0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.33 % Computer : n020.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 1200 0.13/0.33 % DateTime : Tue Jul 13 15:18:51 EDT 2021 0.13/0.33 % CPUTime : 1.98/2.32 ============================== Prover9 =============================== 1.98/2.32 Prover9 (32) version 2009-11A, November 2009. 1.98/2.32 Process 18182 was started by sandbox2 on n020.cluster.edu, 1.98/2.32 Tue Jul 13 15:18:53 2021 1.98/2.32 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_18011_n020.cluster.edu". 1.98/2.32 ============================== end of head =========================== 1.98/2.32 1.98/2.32 ============================== INPUT ================================= 1.98/2.32 1.98/2.32 % Reading from file /tmp/Prover9_18011_n020.cluster.edu 1.98/2.32 1.98/2.32 set(prolog_style_variables). 1.98/2.32 set(auto2). 1.98/2.32 % set(auto2) -> set(auto). 1.98/2.32 % set(auto) -> set(auto_inference). 1.98/2.32 % set(auto) -> set(auto_setup). 1.98/2.32 % set(auto_setup) -> set(predicate_elim). 1.98/2.32 % set(auto_setup) -> assign(eq_defs, unfold). 1.98/2.32 % set(auto) -> set(auto_limits). 1.98/2.32 % set(auto_limits) -> assign(max_weight, "100.000"). 1.98/2.32 % set(auto_limits) -> assign(sos_limit, 20000). 1.98/2.32 % set(auto) -> set(auto_denials). 1.98/2.32 % set(auto) -> set(auto_process). 1.98/2.32 % set(auto2) -> assign(new_constants, 1). 1.98/2.32 % set(auto2) -> assign(fold_denial_max, 3). 1.98/2.32 % set(auto2) -> assign(max_weight, "200.000"). 1.98/2.32 % set(auto2) -> assign(max_hours, 1). 1.98/2.32 % assign(max_hours, 1) -> assign(max_seconds, 3600). 1.98/2.32 % set(auto2) -> assign(max_seconds, 0). 1.98/2.32 % set(auto2) -> assign(max_minutes, 5). 1.98/2.32 % assign(max_minutes, 5) -> assign(max_seconds, 300). 1.98/2.32 % set(auto2) -> set(sort_initial_sos). 1.98/2.32 % set(auto2) -> assign(sos_limit, -1). 1.98/2.32 % set(auto2) -> assign(lrs_ticks, 3000). 1.98/2.32 % set(auto2) -> assign(max_megs, 400). 1.98/2.32 % set(auto2) -> assign(stats, some). 1.98/2.32 % set(auto2) -> clear(echo_input). 1.98/2.32 % set(auto2) -> set(quiet). 1.98/2.32 % set(auto2) -> clear(print_initial_clauses). 1.98/2.32 % set(auto2) -> clear(print_given). 1.98/2.32 assign(lrs_ticks,-1). 1.98/2.32 assign(sos_limit,10000). 1.98/2.32 assign(order,kbo). 1.98/2.32 set(lex_order_vars). 1.98/2.32 clear(print_given). 1.98/2.32 1.98/2.32 % formulas(sos). % not echoed (916 formulas) 1.98/2.32 1.98/2.32 ============================== end of input ========================== 1.98/2.32 1.98/2.32 % From the command line: assign(max_seconds, 1200). 1.98/2.32 1.98/2.32 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 1.98/2.32 1.98/2.32 % Formulas that are not ordinary clauses: 1.98/2.32 1 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(R) <-> p(Q)) -> Q = R))))) # label(boolext) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 2 (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]. 1.98/2.32 3 (all A (ne(A) -> (all B (ne(B) -> ne(arr(A,B)))))) # label(arr_ne) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 4 (all A all X (mem(X,A) -> ap(i(A),X) = X)) # label(ibeta) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 5 (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]. 1.98/2.32 6 (all A all Y all X (mem(X,A) -> ap(k(A,Y),X) = Y)) # label(kbeta) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 7 (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]. 1.98/2.32 8 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> ((p(Q) -> p(R)) <-> p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))))))) # label(ax_imp_p) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 9 (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]. 1.98/2.32 10 (all A (ne(A) -> (all X (mem(X,A) -> (all Y (mem(Y,A) -> (p(ap(ap(c_2Emin_2E_3D(A),X),Y)) <-> Y = X))))))) # label(ax_eq_p) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 11 (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(V0P) <-> p(V1P_27))) -> (p(V0P) | p(V2Q) <-> p(V1P_27) | p(V3Q_27))))))))))) # label(conj_thm_2Ebool_2EOR__CONG) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 12 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> ((all V4x (mem(V4x,A_27a) -> p(V1Q))) | (all V3x (mem(V3x,A_27a) -> p(V0P))) <-> (all V2x (mem(V2x,A_27a) -> p(V1Q) | p(V0P)))))))))) # label(conj_thm_2Ebool_2EBOTH__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 13 (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]. 1.98/2.32 14 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(Q) & p(R) <-> p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))))))) # label(ax_and_p) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 15 (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]. 1.98/2.32 16 (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]. 1.98/2.32 17 (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 (p(ap(V0P,V2x)) & V2x = V1a & mem(V2x,A_27a)))))))))) # label(conj_thm_2Ebool_2EUNWIND__THM1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 18 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V2x ((p(ap(V0P,V2x)) -> p(V1Q)) & mem(V2x,A_27a))) <-> ((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]. 1.98/2.32 19 (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]. 1.98/2.32 20 (all V0P (mem(V0P,arr(bool,bool)) -> ((all V1b (mem(V1b,bool) -> p(ap(V0P,V1b)))) <-> p(ap(V0P,c_2Ebool_2EF)) & p(ap(V0P,c_2Ebool_2ET))))) # label(conj_thm_2Ebool_2EFORALL__BOOL) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 21 (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]. 1.98/2.32 22 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0M (mem(V0M,arr(A_27a,A_27b)) -> V0M = f47(A_27b,A_27a,V0M))))))) # label(conj_thm_2Ebool_2EETA__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 23 (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(ap(V1Q,V2x)))) & p(V0P) <-> (all V3x (mem(V3x,A_27a) -> p(V0P) & p(ap(V1Q,V3x))))))))))) # label(conj_thm_2Ebool_2ERIGHT__AND__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 24 (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]. 1.98/2.32 25 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) -> (p(V1t2) -> p(V0t1) & p(V1t2))))))) # label(conj_thm_2Ebool_2EAND__INTRO__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 26 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V2x ap(f58(A_27a,V0P,V1Q),V2x) = ap(ap(c_2Ebool_2E_5C_2F,ap(V0P,V2x)),ap(V1Q,V2x))))))) # label(lameq_f58) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 27 (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]. 1.98/2.32 28 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(f34(A_27a,V0p,V1m),V2x) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x))))))) # label(lameq_f34) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 29 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ap(c_2Emin_2E_40(A_27a),f51(A_27a,V0x)) = V0x)))) # label(conj_thm_2Ebool_2ESELECT__REFL__2) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 30 (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]. 1.98/2.32 31 (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]. 1.98/2.32 32 (all V0t (mem(V0t,bool) -> ($T <-> $T | p(V0t)) & (p(V0t) <-> p(V0t) | p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) | $T <-> $T))) # label(conj_thm_2Ebool_2EOR__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 33 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2Ebool_2EFALSITY) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 34 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V1B) & p(V0A) | p(V2C) & p(V0A) <-> (p(V2C) | p(V1B)) & p(V0A)))))))) # label(conj_thm_2Ebool_2ELEFT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 35 (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]. 1.98/2.32 36 (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(V0P,ap(ap(c_2Ebool_2ELET(A_27a,A_27b),f53(A_27b,A_27a,V1N)),V2M))) <-> p(ap(ap(c_2Ebool_2ELET(A_27a,bool),f54(A_27b,A_27a,V1N,V0P)),V2M))))))))))))) # label(conj_thm_2Ebool_2ELET__RAND) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 37 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((p(V0A) <-> p(V0A) | p(V1B)) <-> (p(V1B) -> p(V0A))))))) # label(conj_thm_2Ebool_2EOR__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 38 (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]. 1.98/2.32 39 (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(c_2Ebool_2Eliteral__case(A_27a,A_27c),f56(A_27b,A_27c,A_27a,V0N,V2b)),V1M) = ap(ap(ap(c_2Ebool_2Eliteral__case(A_27a,arr(A_27b,A_27c)),f55(A_27c,A_27b,A_27a,V0N)),V1M),V2b))))))))))))) # label(conj_thm_2Ebool_2Eliteral__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 40 (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__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 41 (all A_27a all V0p f43(A_27a,V0p) = ap(f44(A_27a),V0p)) # label(lameq_f44) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 42 (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]. 1.98/2.32 43 (all A_27a all V0t (mem(V0t,bool) -> (all V1t1 (mem(V1t1,A_27a) -> (all V2t2 ap(f16(A_27a,V0t,V1t1),V2t2) = ap(c_2Emin_2E_40(A_27a),f15(A_27a,V1t1,V2t2,V0t))))))) # label(lameq_f16) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 44 (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]. 1.98/2.32 45 (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]. 1.98/2.32 46 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> ((p(V0A) -> p(V1B)) <-> p(V1B) | -p(V0A)))))) # label(conj_thm_2Ebool_2EIMP__DISJ__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 47 (all A_27a all A_27b all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1y ap(f23(A_27a,A_27b,V0f),V1y) = ap(c_2Ebool_2E_3F(A_27a),f22(A_27b,A_27a,V0f,V1y))))) # label(lameq_f23) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 48 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($T <-> p(ap(c_2Ebool_2EDATATYPE(A_27a),V0x))))))) # label(conj_thm_2Ebool_2EDATATYPE__TAG__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 49 (all A_27b all A_27a all V1N (mem(V1N,arr(A_27a,A_27b)) -> (all V3x ap(f53(A_27b,A_27a,V1N),V3x) = ap(V1N,V3x)))) # label(lameq_f53) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 50 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((exists V2x ((p(ap(V0P,V2x)) | p(ap(V1Q,V2x))) & mem(V2x,A_27a))) <-> (exists V3x (mem(V3x,A_27a) & p(ap(V0P,V3x)))) | (exists V4x (mem(V4x,A_27a) & p(ap(V1Q,V4x))))))))))) # label(conj_thm_2Ebool_2EEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 51 (all V0bool (mem(V0bool,arr(bool,arr(bool,bool))) -> ($T <-> p(ap(c_2Ebool_2EDATATYPE(bool),ap(ap(V0bool,c_2Ebool_2ET),c_2Ebool_2EF)))))) # label(conj_thm_2Ebool_2EDATATYPE__BOOL) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 52 (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]. 1.98/2.32 53 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (all V2t3 (mem(V2t3,bool) -> ((p(V0t1) & p(V1t2) -> p(V2t3)) <-> (p(V0t1) -> (p(V1t2) -> p(V2t3)))))))))) # label(conj_thm_2Ebool_2EAND__IMP__INTRO) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 54 (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_2ECOND__ID) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 55 (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]. 1.98/2.32 56 (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))) -> V1g = V0f))))))))) # label(conj_thm_2Ebool_2EEQ__EXT) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 57 (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(ap(V0P,V3x)) | p(V1Q)))) <-> 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]. 1.98/2.32 58 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(V1m,V2x) = ap(f40(A_27a,V1m),V2x)))) # label(lameq_f40) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 59 (all A_27a (ne(A_27a) -> (all V0a (mem(V0a,A_27a) -> (exists V1x (mem(V1x,A_27a) & V1x = V0a)))))) # label(conj_thm_2Ebool_2EEXISTS__REFL) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 60 (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_2Eliteral__case(A_27a,A_27b),V0f),V1x))))))))) # label(conj_thm_2Ebool_2Eliteral__case__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 61 (all A_27a all V1Q (mem(V1Q,arr(A_27a,bool)) -> (all V4x ap(V1Q,V4x) = ap(f60(A_27a,V1Q),V4x)))) # label(lameq_f60) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 62 (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]. 1.98/2.32 63 (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(V0x)) & (p(V1x_27) -> (p(V2y) <-> p(V3y_27))) -> ((p(V0x) -> p(V2y)) <-> (p(V1x_27) -> p(V3y_27)))))))))))) # label(conj_thm_2Ebool_2EIMP__CONG) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 64 (all A_27b all A_27a all V0M (mem(V0M,arr(A_27a,A_27b)) -> (all V1x ap(f47(A_27b,A_27a,V0M),V1x) = ap(V0M,V1x)))) # label(lameq_f47) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 65 (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]. 1.98/2.32 66 (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__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 67 (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) -> (V2y = V1x <-> p(ap(V0P,V2y))))) -> ap(c_2Emin_2E_40(A_27a),V0P) = V1x))))))) # label(conj_thm_2Ebool_2ESELECT__UNIQUE) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 68 (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]. 1.98/2.32 69 (all V0t (mem(V0t,bool) -> (($F <-> p(V0t)) <-> -p(V0t)))) # label(conj_thm_2Ebool_2EIMP__F__EQ__F) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 70 (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]. 1.98/2.32 71 (all A_27a (ne(A_27a) -> c_2Ebool_2ERES__SELECT(A_27a) = f46(A_27a))) # label(ax_thm_2Ebool_2ERES__SELECT__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 72 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V1t2) -> p(V1t2) | p(V0t1)))))) # label(conj_thm_2Ebool_2EOR__INTRO__THM2) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 73 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((exists V2x (-p(ap(V0P,V2x)) & mem(V2x,A_27a))) <-> -(all V1x (mem(V1x,A_27a) -> p(ap(V0P,V1x))))))))) # label(conj_thm_2Ebool_2ENOT__FORALL__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 74 (exists V0f (mem(V0f,arr(ind,ind)) & p(ap(c_2Ebool_2EONE__ONE(ind,ind),V0f)) & -p(ap(c_2Ebool_2EONTO(ind,ind),V0f)))) # label(ax_thm_2Ebool_2EINFINITY__AX) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 75 (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]. 1.98/2.32 76 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Ebool_2Eitself(A_27a),bool)) -> ((all 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_2EFORALL__itself) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 77 (all V4b ap(f65,V4b) = ap(c_2Ebool_2E_7E,V4b)) # label(lameq_f65) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 78 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((exists V3x (mem(V3x,A_27a) & (p(V0P) | p(ap(V1Q,V3x))))) <-> (exists V2x (p(ap(V1Q,V2x)) & mem(V2x,A_27a))) | p(V0P)))))))) # label(conj_thm_2Ebool_2ERIGHT__OR__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 79 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> p(ap(V1Q,V3x)))) | p(V0P) <-> (all V2x (mem(V2x,A_27a) -> p(ap(V1Q,V2x)) | p(V0P)))))))))) # label(conj_thm_2Ebool_2ERIGHT__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 80 $T # label(conj_thm_2Ebool_2ETRUTH) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 81 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EIMP__F) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 82 (all A_27a (ne(A_27a) -> k(A_27a,c_2Ebool_2ET) = c_2Ebool_2EDATATYPE(A_27a))) # label(ax_thm_2Ebool_2EDATATYPE__TAG__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 83 (all V0y (mem(V0y,bool) -> (all V1x (mem(V1x,bool) -> (all V2z (mem(V2z,bool) -> (all V3w (mem(V3w,bool) -> ((p(V2z) -> p(V3w)) & (p(V0y) -> p(V1x)) -> ((p(V1x) -> p(V2z)) -> (p(V0y) -> p(V3w)))))))))))) # label(conj_thm_2Ebool_2EMONO__IMP) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 84 (all V1t2 (mem(V1t2,bool) -> (all V0t1 (mem(V0t1,bool) -> (all V2t ap(f3(V1t2,V0t1),V2t) = ap(ap(c_2Emin_2E_3D_3D_3E,ap(ap(c_2Emin_2E_3D_3D_3E,V0t1),ap(ap(c_2Emin_2E_3D_3D_3E,V1t2),V2t))),V2t)))))) # label(lameq_f3) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 85 (all A_27a (ne(A_27a) -> (all V0t (mem(V0t,bool) -> ((all V2x (mem(V2x,A_27a) -> (all V3y (mem(V3y,A_27a) -> V3y = V2x)))) & p(V0t) <-> p(ap(c_2Ebool_2E_3F_21(A_27a),k(A_27a,V0t)))))))) # label(conj_thm_2Ebool_2EUEXISTS__SIMP) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 86 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (p(ap(c_2Ebool_2E_21(A_27a),V0f)) <-> (all V1x (mem(V1x,A_27a) -> p(ap(V0f,V1x))))))))) # label(conj_thm_2Ebool_2EFORALL__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 87 (all V0t1 f7(V0t1) = ap(f8,V0t1)) # label(lameq_f8) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 88 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t)) & (p(V0t) <-> p(V0t) & p(V0t)) & ($F & p(V0t) <-> $F) & ($F <-> p(V0t) & $F))) # label(conj_thm_2Ebool_2EAND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 89 i(bool) = i(bool) <-> $T # label(ax_thm_2Ebool_2ET__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 90 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x1 (mem(V1x1,A_27a) -> (all V2x2 ap(f19(A_27b,A_27a,V0f,V1x1),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))))))) # label(lameq_f19) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 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)) -> ((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) -> V2x_27 = V3x_27_27))))) & (all V4x (mem(V4x,A_27a) -> (p(ap(V0P,V4x)) <-> (exists V5x_27 (mem(V5x_27,A_27b) & V4x = ap(V1rep,V5x_27)))))) <-> p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b),V0P),V1rep))))))))))) # label(conj_thm_2Ebool_2ETYPE__DEFINITION__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 92 (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) -> V3t2 = ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V2t1),V3t2))))))) # label(conj_thm_2Ebool_2Ebool__case__thm) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 93 (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]. 1.98/2.32 94 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V0A) & (p(V2C) | p(V1B)) <-> p(V2C) & p(V0A) | p(V1B) & p(V0A)))))))) # label(conj_thm_2Ebool_2ERIGHT__AND__OVER__OR) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 95 (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]. 1.98/2.32 96 (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]. 1.98/2.32 97 (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]. 1.98/2.32 98 (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(ap(c_2Ebool_2EIN(A_27a),V2x),V0P)) & p(ap(V1f,V2x))))))))))) # label(conj_thm_2Ebool_2ERES__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 99 (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]. 1.98/2.32 100 (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]. 1.98/2.32 101 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (all V1v (mem(V1v,A_27a) -> ((all V2x (mem(V2x,A_27a) -> (V2x = V1v -> p(ap(V0f,V2x))))) <-> p(ap(V0f,V1v))))))))) # label(conj_thm_2Ebool_2EUNWIND__FORALL__THM1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 102 (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),f59(A_27a,V0P))) | p(ap(c_2Ebool_2E_3F_21(A_27a),f60(A_27a,V1Q)))))))))) # label(conj_thm_2Ebool_2EUEXISTS__OR__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 103 (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]. 1.98/2.32 104 (all A_27a all V0t ap(f18(A_27a),V0t) = f17(A_27a,V0t)) # label(lameq_f18) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 105 (all A_27a all V0p f38(A_27a,V0p) = ap(f39(A_27a),V0p)) # label(lameq_f39) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 106 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f24(A_27a,A_27b) = c_2Ebool_2EONTO(A_27a,A_27b))))) # label(ax_thm_2Ebool_2EONTO__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 107 (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_2ELET(A_27a,A_27b),V0f),V1x) = ap(V0f,V1x))))))))) # label(conj_thm_2Ebool_2ELET__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 108 (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]. 1.98/2.32 109 (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)) & p(V0P) & mem(V2x,A_27a))) <-> p(V0P) & (exists V3x (mem(V3x,A_27a) & p(ap(V1Q,V3x))))))))))) # label(conj_thm_2Ebool_2ERIGHT__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 110 (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]. 1.98/2.32 111 (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(V0f,V2x) = ap(V1g,V2x))) <-> V1g = V0f))))))))) # label(conj_thm_2Ebool_2EFUN__EQ__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 112 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V1B) & p(V2C) | p(V0A) <-> (p(V1B) | p(V0A)) & (p(V2C) | p(V0A))))))))) # label(conj_thm_2Ebool_2ELEFT__OR__OVER__AND) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 113 (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_2EONE__ONE(A_27a,A_27b),V0f)) <-> (all V1x1 (mem(V1x1,A_27a) -> (all V2x2 (mem(V2x2,A_27a) -> (ap(V0f,V1x1) = ap(V0f,V2x2) -> V1x1 = V2x2)))))))))))) # label(conj_thm_2Ebool_2EONE__ONE__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 114 (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]. 1.98/2.32 115 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27b) -> V0t1 = ap(k(A_27b,V0t1),V1t2))))))))) # label(conj_thm_2Ebool_2EABS__SIMP) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 116 (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]. 1.98/2.32 117 (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),V1Q),V3x_27),V5y_27) = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0P),V2x),V4y)))))))))))))))) # label(conj_thm_2Ebool_2ECOND__CONG) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 118 (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]. 1.98/2.32 119 (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]. 1.98/2.32 120 (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 (mem(V3x,A_27a) & p(V0P))) -> (all V4x (mem(V4x,A_27a) -> p(V1Q))))))))))) # label(conj_thm_2Ebool_2EBOTH__FORALL__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 121 (all A_27a (ne(A_27a) -> f39(A_27a) = c_2Ebool_2ERES__EXISTS(A_27a))) # label(ax_thm_2Ebool_2ERES__EXISTS__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 122 (all A_27a all V1f (mem(V1f,arr(A_27a,bool)) -> (all V2x ap(V1f,V2x) = ap(f61(A_27a,V1f),V2x)))) # label(lameq_f61) # label(axiom) # label(non_clause). [assumption]. 1.98/2.32 123 (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]. 1.98/2.32 124 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> (exists V2fn (V0t1 = ap(V2fn,c_2Ebool_2ET) & V1t2 = ap(V2fn,c_2Ebool_2EF) & mem(V2fn,arr(bool,A_27a)))))))))) # label(conj_thm_2Ebool_2EboolAxiom) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 125 (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]. 1.98/2.33 126 (all A_27a all V1t1 (mem(V1t1,A_27a) -> (all V2t2 (mem(V2t2,A_27a) -> (all V0t (mem(V0t,bool) -> (all 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))) = ap(f15(A_27a,V1t1,V2t2,V0t),V3x)))))))) # label(lameq_f15) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 127 (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]. 1.98/2.33 128 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V1B) | p(V0A) <-> p(V1B) | p(V0A)))))) # label(conj_thm_2Ebool_2EDISJ__SYM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 129 (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]. 1.98/2.33 130 (all V0t (mem(V0t,bool) -> (-p(V0t) -> ($F <-> p(V0t))))) # label(conj_thm_2Ebool_2ENOT__F) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 131 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (-p(V1B) | -p(V0A) <-> -(p(V0A) & p(V1B))) & (-p(V1B) & -p(V0A) <-> -(p(V1B) | p(V0A))))))) # label(conj_thm_2Ebool_2EDE__MORGAN__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 132 (all V0b (mem(V0b,bool) -> (all V1t1 (mem(V1t1,bool) -> (all V2t2 (mem(V2t2,bool) -> ((p(V1t1) | -p(V0b)) & (p(V2t2) | p(V0b)) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0b),V1t1),V2t2))))))))) # label(conj_thm_2Ebool_2ECOND__EXPAND) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 133 (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]. 1.98/2.33 134 (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]. 1.98/2.33 135 (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]. 1.98/2.33 136 (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]. 1.98/2.33 137 (all V0t (mem(V0t,bool) -> -(p(V0t) & -p(V0t)))) # label(conj_thm_2Ebool_2ENOT__AND) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 138 (all V0t (mem(V0t,bool) -> (-p(V0t) -> -p(V0t)))) # label(conj_thm_2Ebool_2EF__IMP) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 139 (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]. 1.98/2.33 140 (all V0t (mem(V0t,bool) -> p(V0t))) <-> $F # label(ax_thm_2Ebool_2EF__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 141 (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]. 1.98/2.33 142 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (V0x = V1y -> V0x = V1y))))))) # label(conj_thm_2Ebool_2EEQ__SYM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 143 (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))) <-> p(V1Q) & (exists V3x (mem(V3x,A_27a) & p(ap(V0P,V3x))))))))))) # label(conj_thm_2Ebool_2ELEFT__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 144 (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]. 1.98/2.33 145 (all A0 (ne(A0) -> ne(ty_2Ebool_2Eitself(A0)))) # label(ne_ty_2Ebool_2Eitself) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 146 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) & p(V1t2) -> p(V0t1)))))) # label(conj_thm_2Ebool_2EAND1__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 147 (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(V3Q_27) & p(V1P_27) <-> p(V2Q) & p(V0P))))))))))) # label(conj_thm_2Ebool_2EAND__CONG) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 148 (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(V1Q) -> p(V2R))))))))) # label(conj_thm_2Ebool_2EDISJ__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 149 (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]. 1.98/2.33 150 (all A_27a all V0p f45(A_27a,V0p) = ap(f46(A_27a),V0p)) # label(lameq_f46) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 151 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($T <-> V0x = V0x))))) # label(conj_thm_2Ebool_2EREFL__CLAUSE) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 152 (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 & ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2)))))) # label(conj_thm_2Ebool_2ECOND__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 153 (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]. 1.98/2.33 154 (all A_27a (ne(A_27a) -> c_2Ebool_2E_21(A_27a) = f1(A_27a))) # label(ax_thm_2Ebool_2EFORALL__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 155 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m ap(f45(A_27a,V0p),V1m) = ap(c_2Emin_2E_40(A_27a),f37(A_27a,V0p,V1m))))) # label(lameq_f45) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 156 (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 V4a (mem(V4a,A_27b) -> V4a = ap(V3abs,ap(V2rep,V4a)))) & (all V5r (mem(V5r,A_27a) -> (V5r = ap(V2rep,ap(V3abs,V5r)) <-> p(ap(V0P,V5r))))) & mem(V3abs,arr(A_27a,A_27b))))))))))))) # label(conj_thm_2Ebool_2EABS__REP__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 157 (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]. 1.98/2.33 158 (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(V2Q) <-> p(V3Q_27))) -> (p(V3Q_27) | p(V1P_27) <-> p(V0P) | p(V2Q))))))))))) # label(conj_thm_2Ebool_2ELEFT__OR__CONG) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 159 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27a) -> (all V2z (mem(V2z,A_27a) -> (V1y = V0x & V1y = V2z -> V2z = V0x))))))))) # label(conj_thm_2Ebool_2EEQ__TRANS) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 160 (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]. 1.98/2.33 161 (all A_27a (ne(A_27a) -> f18(A_27a) = c_2Ebool_2ECOND(A_27a))) # label(ax_thm_2Ebool_2ECOND__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 162 (all A_27a all V0p (mem(V0p,arr(A_27a,bool)) -> (all V1m (mem(V1m,arr(A_27a,bool)) -> (all V2x ap(f37(A_27a,V0p,V1m),V2x) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0p)),ap(V1m,V2x))))))) # label(lameq_f37) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 163 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27a,bool)) -> ((all V4x (mem(V4x,A_27a) -> p(ap(V1Q,V4x)))) & (all V3x (mem(V3x,A_27a) -> p(ap(V0P,V3x)))) <-> (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]. 1.98/2.33 164 (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,ap(ap(V0f,V1x),V2y)),V3z) = ap(ap(V0f,V1x),ap(ap(V0f,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]. 1.98/2.33 165 (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]. 1.98/2.33 166 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1x ap(f49(A_27a,V0P),V1x) = ap(V0P,V1x)))) # label(lameq_f49) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 167 (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]. 1.98/2.33 168 (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_27b) -> (exists V2x (mem(V2x,A_27a) & V1y = ap(V0f,V2x))))) <-> p(ap(c_2Ebool_2EONTO(A_27a,A_27b),V0f))))))))) # label(conj_thm_2Ebool_2EONTO__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 169 (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(V1Q) & p(ap(V0P,V3x)))) <-> (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]. 1.98/2.33 170 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)) & ($T <-> (p(V0t) -> $T)) & ($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]. 1.98/2.33 171 (all A_27a all V1f (mem(V1f,arr(A_27a,bool)) -> (all V3x (mem(V3x,A_27a) -> (all V4y ap(f62(A_27a,V1f,V3x),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))))))) # label(lameq_f62) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 172 (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]. 1.98/2.33 173 (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]. 1.98/2.33 174 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x ap(f13(A_27b,A_27a,V0f),V1x) = ap(V0f,V1x)))) # label(lameq_f13) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 175 (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]. 1.98/2.33 176 (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]. 1.98/2.33 177 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> (all V4y (mem(V4y,A_27a) -> (p(ap(V0P,V4y)) & p(ap(V0P,V3x)) -> V3x = V4y))))) & (exists V2x (mem(V2x,A_27a) & p(ap(V0P,V2x)))) <-> p(ap(c_2Ebool_2E_3F_21(A_27a),f49(A_27a,V0P)))))))) # label(conj_thm_2Ebool_2EEXISTS__UNIQUE__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 178 (all A_27a (ne(A_27a) -> (all V0Q (mem(V0Q,bool) -> (all V1P (mem(V1P,arr(A_27a,bool)) -> ((all V3x (mem(V3x,A_27a) -> p(ap(V1P,V3x)))) | p(V0Q) <-> (all V2x (mem(V2x,A_27a) -> p(V0Q) | p(ap(V1P,V2x))))))))))) # label(conj_thm_2Ebool_2ELEFT__FORALL__OR__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 179 (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]. 1.98/2.33 180 (all V0P (mem(V0P,arr(bool,bool)) -> (p(ap(V0P,c_2Ebool_2EF)) & p(ap(V0P,c_2Ebool_2ET)) -> (all V1b (mem(V1b,bool) -> p(ap(V0P,V1b))))))) # label(conj_thm_2Ebool_2Ebool__INDUCT) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 181 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,bool) -> (all V1Q (mem(V1Q,bool) -> ((exists V2x (mem(V2x,A_27a) & (p(V0P) -> p(V1Q)))) <-> ((all V3x (mem(V3x,A_27a) -> p(V0P))) -> (exists V4x (mem(V4x,A_27a) & p(V1Q))))))))))) # label(conj_thm_2Ebool_2EBOTH__EXISTS__IMP__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 182 (all V0v (mem(V0v,bool) -> ($T <-> p(ap(c_2Ebool_2EBOUNDED,V0v))))) # label(conj_thm_2Ebool_2EBOUNDED__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 183 (all A_27a (ne(A_27a) -> f33(A_27a) = c_2Ebool_2EIN(A_27a))) # label(ax_thm_2Ebool_2EIN__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 184 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> mem(c_2Ebool_2Eliteral__case(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(A_27a,A_27b))))))) # label(mem_c_2Ebool_2Eliteral__case) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 185 (all A_27a all V0P ap(f12(A_27a),V0P) = ap(ap(c_2Ebool_2E_2F_5C,ap(c_2Ebool_2E_3F(A_27a),V0P)),ap(c_2Ebool_2E_21(A_27a),f11(A_27a,V0P)))) # label(lameq_f12) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 186 (all A (ne(A) -> (all Q (mem(Q,arr(A,bool)) -> ((exists X (mem(X,A) & p(ap(Q,X)))) <-> p(ap(c_2Ebool_2E_3F(A),Q))))))) # label(ax_ex_p) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 187 -($F <-> $T) # label(conj_thm_2Ebool_2EBOOL__EQ__DISTINCT_AndLHS) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 188 -($T <-> $F) # label(conj_thm_2Ebool_2EBOOL__EQ__DISTINCT_AndRHS) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 189 (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]. 1.98/2.33 190 (all Q (mem(Q,bool) -> (all R (mem(R,bool) -> (p(ap(ap(c_2Ebool_2E_5C_2F,Q),R)) <-> p(R) | p(Q)))))) # label(ax_or_p) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 191 (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]. 1.98/2.33 192 (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]. 1.98/2.33 193 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (p(V1B) | p(V0A) <-> p(V1B) | p(V0A)))))) # label(conj_thm_2Ebool_2EDISJ__COMM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 194 (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]. 1.98/2.33 195 (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(f28(A_27b,A_27a,V0P,V1rep),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)))))))) # label(lameq_f28) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 196 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((exists V5x (p(V1Q) & p(ap(V0P,V5x)) & mem(V5x,A_27a))) <-> (exists V4x (p(ap(V0P,V4x)) & mem(V4x,A_27a))) & p(V1Q)) & ((exists V6x (mem(V6x,A_27a) & p(ap(V0P,V6x)))) & p(V1Q) <-> (exists V7x (p(V1Q) & p(ap(V0P,V7x)) & mem(V7x,A_27a)))) & ((all V3x (mem(V3x,A_27a) -> (p(ap(V0P,V3x)) -> p(V1Q)))) <-> ((exists V2x (p(ap(V0P,V2x)) & mem(V2x,A_27a))) -> p(V1Q))))))))) # label(conj_thm_2Ebool_2EPULL__EXISTS) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 197 (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__EQ) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 198 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndLHS) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 199 $T <-> -$F # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 200 $F <-> -$T # label(conj_thm_2Ebool_2ENOT__CLAUSES_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 201 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (-p(V1t2) & -p(V0t1) | p(V0t1) & p(V1t2) <-> (p(V0t1) <-> p(V1t2))))))) # label(conj_thm_2Ebool_2EEQ__EXPAND) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 202 (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]. 1.98/2.33 203 (all V0t1 ap(f5,V0t1) = f4(V0t1)) # label(lameq_f5) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 204 (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]. 1.98/2.33 205 (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]. 1.98/2.33 206 (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]. 1.98/2.33 207 (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]. 1.98/2.33 208 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1a (mem(V1a,A_27a) -> ((exists V2x (mem(V2x,A_27a) & V1a = V2x & p(ap(V0P,V2x)))) <-> p(ap(V0P,V1a))))))))) # label(conj_thm_2Ebool_2EUNWIND__THM2) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 209 (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]. 1.98/2.33 210 (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]. 1.98/2.33 211 (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) -> (V2M = V3N & (all V4x (mem(V4x,A_27a) -> (V4x = V3N -> ap(V0f,V4x) = ap(V1g,V4x)))) -> ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),V1g),V3N) = ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),V0f),V2M)))))))))))))) # label(conj_thm_2Ebool_2Eliteral__case__CONG) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 212 (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(ap(c_2Ebool_2ECOND(arr(A_27a,A_27b)),V0b),V1f),V2g),V3x) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),V0b),ap(V1f,V3x)),ap(V2g,V3x)))))))))))))) # label(conj_thm_2Ebool_2ECOND__RATOR) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 213 (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))))))))) # label(conj_thm_2Ebool_2EIMP__CONJ__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 214 (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]. 1.98/2.33 215 (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]. 1.98/2.33 216 (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]. 1.98/2.33 217 (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]. 1.98/2.33 218 (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]. 1.98/2.33 219 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (all V2t3 (mem(V2t3,bool) -> (p(V0t1) & p(V1t2) & p(V2t3) <-> p(V0t1) & p(V2t3) & p(V1t2)))))))) # label(conj_thm_2Ebool_2ECONJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 220 (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]. 1.98/2.33 221 (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]. 1.98/2.33 222 (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]. 1.98/2.33 223 (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]. 1.98/2.33 224 (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]. 1.98/2.33 225 (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]. 1.98/2.33 226 (all V0t1 (mem(V0t1,bool) -> (all V1t2 (mem(V1t2,bool) -> (p(V0t1) -> p(V0t1) | p(V1t2)))))) # label(conj_thm_2Ebool_2EOR__INTRO__THM1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 227 (all V0t (mem(V0t,bool) -> (p(V0t) <-> ($T <-> p(V0t))) & (p(V0t) <-> (p(V0t) <-> $T)) & ((p(V0t) <-> $F) <-> -p(V0t)) & (-p(V0t) <-> ($F <-> p(V0t))))) # label(conj_thm_2Ebool_2EEQ__CLAUSES) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 228 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ((exists V2x (mem(V2x,A_27a) & p(ap(V0P,V2x)))) <-> 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]. 1.98/2.33 229 (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]. 1.98/2.33 230 (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]. 1.98/2.33 231 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f14(A_27b,A_27a) = c_2Ebool_2Eliteral__case(A_27a,A_27b))))) # label(ax_thm_2Ebool_2Eliteral__case__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 232 (all A_27a (ne(A_27a) -> (exists V0rep (mem(V0rep,arr(ty_2Ebool_2Eitself(A_27a),A_27a)) & 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)))))) # label(ax_thm_2Ebool_2Eitself__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 233 (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]. 1.98/2.33 234 (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]. 1.98/2.33 235 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,bool) -> ((all V5x (mem(V5x,A_27a) -> p(ap(V0P,V5x)) & p(V1Q))) <-> p(V1Q) & (all V4x (mem(V4x,A_27a) -> p(ap(V0P,V4x))))) & ((all V7x (mem(V7x,A_27a) -> p(V1Q) & p(ap(V0P,V7x)))) <-> p(V1Q) & (all V6x (mem(V6x,A_27a) -> p(ap(V0P,V6x))))) & ((p(V1Q) -> (all V2x (mem(V2x,A_27a) -> p(ap(V0P,V2x))))) <-> (all V3x (mem(V3x,A_27a) -> (p(V1Q) -> p(ap(V0P,V3x)))))))))))) # label(conj_thm_2Ebool_2EPULL__FORALL) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 236 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> c_2Ebool_2ETYPE__DEFINITION(A_27a,A_27b) = f30(A_27b,A_27a))))) # label(ax_thm_2Ebool_2ETYPE__DEFINITION) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 237 (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(V2t2) & -p(V0b) | p(V0b) & p(V1t1)))))))) # label(conj_thm_2Ebool_2ECOND__EXPAND__OR) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 238 (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]. 1.98/2.33 239 (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]. 1.98/2.33 240 (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]. 1.98/2.33 241 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((exists V3f ((all V4x (mem(V4x,A_27a) -> p(ap(ap(V0P,V4x),ap(V3f,V4x))))) & mem(V3f,arr(A_27a,A_27b)))) <-> (all V1x (mem(V1x,A_27a) -> (exists V2y (mem(V2y,A_27b) & p(ap(ap(V0P,V1x),V2y))))))))))))) # label(conj_thm_2Ebool_2ESKOLEM__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 242 (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]. 1.98/2.33 243 (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]. 1.98/2.33 244 (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(V2Q) & p(V0P) <-> p(V1P_27) & p(V3Q_27))))))))))) # label(conj_thm_2Ebool_2ELEFT__AND__CONG) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 245 (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]. 1.98/2.33 246 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> ($F <-> p(ap(ap(c_2Ebool_2ERES__EXISTS(A_27a),V0P),k(A_27a,c_2Ebool_2EF)))))))) # label(conj_thm_2Ebool_2ERES__EXISTS__FALSE) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 247 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V3x ap(V0P,V3x) = ap(f59(A_27a,V0P),V3x)))) # label(lameq_f59) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 248 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (-(p(V0A) -> p(V1B)) <-> p(V0A) & -p(V1B)))))) # label(conj_thm_2Ebool_2ENOT__IMP) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 249 (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]. 1.98/2.33 250 (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(V0P,ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),f53(A_27b,A_27a,V1N)),V2M)) = ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27c),f66(A_27b,A_27c,A_27a,V1N,V0P)),V2M))))))))))))) # label(conj_thm_2Ebool_2Eliteral__case__RAND) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 251 (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]. 1.98/2.33 252 (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]. 1.98/2.33 253 (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]. 1.98/2.33 254 (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 (p(ap(V1Q,V4x)) & mem(V4x,A_27a))))))))))) # label(conj_thm_2Ebool_2EMONO__EXISTS) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 255 (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]. 1.98/2.33 256 (all A_27a all V0p f35(A_27a,V0p) = ap(f36(A_27a),V0p)) # label(lameq_f36) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 257 (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]. 1.98/2.33 258 (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(ap(V0P,V3x)))) -> 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]. 1.98/2.33 259 (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]. 1.98/2.33 260 (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]. 1.98/2.33 261 (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]. 1.98/2.33 262 (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]. 1.98/2.33 263 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V0A) | p(V2C) | p(V1B) <-> p(V2C) | p(V1B) | p(V0A)))))))) # label(conj_thm_2Ebool_2EDISJ__ASSOC) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 264 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f14(A_27b,A_27a) = c_2Ebool_2ELET(A_27a,A_27b))))) # label(ax_thm_2Ebool_2ELET__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 265 (all A_27a all V1m (mem(V1m,arr(A_27a,bool)) -> (all V0p (mem(V0p,arr(A_27a,bool)) -> (all V3x ap(f42(A_27a,V1m,V0p),V3x) = ap(ap(c_2Ebool_2ERES__FORALL(A_27a),V0p),f41(A_27a,V1m,V3x))))))) # label(lameq_f42) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 266 (all A_27a all V0x f32(A_27a,V0x) = ap(f33(A_27a),V0x)) # label(lameq_f33) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 267 (all V0f (mem(V0f,arr(bool,bool)) -> V0f = k(bool,c_2Ebool_2ET) | V0f = k(bool,c_2Ebool_2EF) | V0f = f65 | i(bool) = V0f)) # label(conj_thm_2Ebool_2EBOOL__FUN__CASES__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 268 (all V0t (mem(V0t,bool) -> (p(V0t) <-> $T) | ($F <-> p(V0t)))) # label(ax_thm_2Ebool_2EBOOL__CASES__AX) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 269 (all Q (mem(Q,bool) -> (p(ap(c_2Ebool_2E_7E,Q)) <-> -p(Q)))) # label(ax_neg_p) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 270 (all V0t (mem(V0t,bool) -> -p(V0t) | p(V0t))) # label(conj_thm_2Ebool_2EEXCLUDED__MIDDLE) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 271 (all A_27a all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1f (mem(V1f,arr(A_27a,bool)) -> (all V2x ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Ebool_2EIN(A_27a),V2x),V0P)),ap(V1f,V2x)) = ap(f64(A_27a,V0P,V1f),V2x)))))) # label(lameq_f64) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 272 (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) -> ap(ap(c_2Ebool_2Eliteral__case(A_27a,A_27b),f67(A_27b,A_27a,V1t,V0a,V2u)),V0a) = V1t)))))))))) # label(conj_thm_2Ebool_2Eliteral__case__id) # label(axiom) # label(non_clause). [assumption]. 1.98/2.33 273 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> f21(A_27b,A_27a) = c_2Ebool_2EONE__ONE(A_27a,A_27b))))) # label(ax_thm_2Ebool_2EONE__ONE__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 274 (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))) <-> (exists V3x (p(V0P) & mem(V3x,A_27a))) & (exists V4x (mem(V4x,A_27a) & p(V1Q)))))))))) # label(conj_thm_2Ebool_2EBOTH__EXISTS__AND__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 275 (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) -> V4y = V5y_27) & (p(V1Q) -> V2x = V3x_27) -> 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]. 1.98/2.34 276 (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(V2t2)) & (p(V0b) -> p(V1t1))))))))) # label(conj_thm_2Ebool_2ECOND__EXPAND__IMP) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 277 (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) -> (V2M = V3N & (all V4x (mem(V4x,A_27a) -> (V4x = V3N -> ap(V1g,V4x) = ap(V0f,V4x)))) -> ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V1g),V3N) = ap(ap(c_2Ebool_2ELET(A_27a,A_27b),V0f),V2M)))))))))))))) # label(conj_thm_2Ebool_2ELET__CONG) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 278 (all A_27b all A_27a all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V2x ap(V0f,V2x) = ap(f48(A_27b,A_27a,V0f),V2x)))) # label(lameq_f48) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 279 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> (p(V2C) & p(V1B) | p(V0A) <-> (p(V1B) | p(V0A)) & (p(V2C) | p(V0A))))))))) # label(conj_thm_2Ebool_2ERIGHT__OR__OVER__AND) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 280 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0P (mem(V0P,arr(A_27a,arr(A_27b,bool))) -> ((exists V3y ((exists V4x (p(ap(ap(V0P,V4x),V3y)) & mem(V4x,A_27a))) & mem(V3y,A_27b))) <-> (exists V1x (mem(V1x,A_27a) & (exists V2y (mem(V2y,A_27b) & p(ap(ap(V0P,V1x),V2y))))))))))))) # label(conj_thm_2Ebool_2ESWAP__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 281 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(A_27a,bool)) -> (-(exists V1x (mem(V1x,A_27a) & p(ap(V0P,V1x)))) <-> (all V2x (mem(V2x,A_27a) -> -p(ap(V0P,V2x))))))))) # label(conj_thm_2Ebool_2ENOT__EXISTS__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 282 (all A_27a (ne(A_27a) -> f12(A_27a) = c_2Ebool_2E_3F_21(A_27a))) # label(ax_thm_2Ebool_2EEXISTS__UNIQUE__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 283 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(c_2Emin_2E_40(A_27a),f50(A_27a,V0x)))))) # label(conj_thm_2Ebool_2ESELECT__REFL) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 284 (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]. 1.98/2.34 285 (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]. 1.98/2.34 286 (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]. 1.98/2.34 287 (all V0y (mem(V0y,bool) -> (all V1x (mem(V1x,bool) -> (p(ap(ap(c_2EConseqConv_2EASM__MARKER,V0y),V1x)) <-> p(V1x)))))) # label(conj_thm_2EConseqConv_2EASM__MARKER__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 288 (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(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]. 1.98/2.34 289 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 290 (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]. 1.98/2.34 291 (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]. 1.98/2.34 292 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (p(V0c) & p(V1x) <-> p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V1x),c_2Ebool_2EF))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__FF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 293 (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(V1x_27)) & (p(V1x_27) -> (p(V3y_27) -> p(V2y))) -> ((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]. 1.98/2.34 294 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 295 (all V0t (mem(V0t,bool) -> ($F -> p(V0t)))) # label(conj_thm_2EConseqConv_2Efalse__imp) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 296 (all V0t (mem(V0t,bool) -> (p(V0t) -> $T))) # label(conj_thm_2EConseqConv_2Etrue__imp) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 297 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),V1x),c_2Ebool_2ET)) <-> (p(V0c) -> p(V1x))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__FT) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 298 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V2y) -> (p(V0x) -> p(V1x_27))) & (p(V1x_27) -> (p(V2y) -> p(V3y_27))) -> (p(V0x) & p(V2y) -> p(V3y_27) & p(V1x_27))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__conj__weaken) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 299 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) -> (p(V3y_27) -> p(V2y))) & (p(V2y) -> (p(V1x_27) -> p(V0x))) -> (p(V3y_27) & p(V1x_27) -> p(V2y) & p(V0x))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__conj__strengthen) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 300 (all V0t (mem(V0t,bool) -> ($F & p(V0t) <-> $F))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 301 -$F <-> $T # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__F) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 302 (all V0x (mem(V0x,bool) -> (all V1x_27 (mem(V1x_27,bool) -> (all V2y (mem(V2y,bool) -> (all V3y_27 (mem(V3y_27,bool) -> ((p(V1x_27) -> p(V0x)) & (p(V1x_27) -> (p(V2y) -> p(V3y_27))) -> ((p(V0x) -> p(V2y)) -> (p(V1x_27) -> p(V3y_27)))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__simple__imp__weaken) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 303 (all V0t (mem(V0t,bool) -> ($F <-> $F & p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 304 (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]. 1.98/2.34 305 (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(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]. 1.98/2.34 306 (all V0t (mem(V0t,bool) -> (p(V0t) & p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 307 (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]. 1.98/2.34 308 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EAND__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 309 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 310 (all V0t (mem(V0t,bool) -> (p(V0t) | $T <-> $T))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 311 -$T <-> $F # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__T) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 312 (all A_27a (ne(A_27a) -> (all V0b (mem(V0b,bool) -> (all V1t (mem(V1t,A_27a) -> V1t = ap(ap(ap(c_2Ebool_2ECOND(A_27a),V0b),V1t),V1t))))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__ID) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 313 (all V0t (mem(V0t,bool) -> ($T <-> (p(V0t) -> $T)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XT) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 314 (all V0t (mem(V0t,bool) -> (-p(V0t) <-> -p(V0t)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 315 (all A_27a (ne(A_27a) -> (all V0t1 (mem(V0t1,A_27a) -> (all V1t2 (mem(V1t2,A_27a) -> ap(ap(ap(c_2Ebool_2ECOND(A_27a),c_2Ebool_2EF),V0t1),V1t2) = V1t2)))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__CF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 316 (all V0t (mem(V0t,bool) -> (p(V0t) | p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 317 (all V0c (mem(V0c,bool) -> (all V1x (mem(V1x,bool) -> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V0c),c_2Ebool_2EF),V1x)) <-> p(V1x) & -p(V0c)))))) # label(conj_thm_2EConseqConv_2ECOND__CLAUSES__TF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 318 (all V0t (mem(V0t,bool) -> ($T <-> (p(V0t) -> p(V0t))))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__XX) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 319 (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(V1Q,V2s)) <-> p(ap(V0P,V2s))))) -> ((exists V3s (mem(V3s,A_27a) & p(ap(V0P,V3s)))) <-> (exists V4s (p(ap(V1Q,V4s)) & mem(V4s,A_27a))))))))))) # label(conj_thm_2EConseqConv_2Eexists__eq__thm) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 320 (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__disj__weaken) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 321 (all V0t (mem(V0t,bool) -> ($T <-> ($F -> p(V0t))))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__FX) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 322 (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(V3y_27) | p(V1x_27) -> p(V2y) | p(V0x))))))))))) # label(conj_thm_2EConseqConv_2EIMP__CONG__disj__strengthen) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 323 (all V0t (mem(V0t,bool) -> (p(V0t) | $T <-> $T))) # label(conj_thm_2EConseqConv_2EOR__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 324 (all V0t (mem(V0t,bool) -> (p(V0t) <-> p(V0t)))) # label(conj_thm_2EConseqConv_2EIMP__CLAUSES__TX) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 325 (all V0t (mem(V0t,bool) -> (p(V0t) <-> --p(V0t)))) # label(conj_thm_2EConseqConv_2ENOT__CLAUSES__X) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 326 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (--(p(V0A) | p(V1B)) <-> (-p(V0A) -> --p(V1B))))))) # label(conj_thm_2Esat_2EOR__DUAL) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 327 (all V0p (mem(V0p,bool) -> (--p(V0p) -> p(V0p)))) # label(conj_thm_2Esat_2Epth__nn) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 328 (all V0A (mem(V0A,bool) -> (--p(V0A) <-> p(V0A)))) # label(conj_thm_2Esat_2ENOT__ELIM2) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 329 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> ((-p(V0p) | -p(V1q)) & (p(V0p) | p(V1q)) <-> (p(V0p) <-> -p(V1q))))))) # label(conj_thm_2Esat_2Edc__neg) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 330 (all V0A (mem(V0A,bool) -> (-p(V0A) & p(V0A) <-> $F))) # label(conj_thm_2Esat_2EAND__INV) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 331 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V0p) | -p(V1q)) & (p(V1q) | -p(V0p) | p(V2r)) & (-p(V2r) | p(V0p)) <-> (p(V1q) | p(V2r) <-> p(V0p))))))))) # label(conj_thm_2Esat_2Edc__disj) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 332 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V1q) | p(V0p)) -> -p(V1q)))))) # label(conj_thm_2Esat_2Epth__no2) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 333 (all V0b (mem(V0b,bool) -> (p(V0b) -> (p(V0b) <-> $T)))) # label(conj_thm_2Esat_2EEQT__Imp1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 334 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V1q) | p(V0p)) & (p(V2r) | -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]. 1.98/2.34 335 (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]. 1.98/2.34 336 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V1q) | p(V2r) | p(V0p)) & (-p(V1q) | -p(V2r) | p(V0p)) & (-p(V2r) | -p(V0p) | p(V1q)) & (p(V2r) | -p(V1q) | -p(V0p)) <-> (p(V0p) <-> (p(V2r) <-> p(V1q)))))))))) # label(conj_thm_2Esat_2Edc__eq) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 337 (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]. 1.98/2.34 338 (all V0A (mem(V0A,bool) -> (p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV__IMP) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 339 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> ((p(V0p) | -p(V1q) | -p(V2r)) & (p(V1q) | -p(V0p)) & (p(V2r) | -p(V0p)) <-> (p(V0p) <-> p(V2r) & p(V1q))))))))) # label(conj_thm_2Esat_2Edc__conj) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 340 (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]. 1.98/2.34 341 (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]. 1.98/2.34 342 (all V0t (mem(V0t,bool) -> (--p(V0t) <-> p(V0t)))) # label(conj_thm_2Esat_2ENOT__NOT) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 343 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (-(p(V1q) | p(V0p)) -> -p(V0p)))))) # label(conj_thm_2Esat_2Epth__no1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 344 (all V0A (mem(V0A,bool) -> (all V1B (mem(V1B,bool) -> (all V2C (mem(V2C,bool) -> ((p(V1B) & p(V0A) -> p(V2C)) <-> (p(V0A) -> (p(V1B) -> p(V2C)))))))))) # label(conj_thm_2Esat_2EAND__IMP) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 345 (all V0A (mem(V0A,bool) -> (--p(V0A) -> --p(V0A)))) # label(conj_thm_2Esat_2EAND__INV2) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 346 (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]. 1.98/2.34 347 (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]. 1.98/2.34 348 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2r (mem(V2r,bool) -> (all V3s (mem(V3s,bool) -> ((-p(V1q) | -p(V0p) | p(V2r)) & (p(V1q) | p(V3s) | -p(V0p)) & (-p(V2r) | -p(V3s) | p(V0p)) & (-p(V2r) | -p(V1q) | p(V0p)) & (-p(V3s) | p(V1q) | p(V0p)) <-> (p(ap(ap(ap(c_2Ebool_2ECOND(bool),V1q),V2r),V3s)) <-> p(V0p))))))))))) # label(conj_thm_2Esat_2Edc__cond) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 349 (all V0b (mem(V0b,bool) -> (-p(V0b) -> (p(V0b) <-> $F)))) # label(conj_thm_2Esat_2EEQF__Imp1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 350 (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]. 1.98/2.34 351 (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]. 1.98/2.34 352 (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(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)) -> V1g = V0f))))))))) # label(ax_thm_2EnormalForms_2EEXT__POINT__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 353 (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]. 1.98/2.34 354 (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)) -> (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]. 1.98/2.34 355 (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]. 1.98/2.34 356 (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(V1q) <-> p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V1q) & p(V0p)) & (p(V0p) & p(V1q) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) <-> p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V1q) & p(V0p)) & (p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V0p) <-> p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V0p)))))))) # label(conj_thm_2Emarker_2Emove__left__conj) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 357 (all V0lab (mem(V0lab,ind) -> (all V1argument (mem(V1argument,bool) -> (p(V1argument) <-> p(ap(ap(c_2Emarker_2E_3A_2D,V0lab),V1argument))))))) # label(ax_thm_2Emarker_2Elabel__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 358 (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]. 1.98/2.34 359 (all V0x (mem(V0x,bool) -> (p(V0x) <-> p(ap(c_2Emarker_2ECong,V0x))))) # label(ax_thm_2Emarker_2ECong__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 360 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2m (mem(V2m,bool) -> (p(V1q) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V0p) <-> p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V1q)) & (p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V1q) <-> p(V1q) | 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))))))))) # label(conj_thm_2Emarker_2Emove__right__disj) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 361 (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]. 1.98/2.34 362 p(c_2Emarker_2EIfCases) <-> $T # label(ax_thm_2Emarker_2EIfCases__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 363 (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]. 1.98/2.34 364 (all V0p (mem(V0p,bool) -> (all V1q (mem(V1q,bool) -> (all V2m (mem(V2m,bool) -> (p(V1q) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) | p(V0p) <-> p(V1q) | p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m))) & (p(V1q) | p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) <-> p(V0p) | p(V1q) | p(ap(c_2Emarker_2Estmarker(bool),V2m))) & (p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m)) <-> p(V0p) | p(ap(c_2Emarker_2Estmarker(bool),V2m))))))))) # label(conj_thm_2Emarker_2Emove__left__disj) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 365 (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(V0p) & p(ap(c_2Emarker_2Estmarker(bool),V2m))) & (p(V0p) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V1q) <-> p(V0p) & p(V1q) & p(ap(c_2Emarker_2Estmarker(bool),V2m))) & (p(V1q) & p(ap(c_2Emarker_2Estmarker(bool),V2m)) & p(V0p) <-> p(V0p) & p(V1q) & p(ap(c_2Emarker_2Estmarker(bool),V2m))))))))) # label(conj_thm_2Emarker_2Emove__right__conj) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 366 (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]. 1.98/2.34 367 (all V0b1 (mem(V0b1,bool) -> (all V1b2 (mem(V1b2,bool) -> (p(V1b2) & p(V0b1) <-> p(ap(ap(c_2Emarker_2EAC,V0b1),V1b2))))))) # label(ax_thm_2Emarker_2EAC__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 368 (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]. 1.98/2.34 369 (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) -> (all V2y (mem(V2y,A_27a) -> ap(ap(V0f,V1x),V2y) = ap(ap(V0f,V2y),V1x))))) <-> p(ap(c_2Ecombin_2ECOMM(A_27a,A_27b),V0f))))))))) # label(ax_thm_2Ecombin_2ECOMM__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 370 (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]. 1.98/2.34 371 (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) -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),ap(V0f,V1a)),V0f) = V0f)))))))) # label(conj_thm_2Ecombin_2EAPPLY__UPDATE__ID) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 372 (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]. 1.98/2.34 373 (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]. 1.98/2.34 374 (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]. 1.98/2.34 375 (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),ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V2b),V0f)) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f))))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__EQ) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 376 (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]. 1.98/2.34 377 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V1b (mem(V1b,A_27b) -> f79(A_27b,A_27a,V1b,V0a) = ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V0a),V1b))))))))) # label(ax_thm_2Ecombin_2EUPDATE__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 378 (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]. 1.98/2.34 379 (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]. 1.98/2.34 380 (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) -> V3b = V4c & (all V5v (mem(V5v,A_27b) -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V5v),V1f2) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V5v),V0f1)))))))))))))))))) # label(conj_thm_2Ecombin_2EUPD__SAME__KEY__UNWIND) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 381 (all A_27b all A_27c all A_27a all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V2x ap(V0f,V2x) = ap(f84(A_27b,A_27c,A_27a,V0f),V2x)))) # label(lameq_f84) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 382 (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]. 1.98/2.34 383 (all A_27a (ne(A_27a) -> (all V0f (mem(V0f,arr(A_27a,bool)) -> (all V1v (mem(V1v,A_27a) -> (p(ap(ap(c_2Ebool_2Eliteral__case(A_27a,bool),V0f),V1v)) <-> 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)))))))))) # label(conj_thm_2Ecombin_2Eliteral__case__FORALL__ELIM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 384 (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]. 1.98/2.34 385 (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]. 1.98/2.34 386 (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]. 1.98/2.34 387 (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(ap(c_2Ecombin_2EMONOID(A_27a),V0f),V1e)) <-> p(ap(ap(c_2Ecombin_2ERIGHT__ID(A_27a,A_27a),V0f),V1e)) & p(ap(ap(c_2Ecombin_2ELEFT__ID(A_27a,A_27a),V0f),V1e)) & p(ap(c_2Ecombin_2EASSOC(A_27a),V0f))))))))) # label(ax_thm_2Ecombin_2EMONOID__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 388 (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]. 1.98/2.34 389 (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]. 1.98/2.34 390 (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]. 1.98/2.34 391 (all A_27a all A_27c all A_27b all V0f ap(f74(A_27a,A_27c,A_27b),V0f) = f73(A_27a,A_27c,A_27b,V0f)) # label(lameq_f74) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 392 (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]. 1.98/2.34 393 (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]. 1.98/2.34 394 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> c_2Ecombin_2ES(A_27a,A_27b,A_27c) = f71(A_27c,A_27a,A_27b))))))) # label(ax_thm_2Ecombin_2ES__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 395 (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) -> (V1b = ap(V0f,V2a) -> ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V2a),V1b),V0f) = V0f))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__APPLY__IMP__ID) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 396 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0f (mem(V0f,arr(A_27a,A_27b)) -> ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27a),V0f),c_2Ecombin_2EI(A_27a)) = V0f & V0f = ap(ap(c_2Ecombin_2Eo(A_27a,A_27b,A_27b),c_2Ecombin_2EI(A_27b)),V0f))))))) # label(conj_thm_2Ecombin_2EI__o__ID) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 397 (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]. 1.98/2.34 398 (all A_27b all A_27a all V1b (mem(V1b,A_27b) -> (all V0a (mem(V0a,A_27a) -> (all V2f f78(A_27b,A_27a,V1b,V0a,V2f) = ap(f79(A_27b,A_27a,V1b,V0a),V2f)))))) # label(lameq_f79) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 399 (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]. 1.98/2.34 400 (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]. 1.98/2.34 401 (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]. 1.98/2.34 402 (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) -> (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]. 1.98/2.34 403 (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(V0f,ap(V1g,V2x)) = ap(f77(A_27c,A_27b,A_27a,V1g,V0f),V2x)))))) # label(lameq_f77) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 404 (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]. 1.98/2.34 405 (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]. 1.98/2.34 406 (all A_27a (ne(A_27a) -> c_2Ecombin_2EI(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)))) # label(ax_thm_2Ecombin_2EI__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 407 (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(f78(A_27b,A_27a,V1b,V0a,V2f),V3c) = ap(ap(ap(c_2Ebool_2ECOND(A_27b),ap(ap(c_2Emin_2E_3D(A_27a),V0a),V3c)),V1b),ap(V2f,V3c))))))))) # label(lameq_f78) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 408 (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]. 1.98/2.34 409 (all A_27c all A_27a all A_27b all V0f ap(f71(A_27c,A_27a,A_27b),V0f) = f70(A_27c,A_27a,A_27b,V0f)) # label(lameq_f71) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 410 (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]. 1.98/2.34 411 (all A_27b all A_27a all V0f ap(f76(A_27b,A_27a),V0f) = f75(A_27b,A_27a,V0f)) # label(lameq_f76) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 412 (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]. 1.98/2.34 413 (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)) <-> p(ap(ap(c_2Ecombin_2EFCOMM(A_27a,A_27a,A_27a),V0f),V0f))))))) # label(conj_thm_2Ecombin_2EFCOMM__ASSOC) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 414 (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]. 1.98/2.34 415 (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_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]. 1.98/2.34 416 (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]. 1.98/2.34 417 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27a,arr(A_27c,A_27b))) -> (all V1y (mem(V1y,A_27c) -> ap(ap(c_2Ecombin_2EC(A_27a,A_27c,A_27b),f84(A_27b,A_27c,A_27a,V0f)),V1y) = f86(A_27c,A_27b,A_27a,V0f,V1y))))))))))) # label(conj_thm_2Ecombin_2EC__ABS__L) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 418 (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(f86(A_27c,A_27b,A_27a,V0f,V1y),V3x) = ap(ap(V0f,V3x),V1y)))))) # label(lameq_f86) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 419 (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]. 1.98/2.34 420 (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 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]. 1.98/2.34 421 (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]. 1.98/2.34 422 (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) -> (ap(V0f,V1a) = V2b <-> 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]. 1.98/2.34 423 (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,A_27c)) -> (all V1g (mem(V1g,arr(A_27b,A_27a)) -> ap(ap(c_2Ecombin_2Eo(A_27b,A_27c,A_27a),f80(A_27c,A_27a,V0f)),V1g) = f81(A_27a,A_27c,A_27b,V1g,V0f))))))))))) # label(conj_thm_2Ecombin_2Eo__ABS__L) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 424 (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]. 1.98/2.34 425 (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_27c),ap(ap(c_2Ecombin_2Eo(A_27c,A_27b,A_27a),V0f),V1g)),V2h) = 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)))))))))))))))) # label(conj_thm_2Ecombin_2Eo__ASSOC) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 426 (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 V0a (mem(V0a,A_27a) -> (all V1x (mem(V1x,A_27b) -> (all V2f (mem(V2f,arr(A_27a,A_27b)) -> ap(ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V0a),V1x),V2f),V0a) = V1x)))))) & (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)) -> (V4b != V3a -> ap(ap(ap(ap(c_2Ecombin_2EUPDATE(A_27c,A_27d),V3a),V5x),V6f),V4b) = ap(V6f,V4b)))))))))))))))))) # label(conj_thm_2Ecombin_2EUPDATE__APPLY) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 427 (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))) -> (p(ap(ap(c_2Ecombin_2EFCOMM(A_27a,A_27b,A_27c),V0f),V1g)) <-> (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))))))))))))))))))) # label(ax_thm_2Ecombin_2EFCOMM__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 428 (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),V5c),V0f) != ap(ap(ap(c_2Ecombin_2EUPDATE(A_27c,A_27d),V3a),V4b),V0f)))))))))))))))))))))) # label(conj_thm_2Ecombin_2ESAME__KEY__UPDATE__DIFFER) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 429 (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]. 1.98/2.34 430 (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]. 1.98/2.34 431 (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) -> (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) & V2b != V1a | V2b = V1a & V3c = V4d <-> 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]. 1.98/2.34 432 (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_2ELET(A_27b,A_27a),ap(ap(c_2Ecombin_2EC(A_27b,A_27c,A_27a),V0f),V2x)),V1v) = ap(ap(ap(c_2Ebool_2ELET(A_27b,arr(A_27c,A_27a)),V0f),V1v),V2x))))))))))))) # label(conj_thm_2Ecombin_2EGEN__LET__RATOR) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 433 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all A_27c (ne(A_27c) -> (all V0f (mem(V0f,arr(A_27b,arr(A_27c,A_27a))) -> (all V1v (mem(V1v,A_27b) -> (all V2x (mem(V2x,A_27c) -> ap(ap(ap(c_2Ebool_2Eliteral__case(A_27b,arr(A_27c,A_27a)),V0f),V1v),V2x) = ap(ap(c_2Ebool_2Eliteral__case(A_27b,A_27a),ap(ap(c_2Ecombin_2EC(A_27b,A_27c,A_27a),V0f),V2x)),V1v))))))))))))) # label(conj_thm_2Ecombin_2EGEN__literal__case__RATOR) # label(axiom) # label(non_clause). [assumption]. 1.98/2.34 434 (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]. 1.98/2.34 435 (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]. 1.98/2.34 436 (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),V2b),V0f) = ap(ap(ap(c_2Ecombin_2EUPDATE(A_27a,A_27b),V1a),V3c),V0f) <-> V2b = V3c))))))))))))) # label(conj_thm_2Ecombin_2EUPD11__SAME__KEY__AND__BASE) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 437 (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),f84(A_27b,A_27c,A_27a,V0f)),V1g) = f85(A_27c,A_27b,A_27a,V0f,V1g))))))))))) # label(conj_thm_2Ecombin_2ES__ABS__L) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 438 (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(ap(V0f,V3x),ap(V1g,V3x)) = ap(f85(A_27c,A_27b,A_27a,V0f,V1g),V3x)))))) # label(lameq_f85) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 439 (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(f81(A_27a,A_27c,A_27b,V1g,V0f),V3x) = ap(V0f,ap(V1g,V3x))))))) # label(lameq_f81) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 440 (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]. 1.98/2.35 441 (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]. 1.98/2.35 442 (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]. 1.98/2.35 443 (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]. 1.98/2.35 444 (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]. 1.98/2.35 445 (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]. 1.98/2.35 446 (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 V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1v (mem(V1v,A_27c) -> ap(c_2Ecombin_2EK(A_27c,A_27a),V1v) = ap(ap(c_2Ecombin_2Eo(A_27a,A_27c,A_27b),ap(c_2Ecombin_2EK(A_27c,A_27b),V1v)),V0f))))) & (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)))))))))))))))))) # label(conj_thm_2Ecombin_2EK__o__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 447 (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),V0f),f82(A_27c,A_27a,V1g)))))))))))) # label(conj_thm_2Ecombin_2ES__ABS__R) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 448 (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]. 1.98/2.35 449 (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(V0f,V2x),ap(V1g,V2x)) = ap(ap(ap(c_2Ecombin_2ES(A_27a,A_27b,A_27c),V0f),V1g),V2x))))))))))))) # label(conj_thm_2Ecombin_2ES__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 450 (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) -> (p(ap(ap(c_2Ecombin_2ERIGHT__ID(A_27a,A_27b),V0f),V1e)) <-> (all V2x (mem(V2x,A_27a) -> V2x = ap(ap(V0f,V2x),V1e)))))))))))) # label(ax_thm_2Ecombin_2ERIGHT__ID__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 451 (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]. 1.98/2.35 452 (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]. 1.98/2.35 453 (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]. 1.98/2.35 454 (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_AndLHS) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 455 (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_AndRHS) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 456 (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]. 1.98/2.35 457 (all V0P (mem(V0P,arr(ty_2Enum_2Enum,bool)) -> ((all V1n (mem(V1n,ty_2Enum_2Enum) -> (p(ap(V0P,V1n)) -> p(ap(V0P,ap(c_2Enum_2ESUC,V1n)))))) & p(ap(V0P,c_2Enum_2E0)) -> (all V2n (mem(V2n,ty_2Enum_2Enum) -> p(ap(V0P,V2n))))))) # label(conj_thm_2Enum_2EINDUCTION) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 458 (all V0y (mem(V0y,ind) -> c_2Enum_2EZERO__REP != ap(c_2Enum_2ESUC__REP,V0y))) # label(ax_thm_2Enum_2EZERO__REP__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 459 (all V0m (mem(V0m,ind) -> (p(ap(c_2Enum_2EIS__NUM__REP,V0m)) <-> (all V1P (mem(V1P,arr(ind,bool)) -> (p(ap(V1P,c_2Enum_2EZERO__REP)) & (all V2n (mem(V2n,ind) -> (p(ap(V1P,V2n)) -> p(ap(V1P,ap(c_2Enum_2ESUC__REP,V2n)))))) -> p(ap(V1P,V0m)))))))) # label(ax_thm_2Enum_2EIS__NUM__REP) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 460 (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]. 1.98/2.35 461 (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]. 1.98/2.35 462 (exists V0rep (p(ap(ap(c_2Ebool_2ETYPE__DEFINITION(bool,ty_2Eone_2Eone),i(bool)),V0rep)) & mem(V0rep,arr(ty_2Eone_2Eone,bool)))) # label(ax_thm_2Eone_2Eone__TY__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 463 (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]. 1.98/2.35 464 (all V0P (mem(V0P,arr(ty_2Eone_2Eone,bool)) -> ((all V1x (mem(V1x,ty_2Eone_2Eone) -> p(ap(V0P,V1x)))) <-> p(ap(V0P,c_2Eone_2Eone))))) # label(conj_thm_2Eone_2EFORALL__ONE) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 465 (all A_27a all V0e (mem(V0e,A_27a) -> (all V1fn ap(ap(c_2Emin_2E_3D(A_27a),ap(V1fn,c_2Eone_2Eone)),V0e) = ap(f87(A_27a,V0e),V1fn)))) # label(lameq_f87) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 466 (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]. 1.98/2.35 467 (all A_27a (ne(A_27a) -> (all V0e (mem(V0e,A_27a) -> (exists V1fn (mem(V1fn,arr(ty_2Eone_2Eone,A_27a)) & V0e = ap(V1fn,c_2Eone_2Eone))))))) # label(conj_thm_2Eone_2Eone__prim__rec) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 468 (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]. 1.98/2.35 469 (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)) -> V1g = V0f)))))) # label(conj_thm_2Eone_2Eone__axiom) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 470 (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]. 1.98/2.35 471 (all V0v (mem(V0v,ty_2Eone_2Eone) -> c_2Eone_2Eone = V0v)) # label(conj_thm_2Eone_2Eone) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 472 (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]. 1.98/2.35 473 (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]. 1.98/2.35 474 (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_2EINR(A_27a,A_27b),V1y) != ap(c_2Esum_2EINL(A_27a,A_27b),V0x))))))))) # label(conj_thm_2Esum_2Esum__distinct) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 475 (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]. 1.98/2.35 476 (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]. 1.98/2.35 477 (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 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_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]. 1.98/2.35 478 (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]. 1.98/2.35 479 (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(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)) = ap(f96(A_27a,A_27b,A_27c,V0f,V1g),V2h)))))) # label(lameq_f96) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 480 (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]. 1.98/2.35 481 (all A_27a all A_27b all V1v1 (mem(V1v1,A_27a) -> (all V3b ap(f89(A_27a,A_27b,V1v1),V3b) = f88(A_27b,A_27a,V1v1,V3b)))) # label(lameq_f89) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 482 (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]. 1.98/2.35 483 (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]. 1.98/2.35 484 (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]. 1.98/2.35 485 (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_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)) = 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__CASE) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 486 (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]. 1.98/2.35 487 (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__ISL__ISR) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 488 (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)) -> 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]. 1.98/2.35 489 (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]. 1.98/2.35 490 (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]. 1.98/2.35 491 (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)) -> ((all V6a (mem(V6a,A_27a) -> (V1s_27 = ap(c_2Esum_2EINL(A_27a,A_27b),V6a) -> (p(ap(V3P_27,V6a)) <-> p(ap(V2P,V6a)))))) & (all V7b (mem(V7b,A_27b) -> (ap(c_2Esum_2EINR(A_27a,A_27b),V7b) = V1s_27 -> (p(ap(V5Q_27,V7b)) <-> p(ap(V4Q,V7b)))))) & V1s_27 = V0s -> (p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V2P),V4Q),V0s)) <-> p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V3P_27),V5Q_27),V1s_27)))))))))))))))))))) # label(conj_thm_2Esum_2ESUM__ALL__CONG) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 492 (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]. 1.98/2.35 493 (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)))) -> (ap(c_2Esum_2EREP__sum(A_27a,A_27b),ap(c_2Esum_2EABS__sum(A_27a,A_27b),V1r)) = 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]. 1.98/2.35 494 (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 (ap(c_2Esum_2EINL(A_27a,A_27b),V1x) = V0ss & 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]. 1.98/2.35 495 (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]. 1.98/2.35 496 (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)) -> V0x = ap(c_2Esum_2EINR(A_27a,A_27b),ap(c_2Esum_2EOUTR(A_27a,A_27b),V0x))))))))) # label(conj_thm_2Esum_2EINR) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 497 (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 V3y (p(ap(V0P,ap(c_2Esum_2EINR(A_27a,A_27b),V3y))) & mem(V3y,A_27b))) | (exists V2x (p(ap(V0P,ap(c_2Esum_2EINL(A_27a,A_27b),V2x))) & mem(V2x,A_27a))) <-> (exists V1s (mem(V1s,ty_2Esum_2Esum(A_27a,A_27b)) & p(ap(V0P,V1s))))))))))) # label(conj_thm_2Esum_2EEXISTS__SUM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 498 (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]. 1.98/2.35 499 (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 = f91(A_27b,A_27a,V2v2) | V0f = f89(A_27a,A_27b,V1v1)))))) <-> 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]. 1.98/2.35 500 (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]. 1.98/2.35 501 (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]. 1.98/2.35 502 (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]. 1.98/2.35 503 (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]. 1.98/2.35 504 (all A_27b all A_27a all V0e (mem(V0e,A_27a) -> (all V1b (mem(V1b,bool) -> (all V2x k(A_27b,ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27a),V2x),V0e)),V1b)) = ap(f92(A_27b,A_27a,V0e,V1b),V2x)))))) # label(lameq_f92) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 505 (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]. 1.98/2.35 506 (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]. 1.98/2.35 507 (all A_27b all A_27a all V0e (mem(V0e,A_27b) -> (all V1b k(A_27a,f94(A_27b,V0e,V1b)) = ap(f95(A_27b,A_27a,V0e),V1b)))) # label(lameq_f95) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 508 (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]. 1.98/2.35 509 (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]. 1.98/2.35 510 (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]. 1.98/2.35 511 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0y (mem(V0y,A_27a) -> (all V1x (mem(V1x,A_27a) -> (ap(c_2Esum_2EINL(A_27a,A_27b),V1x) = ap(c_2Esum_2EINL(A_27a,A_27b),V0y) <-> V0y = V1x))))) & (all V2y (mem(V2y,A_27b) -> (all V3x (mem(V3x,A_27b) -> (ap(c_2Esum_2EINR(A_27a,A_27b),V2y) = ap(c_2Esum_2EINR(A_27a,A_27b),V3x) <-> V3x = V2y))))))))) # label(conj_thm_2Esum_2EINR__INL__11) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 512 (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]. 1.98/2.35 513 (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]. 1.98/2.35 514 (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]. 1.98/2.35 515 (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 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))))) <-> (all V1s (mem(V1s,ty_2Esum_2Esum(A_27a,A_27b)) -> p(ap(V0P,V1s))))))))))) # label(conj_thm_2Esum_2EFORALL__SUM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 516 (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(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),ap(c_2Esum_2EINL(A_27a,A_27b),V0x)),V1f),V2f1) = ap(V1f,V0x))))))) & (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]. 1.98/2.35 517 (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]. 1.98/2.35 518 (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]. 1.98/2.35 519 (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 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 V7x (mem(V7x,A_27e) -> (all V8y (mem(V8y,A_27f) -> (all V9z (mem(V9z,A_27e) -> (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)) <-> p(V0P) & V7x = V9z))))))) & (all V10x (mem(V10x,A_27g) -> (all V11y (mem(V11y,A_27h) -> (all V12z (mem(V12z,A_27h) -> (V12z = V11y & -p(V0P) <-> 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))))))))) & (all V4x (mem(V4x,A_27c) -> (all V5y (mem(V5y,A_27d) -> (all V6z (mem(V6z,A_27d) -> (-p(V0P) & V6z = V5y <-> 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))))))))) & (all V1x (mem(V1x,A_27a) -> (all V2y (mem(V2y,A_27b) -> (all V3z (mem(V3z,A_27a) -> (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) <-> p(V0P) & V3z = V1x))))))))))))))))))))))))) # label(conj_thm_2Esum_2Econd__sum__expand) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 520 (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 ((all V4y (mem(V4y,A_27b) -> ap(V1g,V4y) = ap(V2h,ap(c_2Esum_2EINR(A_27a,A_27b),V4y)))) & (all V3x (mem(V3x,A_27a) -> ap(V2h,ap(c_2Esum_2EINL(A_27a,A_27b),V3x)) = ap(V0f,V3x))) & mem(V2h,arr(ty_2Esum_2Esum(A_27a,A_27b),A_27c)))))))))))))) # label(conj_thm_2Esum_2Esum__Axiom) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 521 (all A_27b all V0e (mem(V0e,A_27b) -> (all V1b (mem(V1b,bool) -> (all V3y ap(f94(A_27b,V0e,V1b),V3y) = ap(ap(c_2Ebool_2E_2F_5C,ap(ap(c_2Emin_2E_3D(A_27b),V3y),V0e)),ap(c_2Ebool_2E_7E,V1b))))))) # label(lameq_f94) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 522 (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]. 1.98/2.35 523 (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 V1x (mem(V1x,A_27a) -> p(ap(V0P,ap(c_2Esum_2EINL(A_27a,A_27b),V1x))))) & (all V2y (mem(V2y,A_27b) -> p(ap(V0P,ap(c_2Esum_2EINR(A_27a,A_27b),V2y))))) -> (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]. 1.98/2.35 524 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V3P (mem(V3P,arr(A_27a,bool)) -> (all V4Q (mem(V4Q,arr(A_27b,bool)) -> (all V5y (mem(V5y,A_27b) -> (p(ap(V4Q,V5y)) <-> p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V3P),V4Q),ap(c_2Esum_2EINR(A_27a,A_27b),V5y)))))))))) & (all V0P (mem(V0P,arr(A_27a,bool)) -> (all V1Q (mem(V1Q,arr(A_27b,bool)) -> (all V2x (mem(V2x,A_27a) -> (p(ap(ap(ap(c_2Esum_2ESUM__ALL(A_27a,A_27b),V0P),V1Q),ap(c_2Esum_2EINL(A_27a,A_27b),V2x))) <-> p(ap(V0P,V2x))))))))))))) # label(ax_thm_2Esum_2ESUM__ALL__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 525 (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),V0x) = ap(c_2Esum_2EINR(A_27a,A_27b),V1y) <-> V1y = V0x))))))))) # label(conj_thm_2Esum_2EINR__11) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 526 (all A_27b all A_27a all V2v2 (mem(V2v2,A_27b) -> (all V6b ap(f91(A_27b,A_27a,V2v2),V6b) = k(A_27a,f90(A_27b,V2v2,V6b))))) # label(lameq_f91) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 527 (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 V7y (mem(V7y,A_27b) -> (ap(c_2Esum_2EINR(A_27a,A_27b),V7y) = V3M_27 -> ap(V5f1,V7y) = ap(V1f1_27,V7y)))) & (all V6x (mem(V6x,A_27a) -> (V3M_27 = ap(c_2Esum_2EINL(A_27a,A_27b),V6x) -> ap(V0f_27,V6x) = ap(V4f,V6x)))) & V2M = V3M_27 -> ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),V2M),V4f),V5f1) = ap(ap(ap(c_2Esum_2Esum__CASE(A_27a,A_27b,A_27c),V3M_27),V0f_27),V1f1_27)))))))))))))))))))) # label(conj_thm_2Esum_2Esum__case__cong) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 528 (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]. 1.98/2.35 529 (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]. 1.98/2.35 530 (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]. 1.98/2.35 531 (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))) -> (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]. 1.98/2.35 532 (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(V0R1,V4y),V3z)) & p(ap(ap(V1R2,V2x),V4y)) & mem(V4y,A_27h)))))))))))))))))) # label(ax_thm_2Erelation_2EO__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 533 (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]. 1.98/2.35 534 (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]. 1.98/2.35 535 (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)) <-> (exists V3y (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3y),V2z)) & p(ap(ap(V0R,V1x),V3y)) & mem(V3y,A_27a))) | p(ap(ap(V0R,V1x),V2z))))))))))) # label(conj_thm_2Erelation_2ETC__CASES1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 536 (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]. 1.98/2.35 537 (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]. 1.98/2.35 538 (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]. 1.98/2.35 539 (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]. 1.98/2.35 540 (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]. 1.98/2.35 541 (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]. 1.98/2.35 542 (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]. 1.98/2.35 543 (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_2ERC(A_27a),V1R),V4x),V5y)) -> p(ap(V0P,V5y)))))))))))))) # label(conj_thm_2Erelation_2ERC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 544 (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]. 1.98/2.35 545 (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)) -> V1x != V2y)))))))))) # label(conj_thm_2Erelation_2EWF__NOT__REFL) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 546 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1x (mem(V1x,A_27a) -> (all V2z (mem(V2z,A_27a) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2z)) -> (exists V3y (mem(V3y,A_27a) & p(ap(ap(V0R,V1x),V3y)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V3y),V2z)))) | p(ap(ap(V0R,V1x),V2z))))))))))) # label(conj_thm_2Erelation_2ETC__CASES1__E) # label(axiom) # label(non_clause). [assumption]. 1.98/2.35 547 (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]. 1.98/2.35 548 (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]. 1.98/2.35 549 (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]. 1.98/2.35 550 (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]. 1.98/2.35 551 (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]. 1.98/2.35 552 (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]. 1.98/2.35 553 (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]. 1.98/2.35 554 (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]. 1.98/2.35 555 (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]. 1.98/2.35 556 (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]. 1.98/2.35 557 (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]. 1.98/2.35 558 (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]. 1.98/2.35 559 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1a (mem(V1a,A_27a) -> ((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))))) <-> p(ap(ap(c_2Erelation_2EWFP(A_27a),V0R),V1a))))))))) # label(ax_thm_2Erelation_2EWFP__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 560 (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]. 1.98/2.36 561 (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 V3u (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3u),V2y)) & p(ap(ap(V0R,V1x),V3u)) & mem(V3u,A_27a))) | V1x = V2y <-> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__CASES1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 562 (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]. 1.98/2.36 563 (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]. 1.98/2.36 564 (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]. 1.98/2.36 565 (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(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)),V0R))))))) # label(conj_thm_2Erelation_2Esymmetric__inv__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 566 (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 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))))))))))))))) # label(ax_thm_2Erelation_2EWF__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 567 (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]. 1.98/2.36 568 (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]. 1.98/2.36 569 (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]. 1.98/2.36 570 (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,V4x),V5y)) & p(ap(ap(V1P,V5y),V6z)) -> 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]. 1.98/2.36 571 (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))) -> ((all V4f (mem(V4f,arr(A_27a,A_27b)) -> (all V5x (mem(V5x,A_27a) -> (p(ap(V1D,V5x)) & (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(ap(V2P,V5x),ap(ap(V3M,V4f),V5x)))))))) <-> p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V0R),V1D),V2P),V3M))))))))))))))) # label(ax_thm_2Erelation_2EINDUCTIVE__INVARIANT__ON__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 572 (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(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) = ap(f104(A_27b,A_27a,V1M,V0R),V2x)))))) # label(lameq_f104) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 573 (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]. 1.98/2.36 574 (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]. 1.98/2.36 575 (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]. 1.98/2.36 576 (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]. 1.98/2.36 577 (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]. 1.98/2.36 578 (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]. 1.98/2.36 579 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0x (mem(V0x,A_27a) -> (all V1y (mem(V1y,A_27b) -> (p(ap(ap(c_2Erelation_2ERUNIV(A_27a,A_27b),V0x),V1y)) <-> $T))))))))) # label(ax_thm_2Erelation_2ERUNIV) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 580 (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]. 1.98/2.36 581 (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]. 1.98/2.36 582 (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]. 1.98/2.36 583 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ETC(A_27a),V0R) = ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ETC__IDEM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 584 (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]. 1.98/2.36 585 (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]. 1.98/2.36 586 (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]. 1.98/2.36 587 (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]. 1.98/2.36 588 (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]. 1.98/2.36 589 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(ap(c_2Erelation_2ERINTER(A_27a,A_27a),V0R),ap(c_2Erelation_2ERCOMPL(A_27a,A_27a),c_2Emin_2E_3D(A_27a))) = ap(c_2Erelation_2ESTRORD(A_27a),V0R))))) # label(conj_thm_2Erelation_2ESTRORD__AND__NOT__Id) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 590 (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]. 1.98/2.36 591 (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_2ETC(A_27a),ap(c_2Erelation_2ERC(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_2ESC(A_27a),V0R)) = ap(c_2Erelation_2ESC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ERC__MOVES__OUT) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 592 (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 | (exists V3u (mem(V3u,A_27a) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V3u)) & p(ap(ap(V0R,V3u),V2y)))) <-> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__CASES2) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 593 (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_2Eirreflexive(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))))) # label(conj_thm_2Erelation_2Eirreflexive__inv) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 594 (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]. 1.98/2.36 595 (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]. 1.98/2.36 596 (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]. 1.98/2.36 597 (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]. 1.98/2.36 598 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (c_2Erelation_2EEMPTY__REL(A_27a) = V0R <-> p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27a),V0R),c_2Erelation_2EEMPTY__REL(A_27a)))) & 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]. 1.98/2.36 599 (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,V5y) = ap(V1f,V4x))))))))))))))) # label(conj_thm_2Erelation_2ETC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 600 (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) -> (p(ap(ap(V0R,V1y),V2z)) & p(ap(ap(V0R,V2z),V1y)) <-> V1y = V2z)))))))))) # label(conj_thm_2Erelation_2EWeakOrder__EQ) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 601 (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(ap(V1M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V3f),V0R),V4y)),V4y) = ap(f100(A_27b,A_27a,V1M,V0R,V3f),V4y)))))))) # label(lameq_f100) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 602 (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]. 1.98/2.36 603 (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]. 1.98/2.36 604 (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]. 1.98/2.36 605 (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__CASES) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 606 (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]. 1.98/2.36 607 (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(ap(ap(c_2Erelation_2ERRESTRICT(A_27a,A_27b),V0R),V1s),V2x),V3y)) <-> p(ap(ap(c_2Ebool_2EIN(A_27a),V2x),V1s)) & p(ap(ap(V0R,V2x),V3y))))))))))))))) # label(ax_thm_2Erelation_2ERRESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 608 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EStrongOrder(A_27a),ap(c_2Erelation_2ESTRORD(A_27a),V0R))) <-> p(ap(c_2Erelation_2EOrder(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ESTRORD__Strong) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 609 (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]. 1.98/2.36 610 (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]. 1.98/2.36 611 (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 (mem(V2y,A_27b) & p(ap(ap(V0R,V1x),V2y)))) <-> p(ap(ap(c_2Erelation_2ERDOM(A_27a,A_27b),V0R),V1x))))))))))) # label(ax_thm_2Erelation_2ERDOM__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 612 (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__EQ__INDUCTION__THM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 613 (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]. 1.98/2.36 614 (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]. 1.98/2.36 615 (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_2ERC(A_27a),V0R))) <-> p(ap(c_2Erelation_2Eantisymmetric(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Eantisymmetric__RC) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 616 (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]. 1.98/2.36 617 (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),V1R2),V0R1)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0R1),V1R2)) -> V1R2 = V0R1))))))))) # label(conj_thm_2Erelation_2ERSUBSET__ANTISYM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.36 618 (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]. 1.98/2.36 619 (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]. 1.98/2.38 620 (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]. 1.98/2.38 621 (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_2ESC(A_27a),V0R) = V0R))))) # label(conj_thm_2Erelation_2Esymmetric__SC__identity) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 622 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2ERC(A_27a),V0R) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2ERC__IDEM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 623 (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(ap(c_2Erelation_2ERTC(A_27a),V0R),V4y),V5z)) & p(ap(ap(V1P,V4y),V5z)) & p(ap(ap(V0R,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__STRONG__INDUCT) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 624 (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]. 1.98/2.38 625 (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]. 1.98/2.38 626 (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)) -> (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]. 1.98/2.38 627 (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_2ESC(A_27a),V0R),V1x),V2y)) <-> p(ap(ap(V0R,V2y),V1x)) | p(ap(ap(V0R,V1x),V2y))))))))))) # label(ax_thm_2Erelation_2ESC__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 628 (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_2Ereflexive(A_27a),V0R)) <-> p(ap(c_2Erelation_2EPreOrder(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EPreOrder) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 629 (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 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 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),V7x),V8y)) & p(ap(ap(ap(c_2Erelation_2EEQC(A_27a),V0R),V8y),V9z)) -> p(ap(ap(V1P,V7x),V9z))))))))) & (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]. 1.98/2.38 630 (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]. 1.98/2.38 631 (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 (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2y),V4u)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3z),V4u)) & mem(V4u,A_27a)))))))))) <-> p(ap(c_2Erelation_2EWCR(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EWCR__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 632 (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__EQN) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 633 (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]. 1.98/2.38 634 (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]. 1.98/2.38 635 (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]. 1.98/2.38 636 (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_2ERTC(A_27a),V0R),V1a),V2b)) <-> (all V3Q (mem(V3Q,arr(A_27a,bool)) -> ((all V4y (mem(V4y,A_27a) -> (all V5z (mem(V5z,A_27a) -> (p(ap(V3Q,V4y)) & p(ap(ap(V0R,V4y),V5z)) -> p(ap(V3Q,V5z))))))) & p(ap(V3Q,V1a)) -> p(ap(V3Q,V2b)))))))))))))) # label(conj_thm_2Erelation_2ERTC__ALT__RIGHT__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 637 (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]. 1.98/2.38 638 (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)) -> ap(c_2Erelation_2Einv(A_27a,A_27a),V0R) = V0R))))) # label(conj_thm_2Erelation_2Eequivalence__inv__identity) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 639 (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_2ETC(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_2ERC(A_27a),V0R)) = ap(c_2Erelation_2EEQC(A_27a),V0R))))) # label(conj_thm_2Erelation_2EEQC__MOVES__IN) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 640 (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))) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0y),ap(c_2Erelation_2ERRANGE(A_27b,A_27a),V1R))) <-> (exists V2x (mem(V2x,A_27b) & p(ap(ap(V1R,V2x),V0y))))))))))))) # label(conj_thm_2Erelation_2EIN__RRANGE) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 641 (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]. 1.98/2.38 642 (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(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V2y)) <-> (exists V3u (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V3u)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3u),V2y)) & mem(V3u,A_27a)))))))))))) # label(conj_thm_2Erelation_2ERTC__CASES__RTC__TWICE) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 643 (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]. 1.98/2.38 644 (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]. 1.98/2.38 645 (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]. 1.98/2.38 646 (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]. 1.98/2.38 647 (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]. 1.98/2.38 648 (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]. 1.98/2.38 649 (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]. 1.98/2.38 650 (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]. 1.98/2.38 651 (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]. 1.98/2.38 652 (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_27a,A_27b),V0R1),V1R2)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27c,A_27a),V2S1),V3S2)) -> 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]. 1.98/2.38 653 (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]. 1.98/2.38 654 (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)) <-> (all V1x (mem(V1x,A_27a) -> p(ap(ap(V0R,V1x),V1x))))))))) # label(ax_thm_2Erelation_2Ereflexive__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 655 (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]. 1.98/2.38 656 (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(c_2Erelation_2Einv(A_27b,A_27a),ap(c_2Erelation_2Einv(A_27a,A_27b),V0R)))))))) # label(conj_thm_2Erelation_2Einv__inv) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 657 (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),ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V1R1),V2R2)))) <-> 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),V1R1)))))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM__RUNION) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 658 (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]. 1.98/2.38 659 (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(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) & p(ap(ap(V1P,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]. 1.98/2.38 660 (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]. 1.98/2.38 661 (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]. 1.98/2.38 662 (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]. 1.98/2.38 663 (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]. 1.98/2.38 664 (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]. 1.98/2.38 665 (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_2ERC(A_27a),V0R),V1x),V2y)) | p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V1x),V2y))))))))))) # label(conj_thm_2Erelation_2ERTC__TC__RC) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 666 (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]. 1.98/2.38 667 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> (p(ap(c_2Erelation_2EIDEM(A_27z),V0f)) <-> (all V1x (mem(V1x,A_27z) -> ap(V0f,ap(V0f,V1x)) = ap(V0f,V1x)))))))) # label(conj_thm_2Erelation_2EIDEM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 668 (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]. 1.98/2.38 669 (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]. 1.98/2.38 670 (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)) -> V0R = ap(c_2Erelation_2ERC(A_27a),V0R)))))) # label(conj_thm_2Erelation_2Ereflexive__RC__identity) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 671 (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_2ETC(A_27a),V0R),V1x),V3y)) & p(ap(ap(V0R,V3y),V2z)))) | p(ap(ap(V0R,V1x),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]. 1.98/2.38 672 (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(ap(c_2Erelation_2ETC(A_27a),V0R),V5y),V6z)) & p(ap(ap(V1P,V5y),V6z)) & p(ap(ap(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__LEFT1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 673 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Etransitive(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R))) <-> p(ap(c_2Erelation_2Etransitive(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Etransitive__inv) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 674 (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_2Einv(A_27a,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]. 1.98/2.38 675 (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))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V1z),V0y)) & p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),V0y),V1z)) <-> V1z = V0y))))))))) # label(conj_thm_2Erelation_2EEqIsBothRSUBSET) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 676 (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]. 1.98/2.38 677 (all A_27g (ne(A_27g) -> (all V0Z (mem(V0Z,arr(A_27g,arr(A_27g,bool))) -> (p(ap(c_2Erelation_2Ereflexive(A_27g),V0Z)) & p(ap(c_2Erelation_2Eantisymmetric(A_27g),V0Z)) & p(ap(c_2Erelation_2Etransitive(A_27g),V0Z)) <-> p(ap(c_2Erelation_2EWeakOrder(A_27g),V0Z))))))) # label(ax_thm_2Erelation_2EWeakOrder) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 678 (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(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 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__STRONG__INDUCT__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 679 (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),V0R1),V1R2) = ap(ap(c_2Erelation_2ERINTER(A_27a,A_27b),V1R2),V0R1))))))))) # label(conj_thm_2Erelation_2ERINTER__COMM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 680 (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]. 1.98/2.38 681 (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]. 1.98/2.38 682 (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),V2s)) & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V1R)))))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM__RRESTRICT) # label(axiom) # label(non_clause). [assumption]. 1.98/2.38 683 (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]. 1.98/2.38 684 (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)) -> V0R = ap(c_2Erelation_2ESTRORD(A_27a),ap(c_2Erelation_2ERC(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ESTRORD__RC) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 685 (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]. 1.98/2.39 686 (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(ap(c_2Erelation_2ERCOMPL(A_27a,A_27b),V0R),V1x),V2y)) <-> -p(ap(ap(V0R,V1x),V2y))))))))))))) # label(ax_thm_2Erelation_2ERCOMPL) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 687 (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]. 1.98/2.39 688 (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]. 1.98/2.39 689 (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,V4x),V5y)) & p(ap(ap(V0R,V5y),V6z)) -> 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 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]. 1.98/2.39 690 (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]. 1.98/2.39 691 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> ap(ap(c_2Erelation_2EO(A_27a,A_27a,A_27b),V0R),c_2Emin_2E_3D(A_27a)) = V0R)))))) # label(conj_thm_2Erelation_2EO__Id) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 692 (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]. 1.98/2.39 693 (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]. 1.98/2.39 694 (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]. 1.98/2.39 695 (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]. 1.98/2.39 696 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2EStrongLinearOrder(A_27a),V0R)) <-> p(ap(c_2Erelation_2EStrongOrder(A_27a),V0R)) & p(ap(c_2Erelation_2Etrichotomous(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EStrongLinearOrder) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 697 (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]. 1.98/2.39 698 (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_2ERC(A_27a),ap(c_2Erelation_2ETC(A_27a),ap(c_2Erelation_2ESC(A_27a),V0R))))))) # label(ax_thm_2Erelation_2EEQC__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 699 (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]. 1.98/2.39 700 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ercdiamond(A_27a),V0R)) -> p(ap(c_2Erelation_2ECR(A_27a),V0R))) & (p(ap(c_2Erelation_2Ediamond(A_27a),V0R)) -> p(ap(c_2Erelation_2ECR(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Eestablish__CR) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 701 (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)) & V2y != V1x -> (exists V3z (mem(V3z,A_27a) & V1x != V3z & p(ap(ap(V0R,V1x),V3z))))))))))))) # label(conj_thm_2Erelation_2ETC__implies__one__step) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 702 (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]. 1.98/2.39 703 (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)) -> f98(A_27b,A_27a,V0R,V1f) = ap(ap(c_2Erelation_2Einv__image(A_27a,A_27b),V0R),V1f))))))))) # label(ax_thm_2Erelation_2Einv__image__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 704 (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]. 1.98/2.39 705 (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(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)) = ap(f105(A_27b,A_27a,V0R,V1M,V2f),V3x)))))))) # label(lameq_f105) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 706 (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]. 1.98/2.39 707 (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]. 1.98/2.39 708 (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_2ETC(A_27a),V0R),V1a),V2b)) <-> (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,V7y),V8z)) & p(ap(ap(V3P,V6x),V7y)) -> 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)))))))))))))) # label(ax_thm_2Erelation_2ETC__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 709 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ((all V1x (mem(V1x,A_27a) -> (all 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]. 1.98/2.39 710 (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]. 1.98/2.39 711 (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]. 1.98/2.39 712 (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)) <-> (exists V3y (p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V3y),V2z)) & p(ap(ap(V0R,V1x),V3y)) & mem(V3y,A_27a)))))))))))) # label(conj_thm_2Erelation_2EEXTEND__RTC__TC__EQN) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 713 (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]. 1.98/2.39 714 (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]. 1.98/2.39 715 (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]. 1.98/2.39 716 (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(c_2Erelation_2EWF(A_27a),V1R)) & p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V1R),V2D),V3P),V4M)) & p(ap(V2D,V5x)) & 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]. 1.98/2.39 717 (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]. 1.98/2.39 718 (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)) <-> V2y = V1x & p(ap(ap(c_2Ebool_2EIN(A_27a),V1x),V0A))))))))))) # label(ax_thm_2Erelation_2Ediag__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 719 (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]. 1.98/2.39 720 (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]. 1.98/2.39 721 (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]. 1.98/2.39 722 (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]. 1.98/2.39 723 (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]. 1.98/2.39 724 (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(c_2Erelation_2EWF(A_27a),V0R)) & p(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V0R),V1P),V2M)) -> (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]. 1.98/2.39 725 (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_2Etransitive(A_27a),V0R)) & p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) <-> p(ap(c_2Erelation_2Eequivalence(A_27a),V0R))))))) # label(ax_thm_2Erelation_2Eequivalence__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 726 (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),V2y)) & p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V2y),V3z)) -> 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]. 1.98/2.39 727 (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]. 1.98/2.39 728 (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]. 1.98/2.39 729 (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)) | V1x = V2y))))))))) # label(conj_thm_2Erelation_2ERTC__CASES__TC) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 730 (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]. 1.98/2.39 731 (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,V3x),V4y)) & p(ap(ap(V1P,V4y),V5z)) -> 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) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 732 (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]. 1.98/2.39 733 (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(ap(ap(ap(c_2Erelation_2Eapprox(A_27a,A_27b),V0R),V1M),V2x),V3f) = ap(f101(A_27a,A_27b,V2x,V0R,V1M),V3f)))))))) # label(lameq_f101) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 734 (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(V0R1,V2x),V3y)) | p(ap(ap(V1R2,V2x),V3y)) <-> p(ap(ap(ap(ap(c_2Erelation_2ERUNION(A_27a,A_27b),V0R1),V1R2),V2x),V3y))))))))))))))) # label(ax_thm_2Erelation_2ERUNION) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 735 (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]. 1.98/2.39 736 (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]. 1.98/2.39 737 (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 V4x (mem(V4x,A_27a) -> (all V5y (mem(V5y,A_27a) -> (p(ap(V2Q,V4x)) & p(ap(ap(V1R,V4x),V5y)) -> p(ap(V2Q,V5y))))))) & (all V3y (mem(V3y,A_27a) -> (p(ap(ap(V1R,V0a),V3y)) -> p(ap(V2Q,V3y))))) -> (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]. 1.98/2.39 738 (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 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)))))))) <-> p(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V0R),V1P),V2M))))))))))))) # label(ax_thm_2Erelation_2EINDUCTIVE__INVARIANT__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 739 (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,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))))))))))))) # label(conj_thm_2Erelation_2ERTC__RULES__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 740 (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]. 1.98/2.39 741 (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(c_2Erelation_2EWF(A_27a),V0R)) & p(ap(V3D,V4x)) & p(ap(ap(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT__ON(A_27a,A_27b),V0R),V3D),V1P),V2M)) -> 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]. 1.98/2.39 742 (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]. 1.98/2.39 743 (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]. 1.98/2.39 744 (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]. 1.98/2.39 745 (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(ap(ap(c_2Erelation_2ETC(A_27a),V1R),V4x),V5y)) & p(ap(V0P,V4x)) -> p(ap(V0P,V5y)))))))))))))) # label(conj_thm_2Erelation_2ETC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 746 (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]. 1.98/2.39 747 (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),c_2Emin_2E_3D(A_27a)),V0R)) <-> p(ap(c_2Erelation_2Ereflexive(A_27a),V0R))))))) # label(conj_thm_2Erelation_2Ereflexive__Id__RSUBSET) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 748 (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]. 1.98/2.39 749 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)))))) # label(conj_thm_2Erelation_2Einv__RC) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 750 (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]. 1.98/2.39 751 (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(ap(V0M,ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V2f),V1R),V3x)),V3x) = ap(V2f,V3x))))))))))))))) # label(conj_thm_2Erelation_2EWFREC__COROLLARY) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 752 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Ercdiamond(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(ap(c_2Erelation_2ERC(A_27a),V0R),V3z),V4u)) & p(ap(ap(ap(c_2Erelation_2ERC(A_27a),V0R),V2y),V4u)) & mem(V4u,A_27a))))))))))))))) # label(ax_thm_2Erelation_2Ercdiamond__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 753 (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(V1P,V5y),V6z)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),V4x),V5y)) & p(ap(ap(ap(c_2Erelation_2ETC(A_27a),V0R),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) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 754 (all A_27g (ne(A_27g) -> (all V0Z (mem(V0Z,arr(A_27g,arr(A_27g,bool))) -> (p(ap(c_2Erelation_2EOrder(A_27g),V0Z)) <-> p(ap(c_2Erelation_2Etransitive(A_27g),V0Z)) & p(ap(c_2Erelation_2Eantisymmetric(A_27g),V0Z))))))) # label(ax_thm_2Erelation_2EOrder) # label(axiom) # label(non_clause). [assumption]. 1.98/2.39 755 (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]. 1.98/2.39 756 (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]. 1.98/2.39 757 (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(V0R,V2b),V1a)) | p(ap(ap(V0R,V1a),V2b)))))) & p(ap(c_2Erelation_2EWeakOrder(A_27a),V0R)) <-> p(ap(c_2Erelation_2EWeakLinearOrder(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EWeakLinearOrder__dichotomy) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 758 (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]. 1.98/2.40 759 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all V1Q (mem(V1Q,arr(A_27a,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]. 1.98/2.40 760 (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]. 1.98/2.40 761 (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_2EOrder(A_27a),V0R)) <-> p(ap(c_2Erelation_2ELinearOrder(A_27a),V0R))))))) # label(ax_thm_2Erelation_2ELinearOrder) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 762 (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))) -> f104(A_27b,A_27a,V1M,V0R) = ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V0R),V1M))))))))) # label(ax_thm_2Erelation_2EWFREC__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 763 (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]. 1.98/2.40 764 (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]. 1.98/2.40 765 (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]. 1.98/2.40 766 (all A_27z (ne(A_27z) -> (all V0f (mem(V0f,arr(A_27z,A_27z)) -> (p(ap(c_2Erelation_2EIDEM(A_27z),V0f)) <-> V0f = ap(ap(c_2Ecombin_2Eo(A_27z,A_27z,A_27z),V0f),V0f)))))) # label(ax_thm_2Erelation_2EIDEM__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 767 (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(V0R,ap(V1f,V2x)),ap(V1f,V3y))) <-> p(ap(ap(ap(ap(c_2Erelation_2Einv__image(A_27a,A_27b),V0R),V1f),V2x),V3y))))))))))))))) # label(conj_thm_2Erelation_2Einv__image__thm) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 768 (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]. 1.98/2.40 769 (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(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__RIGHT1) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 770 (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) -> (V2b = ap(V0f,V1a) <-> ap(V0f,V2b) = V1a)))))))))) # label(conj_thm_2Erelation_2EINVOL__ONE__ENO) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 771 (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]. 1.98/2.40 772 (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(ap(V0R,ap(V1f,V2x)),ap(V1f,V3y)) = ap(f97(A_27b,A_27a,V0R,V2x,V1f),V3y)))))))) # label(lameq_f97) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 773 (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]. 1.98/2.40 774 (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))) -> (p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V1R))) <-> (exists V2y (p(ap(ap(V1R,V0x),V2y)) & mem(V2y,A_27b)))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 775 (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]. 1.98/2.40 776 (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]. 1.98/2.40 777 (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) -> (p(ap(ap(ap(c_2Erelation_2ETC(A_27a),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(V0R,V1x),V2z))))))))))) # label(conj_thm_2Erelation_2ETC__CASES2__E) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 778 (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),V1R2)) & p(ap(c_2Erelation_2Etransitive(A_27a),V0R1)) -> 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]. 1.98/2.40 779 (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]. 1.98/2.40 780 (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) -> (V2b = V1a <-> ap(V0f,V1a) = ap(V0f,V2b))))))))))) # label(conj_thm_2Erelation_2EINVOL__ONE__ONE) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 781 (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,V2y),V1x)) & p(ap(ap(V0R,V1x),V2y)) -> V1x = V2y)))))))))) # label(ax_thm_2Erelation_2Eantisymmetric__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 782 (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]. 1.98/2.40 783 (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) -> f99(A_27b,A_27a,V0f,V2x,V1R) = ap(ap(ap(c_2Erelation_2ERESTRICT(A_27a,A_27b),V0f),V1R),V2x))))))))))) # label(ax_thm_2Erelation_2ERESTRICT__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 784 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2ECR(A_27a),V0R)) <-> p(ap(c_2Erelation_2Ediamond(A_27a),ap(c_2Erelation_2ERTC(A_27a),V0R)))))))) # label(ax_thm_2Erelation_2ECR__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 785 (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]. 1.98/2.40 786 (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]. 1.98/2.40 787 (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]. 1.98/2.40 788 (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]. 1.98/2.40 789 (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 f102(A_27b,A_27a,V1M,V0R,V3f) = ap(f103(A_27b,A_27a,V1M,V0R),V3f)))))) # label(lameq_f103) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 790 (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]. 1.98/2.40 791 (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]. 1.98/2.40 792 (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]. 1.98/2.40 793 (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(ap(ap(c_2Erelation_2ERDOM__DELETE(A_27a,A_27b),V0R),V1x),V2u),V3v)) <-> p(ap(ap(V0R,V2u),V3v)) & V2u != V1x))))))))))))) # label(ax_thm_2Erelation_2ERDOM__DELETE__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 794 (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]. 1.98/2.40 795 (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_2ERC(A_27a),V0R)) = ap(c_2Erelation_2ERTC(A_27a),V0R) & ap(c_2Erelation_2ERC(A_27a),ap(c_2Erelation_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ERTC(A_27a),V0R))))) # label(conj_thm_2Erelation_2ETC__RC__EQNS) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 796 (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(ap(ap(c_2Erelation_2ERTC(A_27a),V1R),V4x),V5y)) & p(ap(V0P,V4x)) -> p(ap(V0P,V5y)))))))))))))) # label(conj_thm_2Erelation_2ERTC__lifts__invariants) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 797 (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),ap(ap(c_2Erelation_2ERDOM__DELETE(A_27a,A_27b),V1R),V2k)))) <-> V0x != V2k & p(ap(ap(c_2Ebool_2EIN(A_27a),V0x),ap(c_2Erelation_2ERDOM(A_27a,A_27b),V1R)))))))))))))) # label(conj_thm_2Erelation_2EIN__RDOM__DELETE) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 798 (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]. 1.98/2.40 799 (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]. 1.98/2.40 800 (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]. 1.98/2.40 801 (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]. 1.98/2.40 802 (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]. 1.98/2.40 803 (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]. 1.98/2.40 804 (all A_27g (ne(A_27g) -> (all V0Z (mem(V0Z,arr(A_27g,arr(A_27g,bool))) -> (p(ap(c_2Erelation_2Eirreflexive(A_27g),V0Z)) & p(ap(c_2Erelation_2Etransitive(A_27g),V0Z)) <-> p(ap(c_2Erelation_2EStrongOrder(A_27g),V0Z))))))) # label(ax_thm_2Erelation_2EStrongOrder) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 805 (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]. 1.98/2.40 806 (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]. 1.98/2.40 807 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27b,bool))) -> (p(ap(ap(c_2Erelation_2ERSUBSET(A_27a,A_27b),c_2Erelation_2ERUNIV(A_27a,A_27b)),V0R)) <-> 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]. 1.98/2.40 808 (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)) & p(ap(c_2Erelation_2ESN(A_27a),V0R)) -> p(ap(c_2Erelation_2ECR(A_27a),V0R))))))) # label(conj_thm_2Erelation_2ENewmans__lemma) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 809 (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]. 1.98/2.40 810 (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]. 1.98/2.40 811 (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_2ERTC(A_27a),V0R),V4x),V5y)) -> ap(V1f,V5y) = ap(V1f,V4x))))))))))))))) # label(conj_thm_2Erelation_2ERTC__lifts__equalities) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 812 (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]. 1.98/2.40 813 (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]. 1.98/2.40 814 (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]. 1.98/2.40 815 (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,V2y) = ap(V0R,V1x)))))) <-> p(ap(c_2Erelation_2Eequivalence(A_27a),V0R))))))) # label(conj_thm_2Erelation_2EALT__equivalence) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 816 (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_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERC(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_2ETC(A_27a),V0R)) = ap(c_2Erelation_2ETC(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_2ERTC(A_27a),ap(c_2Erelation_2Einv(A_27a,A_27a),V0R)) = ap(c_2Erelation_2Einv(A_27a,A_27a),ap(c_2Erelation_2ERTC(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))))) # label(conj_thm_2Erelation_2Einv__MOVES__OUT) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 817 (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]. 1.98/2.40 818 (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_2ERTC(A_27a),V0R),V1a),V2b)) <-> (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(V3P,V6y),V7z)) & p(ap(ap(V0R,V5x),V6y)) -> p(ap(ap(V3P,V5x),V7z))))))))) -> p(ap(ap(V3P,V1a),V2b)))))))))))))) # label(ax_thm_2Erelation_2ERTC__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 819 (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,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))))))))) & (all V1x (mem(V1x,A_27a) -> p(ap(ap(ap(c_2Erelation_2ERTC(A_27a),V0R),V1x),V1x)))))))) # label(conj_thm_2Erelation_2ERTC__RULES) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 820 (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]. 1.98/2.40 821 (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]. 1.98/2.40 822 (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]. 1.98/2.40 823 (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(ap(ap(c_2Erelation_2EINDUCTIVE__INVARIANT(A_27a,A_27b),V1R),V2P),V3M)) & p(ap(c_2Erelation_2EWF(A_27a),V1R)) & ap(ap(c_2Erelation_2EWFREC(A_27a,A_27b),V1R),V3M) = V0f -> p(ap(ap(V2P,V4x),ap(V0f,V4x)))))))))))))))))) # label(conj_thm_2Erelation_2ETFL__INDUCTIVE__INVARIANT__WFREC) # label(axiom) # label(non_clause). [assumption]. 1.98/2.40 824 (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]. 1.98/2.40 825 (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) -> (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]. 1.98/2.41 826 (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]. 1.98/2.41 827 (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]. 1.98/2.41 828 (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),V3z)) & p(ap(ap(V0R,V1x),V2y)) -> (exists V4u (p(ap(ap(V0R,V3z),V4u)) & p(ap(ap(V0R,V2y),V4u)) & mem(V4u,A_27a))))))))))))))) # label(ax_thm_2Erelation_2Ediamond__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 829 (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]. 1.98/2.41 830 (all A_27a (ne(A_27a) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (p(ap(c_2Erelation_2Esymmetric(A_27a),V0R)) -> ap(c_2Erelation_2Einv(A_27a,A_27a),V0R) = V0R))))) # label(conj_thm_2Erelation_2Esymmetric__inv__identity) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 831 (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]. 1.98/2.41 832 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all 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]. 1.98/2.41 833 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (all V0R (mem(V0R,arr(A_27a,arr(A_27a,bool))) -> (all 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]. 1.98/2.41 834 (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]. 1.98/2.41 835 (all A_27a (ne(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)) & c_2Eoption_2ENONE(A_27a) = ap(c_2Eoption_2EOPTION__JOIN(A_27a),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a))))) # label(ax_thm_2Eoption_2EOPTION__JOIN__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 836 (all A_27a (ne(A_27a) -> (p(ap(c_2Eoption_2EIS__NONE(A_27a),c_2Eoption_2ENONE(A_27a))) <-> $T) & (all V0x (mem(V0x,A_27a) -> ($F <-> p(ap(c_2Eoption_2EIS__NONE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V0x)))))))) # label(ax_thm_2Eoption_2EIS__NONE__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 837 (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]. 1.98/2.41 838 (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]. 1.98/2.41 839 (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]. 1.98/2.41 840 (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]. 1.98/2.41 841 (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 (ap(V2fn,c_2Eoption_2ENONE(A_27a)) = V0e & (all V3x (mem(V3x,A_27a) -> ap(V2fn,ap(c_2Eoption_2ESOME(A_27a),V3x)) = ap(V1f,V3x))) & mem(V2fn,arr(ty_2Eoption_2Eoption(A_27a),A_27b)))))))))))) # label(conj_thm_2Eoption_2Eoption__Axiom) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 842 (all A_27a (ne(A_27a) -> (all A_27b (ne(A_27b) -> (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)))) & (all V0f (mem(V0f,arr(A_27a,A_27b)) -> (all V1x (mem(V1x,A_27a) -> ap(c_2Eoption_2ESOME(A_27b),ap(V0f,V1x)) = ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V0f),ap(c_2Eoption_2ESOME(A_27a),V1x)))))))))) # label(ax_thm_2Eoption_2EOPTION__MAP__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 843 (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]. 1.98/2.41 844 (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]. 1.98/2.41 845 (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]. 1.98/2.41 846 (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]. 1.98/2.41 847 (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]. 1.98/2.41 848 (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_2Eoption_2EOPTION__MAP2(A_27a,A_27b,A_27c),V0f),V1x),V2y) = 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)))))))))))))) # label(ax_thm_2Eoption_2EOPTION__MAP2__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 849 (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]. 1.98/2.41 850 (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]. 1.98/2.41 851 (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]. 1.98/2.41 852 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> V0x = ap(c_2Eoption_2ETHE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V0x)))))) # label(ax_thm_2Eoption_2ETHE__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 853 (all A_27a (ne(A_27a) -> (all V0opt (mem(V0opt,ty_2Eoption_2Eoption(A_27a)) -> c_2Eoption_2ENONE(A_27a) = V0opt | (exists V1x (mem(V1x,A_27a) & V0opt = ap(c_2Eoption_2ESOME(A_27a),V1x))))))) # label(conj_thm_2Eoption_2Eoption__nchotomy) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 854 (all A_27a (ne(A_27a) -> (all V0P (mem(V0P,arr(ty_2Eoption_2Eoption(A_27a),bool)) -> ((exists V1opt (p(ap(V0P,V1opt)) & mem(V1opt,ty_2Eoption_2Eoption(A_27a)))) <-> (exists V2x (p(ap(V0P,ap(c_2Eoption_2ESOME(A_27a),V2x))) & mem(V2x,A_27a))) | p(ap(V0P,c_2Eoption_2ENONE(A_27a)))))))) # label(conj_thm_2Eoption_2EEXISTS__OPTION) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 855 (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]. 1.98/2.41 856 (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]. 1.98/2.41 857 (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]. 1.98/2.41 858 (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]. 1.98/2.41 859 (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(V4f,V2x) = ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),ap(c_2Eoption_2ESOME(A_27a),V2x)),V3v),V4f))))))) & (all V0v (mem(V0v,A_27b) -> (all V1f (mem(V1f,arr(A_27a,A_27b)) -> ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),c_2Eoption_2ENONE(A_27a)),V0v),V1f) = V0v)))))))) # label(ax_thm_2Eoption_2Eoption__case__def) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 860 (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]. 1.98/2.41 861 (all A_27a (ne(A_27a) -> (all V0x (mem(V0x,A_27a) -> ($T <-> p(ap(c_2Eoption_2EIS__SOME(A_27a),ap(c_2Eoption_2ESOME(A_27a),V0x)))))) & (p(ap(c_2Eoption_2EIS__SOME(A_27a),c_2Eoption_2ENONE(A_27a))) <-> $F))) # label(ax_thm_2Eoption_2EIS__SOME__DEF) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 862 (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]. 1.98/2.41 863 (all A0 (ne(A0) -> ne(ty_2Eoption_2Eoption(A0)))) # label(ne_ty_2Eoption_2Eoption) # label(axiom) # label(non_clause). [assumption]. 1.98/2.41 864 (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_2EoptioAlarm clock 119.90/120.09 Prover9 interrupted 119.90/120.10 EOF