))) # label(conj_thm_2Enumpair_2Enlist__ind) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1982 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(c_2Enumpair_2Etri,ap(ap(c_2Earithmetic_2E_2B,V0y),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Etri,V0y)),V1n)) -> V0y = ap(c_2Enumpair_2Einvtri,V1n)))))) # label(conj_thm_2Enumpair_2Einvtri__unique) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1983 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Enfst,V0n)),V0n)))) # label(conj_thm_2Enumpair_2Enfst__le) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1984 (all V0x1 (mem(V0x1,ty_2Enum_2Enum) -> (all V1y1 (mem(V1y1,ty_2Enum_2Enum) -> (all V2x2 (mem(V2x2,ty_2Enum_2Enum) -> (all V3y2 (mem(V3y2,ty_2Enum_2Enum) -> (ap(ap(c_2Enumpair_2Enpair,V0x1),V1y1) = ap(ap(c_2Enumpair_2Enpair,V2x2),V3y2) <-> V2x2 = V0x1 & V1y1 = V3y2))))))))) # label(conj_thm_2Enumpair_2Enpair__11) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1985 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V4r ap(ap(c_2Enumpair_2Encons,V2n),V4r) = ap(f247(V2n),V4r)))) # label(lameq_f247) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1986 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Etri,ap(c_2Enumpair_2Einvtri,V0n))),V0n)))) # label(conj_thm_2Enumpair_2Einvtri__lower) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1987 (all V0nlist (mem(V0nlist,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2t (mem(V2t,ty_2Enum_2Enum) -> ap(ap(c_2Enumpair_2Encons,V1h),ap(ap(c_2Enumpair_2Enapp,V2t),V0nlist)) = ap(ap(c_2Enumpair_2Enapp,ap(ap(c_2Enumpair_2Encons,V1h),V2t)),V0nlist) & ap(ap(c_2Enumpair_2Enapp,c_2Enum_2E0),V0nlist) = V0nlist)))))) # label(conj_thm_2Enumpair_2Enapp__thm) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1988 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2t (mem(V2t,ty_2Enum_2Enum) -> ap(ap(c_2Enumpair_2Enmap,V0f),ap(ap(c_2Enumpair_2Encons,V1h),V2t)) = ap(ap(c_2Enumpair_2Encons,ap(V0f,V1h)),ap(ap(c_2Enumpair_2Enmap,V0f),V2t)) & c_2Enum_2E0 = ap(ap(c_2Enumpair_2Enmap,V0f),c_2Enum_2E0))))))) # label(conj_thm_2Enumpair_2Enmap__thm) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1989 (all V2n k(ty_2Enum_2Enum,f247(V2n)) = ap(f248,V2n)) # label(lameq_f248) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1990 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enumpair_2Etri,V0n)),ap(c_2Enumpair_2Etri,V1m)))))))) # label(conj_thm_2Enumpair_2Etri__LT__I) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1991 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,arr(arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))),arr(ty_2Enum_2Enum,bool)))) -> ((all V1n (mem(V1n,A_27a) -> (all V2f (mem(V2f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a)))) -> (all V3l (mem(V3l,ty_2Enum_2Enum) -> ((c_2Enum_2E0 != V3l -> p(ap(ap(ap(V0P,V1n),V2f),ap(c_2Enumpair_2Ensnd,ap(ap(c_2Earithmetic_2E_2D,V3l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) -> p(ap(ap(ap(V0P,V1n),V2f),V3l))))))))) -> (all V4v (mem(V4v,A_27a) -> (all V5v1 (mem(V5v1,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a)))) -> (all V6v2 (mem(V6v2,ty_2Enum_2Enum) -> p(ap(ap(ap(V0P,V4v),V5v1),V6v2))))))))))))) # label(conj_thm_2Enumpair_2Enlistrec__ind) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1992 (all A_27a all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V4n k(ty_2Enum_2Enum,f245(A_27a,V0f,V4n)) = ap(f246(A_27a,V0f),V4n)))) # label(lameq_f246) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1993 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> ap(ap(c_2Enumpair_2Einvtri0,V0n),V1a) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Epair_2Eprod(ty_2Enum_2Enum,ty_2Enum_2Enum)),ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(ap(c_2Earithmetic_2E_2B,V1a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),V0n),V1a)),ap(ap(c_2Enumpair_2Einvtri0,ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2E_2B,V1a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2B,V1a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))) # label(conj_thm_2Enumpair_2Einvtri0__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1994 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Enumpair_2Etri,V1a)) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Etri,ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Enumpair_2Einvtri0,V0n),V1a)))),ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Enumpair_2Einvtri0,V0n),V1a))))))) # label(conj_thm_2Enumpair_2Einvtri0__thm) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1995 (all A_27a (ne(A_27a) -> mem(c_2Enumpair_2Enfoldl(A_27a),arr(arr(ty_2Enum_2Enum,arr(A_27a,A_27a)),arr(A_27a,arr(ty_2Enum_2Enum,A_27a)))))) # label(mem_c_2Enumpair_2Enfoldl) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1996 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enumpair_2Einvtri,V0n)),V0n)))) # label(conj_thm_2Enumpair_2Einvtri__le) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1997 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Epair_2EFST(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Enumpair_2Einvtri0,V0n),V1a))),ap(c_2Enum_2ESUC,ap(c_2Epair_2ESND(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Enumpair_2Einvtri0,V0n),V1a))))))))) # label(conj_thm_2Enumpair_2ESND__invtri0) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1998 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,V0n),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))) = ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enumpair_2Etri,V0n)))) # label(conj_thm_2Enumpair_2Etwotri__formula) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 1999 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,A_27a))) -> (all V1a (mem(V1a,A_27a) -> (all V2h (mem(V2h,ty_2Enum_2Enum) -> (all V3t (mem(V3t,ty_2Enum_2Enum) -> ap(ap(ap(c_2Enumpair_2Enfoldl(A_27a),V0f),V1a),ap(ap(c_2Enumpair_2Encons,V2h),V3t)) = ap(ap(ap(c_2Enumpair_2Enfoldl(A_27a),V0f),ap(ap(V0f,V2h),V1a)),V3t) & V1a = ap(ap(ap(c_2Enumpair_2Enfoldl(A_27a),V0f),V1a),c_2Enum_2E0))))))))))) # label(conj_thm_2Enumpair_2Enfoldl__thm) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2000 (all V0n (mem(V0n,ty_2Enum_2Enum) -> V0n = c_2Enum_2E0 | (exists V1h (mem(V1h,ty_2Enum_2Enum) & (exists V2t (mem(V2t,ty_2Enum_2Enum) & ap(ap(c_2Enumpair_2Encons,V1h),V2t) = V0n)))))) # label(conj_thm_2Enumpair_2Enlist__cases) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2001 (all V2r ap(ap(c_2Earithmetic_2E_2B,V2r),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(f241,V2r)) # label(lameq_f241) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2002 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,A_27a) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2f (mem(V2f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a)))) -> ap(ap(ap(c_2Enumpair_2Enlistrec(A_27a),V0n),V2f),V1l) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),V1l),c_2Enum_2E0)),V0n),ap(ap(ap(V2f,ap(c_2Enumpair_2Enfst,ap(ap(c_2Earithmetic_2E_2D,V1l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Enumpair_2Ensnd,ap(ap(c_2Earithmetic_2E_2D,V1l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(ap(c_2Enumpair_2Enlistrec(A_27a),V0n),V2f),ap(c_2Enumpair_2Ensnd,ap(ap(c_2Earithmetic_2E_2D,V1l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))))))))))) # label(conj_thm_2Enumpair_2Enlistrec__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2003 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(c_2Enumpair_2Etri,ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Einvtri,V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))) # label(conj_thm_2Enumpair_2Einvtri__upper) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2004 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,bool))) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> ((-p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2E_2B,V2a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) -> p(ap(ap(V0P,ap(ap(c_2Earithmetic_2E_2D,V1n),ap(ap(c_2Earithmetic_2E_2B,V2a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2E_2B,V2a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))) -> p(ap(ap(V0P,V1n),V2a))))))) -> (all V3v (mem(V3v,ty_2Enum_2Enum) -> (all V4v1 (mem(V4v1,ty_2Enum_2Enum) -> p(ap(ap(V0P,V3v),V4v1))))))))) # label(conj_thm_2Enumpair_2Einvtri0__ind) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2005 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Einvtri,ap(c_2Enumpair_2Etri,V0n)) = V0n)) # label(conj_thm_2Enumpair_2Einvtri__linverse) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2006 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2A,V0n),ap(ap(c_2Earithmetic_2E_2B,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Enumpair_2Etri,V0n))) # label(conj_thm_2Enumpair_2Etri__formula) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2007 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (V0m = V1n <-> ap(c_2Enumpair_2Etri,V0m) = ap(c_2Enumpair_2Etri,V1n)))))) # label(conj_thm_2Enumpair_2Etri__11) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2008 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,ty_2Enum_2Enum)) -> ap(ap(c_2Enumpair_2Enlistrec(ty_2Enum_2Enum),c_2Enum_2E0),f243(V0f)) = ap(c_2Enumpair_2Enmap,V0f))) # label(ax_thm_2Enumpair_2Enmap__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2009 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Enumpair_2Enpair,V0m),V1n) = ap(ap(c_2Earithmetic_2E_2B,ap(c_2Enumpair_2Etri,ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))),V1n))))) # label(ax_thm_2Enumpair_2Enpair__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2010 (all A_27a (ne(A_27a) -> (all V0n (mem(V0n,A_27a) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,arr(ty_2Enum_2Enum,arr(A_27a,A_27a)))) -> (all V2h (mem(V2h,ty_2Enum_2Enum) -> (all V3t (mem(V3t,ty_2Enum_2Enum) -> ap(ap(ap(V1f,V2h),V3t),ap(ap(ap(c_2Enumpair_2Enlistrec(A_27a),V0n),V1f),V3t)) = ap(ap(ap(c_2Enumpair_2Enlistrec(A_27a),V0n),V1f),ap(ap(c_2Enumpair_2Encons,V2h),V3t)) & ap(ap(ap(c_2Enumpair_2Enlistrec(A_27a),V0n),V1f),c_2Enum_2E0) = V0n)))))))))) # label(conj_thm_2Enumpair_2Enlistrec__thm) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2011 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Enfst,ap(ap(c_2Enumpair_2Enpair,V0x),V1y)) = V0x)))) # label(conj_thm_2Enumpair_2Enfst__npair) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2012 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> ap(c_2Enumpair_2Ensnd,ap(ap(c_2Enumpair_2Enpair,V0x),V1y)) = V1y)))) # label(conj_thm_2Enumpair_2Ensnd__npair) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2013 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0n),ap(c_2Enumpair_2Etri,V0n))))) # label(conj_thm_2Enumpair_2Etri__le) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2014 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Ebit_2ELOG2,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) = V0n)) # label(conj_thm_2Ebit_2ELOG2__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2015 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (c_2Enum_2E0 != ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0n) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0n))))))) # label(conj_thm_2Ebit_2EMOD__ADD__1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2016 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2ESLICE,V1h),V2l),V0n) = ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2EBITS,V1h),V2l),V0n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2l)))))))) # label(conj_thm_2Ebit_2ESLICE__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2017 (all V0h1 (mem(V0h1,ty_2Enum_2Enum) -> (all V1l1 (mem(V1l1,ty_2Enum_2Enum) -> (all V2h2 (mem(V2h2,ty_2Enum_2Enum) -> (all V3l2 (mem(V3l2,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V2h2),V1l1)),V0h1)) -> ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2E_2B,V2h2),V1l1)),ap(ap(c_2Earithmetic_2E_2B,V3l2),V1l1)),V4n) = ap(ap(ap(c_2Ebit_2EBITS,V2h2),V3l2),ap(ap(ap(c_2Ebit_2EBITS,V0h1),V1l1),V4n))))))))))))) # label(conj_thm_2Ebit_2EBITS__COMP__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2018 (all V0l (mem(V0l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V3m ap(f250(V0l,V2n,V1h),V3m) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,V0l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2n)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1h)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0l))),V3m)),V3m)))))))) # label(lameq_f250) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2019 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0h),V1l)) -> c_2Enum_2E0 = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)))))))) # label(conj_thm_2Ebit_2EBITS__ZERO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2020 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (ap(ap(c_2Ebit_2EMOD__2EXP,V0n),V2b) = ap(ap(c_2Ebit_2EMOD__2EXP,V0n),V1a) <-> p(ap(ap(ap(c_2Ebit_2EMOD__2EXP__EQ,V0n),V1a),V2b))))))))) # label(ax_thm_2Ebit_2EMOD__2EXP__EQ__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2021 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) != ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) <-> ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = c_2Enum_2E0))) # label(conj_thm_2Ebit_2ENOT__MOD2__LEM2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2022 (all V0b (mem(V0b,bool) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Ebit_2ESBIT,V0b),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)) = ap(ap(c_2Ebit_2ESBIT,V0b),ap(ap(c_2Earithmetic_2E_2B,V2n),V1m)))))))) # label(conj_thm_2Ebit_2ESBIT__MULT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2023 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)),V2n)))))))) # label(conj_thm_2Ebit_2EBITS__LEQ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2024 (all V0r (mem(V0r,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0r),V1n)) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2B,V1n),V0r)),V1n)))))) # label(conj_thm_2Ebit_2EDIV__MULT__1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2025 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))) -> ap(ap(c_2Earithmetic_2EDIV,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)))))))) # label(conj_thm_2Ebit_2EBITS__LT__HIGH) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2026 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (c_2Enum_2E0 != V0m -> (exists V1p (ap(c_2Enum_2ESUC,V1p) = V0m & mem(V1p,ty_2Enum_2Enum)))))) # label(conj_thm_2Ebit_2ENOT__ZERO__ADD1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2027 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(ap(ap(c_2Ebit_2ESLICE,V0b),V0b),V1n) = c_2Enum_2E0 <-> -p(ap(ap(c_2Ebit_2EBIT,V0b),V1n))))))) # label(conj_thm_2Ebit_2EBIT__SLICE__THM3) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2028 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) <-> ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) != c_2Enum_2E0))) # label(conj_thm_2Ebit_2ENOT__MOD2__LEM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2029 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,V1i),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))) <-> V1i = V0n & c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) | -p(ap(ap(c_2Ebit_2EBIT,V1i),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))) & p(ap(ap(c_2Eprim__rec_2E_3C,V1i),V0n)) & ap(ap(c_2Earithmetic_2EMOD,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) != c_2Enum_2E0))))))) # label(conj_thm_2Ebit_2EBIT__COMPLEMENT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2030 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0a),V1b)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)))))))) # label(conj_thm_2Ebit_2ETWOEXP__MONO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2031 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0b) = ap(ap(ap(c_2Ebit_2ESLICE,V0b),V0b),V1n) <-> p(ap(ap(c_2Ebit_2EBIT,V0b),V1n))))))) # label(conj_thm_2Ebit_2EBIT__SLICE__THM2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2032 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (ap(ap(ap(c_2Ebit_2ESLICE,V0n),V0n),V1a) = ap(ap(ap(c_2Ebit_2ESLICE,V0n),V0n),V2b) <-> (p(ap(ap(c_2Ebit_2EBIT,V0n),V1a)) <-> p(ap(ap(c_2Ebit_2EBIT,V0n),V2b)))))))))) # label(conj_thm_2Ebit_2EBIT__SLICE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2033 (all V0i (mem(V0i,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0i))) -> -p(ap(ap(c_2Ebit_2EBIT,V0i),V1n))))))) # label(conj_thm_2Ebit_2ENOT__BIT__GT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2034 (all V0x (mem(V0x,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EBIT__REVERSE,c_2Enum_2E0),V0x) = c_2Enum_2E0)) # label(ax_thm_2Ebit_2EBIT__REVERSE__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2035 (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Ebit_2EBIT__REVERSE,V1n),V2x)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V1n),V2x)),c_2Enum_2E0)) = ap(ap(c_2Ebit_2EBIT__REVERSE,ap(c_2Enum_2ESUC,V1n)),V2x))))) # label(ax_thm_2Ebit_2EBIT__REVERSE__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2036 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2x)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V3n)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),ap(ap(c_2Earithmetic_2E_2B,V1l),V3n)),V2x))))))))) # label(conj_thm_2Ebit_2EBITS__DIV__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2037 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)))))))) # label(conj_thm_2Ebit_2ETWOEXP__MONO2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.85 2038 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Ebit_2EMOD__2EXP,ap(c_2Enum_2ESUC,V0h)),V2n)),ap(ap(c_2Ebit_2EMOD__2EXP,V1l),V2n)))))))) # label(ax_thm_2Ebit_2ESLICE__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2039 (all V0l (mem(V0l,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3i (mem(V3i,ty_2Enum_2Enum) -> (V0l != c_2Enum_2E0 -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Earithmetic_2E_3C_3D,V0l),V1h)),ap(ap(c_2Eprim__rec_2E_3C,V3i),V0l))),ap(ap(c_2Ebit_2EBIT,V3i),ap(ap(c_2Earithmetic_2EMOD,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0l)))),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Eprim__rec_2E_3C,V3i),V1h)),ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,V0l),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V2n)))) <-> p(ap(ap(c_2Ebit_2EBIT,V3i),ap(ap(ap(c_2Ebit_2ESIGN__EXTEND,V0l),V1h),V2n))))))))))))) # label(conj_thm_2Ebit_2EBIT__SIGN__EXTEND) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2040 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0h)),V1l),V2n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Enum_2ESUC,V0h)),V1l)),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0h)),V2n)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l))),ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n))))))))) # label(conj_thm_2Ebit_2EBITS__SUC__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2041 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1j (mem(V1j,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1j),ap(ap(c_2Earithmetic_2EMOD,V2k),V0n))),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1j),V2k)),V0n)))))))) # label(conj_thm_2Ebit_2EMOD__PLUS__RIGHT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2042 (all V0a (mem(V0a,ty_2Enum_2Enum) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0a)),V0a))) # label(conj_thm_2Ebit_2ESUC__SUB) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2043 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (V0a != V1b -> -p(ap(ap(c_2Ebit_2EBIT,V0a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)))))))) # label(conj_thm_2Ebit_2EBIT__B__NEQ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2044 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0b),V1n)) <-> p(ap(ap(c_2Ebit_2EBIT,V0b),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))))))))) # label(conj_thm_2Ebit_2EBIT__EXP__SUB1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2045 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n)) -> (p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,V1n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0x)),V2a)) <-> p(ap(ap(c_2Ebit_2EBIT,V0x),ap(ap(c_2Ebit_2EBIT__REVERSE,V1n),V2a))))))))))) # label(conj_thm_2Ebit_2EBIT__REVERSE__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2046 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2ETIMES__2EXP,V0x),V1n) = ap(ap(c_2Earithmetic_2E_2A,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)))))) # label(ax_thm_2Ebit_2ETIMES__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2047 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMOD,V0a),V1b)),V0a))))))) # label(conj_thm_2Ebit_2EMOD__LEQ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2048 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0h),ap(ap(c_2Earithmetic_2E_2B,V1l),V2x))) -> -p(ap(ap(c_2Ebit_2EBIT,V2x),ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V3n)))))))))))) # label(conj_thm_2Ebit_2EBIT__OF__BITS__THM2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2049 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) != c_2Enum_2E0 <-> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a)))))) # label(conj_thm_2Ebit_2ENOT__BITS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2050 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1j (mem(V1j,ty_2Enum_2Enum) -> (all V2k (mem(V2k,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V2k),V0n)),V1j)),V0n) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V2k),V1j)),V0n)))))))) # label(conj_thm_2Ebit_2EMOD__PLUS__LEFT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2051 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V0b)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0b),V1h)) & p(ap(ap(c_2Ebit_2EBIT,V0b),V3n)) <-> p(ap(ap(c_2Ebit_2EBIT,V0b),ap(ap(ap(c_2Ebit_2ESLICE,V1h),V2l),V3n)))))))))))) # label(conj_thm_2Ebit_2EBIT__SLICE__THM4) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2052 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V1h)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EMOD,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2l))),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V1h)))))))))))) # label(conj_thm_2Ebit_2EMOD__2EXP__MONO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2053 (all V0i (mem(V0i,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,V0i),V1n)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0i)),V1n))))))) # label(conj_thm_2Ebit_2EBIT__IMP__GE__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2054 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) = c_2Enum_2E0))))))) # label(conj_thm_2Ebit_2EBITS__LT__LOW) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2055 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2op (mem(V2op,arr(bool,arr(bool,bool))) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (all V4b (mem(V4b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n)) -> (-p(ap(ap(V2op,ap(ap(c_2Ebit_2EBIT,V0x),V3a)),ap(ap(c_2Ebit_2EBIT,V0x),V4b))) -> c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))))))) # label(conj_thm_2Ebit_2EBITWISE__NOT__COR) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2056 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V2b)))),ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V1a)),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V2b))),ap(c_2Ebool_2E_7E,ap(ap(c_2Emin_2E_3D(bool),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V1a)),ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V2b))))) <-> p(ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,V1a),V2b)))))))))) # label(conj_thm_2Ebit_2EADD__BIT__SUC) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2057 (all V0l (mem(V0l,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2ESIGN__EXTEND,V0l),V1h),V2n) = ap(ap(c_2Ebool_2ELET(ty_2Enum_2Enum,ty_2Enum_2Enum),f250(V0l,V2n,V1h)),ap(ap(c_2Earithmetic_2EMOD,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0l))))))))) # label(ax_thm_2Ebit_2ESIGN__EXTEND__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2058 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2E_2B,V2l),V0n)),V1h)) -> (p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(ap(c_2Ebit_2EBITS,V1h),V2l),V3a))) <-> p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V2l),V0n)),V3a)))))))))))) # label(conj_thm_2Ebit_2EBIT__OF__BITS__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2059 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2s (mem(V2s,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2s),V0n)) -> (p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2D,V0n),V2s)),V1a)) <-> p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2E_2A,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2s)))))))))))) # label(conj_thm_2Ebit_2EBIT__SHIFT__THM2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2060 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) <-> ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) != ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) # label(conj_thm_2Ebit_2ENOT__BITS2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2061 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1h2 (mem(V1h2,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0h),V1h2)) -> ap(ap(ap(c_2Ebit_2EBITS,V1h2),V2l),ap(ap(ap(c_2Ebit_2ESLICE,V0h),V2l),V3n)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V2l),V3n)))))))))) # label(conj_thm_2Ebit_2EBITS__SLICE__THM2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2062 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))))))))) # label(conj_thm_2Ebit_2ESLICELT__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2063 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V2b))) = ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,V1a),V2b)))))))) # label(conj_thm_2Ebit_2EBITS__SUM3) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2064 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1m)),V0h)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V1m)) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2ESLICE,V0h),ap(c_2Enum_2ESUC,V1m)),V3n)),ap(ap(ap(c_2Ebit_2ESLICE,V1m),V2l),V3n)) = ap(ap(ap(c_2Ebit_2ESLICE,V0h),V2l),V3n)))))))))) # label(conj_thm_2Ebit_2ESLICE__COMP__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2065 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (V0n != c_2Enum_2E0 -> p(ap(ap(c_2Ebit_2EBIT,ap(c_2Ebit_2ELOG2,V0n)),V0n))))) # label(conj_thm_2Ebit_2EBIT__LOG2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2066 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))))))))) # label(conj_thm_2Ebit_2EBITSLT__THM2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2067 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),c_2Enum_2E0))))) # label(conj_thm_2Ebit_2EBITS__ZERO2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2068 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a)),V2n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b))) & V2n != c_2Enum_2E0 -> (exists V3i (mem(V3i,ty_2Enum_2Enum) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V3i)) & p(ap(ap(c_2Eprim__rec_2E_3C,V3i),V1b)) & p(ap(ap(c_2Ebit_2EBIT,V3i),V2n))))))))))) # label(conj_thm_2Ebit_2EEXISTS__BIT__IN__RANGE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2069 (all V0b (mem(V0b,bool) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2n),V1m)) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Ebit_2ESBIT,V0b),V1m)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2n)) = ap(ap(c_2Ebit_2ESBIT,V0b),ap(ap(c_2Earithmetic_2E_2D,V1m),V2n))))))))) # label(conj_thm_2Ebit_2ESBIT__DIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2070 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))),V3b)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V3b))))))))) # label(conj_thm_2Ebit_2EBITS__SUM2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2071 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EDIVMOD__2EXP,V0x),V1n) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EDIV,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))))))) # label(ax_thm_2Ebit_2EDIVMOD__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2072 (all V3x k(bool,ap(c_2Ebool_2E_7E,V3x)) = ap(f251,V3x)) # label(lameq_f251) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2073 (all V0b (mem(V0b,ty_2Enum_2Enum) -> p(ap(ap(c_2Ebit_2EBIT,V0b),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0b))))) # label(conj_thm_2Ebit_2EBIT__B) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2074 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2l (mem(V2l,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Enum_2ESUC,V1m)),V0h)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V2l),V1m)) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V2l),V3n) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2EBITS,V0h),ap(c_2Enum_2ESUC,V1m)),V3n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V1m)),V2l)))),ap(ap(ap(c_2Ebit_2EBITS,V1m),V2l),V3n))))))))))) # label(conj_thm_2Ebit_2EBIT__COMP__THM3) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2075 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))) # label(conj_thm_2Ebit_2EZERO__LT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2076 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l))) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n))))))) # label(conj_thm_2Ebit_2EBITS__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2077 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EBITV,V1n),V0b) = ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V0b),V1n)),c_2Enum_2E0))))) # label(conj_thm_2Ebit_2EBITV__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2078 (all V0i (mem(V0i,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2op (mem(V2op,arr(bool,arr(bool,bool))) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (all V4b (mem(V4b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1n),V0i)) -> -p(ap(ap(c_2Ebit_2EBIT,V0i),ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b)))))))))))))) # label(conj_thm_2Ebit_2ENOT__BIT__GT__BITWISE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2079 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n))) <-> p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ebit_2ELOG2,V0x)),V1n)) | V0x = c_2Enum_2E0))))) # label(conj_thm_2Ebit_2ELT__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2080 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (V0n = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EMOD,V1x),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) <-> ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,V1x),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),V0n) = c_2Enum_2E0)))))) # label(conj_thm_2Ebit_2EMOD__PLUS__1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2081 (all V0l (mem(V0l,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(ap(c_2Ebit_2ESLICE,V1h),V0l),c_2Enum_2E0))))) # label(conj_thm_2Ebit_2ESLICE__ZERO2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2082 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1l),V0h)) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))) = ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2E_2D,V0h),V1l)),c_2Enum_2E0),V2a)))))))) # label(conj_thm_2Ebit_2EBITS__ZERO4) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2083 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2ESLICE,V0x),V0x),V1n) = ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V0x),V1n)),V0x))))) # label(conj_thm_2Ebit_2EBIT__SLICE__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2084 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1i ap(ap(c_2Ebit_2EBIT,V1i),V0n) = ap(f249(V0n),V1i)))) # label(lameq_f249) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2085 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2s (mem(V2s,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V0n),V2s)),ap(ap(c_2Earithmetic_2E_2A,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2s)))) <-> p(ap(ap(c_2Ebit_2EBIT,V0n),V1a))))))))) # label(conj_thm_2Ebit_2EBIT__SHIFT__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2086 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (V1a != c_2Enum_2E0 & ap(ap(c_2Earithmetic_2EMOD,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)) = c_2Enum_2E0 -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),V1a))))))) # label(conj_thm_2Ebit_2EMOD__ZERO__GT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2087 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EDIV,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)) = ap(ap(c_2Earithmetic_2E_2D,V1n),ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))))))) # label(conj_thm_2Ebit_2EDIV__MULT__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2088 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3y (mem(V3y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0a),V2x)) & p(ap(ap(c_2Eprim__rec_2E_3C,V1b),V3y)) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2A,V0a),V1b)),ap(ap(c_2Earithmetic_2E_2A,V2x),V3y)))))))))))) # label(conj_thm_2Ebit_2ELESS__MULT__MONO2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2089 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2s (mem(V2s,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V2s)) -> -p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2E_2A,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2s))))))))))) # label(conj_thm_2Ebit_2EBIT__SHIFT__THM3) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2090 (all V0wl (mem(V0wl,ty_2Enum_2Enum) -> (all V1op (mem(V1op,arr(bool,arr(bool,bool))) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0wl)),V1op),V2a),V3b) = ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0wl)),V1op),ap(ap(ap(c_2Ebit_2EBITS,V0wl),c_2Enum_2E0),V2a)),ap(ap(ap(c_2Ebit_2EBITS,V0wl),c_2Enum_2E0),V3b)))))))))) # label(conj_thm_2Ebit_2EBITWISE__BITS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2091 (all V0y (mem(V0y,ty_2Enum_2Enum) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2ESLICE,V1x),V1x),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0y)) = ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,V1x),V2n)),ap(ap(c_2Earithmetic_2E_2B,V1x),V0y)))))))) # label(conj_thm_2Ebit_2EBIT__SLICE__LEM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2092 (all V0h1 (mem(V0h1,ty_2Enum_2Enum) -> (all V1l1 (mem(V1l1,ty_2Enum_2Enum) -> (all V2h2 (mem(V2h2,ty_2Enum_2Enum) -> (all V3l2 (mem(V3l2,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V2h2),V3l2),ap(ap(ap(c_2Ebit_2EBITS,V0h1),V1l1),V4n)) = ap(ap(ap(c_2Ebit_2EBITS,ap(ap(c_2Earithmetic_2EMIN,V0h1),ap(ap(c_2Earithmetic_2E_2B,V2h2),V1l1))),ap(ap(c_2Earithmetic_2E_2B,V3l2),V1l1)),V4n))))))))))) # label(conj_thm_2Ebit_2EBITS__COMP__THM2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2093 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0n),V1m)) & p(ap(ap(c_2Eprim__rec_2E_3C,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EDIV,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)))))))))) # label(conj_thm_2Ebit_2EDIV__LT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2094 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1h (mem(V1h,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V1h),c_2Enum_2E0),V0n) = ap(ap(ap(c_2Ebit_2ESLICE,V1h),c_2Enum_2E0),V0n))))) # label(conj_thm_2Ebit_2ESLICE__ZERO__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2095 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,V0a),V1b))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a))))))) # label(conj_thm_2Ebit_2EEXP__SUB__LESS__EQ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2096 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h))) = ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1n))))) # label(conj_thm_2Ebit_2EBITS__ZERO3) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2097 (all V0i (mem(V0i,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(c_2Ebit_2ELOG2,V1n)),V0i)) -> -p(ap(ap(c_2Ebit_2EBIT,V0i),V1n))))))) # label(conj_thm_2Ebit_2ENOT__BIT__GT__LOG2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2098 (all V0b (mem(V0b,ty_2Enum_2Enum) -> -p(ap(ap(c_2Ebit_2EBIT,V0b),c_2Enum_2E0)))) # label(conj_thm_2Ebit_2EBIT__ZERO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2099 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> V1k = ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(ap(c_2Earithmetic_2EDIV,V1k),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EMOD,V1k),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))))) # label(conj_thm_2Ebit_2ETWOEXP__DIVISION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2100 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (all V2i (mem(V2i,ty_2Enum_2Enum) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2E_2B,V2i),V0n)),V1m)) & p(ap(ap(c_2Eprim__rec_2E_3C,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))) -> (p(ap(ap(c_2Ebit_2EBIT,V2i),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)),ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2EDIV,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),ap(ap(c_2Emin_2E_3D(ty_2Enum_2Enum),ap(ap(c_2Earithmetic_2EMOD,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),c_2Enum_2E0)),c_2Enum_2E0),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))))) <-> p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V2i),V0n)),ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m)),ap(ap(c_2Earithmetic_2EMOD,V3a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))))))))))))))) # label(conj_thm_2Ebit_2EBIT__SHIFT__THM5) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2101 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2op (mem(V2op,arr(bool,arr(bool,bool))) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (all V4b (mem(V4b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n)) -> (p(ap(ap(V2op,ap(ap(c_2Ebit_2EBIT,V0x),V3a)),ap(ap(c_2Ebit_2EBIT,V0x),V4b))) -> ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2EDIV,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))))))))) # label(conj_thm_2Ebit_2EBITWISE__COR) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2102 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,V1a),V2b)) = ap(ap(c_2Earithmetic_2EMOD,ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),V1a)),ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),V2b))),ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0n)),ap(c_2Enum_2ESUC,V0n)),ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V2b))))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))))))))) # label(conj_thm_2Ebit_2EADD__BITS__SUC) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2103 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0x)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),V1y)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ebit_2ELOG2,V0x)),ap(c_2Ebit_2ELOG2,V1y))))))))) # label(conj_thm_2Ebit_2ELOG2__LE__MONO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2104 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0h),V1l)) -> ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n) = c_2Enum_2E0))))))) # label(conj_thm_2Ebit_2ESLICE__ZERO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2105 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V2n)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n))))))) # label(conj_thm_2Ebit_2EBITS__SLICE__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2106 (all V0b (mem(V0b,bool) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2ESBIT,V0b),V1n) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Enum_2Enum),V0b),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1n)),c_2Enum_2E0))))) # label(ax_thm_2Ebit_2ESBIT__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2107 (all V0n (mem(V0n,ty_2Enum_2Enum) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))) # label(conj_thm_2Ebit_2EONE__LE__TWOEXP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2108 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1a)),ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V2b))) = ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2A,V1a),V2b)))))))) # label(conj_thm_2Ebit_2EBITS__MUL) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2109 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2f (mem(V2f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n)) -> (p(ap(ap(c_2Ebit_2EBIT,V0x),ap(ap(ap(c_2Ebit_2EBIT__MODIFY,V1n),V2f),V3a))) <-> p(ap(ap(V2f,V0x),ap(ap(c_2Ebit_2EBIT,V0x),V3a))))))))))))) # label(conj_thm_2Ebit_2EBIT__MODIFY__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2110 (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBIT__MODIFY,c_2Enum_2E0),V0f),V1x) = c_2Enum_2E0)))) # label(ax_thm_2Ebit_2EBIT__MODIFY__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2111 (all V2n (mem(V2n,ty_2Enum_2Enum) -> (all V3f (mem(V3f,arr(ty_2Enum_2Enum,arr(bool,bool))) -> (all V4x (mem(V4x,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBIT__MODIFY,ap(c_2Enum_2ESUC,V2n)),V3f),V4x) = ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2EBIT__MODIFY,V2n),V3f),V4x)),ap(ap(c_2Ebit_2ESBIT,ap(ap(V3f,V2n),ap(ap(c_2Ebit_2EBIT,V2n),V4x))),V2n)))))))) # label(ax_thm_2Ebit_2EBIT__MODIFY__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2112 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V3b),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l))),V3b)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),ap(ap(c_2Earithmetic_2E_2A,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l)))))))))))) # label(conj_thm_2Ebit_2EBITS__SUM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2113 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l)))))))))) # label(conj_thm_2Ebit_2EBITSLT__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2114 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1m_27 (mem(V1m_27,ty_2Enum_2Enum) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3l (mem(V3l,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V3l),V2m)) & p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V0h)) & V1m_27 = ap(ap(c_2Earithmetic_2E_2B,V2m),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1m_27),V4n)),ap(ap(ap(c_2Ebit_2ESLICE,V2m),V3l),V4n)) = ap(ap(ap(c_2Ebit_2ESLICE,V0h),V3l),V4n)))))))))))) # label(conj_thm_2Ebit_2ESLICE__COMP__RWT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2115 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0a),V1b)) -> (exists V2p (mem(V2p,ty_2Enum_2Enum) & ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b) = ap(ap(c_2Earithmetic_2E_2A,V2p),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0a))))))))) # label(conj_thm_2Ebit_2ELESS__EQ__EXP__MULT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2116 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n) = ap(ap(c_2Ebit_2EMOD__2EXP,ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l)),ap(ap(c_2Ebit_2EDIV__2EXP,V1l),V2n)))))))) # label(ax_thm_2Ebit_2EBITS__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2117 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1p (mem(V1p,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1p)),V0n)) & p(ap(ap(c_2Eprim__rec_2E_3C,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V1p)))) -> ap(c_2Ebit_2ELOG2,V0n) = V1p))))) # label(conj_thm_2Ebit_2ELOG2__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2118 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (ap(ap(c_2Ebit_2EMOD__2EXP,V0n),V1a) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) <-> p(ap(ap(c_2Ebit_2EMOD__2EXP__MAX,V0n),V1a))))))) # label(ax_thm_2Ebit_2EMOD__2EXP__MAX__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2119 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1k (mem(V1k,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(c_2Earithmetic_2EMOD,V1k),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))))) # label(conj_thm_2Ebit_2EMOD__2EXP__LT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2120 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,V0b),V1n)) <-> ap(ap(ap(c_2Ebit_2EBITS,V0b),V0b),V1n) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))))))) # label(ax_thm_2Ebit_2EBIT__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2121 (all V0op (mem(V0op,arr(bool,arr(bool,bool))) -> (all V1x (mem(V1x,ty_2Enum_2Enum) -> (all V2y (mem(V2y,ty_2Enum_2Enum) -> c_2Enum_2E0 = ap(ap(ap(ap(c_2Ebit_2EBITWISE,c_2Enum_2E0),V0op),V1x),V2y))))))) # label(ax_thm_2Ebit_2EBITWISE__def_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2122 (all V3n (mem(V3n,ty_2Enum_2Enum) -> (all V4op (mem(V4op,arr(bool,arr(bool,bool))) -> (all V5x (mem(V5x,ty_2Enum_2Enum) -> (all V6y (mem(V6y,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V3n),V4op),V5x),V6y)),ap(ap(c_2Ebit_2ESBIT,ap(ap(V4op,ap(ap(c_2Ebit_2EBIT,V3n),V5x)),ap(ap(c_2Ebit_2EBIT,V3n),V6y))),V3n)) = ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V3n)),V4op),V5x),V6y))))))))) # label(ax_thm_2Ebit_2EBITWISE__def_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2123 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (c_2Enum_2E0 = ap(ap(c_2Earithmetic_2EMOD,V0a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b)),V0a)) -> ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EDIV,V0a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO))) = ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2E_2D,V0a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1b))))))) # label(conj_thm_2Ebit_2EDIV__SUB1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2124 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> ((all V2i (mem(V2i,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V2i),V0n)) -> -p(ap(ap(c_2Ebit_2EBIT,V2i),V1m))))) -> ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1m) = c_2Enum_2E0))))) # label(conj_thm_2Ebit_2EBITS__ZERO5) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2125 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,V1i),ap(ap(c_2Earithmetic_2EDIV,V2a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n)))) <-> p(ap(ap(c_2Ebit_2EBIT,ap(ap(c_2Earithmetic_2E_2B,V1i),V0n)),V2a))))))))) # label(conj_thm_2Ebit_2EBIT__SHIFT__THM4) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2126 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EMOD__2EXP,V0x),V1n) = ap(ap(c_2Earithmetic_2EMOD,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)))))) # label(ax_thm_2Ebit_2EMOD__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2127 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1m (mem(V1m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1m))) <-> V0n = V1m))))) # label(conj_thm_2Ebit_2EBIT__TWO__POW) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2128 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EDIV__2EXP,V0x),V1n) = ap(ap(c_2Earithmetic_2EDIV,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)))))) # label(ax_thm_2Ebit_2EDIV__2EXP__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2129 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1a),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))) -> ap(ap(ap(c_2Ebit_2EBITS,V0h),c_2Enum_2E0),V1a) = V1a))))) # label(conj_thm_2Ebit_2EBITS__ZEROL) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2130 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V0n)) -> V0n = ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Ebit_2ELOG2,V0n)),c_2Enum_2E0),V0n)))) # label(conj_thm_2Ebit_2EBITS__LOG2__ZERO__ID) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2131 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> (ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2a) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V3b) <-> (all V4x (mem(V4x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V4x),V0h)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V1l),V4x)) -> (p(ap(ap(c_2Ebit_2EBIT,V4x),V3b)) <-> p(ap(ap(c_2Ebit_2EBIT,V4x),V2a))))))))))))))) # label(conj_thm_2Ebit_2EBIT__BITS__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2132 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))) = ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)) <-> p(ap(c_2Earithmetic_2EODD,V0n))))) # label(conj_thm_2Ebit_2EODD__MOD2__LEM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2133 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> ap(ap(ap(c_2Ebit_2EBITS,V1b),V1b),V0n) = ap(ap(c_2Ebit_2EBITV,V0n),V1b))))) # label(ax_thm_2Ebit_2EBITV__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2134 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(c_2Earithmetic_2EDIV,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))) = ap(ap(c_2Earithmetic_2E_2D,V0n),ap(ap(c_2Earithmetic_2EMOD,V0n),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))) # label(conj_thm_2Ebit_2EDIV__MULT__THM2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2135 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2x (mem(V2x,ty_2Enum_2Enum) -> (all V3y (mem(V3y,ty_2Enum_2Enum) -> (all V4n (mem(V4n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V0h),V2x)) & p(ap(ap(c_2Earithmetic_2E_3C_3D,V3y),V1l)) -> ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),V4n) = ap(ap(ap(c_2Ebit_2ESLICE,V0h),V1l),ap(ap(ap(c_2Ebit_2ESLICE,V2x),V3y),V4n))))))))))))) # label(conj_thm_2Ebit_2ESLICE__COMP__THM2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2136 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1op (mem(V1op,arr(bool,arr(bool,bool))) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Earithmetic_2E_2A,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(ap(ap(ap(c_2Ebit_2EBITWISE,V0n),V1op),ap(ap(c_2Earithmetic_2EDIV,V2a),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))),ap(ap(c_2Earithmetic_2EDIV,V3b),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))),ap(ap(c_2Ebit_2ESBIT,ap(ap(V1op,ap(c_2Earithmetic_2EODD,V2a)),ap(c_2Earithmetic_2EODD,V3b))),c_2Enum_2E0)) = ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0n)),V1op),V2a),V3b))))))))) # label(conj_thm_2Ebit_2EBITWISE__EVAL) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2137 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1op (mem(V1op,arr(bool,arr(bool,bool))) -> (all V2a (mem(V2a,ty_2Enum_2Enum) -> (all V3b (mem(V3b,ty_2Enum_2Enum) -> p(ap(ap(c_2Eprim__rec_2E_3C,ap(ap(ap(ap(c_2Ebit_2EBITWISE,V0n),V1op),V2a),V3b)),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))))))))))) # label(conj_thm_2Ebit_2EBITWISE__LT__2EXP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2138 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> ap(ap(c_2Earithmetic_2EDIV,ap(ap(c_2Earithmetic_2EMOD,V2n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0h)))),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V1l)) = ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n))))))) # label(conj_thm_2Ebit_2EBITS__THM2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2139 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (-p(ap(ap(c_2Ebit_2EBIT,V0n),V1a)) <-> ap(ap(ap(c_2Ebit_2EBITS,V0n),V0n),V1a) = c_2Enum_2E0))))) # label(conj_thm_2Ebit_2ENOT__BIT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2140 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1y (mem(V1y,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0x)),V1y)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V0x),ap(c_2Ebit_2ELOG2,V1y)))))))) # label(conj_thm_2Ebit_2ETWOEXP__LE__IMP__LE__LOG2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2141 (all V2y (mem(V2y,ty_2Enum_2Enum) -> (all V3x (mem(V3x,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V3x)) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V3x),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V2y))) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(c_2Ebit_2ELOG2,V3x)),V2y)))))))) # label(conj_thm_2Ebit_2ETWOEXP__LE__IMP__LE__LOG2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2142 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1i (mem(V1i,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0n)),V1i)) <-> p(ap(ap(c_2Ebit_2EBIT,V0n),ap(ap(c_2Earithmetic_2EDIV,V1i),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO)))))))))) # label(conj_thm_2Ebit_2EBIT__DIV2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2143 (all V0a (mem(V0a,ty_2Enum_2Enum) -> (all V1b (mem(V1b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1b),V0a)) & p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),V1b)) -> p(ap(ap(c_2Eprim__rec_2E_3C,c_2Enum_2E0),ap(ap(c_2Earithmetic_2EDIV,V0a),V1b)))))))) # label(conj_thm_2Ebit_2EDIV__GT0) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2144 (all V0m (mem(V0m,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebit_2EBIT,c_2Enum_2E0),ap(ap(c_2Earithmetic_2E_2B,V0m),V1n))) <-> -(p(ap(ap(c_2Ebit_2EBIT,c_2Enum_2E0),V1n)) <-> p(ap(ap(c_2Ebit_2EBIT,c_2Enum_2E0),V0m)))))))) # label(conj_thm_2Ebit_2EADD__BIT0) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2145 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1a (mem(V1a,ty_2Enum_2Enum) -> (all V2b (mem(V2b,ty_2Enum_2Enum) -> ap(ap(ap(ap(c_2Ebit_2EBITWISE,ap(c_2Enum_2ESUC,V0n)),f251),V1a),V2b) = ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2E_2D,ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),ap(c_2Enum_2ESUC,V0n))),ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT1,c_2Earithmetic_2EZERO)))),ap(ap(ap(c_2Ebit_2EBITS,V0n),c_2Enum_2E0),V1a)))))))) # label(conj_thm_2Ebit_2EBITWISE__ONE__COMP__LEM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2146 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> ap(ap(c_2Ebit_2EDIVMOD__2EXP,V0x),V1n) = ap(ap(c_2Epair_2E_2C(ty_2Enum_2Enum,ty_2Enum_2Enum),ap(ap(c_2Ebit_2EDIV__2EXP,V0x),V1n)),ap(ap(c_2Ebit_2EMOD__2EXP,V0x),V1n)))))) # label(conj_thm_2Ebit_2EDIVMOD__2EXP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2147 (all V0n (mem(V0n,ty_2Enum_2Enum) -> ap(c_2Ewhile_2ELEAST,f249(V0n)) = ap(c_2Ebit_2ELOWEST__SET__BIT,V0n))) # label(ax_thm_2Ebit_2ELOWEST__SET__BIT__def) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2148 (all V0n (mem(V0n,ty_2Enum_2Enum) -> (all V1P (mem(V1P,arr(ty_2Enum_2Enum,bool)) -> (p(ap(V1P,V0n)) & (all V2m (mem(V2m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V2m),V0n)) -> -p(ap(V1P,V2m))))) -> ap(c_2Ewhile_2ELEAST,V1P) = V0n))))) # label(conj_thm_2Ebit_2ELEAST__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2149 (all V0n (mem(V0n,ty_2Enum_2Enum) -> c_2Enum_2E0 != ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0n))) # label(conj_thm_2Ebit_2ETWOEXP__NOT__ZERO) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2150 (all V0h (mem(V0h,ty_2Enum_2Enum) -> (all V1l (mem(V1l,ty_2Enum_2Enum) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Earithmetic_2E_3C_3D,V1l),ap(c_2Enum_2ESUC,V0h))) -> ap(ap(c_2Earithmetic_2E_2B,ap(ap(c_2Ebit_2ESBIT,ap(ap(c_2Ebit_2EBIT,ap(c_2Enum_2ESUC,V0h)),V2n)),ap(ap(c_2Earithmetic_2E_2D,ap(c_2Enum_2ESUC,V0h)),V1l))),ap(ap(ap(c_2Ebit_2EBITS,V0h),V1l),V2n)) = ap(ap(ap(c_2Ebit_2EBITS,ap(c_2Enum_2ESUC,V0h)),V1l),V2n)))))))) # label(conj_thm_2Ebit_2EBITS__SUC) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2151 (all V0b (mem(V0b,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V1n),ap(ap(c_2Earithmetic_2EEXP,ap(c_2Earithmetic_2ENUMERAL,ap(c_2Earithmetic_2EBIT2,c_2Earithmetic_2EZERO))),V0b))) & c_2Enum_2E0 != V1n -> (exists V2i (p(ap(ap(c_2Eprim__rec_2E_3C,V2i),V0b)) & p(ap(ap(c_2Ebit_2EBIT,V2i),V1n)) & mem(V2i,ty_2Enum_2Enum)))))))) # label(conj_thm_2Ebit_2EEXISTS__BIT__LT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2152 (all V0x (mem(V0x,ty_2Enum_2Enum) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2op (mem(V2op,arr(bool,arr(bool,bool))) -> (all V3a (mem(V3a,ty_2Enum_2Enum) -> (all V4b (mem(V4b,ty_2Enum_2Enum) -> (p(ap(ap(c_2Eprim__rec_2E_3C,V0x),V1n)) -> (p(ap(ap(V2op,ap(ap(c_2Ebit_2EBIT,V0x),V3a)),ap(ap(c_2Ebit_2EBIT,V0x),V4b))) <-> p(ap(ap(c_2Ebit_2EBIT,V0x),ap(ap(ap(ap(c_2Ebit_2EBITWISE,V1n),V2op),V3a),V4b))))))))))))))) # label(conj_thm_2Ebit_2EBITWISE__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2153 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t)) <-> (exists V2y (p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),V1t)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V2y),V0s)) & mem(V2y,A_27a))) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2EPSUBSET__MEMBER) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2154 (all A_27a (ne(A_27a) -> c_2Epred__set_2EEMPTY(A_27a) = k(A_27a,c_2Ebool_2EF))) # label(ax_thm_2Epred__set_2EEMPTY__DEF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2155 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (V1t = V0s <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s))))))))) # label(conj_thm_2Epred__set_2ESUBSET__SUBSET__EQ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2156 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($F <-> p(ap(c_2Epred__set_2EEMPTY(A_27a),V0x))))))) # label(conj_thm_2Epred__set_2EEMPTY__applied) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2157 (all A_27a all V1s (mem(V1s,arr(A_27a,bool)) -> (all V0x (mem(V0x,A_27a) -> (all V2y ap(ap(c_2Epair_2E_2C(A_27a,bool),V2y),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Emin_2E_3D(A_27a),V2y),V0x)),ap(ap(c_2Ebool_2EIN(A_27a),V2y),V1s))) = ap(f266(A_27a,V1s,V0x),V2y)))))) # label(lameq_f266) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2158 (all A_27a (ne(A_27a) -> c_2Epred__set_2EUNIV(A_27a) = k(A_27a,c_2Ebool_2ET))) # label(ax_thm_2Epred__set_2EUNIV__DEF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2159 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))))))))) # label(conj_thm_2Epred__set_2ESUBSET__OF__INSERT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2160 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1n (mem(V1n,ty_2Enum_2Enum) -> (all V2d (mem(V2d,ty_2Enum_2Enum) -> ((all V3n (mem(V3n,ty_2Enum_2Enum) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,V3n)),ap(V0f,ap(c_2Enum_2ESUC,V3n)))))) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V0f,V1n)),ap(V0f,ap(ap(c_2Earithmetic_2E_2B,V1n),V2d))))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__ADD) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2161 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Epartition(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool)))))) # label(mem_c_2Epred__set_2Epartition) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2162 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x) = ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)),V0x))))))) # label(conj_thm_2Epred__set_2EDELETE__DELETE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2163 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> (all V1y (mem(V1y,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0x),V1y)),V0x) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V1y),V0x) & ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0x),V1y)),V1y) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V1y))))))) # label(conj_thm_2Epred__set_2EDIFF__SAME__UNION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2164 (all A_27a all A_27b all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2y ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V1x),V2y)),ap(ap(V0P,V1x),V2y)) = ap(f254(A_27a,A_27b,V0P,V1x),V2y)))))) # label(lameq_f254) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2165 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (V0s = c_2Epred__set_2EUNIV(A_27a) -> (all V1v (mem(V1v,A_27a) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V1v),V0s))))))))) # label(conj_thm_2Epred__set_2EIN__EQ__UNIV__IMP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2166 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) | p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s))))))))))) # label(conj_thm_2Epred__set_2EIN__UNION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2167 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),c_2Epred__set_2EUNIV(A_27a))) <-> (exists V1x (-p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) & mem(V1x,A_27a)))))))) # label(conj_thm_2Epred__set_2EPSUBSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2168 (all A_27a (ne(A_27a) -> c_2Epred__set_2EUNIV(A_27a) != c_2Epred__set_2EEMPTY(A_27a))) # label(conj_thm_2Epred__set_2EUNIV__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2169 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EDIFF(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2EDIFF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2170 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (c_2Epred__set_2EEMPTY(A_27a) != V0s <-> (exists V1x (p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) & mem(V1x,A_27a)))))))) # label(conj_thm_2Epred__set_2EMEMBER__NOT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2171 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EDELETE(A_27a),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2EDELETE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2172 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EDIFF(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s))))) # label(conj_thm_2Epred__set_2EEMPTY__DIFF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2173 (all A_27a all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2x ap(f252(A_27a,V1P),V2x) = ap(V1P,V2x)))) # label(lameq_f252) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2174 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,bool) -> (all V1y (mem(V1y,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),c_2Epred__set_2EUNIV(A_27a)),V1y)) | -p(V0x) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Ecombin_2EK(bool,A_27a),V0x)),V1y))))))))) # label(conj_thm_2Epred__set_2EK__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2175 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (-p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x) = V0s))))))) # label(conj_thm_2Epred__set_2EDELETE__NON__ELEMENT__RWT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2176 (all A_27a all V1t (mem(V1t,arr(A_27a,bool)) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_5C_2F,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))) = ap(f263(A_27a,V1t,V0s),V2x)))))) # label(lameq_f263) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2177 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EINJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))))))) # label(mem_c_2Epred__set_2EINJ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2178 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> ((all V5x (mem(V5x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V5x),V2t)) -> p(ap(V0P,V5x))))) & (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V1s)) -> p(ap(V0P,V4x))))) <-> (all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t))) -> p(ap(V0P,V3x)))))))))))))) # label(conj_thm_2Epred__set_2EFORALL__IN__UNION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2179 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Epairwise(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2Epairwise) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2180 (all V0s (mem(V0s,arr(ty_2Enum_2Enum,bool)) -> ((exists V2n (mem(V2n,ty_2Enum_2Enum) & (all V3m (mem(V3m,ty_2Enum_2Enum) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V3m),V0s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,V2n),V3m))))) & p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V2n),V0s)))) <-> (exists V1n (mem(V1n,ty_2Enum_2Enum) & p(ap(ap(c_2Ebool_2EIN(ty_2Enum_2Enum),V1n),V0s))))))) # label(conj_thm_2Epred__set_2ENUM__SET__WOP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2181 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2ESURJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))))))) # label(mem_c_2Epred__set_2ESURJ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2182 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ECARD(A_27a),arr(arr(A_27a,bool),ty_2Enum_2Enum)))) # label(mem_c_2Epred__set_2ECARD) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2183 (all A_27a all V1P (mem(V1P,arr(A_27a,bool)) -> (all V2x ap(f256(A_27a,V1P),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(V1P,V2x))))) # label(lameq_f256) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2184 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) | p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) <-> p(ap(ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t),V2x))))))))))) # label(conj_thm_2Epred__set_2EUNION__applied) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2185 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V2u)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V2u)))))))))) # label(conj_thm_2Epred__set_2EINTER__OVER__UNION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2186 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> c_2Epred__set_2EUNIV(A_27a) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),c_2Epred__set_2EUNIV(A_27a)))))) # label(conj_thm_2Epred__set_2EINSERT__UNIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2187 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) != ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))))))) # label(conj_thm_2Epred__set_2ENOT__EMPTY__INSERT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2188 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Eis__measure__maximal(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2Eis__measure__maximal) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2189 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (V1t != V0s <-> (exists V2x (mem(V2x,A_27a) & (-p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)))))))))))) # label(conj_thm_2Epred__set_2ENOT__EQUAL__SETS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2190 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> V0s = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a)))))) # label(conj_thm_2Epred__set_2EDIFF__EMPTY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2191 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f266(A_27a,V1s,V0x)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))))))) # label(ax_thm_2Epred__set_2EINSERT__DEF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2192 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EDELETE(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0x))))) # label(conj_thm_2Epred__set_2EEMPTY__DELETE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2193 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)),V1s)))))))) # label(conj_thm_2Epred__set_2EDELETE__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2194 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EDISJOINT(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2EDISJOINT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2195 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) -> V1s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)))))))) # label(conj_thm_2Epred__set_2EABSORPTION__RWT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2196 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f264(A_27a,V1t,V0s)))))))) # label(ax_thm_2Epred__set_2EINTER__DEF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2197 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),ap(ap(c_2Epred__set_2EUNION(A_27a),V1t),V2u)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u))))))))) # label(conj_thm_2Epred__set_2EUNION__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2198 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),c_2Epred__set_2EEMPTY(A_27a))))))))) # label(ax_thm_2Epred__set_2EDELETE__DEF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2199 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V2u)) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),V2u))))))))) # label(conj_thm_2Epred__set_2EINTER__ASSOC) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2200 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ((all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) -> -p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))))) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__ALT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2201 (all A_27a (ne(A_27a) -> (all V0y (mem(V0y,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f256(A_27a,V1P)))) <-> p(ap(V1P,V0y))))))))) # label(conj_thm_2Epred__set_2EIN__GSPEC__IFF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2202 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1y)),V0x) = ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V0x)),V1y))))))))) # label(conj_thm_2Epred__set_2EDELETE__COMM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2203 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V0s))))) # label(conj_thm_2Epred__set_2EDIFF__EQ__EMPTY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2204 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1a (mem(V1a,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1a),V2s))) -> p(ap(V0P,V3x))))) <-> p(ap(V0P,V1a)) & (all V4x (mem(V4x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V2s)) -> p(ap(V0P,V4x)))))))))))))) # label(conj_thm_2Epred__set_2EFORALL__IN__INSERT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2205 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u)) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V2u)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2EUNION__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2206 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a))))))) # label(conj_thm_2Epred__set_2EDISJOINT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2207 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V0s) = V0s))))))) # label(conj_thm_2Epred__set_2ESUBSET__INTER2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2208 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ESUM__IMAGE(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27a,bool),ty_2Enum_2Enum))))) # label(mem_c_2Epred__set_2ESUM__IMAGE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2209 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V1t))))))) # label(conj_thm_2Epred__set_2EDIFF__DIFF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2210 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2t),V0x))) <-> -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__DELETE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2211 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (V1x != V2y & p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y)))))))))))) # label(conj_thm_2Epred__set_2EIN__DELETE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2212 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> p(ap(c_2Epred__set_2EUNIV(A_27a),V0x)))))) # label(conj_thm_2Epred__set_2EUNIV__applied) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2213 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)))))))) # label(conj_thm_2Epred__set_2EINSERT__INSERT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2214 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <-> (all V2x (mem(V2x,A_27a) -> (p(ap(V0s,V2x)) -> p(ap(V1t,V2x)))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__applied) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2215 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),c_2Epred__set_2EUNIV(A_27a))))))) # label(conj_thm_2Epred__set_2ESUBSET__UNIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2216 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),f252(A_27a,V1P))) <-> p(ap(V1P,V0x))))))))) # label(conj_thm_2Epred__set_2EIN__ABS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2217 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))))))) # label(conj_thm_2Epred__set_2ENOT__IN__EMPTY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2218 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),c_2Epred__set_2EUNIV(A_27a))))))) # label(conj_thm_2Epred__set_2EIN__UNIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2219 (all A_27b all A_27a all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> (all V1x f254(A_27a,A_27b,V0P,V1x) = ap(f255(A_27b,A_27a,V0P),V1x)))) # label(lameq_f255) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2220 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (all V2P (mem(V2P,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(V2P,V0x),V1y)) <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0x),V1y)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f258(A_27b,A_27a,V2P)))))))))))))))) # label(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__IFF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.86 2221 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EBIGUNION(A_27a),arr(arr(arr(A_27a,bool),bool),arr(A_27a,bool))))) # label(mem_c_2Epred__set_2EBIGUNION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2222 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EREL__RESTRICT(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),arr(A_27a,arr(A_27a,bool))))))) # label(mem_c_2Epred__set_2EREL__RESTRICT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2223 (all A_27a (ne(A_27a) -> (all V0g (mem(V0g,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V1f (mem(V1f,arr(ty_2Enum_2Enum,arr(A_27a,bool))) -> (all V2m (mem(V2m,ty_2Enum_2Enum) -> (all V3n (mem(V3n,ty_2Enum_2Enum) -> ((all V4n (mem(V4n,ty_2Enum_2Enum) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(V1f,V4n)),ap(V1f,ap(c_2Enum_2ESUC,V4n)))))) & (all V5n (mem(V5n,ty_2Enum_2Enum) -> ap(V0g,V5n) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(V1f,ap(c_2Enum_2ESUC,V5n))),ap(V1f,V5n)))) & V2m != V3n -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(V0g,V2m)),ap(V0g,V3n)))))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__DIFFS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2224 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EGSPEC(A_27a,A_27b),arr(arr(A_27b,ty_2Epair_2Eprod(A_27a,bool)),arr(A_27a,bool))))))) # label(mem_c_2Epred__set_2EGSPEC) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2225 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> V0P = ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f253(A_27a,V0P)))))) # label(conj_thm_2Epred__set_2EGSPEC__ETA) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2226 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (p(ap(V0P,V1x)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0P))))))))) # label(conj_thm_2Epred__set_2ESPECIFICATION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2227 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V1t),V2u)) & p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t)) -> p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2EPSUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2228 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) <-> p(ap(ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t),V2x))))))))))) # label(conj_thm_2Epred__set_2EDIFF__applied) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2229 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t) = c_2Epred__set_2EEMPTY(A_27a) <-> V1t = c_2Epred__set_2EEMPTY(A_27a) & V0s = c_2Epred__set_2EEMPTY(A_27a)))))))) # label(conj_thm_2Epred__set_2EEMPTY__UNION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2230 (all A_27a (ne(A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),c_2Epred__set_2EEMPTY(A_27a)) = V1s)) & (all V0s (mem(V0s,arr(A_27a,bool)) -> V0s = ap(ap(c_2Epred__set_2EUNION(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s))))) # label(conj_thm_2Epred__set_2EUNION__EMPTY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2231 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) != ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))))))) # label(conj_thm_2Epred__set_2ENOT__INSERT__EMPTY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2232 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t)) <-> -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1s),V2t))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__INSERT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2233 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) -> (all V1v (mem(V1v,A_27a) -> (p(ap(ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f),V1v)) <-> (exists V2x (mem(V2x,A_27b) & ap(V0f,V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V1v),c_2Ebool_2ET)))))))))))) # label(conj_thm_2Epred__set_2EGSPECIFICATION__applied) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2234 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V0s))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__SYM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2235 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EREST(A_27a),arr(arr(A_27a,bool),arr(A_27a,bool))))) # label(mem_c_2Epred__set_2EREST) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2236 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ESING(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Epred__set_2ESING) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2237 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),c_2Epred__set_2EUNIV(A_27a)))))) # label(conj_thm_2Epred__set_2EDIFF__UNIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2238 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Eenumerate(A_27a),arr(arr(A_27a,bool),arr(ty_2Enum_2Enum,A_27a))))) # label(mem_c_2Epred__set_2Eenumerate) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2239 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <-> V0s = ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)))))))) # label(conj_thm_2Epred__set_2ESUBSET__INTER__ABSORPTION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2240 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> -p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a))))))) # label(conj_thm_2Epred__set_2ENOT__PSUBSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2241 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (-p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) <-> V1s = ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)))))))) # label(conj_thm_2Epred__set_2EDELETE__NON__ELEMENT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2242 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (V0s = V1t <-> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)))))))))))) # label(conj_thm_2Epred__set_2EEXTENSION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2243 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> (all V1y (mem(V1y,arr(A_27a,bool)) -> (all V2z (mem(V2z,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V1y)),V2z) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1y),V2z)))))))))) # label(conj_thm_2Epred__set_2EDIFF__UNION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2244 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (V1t = ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2ESUBSET__UNION__ABSORPTION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2245 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)))))))))) # label(conj_thm_2Epred__set_2EINSERT__UNION__EQ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2246 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2ERINV(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,A_27a)))))))) # label(mem_c_2Epred__set_2ERINV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2247 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) & V0x != ap(c_2Epred__set_2ECHOICE(A_27a),V1s) <-> p(ap(ap(c_2Epred__set_2EREST(A_27a),V1s),V0x))))))))) # label(conj_thm_2Epred__set_2EREST__applied) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2248 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1a (mem(V1a,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(V0P,V1a)) | (exists V4x (mem(V4x,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V4x),V2s)) & p(ap(V0P,V4x)))) <-> (exists V3x (p(ap(V0P,V3x)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1a),V2s))) & mem(V3x,A_27a)))))))))))) # label(conj_thm_2Epred__set_2EEXISTS__IN__INSERT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2249 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x ap(f253(A_27a,V0P),V1x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V1x),ap(V0P,V1x))))) # label(lameq_f253) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2250 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ap(c_2Epair_2EUNCURRY(A_27a,A_27b,bool),V0P) = ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),ty_2Epair_2Eprod(A_27a,A_27b)),ap(c_2Epair_2EUNCURRY(A_27a,A_27b,ty_2Epair_2Eprod(ty_2Epair_2Eprod(A_27a,A_27b),bool)),f255(A_27b,A_27a,V0P))))))))) # label(conj_thm_2Epred__set_2EGSPEC__PAIR__ETA) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2251 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V1b (mem(V1b,A_27b) -> (all V2x (mem(V2x,A_27a) -> (all V3P (mem(V3P,arr(A_27b,bool)) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0a),V1b)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),A_27b),f261(A_27a,A_27b,V2x,V3P)))) <-> p(ap(V3P,V1b)) & V2x = V0a))))))))))))) # label(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2252 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),c_2Epred__set_2EEMPTY(A_27a))) <-> V0s = c_2Epred__set_2EEMPTY(A_27a)))))) # label(conj_thm_2Epred__set_2ESUBSET__EMPTY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2253 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EINTER(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2EINTER) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2254 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EBIGINTER(A_27a),arr(arr(arr(A_27a,bool),bool),arr(A_27a,bool))))) # label(mem_c_2Epred__set_2EBIGINTER) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2255 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> (all V1y (mem(V1y,bool) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0x),ap(c_2Ecombin_2EK(bool,A_27a),V1y))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0x),c_2Epred__set_2EEMPTY(A_27a))) | p(V1y)))))))) # label(conj_thm_2Epred__set_2ESUBSET__K) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2256 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EPREIMAGE(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),arr(A_27a,bool)))))))) # label(mem_c_2Epred__set_2EPREIMAGE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2257 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (V0x != ap(c_2Epred__set_2ECHOICE(A_27a),V1s) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Epred__set_2EREST(A_27a),V1s)))))))))) # label(conj_thm_2Epred__set_2EIN__REST) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2258 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> (all V1b (mem(V1b,A_27a) -> (all V2P (mem(V2P,arr(A_27a,bool)) -> (p(ap(V2P,V0a)) & V1b = V0a <-> p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27a)),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V0a),V1b)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27a),A_27a),f262(A_27a,V2P))))))))))))) # label(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__same) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2259 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s) = V1s <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s))))))))) # label(conj_thm_2Epred__set_2EABSORPTION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2260 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t)) <-> (exists V2x (mem(V2x,A_27a) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V0s)),V1t))))))))))) # label(conj_thm_2Epred__set_2EPSUBSET__INSERT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2261 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u)) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V2u))) & (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2u),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V2u)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__UNION__BOTH) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2262 (all A_27a (ne(A_27a) -> c_2Epred__set_2EUNIV(A_27a) != c_2Epred__set_2EEMPTY(A_27a))) # label(conj_thm_2Epred__set_2EEMPTY__NOT__UNIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2263 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2t),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V2t),V1s)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__INSERT_27) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2264 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),ap(ap(c_2Epred__set_2EUNION(A_27a),V1t),V2u)) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V2u)))))))))) # label(conj_thm_2Epred__set_2EUNION__OVER__INTER) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2265 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2g (mem(V2g,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V2g) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V2g)),V1t))))))))) # label(conj_thm_2Epred__set_2EDIFF__INTER) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2266 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V0s) = ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t))))))) # label(conj_thm_2Epred__set_2EINTER__COMM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2267 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V1t)) <-> V1t != V0s & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(ax_thm_2Epred__set_2EPSUBSET__DEF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2268 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V3P (mem(V3P,arr(A_27a,bool)) -> (all V4x ap(ap(c_2Epair_2E_2C(A_27b,bool),ap(V0f,V4x)),ap(V3P,V4x)) = ap(f259(A_27b,A_27a,V0f,V3P),V4x)))))) # label(lameq_f259) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2269 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Echooser(A_27a),arr(arr(A_27a,bool),arr(ty_2Enum_2Enum,A_27a))))) # label(mem_c_2Epred__set_2Echooser) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2270 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V2t))),ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),V2t)))))))))) # label(conj_thm_2Epred__set_2EINSERT__INTER) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2271 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)))))))))))) # label(conj_thm_2Epred__set_2EIN__INTER) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2272 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) <-> p(ap(ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t),V2x))))))))))) # label(conj_thm_2Epred__set_2EINTER__applied) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2273 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V0s)))))) # label(conj_thm_2Epred__set_2ESUBSET__REFL) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2274 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EFUNSET(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(arr(A_27a,A_27b),bool)))))))) # label(mem_c_2Epred__set_2EFUNSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2275 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s))))))))) # label(conj_thm_2Epred__set_2ECOMPONENT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2276 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V0s)),V1t) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t))))))))))) # label(conj_thm_2Epred__set_2EINSERT__DIFF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2277 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (c_2Epred__set_2EEMPTY(A_27a) = V0s <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V0s))))))) # label(conj_thm_2Epred__set_2EDISJOINT__EMPTY__REFL) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2278 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> -p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),V0s),V0s)))))) # label(conj_thm_2Epred__set_2EPSUBSET__IRREFL) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2279 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (c_2Epred__set_2EEMPTY(A_27a) != V0s -> V0s = ap(ap(c_2Epred__set_2EINSERT(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),ap(c_2Epred__set_2EREST(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2ECHOICE__INSERT__REST) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2280 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Eequiv__on(A_27a),arr(arr(A_27a,arr(A_27a,bool)),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2Eequiv__on) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2281 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2x_27 (mem(V2x_27,A_27a) -> ((p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x_27),V0s))) <-> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x_27),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V1x))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x_27))))))))))))) # label(conj_thm_2Epred__set_2EIN__DELETE__EQ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2282 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EFINITE(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Epred__set_2EFINITE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2283 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> -p(ap(ap(c_2Epred__set_2EPSUBSET(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s)))))) # label(conj_thm_2Epred__set_2ENOT__UNIV__PSUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2284 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Ecountable(A_27a),arr(arr(A_27a,bool),bool)))) # label(mem_c_2Epred__set_2Ecountable) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2285 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),V2x) = ap(ap(c_2Epred__set_2EINTER(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x)),V1t))))))))) # label(conj_thm_2Epred__set_2EDELETE__INTER) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2286 (all A_27a (ne(A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),c_2Epred__set_2EEMPTY(A_27a)))) & (all V0s (mem(V0s,arr(A_27a,bool)) -> c_2Epred__set_2EEMPTY(A_27a) = ap(ap(c_2Epred__set_2EINTER(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s))))) # label(conj_thm_2Epred__set_2EINTER__EMPTY) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2287 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EPOW(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2EPOW) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2288 (all A_27a all A_27b all V2x (mem(V2x,A_27a) -> (all V3P (mem(V3P,arr(A_27b,bool)) -> (all V4y ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V2x),V4y)),ap(V3P,V4y)) = ap(f261(A_27a,A_27b,V2x,V3P),V4y)))))) # label(lameq_f261) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2289 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) = c_2Epred__set_2EEMPTY(A_27a) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t))))))))) # label(ax_thm_2Epred__set_2EDISJOINT__DEF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2290 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ESUBSET(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2ESUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2291 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (V0s = V1t -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t))))))))) # label(conj_thm_2Epred__set_2EEQ__SUBSET__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2292 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EUNIV(A_27a),arr(A_27a,bool)))) # label(mem_c_2Epred__set_2EUNIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2293 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2u),V1t)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2294 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (-p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2t))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t)))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__INSERT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2295 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))))))) & (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3t (mem(V3t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V2s),ap(ap(c_2Epred__set_2EUNION(A_27a),V3t),V2s))))))))) # label(conj_thm_2Epred__set_2ESUBSET__UNION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2296 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> V0s = ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V0s))))) # label(conj_thm_2Epred__set_2EUNION__IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2297 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2t))) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)),V2t))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__INSERT__DELETE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2298 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2s)) = ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),V2s)))))))))) # label(conj_thm_2Epred__set_2EINSERT__COMM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2299 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V2u)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V2u))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__TRANS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2300 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2Eschroeder__close(A_27a),arr(arr(A_27a,A_27a),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2Eschroeder__close) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2301 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27a) -> (p(ap(ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2y),V1x)) <-> V1x != V2y & p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s))))))))))) # label(conj_thm_2Epred__set_2EDELETE__applied) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2302 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EIMAGE(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,bool)))))))) # label(mem_c_2Epred__set_2EIMAGE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2303 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V0s)) <-> c_2Epred__set_2EEMPTY(A_27a) = V0s))))) # label(conj_thm_2Epred__set_2EDISJOINT__EMPTY__REFL__RWT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2304 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> V1t = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1t),V0s)),V0s) & ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),ap(ap(c_2Epred__set_2EDIFF(A_27a),V1t),V0s)) = V1t))))))) # label(conj_thm_2Epred__set_2EUNION__DIFF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2305 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1s),V2t)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t))))))))))) # label(conj_thm_2Epred__set_2EINSERT__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2306 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),V1t),V0s) = ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))))))) # label(conj_thm_2Epred__set_2EUNION__COMM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2307 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2ECROSS(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),arr(ty_2Epair_2Eprod(A_27a,A_27b),bool)))))))) # label(mem_c_2Epred__set_2ECROSS) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2308 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EPSUBSET(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),bool))))) # label(mem_c_2Epred__set_2EPSUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2309 (all A_27b all A_27a all V2x (mem(V2x,A_27b) -> (all V3P (mem(V3P,arr(A_27a,bool)) -> (all V4y ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V4y),V2x)),ap(V3P,V4y)) = ap(f260(A_27b,A_27a,V2x,V3P),V4y)))))) # label(lameq_f260) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2310 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EBIJ(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool)))))))) # label(mem_c_2Epred__set_2EBIJ) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2311 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1M (mem(V1M,arr(A_27a,ty_2Enum_2Enum)) -> ((exists V3x (mem(V3x,A_27a) & p(ap(ap(c_2Ebool_2EIN(A_27a),V3x),V0s)) & (all V4y (mem(V4y,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V4y),V0s)) -> p(ap(ap(c_2Earithmetic_2E_3C_3D,ap(V1M,V3x)),ap(V1M,V4y)))))))) <-> (exists V2x (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Epred__set_2ESET__MINIMUM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2312 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ((all V1x (mem(V1x,A_27a) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s)))) <-> c_2Epred__set_2EUNIV(A_27a) = V0s))))) # label(conj_thm_2Epred__set_2EEQ__UNIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2313 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EPROD__IMAGE(A_27a),arr(arr(A_27a,ty_2Enum_2Enum),arr(arr(A_27a,bool),ty_2Enum_2Enum))))) # label(mem_c_2Epred__set_2EPROD__IMAGE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2314 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1x (mem(V1x,A_27a) -> ((exists V2t (mem(V2t,arr(A_27a,bool)) & V0s = ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V2t) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2t)))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0s))))))))) # label(conj_thm_2Epred__set_2EDECOMPOSITION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2315 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V1t)) <-> -(exists V2x (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) & mem(V2x,A_27a)))))))))) # label(conj_thm_2Epred__set_2EIN__DISJOINT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2316 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> -p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),ap(c_2Epred__set_2EREST(A_27a),V0s))))))) # label(conj_thm_2Epred__set_2ECHOICE__NOT__IN__REST) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2317 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EITSET(A_27a,A_27b),arr(arr(A_27a,arr(A_27b,A_27b)),arr(arr(A_27a,bool),arr(A_27b,A_27b)))))))) # label(mem_c_2Epred__set_2EITSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2318 (all A_27a all A_27b all V2P (mem(V2P,arr(A_27a,arr(A_27b,bool))) -> (all V3x (mem(V3x,A_27a) -> (all V4y ap(f257(A_27a,A_27b,V2P,V3x),V4y) = ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27b),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V3x),V4y)),ap(ap(V2P,V3x),V4y))))))) # label(lameq_f257) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2319 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V0s),V2u)) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),V2u)) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t)),V2u))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__UNION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2320 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ECHOICE(A_27a),arr(arr(A_27a,bool),A_27a)))) # label(mem_c_2Epred__set_2ECHOICE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2321 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s)) <-> c_2Epred__set_2EUNIV(A_27a) = V0s))))) # label(conj_thm_2Epred__set_2EUNIV__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2322 (all A_27a all V2P (mem(V2P,arr(A_27a,bool)) -> (all V3x ap(ap(c_2Epair_2E_2C(ty_2Epair_2Eprod(A_27a,A_27a),bool),ap(ap(c_2Epair_2E_2C(A_27a,A_27a),V3x),V3x)),ap(V2P,V3x)) = ap(f262(A_27a,V2P),V3x)))) # label(lameq_f262) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2323 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)) = V1t))))))) # label(conj_thm_2Epred__set_2EDIFF__DIFF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2324 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1y (mem(V1y,A_27a) -> (all V2x (mem(V2x,A_27b) -> (all V3P (mem(V3P,arr(A_27a,bool)) -> (p(ap(V3P,V1y)) & V2x = ap(V0f,V1y) -> p(ap(ap(c_2Ebool_2EIN(A_27b),V2x),ap(c_2Epred__set_2EGSPEC(A_27b,A_27a),f259(A_27b,A_27a,V0f,V3P))))))))))))))))) # label(conj_thm_2Epred__set_2EIN__GSPEC) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2325 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2ELINV(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,A_27a)))))))) # label(mem_c_2Epred__set_2ELINV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2326 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2u (mem(V2u,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V2u)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <-> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V2u)))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__INTER) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2327 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (all V2t (mem(V2t,arr(A_27a,bool)) -> ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2t)),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),V2t))) = ap(ap(c_2Epred__set_2EUNION(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V1s)),V2t))))))))) # label(conj_thm_2Epred__set_2EINSERT__UNION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2328 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1t),V2x)),V0s)) <-> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x)),V1t))))))))))) # label(conj_thm_2Epred__set_2EDISJOINT__DELETE__SYM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2329 (all A_27b all A_27a all V2P (mem(V2P,arr(A_27a,arr(A_27b,bool))) -> (all V3x ap(f258(A_27b,A_27a,V2P),V3x) = f257(A_27a,A_27b,V2P,V3x)))) # label(lameq_f258) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2330 (all A_27a (ne(A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> c_2Epred__set_2EUNIV(A_27a) = ap(ap(c_2Epred__set_2EUNION(A_27a),V1s),c_2Epred__set_2EUNIV(A_27a)))) & (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EUNION(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s) = c_2Epred__set_2EUNIV(A_27a))))) # label(conj_thm_2Epred__set_2EUNION__UNIV) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2331 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (c_2Epred__set_2EEMPTY(A_27a) != V0s -> p(ap(ap(c_2Ebool_2EIN(A_27a),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)),V0s))))))) # label(ax_thm_2Epred__set_2ECHOICE__DEF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2332 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V1t),V0s)) & p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> V1t = V0s))))))) # label(conj_thm_2Epred__set_2ESUBSET__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2333 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t) = V0s))))))) # label(conj_thm_2Epred__set_2ESUBSET__INTER1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2334 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> (p(ap(V1P,V0x)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1P))))))))) # label(conj_thm_2Epred__set_2EIN__APP) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2335 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0P),V1Q)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1Q)))))))))))) # label(conj_thm_2Epred__set_2ESUBSET__THM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2336 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V1b (mem(V1b,A_27b) -> (all V2x (mem(V2x,A_27b) -> (all V3P (mem(V3P,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(ty_2Epair_2Eprod(A_27a,A_27b)),ap(ap(c_2Epair_2E_2C(A_27a,A_27b),V0a),V1b)),ap(c_2Epred__set_2EGSPEC(ty_2Epair_2Eprod(A_27a,A_27b),A_27a),f260(A_27b,A_27a,V2x,V3P)))) <-> p(ap(V3P,V0a)) & V2x = V1b))))))))))))) # label(conj_thm_2Epred__set_2EPAIR__IN__GSPEC__1) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2337 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),V0s),V1t)) <-> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) -> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)))))))))))) # label(ax_thm_2Epred__set_2ESUBSET__DEF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2338 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27b,ty_2Epair_2Eprod(A_27a,bool))) -> (all V1v (mem(V1v,A_27a) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V1v),ap(c_2Epred__set_2EGSPEC(A_27a,A_27b),V0f))) <-> (exists V2x (ap(ap(c_2Epair_2E_2C(A_27a,bool),V1v),c_2Ebool_2ET) = ap(V0f,V2x) & mem(V2x,A_27b)))))))))))) # label(ax_thm_2Epred__set_2EGSPECIFICATION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2339 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EINSERT(A_27a),V2x),V1t)) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),V2x)),V1t))))))))) # label(conj_thm_2Epred__set_2EDIFF__INSERT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2340 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),V2s)),V1y) = ap(ap(ap(c_2Ebool_2ECOND(arr(A_27a,bool)),ap(ap(c_2Emin_2E_3D(A_27a),V0x),V1y)),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1y)),ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V2s),V1y))))))))))) # label(conj_thm_2Epred__set_2EDELETE__INSERT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2341 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (exists V1x (mem(V1x,A_27a) & (exists V2t (mem(V2t,arr(A_27a,bool)) & -p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V2t)) & ap(ap(c_2Epred__set_2EINSERT(A_27a),V1x),V2t) = V0s)))) | c_2Epred__set_2EEMPTY(A_27a) = V0s)))) # label(conj_thm_2Epred__set_2ESET__CASES) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2342 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2ECOMPL(A_27a),arr(arr(A_27a,bool),arr(A_27a,bool))))) # label(mem_c_2Epred__set_2ECOMPL) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2343 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EINSERT(A_27a),arr(A_27a,arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2EINSERT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2344 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (V1y = V0x | p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s)) <-> p(ap(ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),V2s),V0x))))))))))) # label(conj_thm_2Epred__set_2EINSERT__applied) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2345 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V1t)),V0s)))))) & (all V2s (mem(V2s,arr(A_27a,bool)) -> (all V3t (mem(V3t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EINTER(A_27a),V3t),V2s)),V2s)))))))) # label(conj_thm_2Epred__set_2EINTER__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2346 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2EDFUNSET(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27a,arr(A_27b,bool)),arr(arr(A_27a,A_27b),bool)))))))) # label(mem_c_2Epred__set_2EDFUNSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2347 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),V1t),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t))) & p(ap(ap(c_2Epred__set_2EDISJOINT(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V1t)))))))) # label(conj_thm_2Epred__set_2EDISJOINT__DIFF) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2348 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EUNION(A_27a),arr(arr(A_27a,bool),arr(arr(A_27a,bool),arr(A_27a,bool)))))) # label(mem_c_2Epred__set_2EUNION) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2349 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2s (mem(V2s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EINSERT(A_27a),V1y),V2s))) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V2s)) | V0x = V1y))))))))) # label(conj_thm_2Epred__set_2EIN__INSERT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2350 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),ap(ap(c_2Epred__set_2EINTER(A_27a),V1t),V0s)))))))) # label(conj_thm_2Epred__set_2EDIFF__INTER2) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2351 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)),V0s)))))))) # label(conj_thm_2Epred__set_2EDIFF__SUBSET) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2352 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> V0s = ap(ap(c_2Epred__set_2EINTER(A_27a),V0s),V0s))))) # label(conj_thm_2Epred__set_2EINTER__IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2353 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,arr(A_27a,bool)) -> (all V1y (mem(V1y,arr(A_27a,bool)) -> (all V2z (mem(V2z,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V1y)),V2z) = ap(ap(c_2Epred__set_2EDIFF(A_27a),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0x),V2z)),V1y))))))))) # label(conj_thm_2Epred__set_2EDIFF__COMM) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2354 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> -p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x))))))))) # label(conj_thm_2Epred__set_2EELT__IN__DELETE) # label(axiom) # label(non_clause). [assumption]. 3.74/3.87 2355 (all A_27a (ne(A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),V1s),c_2Epred__set_2EUNIV(A_27a)) = V1s)) & (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EINTER(A_27a),c_2Epred__set_2EUNIV(A_27a)),V0s) = V0s)))) # label(conj_thm_2Epred__set_2EINTER__UNIV) # label(axiom) # label(non_clause). [assumption]. 56.26/56.37 2356 (all A_27a all V1t (mem(V1t,arr(A_27a,bool)) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)),ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))) = ap(f264(A_27a,V1t,V0s),V2x)))))) # label(lameq_f264) # label(axiom) # label(non_clause). [assumption]. 56.26/56.37 2357 (all A_27a (ne(A_27a) -> mem(c_2Epred__set_2EEMPTY(A_27a),arr(A_27a,bool)))) # label(mem_c_2Epred__set_2EEMPTY) # label(axiom) # label(non_clause). [assumption]. 56.26/56.37 2358 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> (all V2x (mem(V2x,A_27a) -> (-p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t)))))))))))) # label(conj_thm_2Epred__set_2EIN__DIFF) # label(axiom) # label(non_clause). [assumption]. 56.26/56.37 2359 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f263(A_27a,V1t,V0s)) = ap(ap(c_2Epred__set_2EUNION(A_27a),V0s),V1t))))))) # label(ax_thm_2Epred__set_2EUNION__DEF) # label(axiom) # label(non_clause). [assumption]. 56.26/56.37 2360 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V1t (mem(V1t,arr(A_27a,bool)) -> ap(c_2Epred__set_2EGSPEC(A_27a,A_27a),f265(A_27a,V1t,V0s)) = ap(ap(c_2Epred__set_2EDIFF(A_27a),V0s),V1t))))))) # label(ax_thm_2Epred__set_2EDIFF__DEF) # label(axiom) # label(non_clause). [assumption]. 56.26/56.37 2361 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Epred__set_2ELINV__OPT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27a,bool),arr(A_27b,ty_2Eoption_2Eoption(A_27a))))))))) # label(mem_c_2Epred__set_2ELINV__OPT) # label(axiom) # label(non_clause). [assumption]. 56.26/56.37 2362 (all A_27a all V1t (mem(V1t,arr(A_27a,bool)) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> (all V2x ap(f265(A_27a,V1t,V0s),V2x) = ap(ap(c_2Epair_2E_2C(A_27a,bool),V2x),ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0s)),ap(c_2Ebool_2E_7E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1t))))))))) # label(lameq_f265) # label(axiom) # label(non_clause). [assumption]. 56.26/56.37 2363 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> ap(ap(c_2Epred__set_2EDELETE(A_27a),V0s),ap(c_2Epred__set_2ECHOICE(A_27a),V0s)) = ap(c_2Epred__set_2EREST(A_27a),V0s))))) # label(ax_thm_2Epred__set_2EREST__DEF) # label(axiom) # label(non_clause). [assumption]. 56.26/56.37 2364 (all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),c_2Epred__set_2EEMPTY(A_27a)),V0s)))))) # label(conj_thm_2Epred__set_2EEMPTY__SUBSET) # label(axiom) # label(non_clause). [assumption]. 56.26/56.37 2365 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1s (mem(V1s,arr(A_27a,bool)) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),V1s)) -> ap(ap(c_2Epred__set_2EINSERT(A_27a),V0x),ap(ap(c_2Epred__set_2EDELETE(A_27a),V1s),V0x)) = V1s))))))) # label(conj_thm_2Epred__set_2EINSERT__DELETE) # label(axiom) # label(non_clause). [assumption]. 56.26/56.37 2366 -(all A_27a (ne(A_27a) -> (all V0s (mem(V0s,arr(A_27a,bool)) -> p(ap(ap(c_2Epred__set_2ESUBSET(A_27a),ap(c_2Epred__set_2EREST(A_27a),V0s)),V0s)))))) # label(conj_thm_2Epred__set_2EREST__SUBSET) # label(negated_conjecture) # label(non_clause). [assumption]. 56.26/56.37 56.26/56.37 ============================== end of process non-clausal formulas === 56.26/56.37 56.26/56.37 ============================== PROCESS INITIAL CLAUSES =============== 56.26/56.37 56.26/56.37 ============================== PREDICATE ELIMINATION ================= 56.26/56.37 56.26/56.37 ============================== end predicate elimination ============= 56.26/56.37 56.26/56.37 Auto_denials: (non-Horn, no changes). 56.26/56.37 56.26/56.37 Term ordering decisions: 56.26/56.37 Function symbol KB weights: bool=1. ty_2Enum_2Enum=1. c_2Enum_2E0=1. c_2Eprim__rec_2E_3C=1. c_2Earithmetic_2ENUMERAL=1. c_2Earithmetic_2EZERO=1. c_2Earithmetic_2EBIT1=1. c_2Earithmetic_2E_3C_3D=1. c_2Enum_2ESUC=1. c_2Earithmetic_2E_2B=1. c_2Earithmetic_2EBIT2=1. c_2Earithmetic_2E_2A=1. c_2Earithmetic_2EEXP=1. c_2Earithmetic_2E_2D=1. c_2Earithmetic_2EMOD=1. c_2Ebit_2EBIT=1. c_2Earithmetic_2EDIV=1. c_2Ebit_2EBITS=1. c_2Edivides_2Edivides=1. c_2Egcd_2Egcd=1. c_2Ebool_2ET=1. c_2Eprim__rec_2EPRE=1. c_2Earithmetic_2EEVEN=1. c_2Earithmetic_2EODD=1. ty_2Eone_2Eone=1. c_2Earithmetic_2EMODEQ=1. c_2Ebool_2E_2F_5C=1. c_2Ebool_2EF=1. c_2Enumpair_2Etri=1. c_2Earithmetic_2EMIN=1. c_2Ebit_2ESLICE=1. c_2Earithmetic_2EMAX=1. c_2Earithmetic_2E_3E=1. c_2Enumeral_2EiSUB=1. ind=1. c_2Emin_2E_3D_3D_3E=1. c_2Ewhile_2ELEAST=1. c_2Elogroot_2ELOG=1. c_2Earithmetic_2EABS__DIFF=1. c_2Edivides_2Eprime=1. c_2Earithmetic_2E_3E_3D=1. c_2Egcd_2Eis__gcd=1. c_2Edivides_2EPRIMES=1. c_2Enumeral_2EiDUB=1. c_2Ewhile_2EOLEAST=1. c_2Enumpair_2Encons=1. c_2Elogroot_2ESQRTd=1. c_2Enumeral_2EiiSUC=1. c_2Enumeral_2Etexp__help=1. c_2Elogroot_2EROOT=1. c_2Ebit_2ESBIT=1. c_2Ebool_2E_7E=1. c_2Eind__type_2ENUMSUM=1. c_2Eone_2Eone=1. c_2Ebit_2EBITWISE=1. c_2Enumeral_2EiZ=1. c_2Ebool_2E_5C_2F=1. c_2Egcd_2Elcm=1. c_2Enumpair_2Enpair=1. c_2Earithmetic_2EDIVMOD=1. c_2Earithmetic_2EFACT=1. c_2Ebit_2ELOG2=1. c_2Ebit_2EMOD__2EXP=1. c_2Eind__type_2ENUMPAIR=1. c_2Enumeral_2Einternal__mult=1. c_2Enum_2EIS__NUM__REP=1. c_2Enumpair_2Einvtri=1. c_2Earithmetic_2EDIV2=1. c_2Earithmetic_2Efindq=1. c_2Enumeral_2Eexactlog=1. c_2Enumeral_2Eonecount=1. c_2Enumpair_2Einvtri0=1. c_2Enumpair_2Ensnd=1. c_2Emarker_2EAbbrev=1. c_2Eoption_2EOPTION__GUARD=1. c_2Ebit_2EBIT__MODIFY=1. c_2Ebit_2EBIT__REVERSE=1. c_2Enum_2EABS__num=1. c_2Enum_2EZERO__REP=1. c_2Enumpair_2Enfst=1. c_2Enum_2EREP__num=1. c_2Enum_2ESUC__REP=1. c_2Enumeral_2EiSQR=1. c_2Enumpair_2Enapp=1. c_2Enumpair_2Enlen=1. c_2Enumpair_2Enmap=1. c_2EConseqConv_2EASM__MARKER=1. c_2Ebit_2EDIV__2EXP=1. c_2Ebit_2ESIGN__EXTEND=1. c_2Eind__type_2ENUMLEFT=1. c_2Eind__type_2ENUMRIGHT=1. c_2Elogroot_2EiSQRT0=1. c_2Elogroot_2EiSQRT1=1. c_2Elogroot_2EiSQRT2=1. c_2Elogroot_2EiSQRT3=1. c_2Emarker_2EAC=1. f159=1. c_2Ebit_2EBITV=1. c_2Ebit_2EDIVMOD__2EXP=1. c_2Ebit_2EMOD__2EXP__EQ=1. c_2Ebit_2EMOD__2EXP__MAX=1. c_2Ebool_2EBOUNDED=1. c_2Eind__type_2ENUMFST=1. c_2Eind__type_2ENUMSND=1. c_2Emarker_2ECong=1. c_2Emarker_2E_3A_2D=1. f151=1. f153=1. f65=1. c_2Earithmetic_2Enat__elim____magic=1. c_2EbasicSize_2Ebool__size=1. c_2EbasicSize_2Eone__size=1. c_2Ebit_2ELOWEST__SET__BIT=1. c_2Ebit_2ETIMES__2EXP=1. c_2Emarker_2EIfCases=1. f173=1. f178=1. f184=1. f202=1. f230=1. f232=1. f236=1. f240=1. f241=1. f248=1. f251=1. f5=1. f8=1. f9=1. c_2Epred__set_2EMAX__SET=1. c_2Epred__set_2EMIN__SET=1. c_2Epred__set_2EPROD__SET=1. c_2Epred__set_2ESUM__SET=1. c_2Epred__set_2Ecount=1. c_2Epred__set_2Enum__to__pair=1. c_2Epred__set_2Epair__to__num=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. ap=1. arr=1. ty_2Epair_2Eprod=1. c_2Epair_2E_2C=1. c_2Epair_2ELEX=1. ty_2Esum_2Esum=1. c_2Epair_2EPROD__ALL=1. c_2Esum_2ESUM__ALL=1. c_2Esum_2EINL=1. c_2Esum_2EINR=1. c_2Ebool_2ELET=1. c_2Ecombin_2EUPDATE=1. c_2Erelation_2Einv=1. c_2Epair_2EFST=1. c_2Epair_2ESND=1. k=1. c_2Ebool_2ETYPE__DEFINITION=1. c_2Eoption_2Eoption__CASE=1. c_2Erelation_2ERSUBSET=1. c_2Eoption_2EOPTION__MAP=1. c_2Epred__set_2EGSPEC=1. c_2Eoption_2EOPTREL=1. c_2Erelation_2ERDOM=1. c_2Eind__type_2EISO=1. c_2Eoption_2EOPTION__BIND=1. c_2Ebool_2Eliteral__case=1. c_2Ecombin_2EK=1. c_2Ebool_2EONE__ONE=1. c_2Eposet_2Efunction=1. c_2Erelation_2ERINTER=1. c_2Erelation_2ERUNION=1. f49=1. c_2Eoption_2EOPTION__APPLY=1. c_2Erelation_2EINDUCTIVE__INVARIANT__ON=1. c_2Eoption_2EOPTION__IGNORE__BIND=1. c_2Erelation_2ERESTRICT=1. c_2Erelation_2EWFREC=1. c_2Ewhile_2EHOARE__SPEC=1. c_2Erelation_2EINDUCTIVE__INVARIANT=1. c_2Erelation_2Einv__image=1. c_2Esum_2EIS__SUM__REP=1. c_2Ebool_2ERES__ABSTRACT=1. c_2EnormalForms_2EEXT__POINT=1. c_2Erelation_2ERRANGE=1. c_2Erelation_2ERRESTRICT=1. c_2Erelation_2ERUNIV=1. c_2Esum_2EISL=1. c_2Ebool_2EONTO=1. c_2Ecombin_2ELEFT__ID=1. c_2Ecombin_2ERIGHT__ID=1. c_2Esum_2EABS__sum=1. c_2Esum_2EISR=1. c_2Ecombin_2ECOMM=1. c_2Epair_2EABS__prod=1. c_2Erelation_2ERDOM__DELETE=1. c_2Epair_2EREP__prod=1. c_2Erelation_2Eapprox=1. c_2Esum_2EOUTL=1. c_2Esum_2EOUTR=1. c_2Esum_2EREP__sum=1. f262=1. c_2EbasicSize_2Esum__size=1. c_2Ecombin_2EFAIL=1. c_2Ecombin_2EW=1. c_2Epair_2ERPROD=1. c_2Eposet_2Epointwise__lift=1. c_2Erelation_2ERCOMPL=1. c_2Erelation_2Enf=1. c_2Erelation_2Ethe__fun=1. f120=1. f14=1. f155=1. f157=1. f252=1. f256=1. f61=1. f68=1. c_2EbasicSize_2Epair__size=1. c_2Ebool_2Eitself__case=1. c_2Ecombin_2E_3A_3E=1. c_2Epair_2ESWAP=1. f108=1. f109=1. f11=1. f110=1. f115=1. f163=1. f17=1. f176=1. f179=1. f182=1. f203=1. f204=1. f206=1. f208=1. f209=1. f21=1. f210=1. f217=1. f218=1. f220=1. f228=1. f233=1. f237=1. f24=1. f242=1. f246=1. f253=1. f3=1. f30=1. f32=1. f35=1. f38=1. f40=1. f43=1. f45=1. f50=1. f51=1. f57=1. f59=1. f6=1. f60=1. f76=1. f87=1. c_2Epred__set_2EBIJ=1. c_2Epred__set_2ECROSS=1. c_2Epred__set_2EDFUNSET=1. c_2Epred__set_2EFUNSET=1. c_2Epred__set_2EIMAGE=1. c_2Epred__set_2EINJ=1. c_2Epred__set_2EITSET=1. c_2Epred__set_2ELINV=1. c_2Epred__set_2ELINV__OPT=1. c_2Epred__set_2EPREIMAGE=1. c_2Epred__set_2ERINV=1. c_2Epred__set_2ESURJ=1. f2=1. f8=1. f23=1. f25=1. f42=1. f52=1. f53=1. f54=1. f55=1. f56=1. f69=1. f70=1. f80=1. f86=1. f88=1. f102=1. f103=1. f111=1. f116=1. f125=1. f126=1. f127=1. f134=1. f156=1. f170=1. f171=1. f172=1. f173=1. f180=1. f181=1. f183=1. f189=1. f194=1. f211=1. f271=1. f273=1. f289=1. f301=1. f302=1. f303=1. f308=1. f309=1. f310=1. f311=1. f312=1. f313=1. f314=1. f317=1. f318=1. f320=1. f321=1. f322=1. f336=1. f337=1. f341=1. f342=1. f343=1. f347=1. f349=1. f358=1. f365=1. f367=1. f368=1. f369=1. f376=1. f424=1. f425=1. f426=1. f427=1. f433=1. f440=1. f441=1. f444=1. f451=1. f452=1. f454=1. f455=1. f456=1. f464=1. f506=1. f520=1. f526=1. f540=1. f547=1. f560=1. f568=1. f572=1. f576=1. f577=1. f582=1. f583=1. f584=1. f590=1. f591=1. f593=1. f595=1. f596=1. f605=1. f611=1. f614=1. f615=1. f618=1. f619=1. f620=1. f625=1. f633=1. f634=1. f642=1. f644=1. f648=1. f656=1. f663=1. f664=1. f665=1. f666=1. f667=1. f668=1. f675=1. f676=1. f677=1. f687=1. f688=1. f689=1. f690=1. f691=1. f692=1. f693=1. f694=1. f710=1. f711=1. f712=1. f719=1. f720=1. f722=1. f723=1. f726=1. f727=1. f731=1. f749=1. f754=1. f755=1. c_2Erelation_2EEQC=1. ty_2Eoption_2Eoption=1. c_2Erelation_2ETC=1. c_2Ebool_2EIN=1. c_2Eposet_2Eposet=1. c_2Ebool_2ECOND=1. c_2Erelation_2ERTC=1. c_2Eoption_2ESOME=1. c_2Eoption_2ENONE=1. c_2Emin_2E_3D=1. c_2Epred__set_2ESUBSET=1. c_2Erelation_2EWF=1. c_2Erelation_2ERC=1. c_2Epred__set_2EUNION=1. c_2Epred__set_2EINSERT=1. c_2Epred__set_2EDISJOINT=1. c_2Erelation_2Etransitive=1. c_2Epred__set_2EDELETE=1. c_2Epred__set_2EEMPTY=1. c_2Ebool_2E_21=1. c_2Epred__set_2EDIFF=1. c_2Epred__set_2EINTER=1. c_2Earithmetic_2ENRC=1. c_2Erelation_2ESC=1. ty_2Eind__type_2Erecspace=1. c_2Erelation_2Ereflexive=1. c_2Ebool_2E_3F=1. c_2Eposet_2Eglb=1. c_2Eposet_2Elub=1. c_2Eind__type_2EZRECSPACE=1. c_2Erelation_2Esymmetric=1. c_2Erelation_2EWFP=1. c_2Ebool_2ERES__FORALL=1. c_2Ebool_2E_3F_21=1. c_2Epred__set_2EUNIV=1. c_2Ewhile_2EOWHILE=1. c_2Eoption_2EOPTION__ALL=1. c_2Erelation_2Eantisymmetric=1. c_2Ebool_2ERES__EXISTS=1. c_2Eposet_2Ecomplete=1. c_2Earithmetic_2Enum__CASE=1. c_2Eind__type_2EZBOT=1. c_2Emin_2E_40=1. c_2Eoption_2EIS__SOME=1. c_2Earithmetic_2EFUNPOW=1. c_2Erelation_2Etrichotomous=1. c_2Erelation_2EWeakOrder=1. c_2Erelation_2Ediamond=1. ty_2Ebool_2Eitself=1. c_2Eposet_2Ecarrier=1. c_2Ecombin_2EASSOC=1. c_2Eoption_2Esome=1. c_2Eposet_2Emonotonic=1. c_2Epred__set_2EPSUBSET=1. c_2Eposet_2Echain=1. c_2Erelation_2Eequivalence=1. c_2Erelation_2Eirreflexive=1. c_2Erelation_2Ercdiamond=1. c_2Eind__type_2ECONSTR=1. c_2Eposet_2Egfp=1. c_2Eposet_2Elfp=1. c_2Erelation_2EINVOL=1. c_2Erelation_2EOrder=1. c_2Ebool_2Ethe__value=1. c_2Eind__type_2EINJP=1. c_2Eind__type_2EZCONSTR=1. c_2Eprim__rec_2ESIMP__REC__REL=1. c_2Erelation_2EIDEM=1. c_2Erelation_2ESTRORD=1. c_2Erelation_2EWCR=1. c_2Erelation_2Etotal=1. c_2Ecombin_2EI=1. c_2Enumpair_2Enlistrec=1. c_2Erelation_2EStrongOrder=1. c_2Erelation_2EWeakLinearOrder=1. i=1. c_2Eind__type_2Edest__rec=1. c_2Eoption_2EIS__NONE=1. c_2Eposet_2Edown__continuous=1. c_2Eposet_2Eup__continuous=1. c_2Ebool_2EDATATYPE=1. c_2Eind__type_2EINJN=1. c_2Eind__type_2Emk__rec=1. c_2Enumeral_2EiBIT__cases=1. c_2Eoption_2ETHE=1. c_2Eprim__rec_2Emeasure=1. c_2Ewhile_2EWHILE=1. c_2Ecombin_2EMONOID=1. c_2Eind__type_2EBOTTOM=1. c_2Eind__type_2EINJA=1. c_2Eind__type_2EINJF=1. c_2Eoption_2EOPTION__CHOICE=1. c_2Eoption_2EOPTION__JOIN=1. c_2Eposet_2Ebottom=1. c_2Eposet_2Etop=1. c_2Epred__set_2EREST=1. c_2Erelation_2EEMPTY__REL=1. c_2Eoption_2Eoption__ABS=1. c_2Epred__set_2ECHOICE=1. c_2Eprim__rec_2EPRIM__REC__FUN=1. c_2Eprim__rec_2ESIMP__REC=1. c_2Eprim__rec_2Ewellfounded=1. c_2Erelation_2ECR=1. c_2Erelation_2Ediag=1. c_2Ebool_2ERES__EXISTS__UNIQUE=1. c_2EnormalForms_2EUNIV__POINT=1. c_2Enumpair_2Enfoldl=1. c_2Eprim__rec_2EPRIM__REC=1. c_2Ebool_2EARB=1. c_2Eind__type_2EFCONS=1. c_2Eoption_2Eoption__REP=1. c_2Eposet_2Econtinuous=1. c_2Erelation_2ELinearOrder=1. c_2Erelation_2EPreOrder=1. c_2Erelation_2ESN=1. c_2Erelation_2EStrongLinearOrder=1. c_2EbasicSize_2Eoption__size=1. c_2Ebool_2ERES__SELECT=1. c_2Eone_2Eone__CASE=1. f188=1. f189=1. c_2Eind__type_2EFNIL=1. c_2Emarker_2Estmarker=1. c_2Emarker_2Eunint=1. c_2Eposet_2Erelation=1. f1=1. f12=1. f149=1. f150=1. f152=1. f158=1. f172=1. f177=1. f18=1. f183=1. f190=1. f191=1. f194=1. f195=1. f196=1. f197=1. f198=1. f199=1. f2=1. f200=1. f201=1. f207=1. f219=1. f229=1. f231=1. f234=1. f235=1. f238=1. f239=1. f243=1. f247=1. f249=1. f33=1. f36=1. f39=1. f4=1. f44=1. f46=1. f7=1. c_2Epred__set_2EBIGINTER=1. c_2Epred__set_2EBIGUNION=1. c_2Epred__set_2ECARD=1. c_2Epred__set_2ECOMPL=1. c_2Epred__set_2EFINITE=1. c_2Epred__set_2EPOW=1. c_2Epred__set_2EPROD__IMAGE=1. c_2Epred__set_2EREL__RESTRICT=1. c_2Epred__set_2ESING=1. c_2Epred__set_2ESUM__IMAGE=1. c_2Epred__set_2Echooser=1. c_2Epred__set_2Ecountable=1. c_2Epred__set_2Eenumerate=1. c_2Epred__set_2Eequiv__on=1. c_2Epred__set_2Eis__measure__maximal=1. c_2Epred__set_2Epairwise=1. c_2Epred__set_2Epartition=1. c_2Epred__set_2Eschroeder__close=1. f16=1. f98=1. f192=1. f193=1. f202=1. f453=1. f567=1. f569=1. f570=1. f571=1. f573=1. f578=1. f579=1. f581=1. f586=1. f587=1. f588=1. f589=1. f594=1. f597=1. f598=1. f599=1. f602=1. f603=1. f604=1. f607=1. f608=1. f609=1. f624=1. f635=1. f636=1. f637=1. f651=1. f652=1. f654=1. f655=1. f657=1. f658=1. f659=1. f660=1. f661=1. f673=1. f695=1. f696=1. f697=1. f698=1. f699=1. f700=1. f701=1. f702=1. f703=1. f704=1. f706=1. f707=1. f708=1. f709=1. f713=1. f714=1. f715=1. f716=1. f717=1. f732=1. f733=1. c_2Epair_2EUNCURRY=1. c_2Ecombin_2Eo=1. c_2Eoption_2EOPTION__MAP2=1. c_2Esum_2Esum__CASE=1. c_2Epair_2Epair__CASE=1. c_2Erelation_2EO=1. c_2Ecombin_2EC=1. c_2Ecombin_2ES=1. f128=1. c_2Ecombin_2EFCOMM=1. c_2Eoption_2EOPTION__MCOMP=1. c_2Epair_2ECURRY=1. f129=1. f166=1. f186=1. f187=1. f53=1. f185=1. f258=1. f37=1. f63=1. f82=1. f89=1. f91=1. f10=1. f107=1. f114=1. f119=1. f13=1. f154=1. f156=1. f16=1. f162=1. f164=1. f165=1. f174=1. f175=1. f181=1. f20=1. f205=1. f212=1. f213=1. f216=1. f23=1. f245=1. f250=1. f255=1. f26=1. f263=1. f264=1. f265=1. f266=1. f29=1. f31=1. f34=1. f41=1. f42=1. f47=1. f48=1. f58=1. f62=1. f64=1. f71=1. f74=1. f75=1. f80=1. f90=1. f93=1. f94=1. f95=1. f3=1. f4=1. f5=1. f6=1. f9=1. f11=1. f12=1. f14=1. f15=1. f17=1. f18=1. f19=1. f21=1. f22=1. f35=1. f36=1. f38=1. f39=1. f40=1. f43=1. f44=1. f45=1. f46=1. f49=1. f50=1. f57=1. f59=1. f60=1. f61=1. f65=1. f66=1. f68=1. f72=1. f73=1. f76=1. f77=1. f78=1. f79=1. f81=1. f83=1. f84=1. f85=1. f92=1. f96=1. f99=1. f101=1. f104=1. f105=1. f106=1. f108=1. f112=1. f113=1. f115=1. f117=1. f118=1. f120=1. f121=1. f122=1. f123=1. f124=1. f130=1. f131=1. f135=1. f136=1. f137=1. f138=1. f139=1. f140=1. f141=1. f142=1. f143=1. f144=1. f145=1. f147=1. f148=1. f149=1. f150=1. f151=1. f152=1. f153=1. f155=1. f157=1. f158=1. f159=1. f160=1. f161=1. f163=1. f167=1. f168=1. f169=1. f184=1. f188=1. f203=1. f204=1. f206=1. f207=1. f208=1. f209=1. f210=1. f217=1. f218=1. f219=1. f220=1. f221=1. f230=1. f231=1. f232=1. f233=1. f234=1. f236=1. f237=1. f238=1. f239=1. f251=1. f253=1. f254=1. f267=1. f268=1. f269=1. f270=1. f272=1. f274=1. f275=1. f276=1. f277=1. f278=1. f279=1. f280=1. f281=1. f282=1. f285=1. f286=1. f296=1. f304=1. f305=1. f306=1. f307=1. f315=1. f316=1. f323=1. f324=1. f325=1. f326=1. f327=1. f334=1. f345=1. f346=1. f348=1. f359=1. f360=1. f361=1. f362=1. f363=1. f364=1. f382=1. f383=1. f384=1. f385=1. f386=1. f387=1. f388=1. f389=1. f390=1. f391=1. f392=1. f393=1. f394=1. f395=1. f396=1. f397=1. f398=1. f399=1. f400=1. f401=1. f402=1. f403=1. f404=1. f405=1. f409=1. f410=1. f411=1. f412=1. f413=1. f414=1. f415=1. f416=1. f417=1. f418=1. f419=1. f420=1. f421=1. f422=1. f423=1. f439=1. f449=1. f467=1. f468=1. f471=1. f472=1. f473=1. f474=1. f475=1. f476=1. f477=1. f478=1. f480=1. f492=1. f493=1. f494=1. f507=1. f508=1. f509=1. f510=1. f511=1. f512=1. f513=1. f514=1. f515=1. f516=1. f517=1. f519=1. f525=1. f527=1. f528=1. f529=1. f530=1. f531=1. f532=1. f533=1. f534=1. f542=1. f543=1. f544=1. f551=1. f554=1. f561=1. f562=1. f564=1. f565=1. f566=1. f601=1. f610=1. f612=1. f613=1. f616=1. f617=1. f621=1. f622=1. f623=1. f626=1. f627=1. f629=1. f630=1. f631=1. f643=1. f662=1. f705=1. f718=1. f724=1. f734=1. f735=1. f738=1. f742=1. f745=1. f747=1. f748=1. f750=1. f751=1. f752=1. c_2Esum_2E_2B_2B=1. c_2Epair_2E_23_23=1. f171=1. f260=1. f261=1. f138=1. f140=1. f54=1. f55=1. f84=1. f103=1. f104=1. f106=1. f112=1. f113=1. f117=1. f118=1. f122=1. f123=1. f124=1. f126=1. f127=1. f131=1. f139=1. f144=1. f148=1. f15=1. f161=1. f169=1. f180=1. f19=1. f192=1. f193=1. f211=1. f215=1. f22=1. f221=1. f227=1. f244=1. f25=1. f254=1. f257=1. f259=1. f27=1. f28=1. f70=1. f73=1. f79=1. f88=1. f92=1. f98=1. f1=1. f7=1. f29=1. f30=1. f31=1. f32=1. f41=1. f100=1. f132=1. f133=1. f174=1. f178=1. f224=1. f225=1. f229=1. f235=1. f240=1. f241=1. f242=1. f250=1. f252=1. f255=1. f256=1. f258=1. f262=1. f263=1. f290=1. f297=1. f298=1. f299=1. f328=1. f331=1. f335=1. f338=1. f339=1. f340=1. f350=1. f355=1. f370=1. f371=1. f372=1. f373=1. f374=1. f375=1. f377=1. f378=1. f379=1. f380=1. f381=1. f406=1. f428=1. f429=1. f438=1. f459=1. f479=1. f487=1. f495=1. f518=1. f522=1. f523=1. f524=1. f535=1. f536=1. f541=1. f545=1. f552=1. f553=1. f556=1. f557=1. f558=1. f559=1. f575=1. f628=1. f632=1. f638=1. f640=1. f645=1. f646=1. f647=1. f653=1. f674=1. f679=1. f680=1. f681=1. f682=1. f683=1. f684=1. f685=1. f686=1. f721=1. f725=1. f728=1. f729=1. f730=1. f736=1. f737=1. f741=1. f743=1. f744=1. f746=1. f753=1. f100=1. f56=1. f85=1. f101=1. f102=1. f105=1. f111=1. f116=1. f121=1. f125=1. f130=1. f135=1. f143=1. f147=1. f160=1. f168=1. f170=1. f214=1. f226=1. f52=1. f66=1. f67=1. f69=1. f72=1. f77=1. f78=1. f81=1. f83=1. f86=1. f96=1. f97=1. f99=1. f24=1. f26=1. f33=1. f146=1. f175=1. f176=1. f177=1. f212=1. f227=1. f228=1. f244=1. f245=1. f246=1. f247=1. f248=1. f249=1. f283=1. f284=1. f287=1. f288=1. f291=1. f292=1. f293=1. f294=1. f295=1. f319=1. f329=1. f330=1. f332=1. f333=1. f344=1. f351=1. f352=1. f353=1. f354=1. f356=1. f357=1. f366=1. f407=1. f408=1. f434=1. f435=1. f443=1. f457=1. f458=1. f460=1. f461=1. f521=1. f538=1. f539=1. f546=1. f548=1. f549=1. f555=1. f563=1. f585=1. f592=1. f606=1. f639=1. f641=1. f649=1. f650=1. f669=1. f670=1. f671=1. f672=1. f678=1. f739=1. f740=1. f133=1. f134=1. f137=1. f142=1. f146=1. f167=1. f223=1. f225=1. f67=1. f97=1. f431=1. f432=1. f445=1. f446=1. f447=1. f448=1. f450=1. f481=1. f482=1. f537=1. f550=1. f580=1. f600=1. f132=1. f136=1. f141=1. f145=1. f222=1. f224=1. f215=1. f216=1. f243=1. f300=1. f462=1. f463=1. f465=1. f466=1. f469=1. f470=1. f504=1. f505=1. f574=1. f213=1. f214=1. f430=1. f442=1. f483=1. f484=1. f485=1. f486=1. f488=1. f489=1. f490=1. f491=1. f222=1. f223=1. f436=1. f437=1. f496=1. f497=1. f498=1. f499=1. f500=1. f501=1. f502=1. f503=1. 56.26/56.37 56.26/56.37 ============================== STATISTICS ============================ 56.26/56.37 56.26/56.37 Given=0. Generated=11676. Kept=9690. proofs=0. 56.26/56.37 Usable=0. Sos=2220. Demods=70. Limbo=7454, Disabled=6016. Hints=0. 56.26/56.37 Kept_by_rule=0, Deleted_by_rule=0. 56.26/56.37 Forward_subsumed=1986. Back_subsumed=4. 56.26/56.37 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 56.26/56.37 New_demodulators=72 (0 lex), Back_demodulated=11. Back_unit_deleted=0. 56.26/56.37 Demod_attempts=424766. Demod_rewrites=1213. 56.26/56.37 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 56.26/56.37 Nonunit_fsub_feature_tests=17132. Nonunit_bsub_feature_tests=5829. 56.26/56.37 Megabytes=419.43. 56.26/56.37 User_CPU=52.99, System_CPU=0.14, Wall_clock=53. 56.26/56.37 56.26/56.37 Megs malloced by palloc(): 400. 56.26/56.37 type (bytes each) gets frees in use bytes 56.26/56.37 chunk ( 104) 135392 135392 0 0.0 K 56.26/56.37 string_buf ( 8) 118686 118686 0 0.0 K 56.26/56.37 token ( 20) 332875 332875 0 0.0 K 56.26/56.37 pterm ( 16) 193493 193493 0 0.0 K 56.26/56.37 hashtab ( 8) 2366 2366 0 0.0 K 56.26/56.37 hashnode ( 8) 21940 21940 0 0.0 K 56.26/56.37 term ( 20) 2105758 1607235 498523 9736.8 K 56.26/56.37 term arg arrays: 2761.5 K 56.26/56.37 attribute ( 12) 29400 492 28908 338.8 K 56.26/56.37 ilist ( 8) 119274579 119255071 19508 152.4 K 56.26/56.37 plist ( 8) 99487 49193 50294 392.9 K 56.26/56.37 i2list ( 12) 1184586 1184586 0 0.0 K 56.26/56.37 just ( 12) 27451 7357 20094 235.5 K 56.26/56.37 parajust ( 16) 0 0 0 0.0 K 56.26/56.37 instancejust ( 8) 0 0 0 0.0 K 56.26/56.37 ivyjust ( 24) 0 0 0 0.0 K 56.26/56.37 formula ( 28) 234570 175418 59152 1617.4 K 56.26/56.37 formula arg arrays: 212.6 K 56.26/56.37 topform ( 52) 20043 1986 18057 917.0 K 56.26/56.37 clist_pos ( 20) 24013 8253 15760 307.8 K 56.26/56.37 clist ( 16) 8 0 8 0.1 K 56.26/56.37 context ( 808) 255534 255533 1 0.8 K 56.26/56.37 trail ( 12) 564211849 564211849 0 0.0 K 56.26/56.37 ac_match_pos (70044) 0 0 0 0.0 K 56.26/56.37 ac_match_free_vars_pos (20020) 56.26/56.37 0 0 0 0.0 K 56.26/56.37 btm_state ( 60) 0 0 0 0.0 K 56.26/56.37 btu_state ( 60) 0 0 0 0.0 K 56.26/56.37 ac_position (285432) 0 0 0 0.0 K 56.26/56.37 fpa_trie ( 20) 42238 98 42140 823.0 K 56.26/56.37 fpa_state ( 28) 324 324 0 0.0 K 56.26/56.37 fpa_index ( 12) 10 0 10 0.1 K 56.26/56.37 fpa_chunk ( 20) 49568 18138 31430 613.9 K 56.26/56.37 fpa_list ( 16) 18610 0 18610 290.8 K 56.26/56.37 fpa_list chunks: 1532.6 K 56.26/56.37 discrim ( 12) 1660 14 1646 19.3 K 56.26/56.37 discrim_pos ( 16) 1421 1421 0 0.0 K 56.26/56.37 flat2 ( 32) 592134 592134 0 0.0 K 56.26/56.37 flat ( 48) 0 0 0 0.0 K 56.26/56.37 flatterm ( 32) 847357 847357 0 0.0 K 56.26/56.37 mindex ( 28) 13 0 13 0.4 K 56.26/56.37 mindex_pos ( 56) 207759 207759 0 0.0 K 56.26/56.37 lindex ( 12) 5 0 5 0.1 K 56.26/56.37 clash ( 40) 0 0 0 0.0 K 56.26/56.37 di_tree ( 12) 33193759 66823 33126936 388206.3 K 56.26/56.37 avl_node ( 20) 2235 15 2220 43.4 K 56.26/56.37 56.26/56.37 Memory report, 20 @ 20 = 400 megs (400.00 megs used). 56.26/56.37 List 1, length 9, 0.0 K 56.26/56.37 List 4, length 10, 0.2 K 56.26/56.37 List 7, length 3, 0.1 K 56.26/56.37 List 8, length 15, 0.5 K 56.26/56.37 List 10, length 2, 0.1 K 56.26/56.37 List 11, length 147, 6.3 K 56.26/56.37 List 14, length 4, 0.2 K 56.26/56.37 List 16, length 44, 2.8 K 56.26/56.37 List 17, length 52, 3.5 K 56.26/56.37 List 18, length 7, 0.5 K 56.26/56.37 List 19, length 1, 0.1 K 56.26/56.37 List 20, length 2, 0.2 K 56.26/56.37 List 21, length 2, 0.2 K 56.26/56.37 List 22, length 2, 0.2 K 56.26/56.37 List 23, length 2, 0.2 K 56.26/56.37 List 24, length 2, 0.2 K 56.26/56.37 List 25, length 2, 0.2 K 56.26/56.37 List 26, length 520, 52.8 K 56.26/56.37 List 28, length 2, 0.2 K 56.26/56.37 List 40, length 2, 0.3 K 56.26/56.37 List 48, length 2, 0.4 K 56.26/56.37 List 50, length 2, 0.4 K 56.26/56.37 List 63, length 2, 0.5 K 56.26/56.37 List 64, length 89, 22.2 K 56.26/56.37 List 80, length 2, 0.6 K 56.26/56.37 List 96, length 2, 0.8 K 56.26/56.38 List 144, length 2, 1.1 K 56.26/56.38 List 189, length 2, 1.5 K 56.26/56.38 List 192, length 2, 1.5 K 56.26/56.38 List 194, length 2, 1.5 K 56.26/56.38 List 202, length 1, 0.8 K 56.26/56.38 List 320, length 2, 2.5 K 56.26/56.38 56.26/56.38 ============================== SELECTOR REPORT ======================= 56.26/56.38 Sos_deleted=0, Sos_displaced=0, Sos_size=2220 56.26/56.38 SELECTOR PART PRIORITY ORDER SIZE SELECTED 56.26/56.38 I 2147483647 high age 2220 0 56.26/56.38 H 1 high weight 0 0 56.26/56.38 A 1 low age 0 0 56.26/56.38 F 4 low weight 0 0 56.26/56.38 T 4 low weight 0 0 56.26/56.38 ============================== end of selector report ================ 56.26/56.38 56.26/56.38 ============================== end of statistics ===================== 56.26/56.38 56.26/56.38 Exiting with failure. 56.26/56.38 56.26/56.38 Process 21189 exit (max_megs) Tue Aug 9 06:38:07 2022 56.26/56.38 Prover9 interrupted 56.26/56.38 EOF