0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.23 % Computer : n169.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 06:33:12 CDT 2018 0.03/0.23 % CPUTime : 13.73/13.81 ============================== Prover9 =============================== 13.73/13.81 Prover9 (32) version 2009-11A, November 2009. 13.73/13.81 Process 47289 was started by sandbox2 on n169.star.cs.uiowa.edu, 13.73/13.81 Sat Jul 14 06:33:23 2018 13.73/13.81 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_47246_n169.star.cs.uiowa.edu". 13.73/13.81 ============================== end of head =========================== 13.73/13.81 13.73/13.81 ============================== INPUT ================================= 13.73/13.81 13.73/13.81 % Reading from file /tmp/Prover9_47246_n169.star.cs.uiowa.edu 13.73/13.81 13.73/13.81 set(prolog_style_variables). 13.73/13.81 set(auto2). 13.73/13.81 % set(auto2) -> set(auto). 13.73/13.81 % set(auto) -> set(auto_inference). 13.73/13.81 % set(auto) -> set(auto_setup). 13.73/13.81 % set(auto_setup) -> set(predicate_elim). 13.73/13.81 % set(auto_setup) -> assign(eq_defs, unfold). 13.73/13.81 % set(auto) -> set(auto_limits). 13.73/13.81 % set(auto_limits) -> assign(max_weight, "100.000"). 13.73/13.81 % set(auto_limits) -> assign(sos_limit, 20000). 13.73/13.81 % set(auto) -> set(auto_denials). 13.73/13.81 % set(auto) -> set(auto_process). 13.73/13.81 % set(auto2) -> assign(new_constants, 1). 13.73/13.81 % set(auto2) -> assign(fold_denial_max, 3). 13.73/13.81 % set(auto2) -> assign(max_weight, "200.000"). 13.73/13.81 % set(auto2) -> assign(max_hours, 1). 13.73/13.81 % assign(max_hours, 1) -> assign(max_seconds, 3600). 13.73/13.81 % set(auto2) -> assign(max_seconds, 0). 13.73/13.81 % set(auto2) -> assign(max_minutes, 5). 13.73/13.81 % assign(max_minutes, 5) -> assign(max_seconds, 300). 13.73/13.81 % set(auto2) -> set(sort_initial_sos). 13.73/13.81 % set(auto2) -> assign(sos_limit, -1). 13.73/13.81 % set(auto2) -> assign(lrs_ticks, 3000). 13.73/13.81 % set(auto2) -> assign(max_megs, 400). 13.73/13.81 % set(auto2) -> assign(stats, some). 13.73/13.81 % set(auto2) -> clear(echo_input). 13.73/13.81 % set(auto2) -> set(quiet). 13.73/13.81 % set(auto2) -> clear(print_initial_clauses). 13.73/13.81 % set(auto2) -> clear(print_given). 13.73/13.81 assign(lrs_ticks,-1). 13.73/13.81 assign(sos_limit,10000). 13.73/13.81 assign(order,kbo). 13.73/13.81 set(lex_order_vars). 13.73/13.81 clear(print_given). 13.73/13.81 13.73/13.81 % formulas(sos). % not echoed (3656 formulas) 13.73/13.81 13.73/13.81 ============================== end of input ========================== 13.73/13.81 13.73/13.81 % From the command line: assign(max_seconds, 300). 13.73/13.81 13.73/13.81 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 13.73/13.81 13.73/13.81 % Formulas that are not ordinary clauses: 13.73/13.81 1 (all Q49892 all Q49893 all F0 all T0 ((all Y (p(s(bool,i(s(fun(fun(Q49893,bool),bool),i(s(fun(Q49893,fun(fun(Q49893,bool),bool)),in),s(Q49893,Y))),s(fun(Q49893,bool),T0)))) -> (exists X (p(s(bool,i(s(fun(fun(Q49892,bool),bool),i(s(fun(Q49892,fun(fun(Q49892,bool),bool)),in),s(Q49892,X))),s(fun(Q49892,bool),s0)))) & s(Q49893,i(s(fun(Q49892,Q49893),F0),s(Q49892,X))) = s(Q49893,Y))))) <-> (exists G0 all Y (p(s(bool,i(s(fun(fun(Q49893,bool),bool),i(s(fun(Q49893,fun(fun(Q49893,bool),bool)),in),s(Q49893,Y))),s(fun(Q49893,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q49892,bool),bool),i(s(fun(Q49892,fun(fun(Q49892,bool),bool)),in),s(Q49892,i(s(fun(Q49893,Q49892),G0),s(Q49893,Y))))),s(fun(Q49892,bool),s0)))) & s(Q49893,i(s(fun(Q49892,Q49893),F0),s(Q49892,i(s(fun(Q49893,Q49892),G0),s(Q49893,Y))))) = s(Q49893,Y))))) # label(aSURJECTIVEu_ONu_RIGHTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 2 (all X all Y (s(int,Y) = s(int,X) <-> s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))) # label(aINTu_SUBu_0) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 3 (all X all Y (s(real,Y) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & s(real,X) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),realu_inv),s(real,X))))),s(real,i(s(fun(real,real),realu_inv),s(real,Y))))))) # label(aREALu_SUBu_INV) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 4 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,N0))),s(num,M0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,i(s(fun(num,num),numeral),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,M0)))))) # label(aARITHu_GTu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 5 (all A all B all F0 all B0 ((all X all Y all S0 (s(A,Y) != s(A,X) -> s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,S0))))) = s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,S0))))))) -> s(B,i(s(fun(B,B),i(s(fun(fun(A,bool),fun(B,B)),i(s(fun(fun(A,fun(B,B)),fun(fun(A,bool),fun(B,B))),itset),s(fun(A,fun(B,B)),F0))),s(fun(A,bool),empty))),s(B,B0))) = s(B,B0) & (all X all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,i(s(fun(B,B),i(s(fun(fun(A,bool),fun(B,B)),i(s(fun(fun(A,fun(B,B)),fun(fun(A,bool),fun(B,B))),itset),s(fun(A,fun(B,B)),F0))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(B,B0))))))),s(B,i(s(fun(B,B),i(s(fun(fun(A,bool),fun(B,B)),i(s(fun(fun(A,fun(B,B)),fun(fun(A,bool),fun(B,B))),itset),s(fun(A,fun(B,B)),F0))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(B,B0))))) = s(B,i(s(fun(B,B),i(s(fun(fun(A,bool),fun(B,B)),i(s(fun(fun(A,fun(B,B)),fun(fun(A,bool),fun(B,B))),itset),s(fun(A,fun(B,B)),F0))),s(fun(A,bool),S0))),s(B,B0))))))) # label(aFINITEu_RECURSIONu_DELETE) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 6 (all Q19958 all Q19957 all U_0 ((all P0 all S0 ((exists X p(s(bool,i(s(fun(Q19957,bool),i(s(fun(Q19958,fun(Q19957,bool)),P0),s(Q19958,X))),s(Q19957,S0))))) <-> p(s(bool,i(s(fun(Q19957,bool),i(s(fun(fun(Q19958,fun(Q19957,bool)),fun(Q19957,bool)),U_0),s(fun(Q19958,fun(Q19957,bool)),P0))),s(Q19957,S0)))))) -> (all P0 all L (p(s(bool,i(s(fun(list(Q19957),bool),i(s(fun(fun(Q19957,bool),fun(list(Q19957),bool)),ex0),s(fun(Q19957,bool),i(s(fun(fun(Q19958,fun(Q19957,bool)),fun(Q19957,bool)),U_0),s(fun(Q19958,fun(Q19957,bool)),P0))))),s(list(Q19957),L)))) <-> (exists X p(s(bool,i(s(fun(list(Q19957),bool),i(s(fun(fun(Q19957,bool),fun(list(Q19957),bool)),ex0),s(fun(Q19957,bool),i(s(fun(Q19958,fun(Q19957,bool)),P0),s(Q19958,X))))),s(list(Q19957),L))))))))) # label(aEXISTSu_EX) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 7 (all A all F0 all S0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(num,i(s(fun(A,num),F0),s(A,X))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aNSUMu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 8 (all Q19765 all Q19764 all L s(Q19764,i(s(fun(Q19764,Q19764),i(s(fun(list(Q19765),fun(Q19764,Q19764)),i(s(fun(fun(Q19765,fun(Q19764,Q19764)),fun(list(Q19765),fun(Q19764,Q19764))),itlist),s(fun(Q19765,fun(Q19764,Q19764)),f))),s(list(Q19765),L))),s(Q19764,i(s(fun(Q19764,Q19764),i(s(fun(Q19765,fun(Q19764,Q19764)),f),s(Q19765,a0))),s(Q19764,b0))))) = s(Q19764,i(s(fun(Q19764,Q19764),i(s(fun(list(Q19765),fun(Q19764,Q19764)),i(s(fun(fun(Q19765,fun(Q19764,Q19764)),fun(list(Q19765),fun(Q19764,Q19764))),itlist),s(fun(Q19765,fun(Q19764,Q19764)),f))),s(list(Q19765),i(s(fun(list(Q19765),list(Q19765)),i(s(fun(list(Q19765),fun(list(Q19765),list(Q19765))),append),s(list(Q19765),L))),s(list(Q19765),i(s(fun(list(Q19765),list(Q19765)),i(s(fun(Q19765,fun(list(Q19765),list(Q19765))),cons),s(Q19765,a0))),s(list(Q19765),nil))))))),s(Q19764,b0)))) # label(aITLISTu_EXTRA) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 9 (all N0 all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aREALu_POWu_1u_LE) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 10 (all Q66845 all X all F0 all S0 (p(s(bool,i(s(fun(fun(Q66845,bool),bool),finite),s(fun(Q66845,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(fun(Q66845,bool),bool),i(s(fun(Q66845,fun(fun(Q66845,bool),bool)),in),s(Q66845,X))),s(fun(Q66845,bool),S0))))),s(num,i(s(fun(fun(Q66845,num),num),i(s(fun(fun(Q66845,bool),fun(fun(Q66845,num),num)),nsum),s(fun(Q66845,bool),S0))),s(fun(Q66845,num),F0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(Q66845,num),F0),s(Q66845,X))))),s(num,i(s(fun(fun(Q66845,num),num),i(s(fun(fun(Q66845,bool),fun(fun(Q66845,num),num)),nsum),s(fun(Q66845,bool),S0))),s(fun(Q66845,num),F0))))))) = s(num,i(s(fun(fun(Q66845,num),num),i(s(fun(fun(Q66845,bool),fun(fun(Q66845,num),num)),nsum),s(fun(Q66845,bool),i(s(fun(fun(Q66845,bool),fun(Q66845,bool)),i(s(fun(Q66845,fun(fun(Q66845,bool),fun(Q66845,bool))),insert),s(Q66845,X))),s(fun(Q66845,bool),S0))))),s(fun(Q66845,num),F0))))) # label(aNSUMu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 11 (all A all B all U_0 ((all P0 all Y (p(s(bool,i(s(fun(B,bool),i(s(fun(prod(A,B),fun(B,bool)),U_0),s(prod(A,B),P0))),s(B,Y)))) <-> (exists X s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y))) = s(prod(A,B),P0)))) -> (all P0 s(B,i(s(fun(prod(A,B),B),snd),s(prod(A,B),P0))) = s(B,i(s(fun(fun(B,bool),B),h_),s(fun(B,bool),i(s(fun(prod(A,B),fun(B,bool)),U_0),s(prod(A,B),P0)))))))) # label(aSNDu_DEF) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 12 (all Q67654 all F0 all S0 all A5 (p(s(bool,i(s(fun(fun(Q67654,bool),bool),i(s(fun(Q67654,fun(fun(Q67654,bool),bool)),in),s(Q67654,A5))),s(fun(Q67654,bool),S0)))) & p(s(bool,i(s(fun(fun(Q67654,bool),bool),finite),s(fun(Q67654,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(Q67654,num),F0),s(Q67654,A5))))),s(num,i(s(fun(fun(Q67654,num),num),i(s(fun(fun(Q67654,bool),fun(fun(Q67654,num),num)),nsum),s(fun(Q67654,bool),i(s(fun(Q67654,fun(Q67654,bool)),i(s(fun(fun(Q67654,bool),fun(Q67654,fun(Q67654,bool))),delete),s(fun(Q67654,bool),S0))),s(Q67654,A5))))),s(fun(Q67654,num),F0))))) = s(num,i(s(fun(fun(Q67654,num),num),i(s(fun(fun(Q67654,bool),fun(fun(Q67654,num),num)),nsum),s(fun(Q67654,bool),S0))),s(fun(Q67654,num),F0))))) # label(aNSUMu_DELETE) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 13 (all Q20978 all Q20979 all F0 all N0 all L (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,i(s(fun(list(Q20979),num),length),s(list(Q20979),L)))))) -> s(Q20978,i(s(fun(list(Q20978),Q20978),i(s(fun(num,fun(list(Q20978),Q20978)),el),s(num,N0))),s(list(Q20978),i(s(fun(list(Q20979),list(Q20978)),i(s(fun(fun(Q20979,Q20978),fun(list(Q20979),list(Q20978))),map0),s(fun(Q20979,Q20978),F0))),s(list(Q20979),L))))) = s(Q20978,i(s(fun(Q20979,Q20978),F0),s(Q20979,i(s(fun(list(Q20979),Q20979),i(s(fun(num,fun(list(Q20979),Q20979)),el),s(num,N0))),s(list(Q20979),L))))))) # label(aELu_MAP) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 14 (all K0 all M0 all N0 s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(fun(num,bool),fun(fun(num,bool),fun(num,bool))),inter),s(fun(num,bool),i(s(fun(num,fun(num,bool)),from),s(num,K0))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))) = s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(fun(num,bool),fun(fun(num,bool),fun(num,bool))),i(s(fun(bool,fun(fun(num,bool),fun(fun(num,bool),fun(num,bool)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,K0))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,K0))),s(num,N0))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0)))))) # label(aFROMu_INTERu_NUMSEGu_GEN) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 15 (exists X ((all Y (p(s(bool,i(s(fun(int,bool),p0),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))))) & p(s(bool,i(s(fun(int,bool),p0),s(int,X)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))))) <-> (exists X (p(s(bool,i(s(fun(int,bool),p0),s(int,X)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))))) # label(aINTu_WOP) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 16 (all N0 all X all Y (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0)))))))) # label(aREALu_POWu_LT2) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 17 (all X all Y s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,i(s(fun(int,int),intu_neg),s(int,Y))))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y)))) # label(aINTu_MAXu_MIN) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 18 (all A all A5 (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),countable),s(fun(fun(A,bool),bool),A5)))) & (all S0 (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),S0))),s(fun(fun(A,bool),bool),A5)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0)))))) -> p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),unions),s(fun(fun(A,bool),bool),A5)))))))) # label(aCOUNTABLEu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 19 (all A all P0 all Q0 ((all X (p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X)))))) <-> (all X p(s(bool,i(s(fun(A,bool),Q0),s(A,X))))) & (all X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) # label(aANDu_FORALLu_THM) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 20 (all M0 all N0 s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),numeral),s(num,M0))))),s(num,i(s(fun(num,num),numeral),s(num,N0)))))) # label(aARITHu_SUBu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 21 (all A all S0 all T0 ((exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) <-> -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))) <-> s(fun(A,bool),T0) != s(fun(A,bool),S0))) # label(aNOTu_EQUALu_SETS) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 22 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y)))))))) # label(aINTu_LETu_ADD) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 23 (all Q53496 all S0 all N0 (s(num,N0) = s(num,i(s(fun(fun(Q53496,bool),num),card),s(fun(Q53496,bool),S0))) & p(s(bool,i(s(fun(fun(Q53496,bool),bool),finite),s(fun(Q53496,bool),S0)))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53496,bool),fun(num,bool)),hasu_size),s(fun(Q53496,bool),S0))),s(num,N0)))))) # label(aHASu_SIZE) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 24 (all T0 ((p(s(bool,T0)) <-> p(s(bool,f0)) | p(s(bool,T0))) & (p(s(bool,T0)) <-> p(s(bool,T0)) | p(s(bool,T0))) & (p(s(bool,T0)) | p(s(bool,f0)) <-> p(s(bool,T0))) & (p(s(bool,t)) <-> p(s(bool,t)) | p(s(bool,T0))) & (p(s(bool,t)) | p(s(bool,T0)) <-> p(s(bool,t))))) # label(aORu_CLAUSES) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 25 (all X1 all X2 all Y1 all Y2 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),X2)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),Y1))),s(prod(hreal,hreal),Y2)))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),Y1))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X2))),s(prod(hreal,hreal),Y2)))))))) # label(aTREALu_MULu_WELLDEF) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 26 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,Y))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y)))))) # label(aINTu_LEu_LNEG) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 27 (all Q66871 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q66871,bool),bool),finite),s(fun(Q66871,bool),S0)))) & p(s(bool,i(s(fun(fun(Q66871,bool),bool),finite),s(fun(Q66871,bool),T0)))) & p(s(bool,i(s(fun(fun(Q66871,bool),bool),i(s(fun(fun(Q66871,bool),fun(fun(Q66871,bool),bool)),disjoint),s(fun(Q66871,bool),S0))),s(fun(Q66871,bool),T0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(Q66871,num),num),i(s(fun(fun(Q66871,bool),fun(fun(Q66871,num),num)),nsum),s(fun(Q66871,bool),S0))),s(fun(Q66871,num),F0))))),s(num,i(s(fun(fun(Q66871,num),num),i(s(fun(fun(Q66871,bool),fun(fun(Q66871,num),num)),nsum),s(fun(Q66871,bool),T0))),s(fun(Q66871,num),F0))))) = s(num,i(s(fun(fun(Q66871,num),num),i(s(fun(fun(Q66871,bool),fun(fun(Q66871,num),num)),nsum),s(fun(Q66871,bool),i(s(fun(fun(Q66871,bool),fun(Q66871,bool)),i(s(fun(fun(Q66871,bool),fun(fun(Q66871,bool),fun(Q66871,bool))),union),s(fun(Q66871,bool),S0))),s(fun(Q66871,bool),T0))))),s(fun(Q66871,num),F0))))) # label(aNSUMu_UNION) # label(axiom) # label(non_clause). [assumption]. 13.73/13.81 28 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0)))))) # label(aSUBu_ADDu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 29 (all X all Y (s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) | s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,Y) <-> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aREALu_ENTIRE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 30 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),infinite),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(prod(A,B),bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(B,bool),T0)))))) # label(aCARDu_MULu_ABSORBu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 31 (all M0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,N0) | p(s(bool,i(s(fun(num,bool),odd),s(num,M0)))) <-> p(s(bool,i(s(fun(num,bool),odd),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,N0)))))))) # label(aODDu_EXP) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 32 (all Q87575 all Q87572 ((all X (p(s(bool,i(s(fun(fun(Q87572,bool),bool),i(s(fun(Q87572,fun(fun(Q87572,bool),bool)),in),s(Q87572,X))),s(fun(Q87572,bool),s0)))) -> s(Q87572,X) = s(Q87572,i(s(fun(Q87575,Q87572),g),s(Q87575,i(s(fun(Q87572,Q87575),f),s(Q87572,X))))))) <-> (all Y all X (p(s(bool,i(s(fun(fun(Q87572,bool),bool),i(s(fun(Q87572,fun(fun(Q87572,bool),bool)),in),s(Q87572,X))),s(fun(Q87572,bool),s0)))) & s(Q87575,i(s(fun(Q87572,Q87575),f),s(Q87572,X))) = s(Q87575,Y) -> s(Q87572,i(s(fun(Q87575,Q87572),g),s(Q87575,Y))) = s(Q87572,X))))) # label(aFLATTENu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 33 (all B all A all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(B,bool),num),dimindex),s(fun(B,bool),univ)))))) -> s(A,i(s(fun(num,A),g),s(num,I0))) = s(A,i(s(fun(num,A),i(s(fun(cart(A,B),fun(num,A)),d_),s(cart(A,B),i(s(fun(fun(num,A),cart(A,B)),lambda),s(fun(num,A),g))))),s(num,I0))))) # label(aLAMBDAu_BETA) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 34 (all Q81150 all Q81151 all Q81216 all P all Q81271 all Q81240 all U_9 ((all C1 all C2 all F0 all X s(fun(Q81271,fun(Q81240,bool)),i(s(fun(P,fun(Q81271,fun(Q81240,bool))),i(s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool))))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))))),U_9),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C2))),s(fun(Q81151,Q81216),F0))),s(P,X))) = s(fun(Q81271,fun(Q81240,bool)),i(s(fun(fun(Q81271,fun(Q81240,bool)),fun(Q81271,fun(Q81240,bool))),i(s(fun(fun(Q81271,fun(Q81240,bool)),fun(fun(Q81271,fun(Q81240,bool)),fun(Q81271,fun(Q81240,bool)))),u_seqpattern),s(fun(Q81271,fun(Q81240,bool)),i(s(fun(P,fun(Q81271,fun(Q81240,bool))),i(s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1),s(fun(Q81151,Q81216),F0))),s(P,X))))),s(fun(Q81271,fun(Q81240,bool)),i(s(fun(P,fun(Q81271,fun(Q81240,bool))),i(s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C2),s(fun(Q81151,Q81216),F0))),s(P,X)))))) -> (all U_8 ((all C1 all C2 all F0 s(fun(P,fun(Q81271,fun(Q81240,bool))),i(s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool))))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))))),U_9),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C2))),s(fun(Q81151,Q81216),F0))) = s(fun(P,fun(Q81271,fun(Q81240,bool))),i(s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool))))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))))),U_8),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C2))),s(fun(Q81151,Q81216),F0)))) -> (all U_7 ((all P0 all C1 all E0 all F0 all X (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))))),U_7),s(fun(fun(Q81151,Q81216),fun(P,bool)),P0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(Q81151,Q81216),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q81151,Q81216),fun(P,bool)),P0),s(fun(Q81151,Q81216),F0))),s(P,X)))) & -(exists Y p(s(bool,i(s(fun(Q81240,bool),i(s(fun(Q81271,fun(Q81240,bool)),i(s(fun(P,fun(Q81271,fun(Q81240,bool))),i(s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1),s(fun(Q81151,Q81216),F0))),s(P,X))),s(Q81271,i(s(fun(P,Q81271),i(s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0),s(fun(Q81151,Q81216),F0))),s(P,X))))),s(Q81240,Y))))))) -> (all U_6 ((all P0 all C1 all E0 all F0 s(fun(P,bool),i(s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))))),U_6),s(fun(fun(Q81151,Q81216),fun(P,bool)),P0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(Q81151,Q81216),F0))) = s(fun(P,bool),i(s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))))),U_7),s(fun(fun(Q81151,Q81216),fun(P,bool)),P0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(Q81151,Q81216),F0)))) -> (all U_5 ((all E0 all C1 all F0 all X s(Q81240,i(s(fun(P,Q81240),i(s(fun(fun(Q81151,Q81216),fun(P,Q81240)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240)))),U_5),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(Q81151,Q81216),F0))),s(P,X))) = s(Q81240,i(s(fun(fun(Q81271,fun(Q81240,bool)),Q81240),i(s(fun(Q81271,fun(fun(Q81271,fun(Q81240,bool)),Q81240)),u_match),s(Q81271,i(s(fun(P,Q81271),i(s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0),s(fun(Q81151,Q81216),F0))),s(P,X))))),s(fun(Q81271,fun(Q81240,bool)),i(s(fun(P,fun(Q81271,fun(Q81240,bool))),i(s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1),s(fun(Q81151,Q81216),F0))),s(P,X)))))) -> (all U_4 ((all E0 all C1 all F0 s(fun(P,Q81240),i(s(fun(fun(Q81151,Q81216),fun(P,Q81240)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240)))),U_4),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(Q81151,Q81216),F0))) = s(fun(P,Q81240),i(s(fun(fun(Q81151,Q81216),fun(P,Q81240)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240)))),U_5),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(Q81151,Q81216),F0)))) -> (all U_3 ((all P0 all C1 all E0 all F0 all X ((exists Y p(s(bool,i(s(fun(Q81240,bool),i(s(fun(Q81271,fun(Q81240,bool)),i(s(fun(P,fun(Q81271,fun(Q81240,bool))),i(s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1),s(fun(Q81151,Q81216),F0))),s(P,X))),s(Q81271,i(s(fun(P,Q81271),i(s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0),s(fun(Q81151,Q81216),F0))),s(P,X))))),s(Q81240,Y))))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q81151,Q81216),fun(P,bool)),P0),s(fun(Q81151,Q81216),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))))),U_3),s(fun(fun(Q81151,Q81216),fun(P,bool)),P0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(Q81151,Q81216),F0))),s(P,X)))))) -> (all U_2 ((all P0 all C1 all E0 all F0 s(fun(P,bool),i(s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))))),U_3),s(fun(fun(Q81151,Q81216),fun(P,bool)),P0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(Q81151,Q81216),F0))) = s(fun(P,bool),i(s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))))),U_2),s(fun(fun(Q81151,Q81216),fun(P,bool)),P0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(Q81151,Q81216),F0)))) -> (all U_1 ((all C1 all E0 all F0 all X (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),U_1),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(Q81151,Q81216),F0))),s(P,X)))) <-> (exists Y p(s(bool,i(s(fun(Q81240,bool),i(s(fun(Q81271,fun(Q81240,bool)),i(s(fun(P,fun(Q81271,fun(Q81240,bool))),i(s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1),s(fun(Q81151,Q81216),F0))),s(P,X))),s(Q81271,i(s(fun(P,Q81271),i(s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0),s(fun(Q81151,Q81216),F0))),s(P,X))))),s(Q81240,Y))))))) -> (all U_0 ((all C1 all E0 all F0 s(fun(P,bool),i(s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),U_0),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(Q81151,Q81216),F0))) = s(fun(P,bool),i(s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),U_1),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(Q81151,Q81216),F0)))) -> (all L_L_ all P0 all S0 all C1 all C2 all E0 (p(s(bool,i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),bool),i(s(fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,bool)),bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,bool)),bool))),i(s(fun(fun(Q81151,fun(Q81150,bool)),fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,bool)),bool)))),admissible),s(fun(Q81151,fun(Q81150,bool)),L_L_))),s(fun(fun(Q81151,Q81216),fun(P,bool)),P0))),s(fun(P,Q81150),S0))),s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),U_0),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0)))))) & p(s(bool,i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool),i(s(fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool))),i(s(fun(fun(Q81151,fun(Q81150,bool)),fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool)))),admissible),s(fun(Q81151,fun(Q81150,bool)),L_L_))),s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))))),U_2),s(fun(fun(Q81151,Q81216),fun(P,bool)),P0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))))),s(fun(P,Q81150),S0))),s(fun(fun(Q81151,Q81216),fun(P,Q81240)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240)))),U_4),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1)))))) & p(s(bool,i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool),i(s(fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool))),i(s(fun(fun(Q81151,fun(Q81150,bool)),fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool)))),admissible),s(fun(Q81151,fun(Q81150,bool)),L_L_))),s(fun(fun(Q81151,Q81216),fun(P,bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(Q81151,Q81216),fun(P,bool))))),U_6),s(fun(fun(Q81151,Q81216),fun(P,bool)),P0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))))),s(fun(P,Q81150),S0))),s(fun(fun(Q81151,Q81216),fun(P,Q81240)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240)))),U_4),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C2)))))) -> p(s(bool,i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool),i(s(fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool))),i(s(fun(fun(Q81151,fun(Q81150,bool)),fun(fun(fun(Q81151,Q81216),fun(P,bool)),fun(fun(P,Q81150),fun(fun(fun(Q81151,Q81216),fun(P,Q81240)),bool)))),admissible),s(fun(Q81151,fun(Q81150,bool)),L_L_))),s(fun(fun(Q81151,Q81216),fun(P,bool)),P0))),s(fun(P,Q81150),S0))),s(fun(fun(Q81151,Q81216),fun(P,Q81240)),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,Q81271)),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,Q81240)))),U_4),s(fun(fun(Q81151,Q81216),fun(P,Q81271)),E0))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool))))),i(s(fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))))),U_8),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C1))),s(fun(fun(Q81151,Q81216),fun(P,fun(Q81271,fun(Q81240,bool)))),C2)))))))))))))))))))))))))))))) # label(aADMISSIBLEu_MATCHu_SEQPATTERN) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 35 (all X all Y all A5 all U all V (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,A5)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,A5)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,V)))) & s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,U))),s(real,V))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,U)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,U))),s(real,X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,V))),s(real,Y))))))),s(real,A5)))))) # label(aREALu_CONVEXu_BOUNDu_LT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 36 (all B all A all B0 all F0 all X all Y s(B,i(s(fun(A,B),F0),s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),i(s(fun(bool,fun(A,fun(A,A))),cond),s(bool,B0))),s(A,X))),s(A,Y))))) = s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,B0))),s(B,i(s(fun(A,B),F0),s(A,X))))),s(B,i(s(fun(A,B),F0),s(A,Y)))))) # label(aCONDu_RAND) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 37 (all M0 all N0 all X (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(int,X)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,M0))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0)))))))) # label(aINTu_POWu_MONO) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 38 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y))))) # label(aREALu_LEu_MULu_EQu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 39 (all M0 all N0 (s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) & s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,N0) <-> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aADDu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 40 (all U_0 ((all U (p(s(bool,i(s(fun(prod(hreal,hreal),bool),U_0),s(prod(hreal,hreal),U)))) <-> (exists X (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(real,fun(prod(hreal,hreal),bool)),destu_real),s(real,x))),s(prod(hreal,hreal),X)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),trealu_inv),s(prod(hreal,hreal),X))))),s(prod(hreal,hreal),U)))))))) -> s(real,i(s(fun(real,real),realu_inv),s(real,x))) = s(real,i(s(fun(fun(prod(hreal,hreal),bool),real),mku_real),s(fun(prod(hreal,hreal),bool),U_0))))) # label(arealu_inv) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 41 (all N0 s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) # label(aMODu_1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 42 p(s(bool,t)) <-> -p(s(bool,f0)) # label(aNOTu_CLAUSESu_WEAKu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 43 (all N0 s(bool,i(s(fun(num,bool),odd),s(num,i(s(fun(num,num),numeral),s(num,N0))))) = s(bool,i(s(fun(num,bool),odd),s(num,N0)))) # label(aARITHu_ODDu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 44 (all A all P0 (p(s(bool,i(s(fun(option(A),bool),P0),s(option(A),none)))) & (all A5 p(s(bool,i(s(fun(option(A),bool),P0),s(option(A),i(s(fun(A,option(A)),some),s(A,A5))))))) -> (all X p(s(bool,i(s(fun(option(A),bool),P0),s(option(A),X))))))) # label(aoptionu_elim) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 45 (all Q47602 all Q47598 s(fun(Q47602,bool),i(s(fun(fun(Q47598,bool),fun(Q47602,bool)),i(s(fun(fun(Q47598,Q47602),fun(fun(Q47598,bool),fun(Q47602,bool))),image),s(fun(Q47598,Q47602),f))),s(fun(Q47598,bool),i(s(fun(fun(Q47598,bool),fun(Q47598,bool)),i(s(fun(Q47598,fun(fun(Q47598,bool),fun(Q47598,bool))),insert),s(Q47598,x))),s(fun(Q47598,bool),s0))))) = s(fun(Q47602,bool),i(s(fun(fun(Q47602,bool),fun(Q47602,bool)),i(s(fun(Q47602,fun(fun(Q47602,bool),fun(Q47602,bool))),insert),s(Q47602,i(s(fun(Q47598,Q47602),f),s(Q47598,x))))),s(fun(Q47602,bool),i(s(fun(fun(Q47598,bool),fun(Q47602,bool)),i(s(fun(fun(Q47598,Q47602),fun(fun(Q47598,bool),fun(Q47602,bool))),image),s(fun(Q47598,Q47602),f))),s(fun(Q47598,bool),s0)))))) # label(aIMAGEu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 46 (all Q73319 all U_0 ((all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(Q73319,real),U_0),s(Q73319,X)))) -> (all S0 (p(s(bool,i(s(fun(fun(Q73319,bool),bool),finite),s(fun(Q73319,bool),S0)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(Q73319,bool),num),card),s(fun(Q73319,bool),S0))))) = s(real,i(s(fun(fun(Q73319,real),real),i(s(fun(fun(Q73319,bool),fun(fun(Q73319,real),real)),sum),s(fun(Q73319,bool),S0))),s(fun(Q73319,real),U_0))))))) # label(aCARDu_EQu_SUM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 47 (all A5 all B0 s(int,i(s(fun(prod(int,int),int),intu_gcd),s(prod(int,int),i(s(fun(int,prod(int,int)),i(s(fun(int,fun(int,prod(int,int))),c_),s(int,i(s(fun(num,int),intu_ofu_num),s(num,A5))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,B0))))))) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(prod(num,num),num),numu_gcd),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,A5))),s(num,B0)))))))) # label(aNUMu_GCD) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 48 (all A s(fun(A,bool),i(s(fun(list(A),fun(A,bool)),setu_ofu_list),s(list(A),nil))) = s(fun(A,bool),empty)) # label(asetu_ofu_listu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 49 (all A all U_0 ((all Z0 s(bool,t) = s(bool,i(s(fun(fun(num,fun(A,bool)),bool),U_0),s(fun(num,fun(A,bool)),Z0)))) -> s(fun(num,fun(A,bool)),zbot) = s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(A,bool)),fun(num,fun(A,bool))),i(s(fun(fun(num,fun(A,bool)),fun(fun(num,fun(A,bool)),fun(num,fun(A,bool)))),injp),s(fun(num,fun(A,bool)),i(s(fun(num,fun(num,fun(A,bool))),injn),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(num,fun(A,bool)),i(s(fun(fun(fun(num,fun(A,bool)),bool),fun(num,fun(A,bool))),h_),s(fun(fun(num,fun(A,bool)),bool),U_0))))))) # label(aZBOT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 50 (all A s(bool,t) = s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,fun(A,bool)),fun(list(A),bool)),pairwise0),s(fun(A,fun(A,bool)),r0))),s(list(A),nil)))) # label(aPAIRWISEu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 51 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X))))))))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,Y))))),s(real,Z0)))))) # label(aREALu_ABSu_TRIANGLEu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 52 (all Q56105 all Q56108 all X all Y all S0 all T0 (p(s(bool,i(s(fun(fun(Q56108,bool),bool),i(s(fun(Q56108,fun(fun(Q56108,bool),bool)),in),s(Q56108,Y))),s(fun(Q56108,bool),T0)))) & p(s(bool,i(s(fun(fun(Q56105,bool),bool),i(s(fun(Q56105,fun(fun(Q56105,bool),bool)),in),s(Q56105,X))),s(fun(Q56105,bool),S0)))) <-> p(s(bool,i(s(fun(fun(prod(Q56105,Q56108),bool),bool),i(s(fun(prod(Q56105,Q56108),fun(fun(prod(Q56105,Q56108),bool),bool)),in),s(prod(Q56105,Q56108),i(s(fun(Q56108,prod(Q56105,Q56108)),i(s(fun(Q56105,fun(Q56108,prod(Q56105,Q56108))),c_),s(Q56105,X))),s(Q56108,Y))))),s(fun(prod(Q56105,Q56108),bool),i(s(fun(fun(Q56108,bool),fun(prod(Q56105,Q56108),bool)),i(s(fun(fun(Q56105,bool),fun(fun(Q56108,bool),fun(prod(Q56105,Q56108),bool))),cross0),s(fun(Q56105,bool),S0))),s(fun(Q56108,bool),T0)))))))) # label(aINu_CROSS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 53 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y))),s(int,X))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Z0))),s(int,X)))))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Z0)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,Z0)))))) # label(aINTu_ABSu_BETWEEN1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 54 (all A ((all X (p(s(bool,i(s(fun(A,bool),p0),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),q0),s(A,X)))))) -> (p(s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,bool),fun(list(A),bool)),all0),s(fun(A,bool),p0))),s(list(A),l0)))) -> p(s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,bool),fun(list(A),bool)),all0),s(fun(A,bool),q0))),s(list(A),l0))))))) # label(aMONOu_ALL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 55 (all A all M all N all U_0 ((all F0 all I0 s(A,i(s(fun(num,A),i(s(fun(cart(A,finite_sum(M,N)),fun(num,A)),d_),s(cart(A,finite_sum(M,N)),F0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))))) = s(A,i(s(fun(num,A),i(s(fun(cart(A,finite_sum(M,N)),fun(num,A)),U_0),s(cart(A,finite_sum(M,N)),F0))),s(num,I0)))) -> (all F0 s(cart(A,N),i(s(fun(cart(A,finite_sum(M,N)),cart(A,N)),sndcart),s(cart(A,finite_sum(M,N)),F0))) = s(cart(A,N),i(s(fun(fun(num,A),cart(A,N)),lambda),s(fun(num,A),i(s(fun(cart(A,finite_sum(M,N)),fun(num,A)),U_0),s(cart(A,finite_sum(M,N)),F0)))))))) # label(asndcart) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 56 (all A all B all F0 all G0 ((all X s(B,i(s(fun(A,B),G0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,X)))) -> s(fun(A,B),G0) = s(fun(A,B),F0))) # label(aEQu_EXT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 57 (all A all B all U_1 ((all T0 all GENR_PVARR_249 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),U_1),s(fun(B,bool),T0))),s(fun(B,bool),GENR_PVARR_249)))) <-> (exists V exists V0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(bool,fun(fun(B,bool),bool)),i(s(fun(fun(B,bool),fun(bool,fun(fun(B,bool),bool))),setspec),s(fun(B,bool),GENR_PVARR_249))),s(bool,V0))),s(fun(B,bool),V)))) & (p(s(bool,V0)) <-> p(s(bool,i(s(fun(fun(B,bool),bool),q0),s(fun(B,bool),V)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),V))),s(fun(B,bool),T0))))))))) -> (all U_0 ((all S0 all GENR_PVARR_248 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))),s(fun(A,bool),GENR_PVARR_248)))) <-> (exists U exists V (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_248))),s(bool,V))),s(fun(A,bool),U)))) & (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),U))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),p0),s(fun(A,bool),U)))) <-> p(s(bool,V))))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) & (all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),p0),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),q0),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0)))))))) -> p(s(bool,i(s(fun(fun(fun(B,bool),bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(fun(B,bool),bool),bool)),l_a_u_c),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))))))),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),gspec),s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),U_1),s(fun(B,bool),T0)))))))))))))) # label(aCARDu_LEu_SUBPOWERSET) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 58 (all B all A all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0)))))))) # label(aCARDu_IMAGEu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 59 (all A all S0 (s(fun(A,bool),S0) = s(fun(A,bool),empty) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),S0))),s(fun(A,bool),S0)))))) # label(aDISJOINTu_EMPTYu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 60 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,m))),s(num,n))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,m))),s(num,n)))))) <-> (exists Q0 exists R0 ((p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,R0))),s(num,n)))) & s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,Q0))),s(num,n))))),s(num,R0))) = s(num,m) | s(num,n) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) & s(num,m) = s(num,R0) & s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,Q0)) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,Q0))),s(num,R0)))))) # label(aDIVMODu_ELIMu_THMi_) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 61 (all M0 all N0 exists V ((p(s(bool,V)) <-> s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),rem),s(int,M0))),s(int,N0))) = s(int,M0) & s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),div0),s(int,M0))),s(int,N0)))) & (exists VI_ ((p(s(bool,VI_)) <-> s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,N0)) & (exists VI_I_ (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,VI_))),s(bool,V))),s(bool,VI_I_)))) & (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),rem),s(int,M0))),s(int,N0)))))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),rem),s(int,M0))),s(int,N0))))),s(int,i(s(fun(int,int),intu_abs),s(int,N0)))))) & s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),div0),s(int,M0))),s(int,N0))))),s(int,N0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),rem),s(int,M0))),s(int,N0))))) = s(int,M0) <-> p(s(bool,VI_I_))))))))) # label(aINTu_DIVISIONu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 62 (all X s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,i(s(fun(int,int),intu_abs),s(int,X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aINTu_POW2u_ABS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 63 (all A all B all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(B,real),G0),s(B,i(s(fun(A,B),F0),s(A,X)))))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(B,real),real),i(s(fun(fun(B,bool),fun(fun(B,real),real)),sum),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,real),G0))))),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(fun(A,B),fun(A,real)),i(s(fun(fun(B,real),fun(fun(A,B),fun(A,real))),o),s(fun(B,real),G0))),s(fun(A,B),F0)))))))))) # label(aSUMu_IMAGEu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.83 64 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),infinite),s(fun(B,bool),T0)))) & s(fun(A,bool),empty) != s(fun(A,bool),S0) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(prod(A,B),bool),fun(fun(B,bool),bool)),a_u_c),s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(B,bool),T0)))))) # label(aCARDu_MULu_ABSORB) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 65 (all B all A all F0 all Y s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,i(s(fun(A,B),F0),s(A,Y)))) # label(aBETAu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 66 (all N0 all M0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,M0))),s(num,N0)))) # label(aGT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 67 (all Q1020 all P0 all A5 ((all X (s(Q1020,X) = s(Q1020,A5) -> p(s(bool,i(s(fun(Q1020,bool),P0),s(Q1020,X)))))) <-> p(s(bool,i(s(fun(Q1020,bool),P0),s(Q1020,A5)))))) # label(aFORALLu_UNWINDu_THM1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 68 (all Q19988 all Q19987 all U_0 ((all P0 all S0 (p(s(bool,i(s(fun(Q19987,bool),i(s(fun(fun(Q19988,fun(Q19987,bool)),fun(Q19987,bool)),U_0),s(fun(Q19988,fun(Q19987,bool)),P0))),s(Q19987,S0)))) <-> (all X p(s(bool,i(s(fun(Q19987,bool),i(s(fun(Q19988,fun(Q19987,bool)),P0),s(Q19988,X))),s(Q19987,S0))))))) -> (all P0 all L (p(s(bool,i(s(fun(list(Q19987),bool),i(s(fun(fun(Q19987,bool),fun(list(Q19987),bool)),all0),s(fun(Q19987,bool),i(s(fun(fun(Q19988,fun(Q19987,bool)),fun(Q19987,bool)),U_0),s(fun(Q19988,fun(Q19987,bool)),P0))))),s(list(Q19987),L)))) <-> (all X p(s(bool,i(s(fun(list(Q19987),bool),i(s(fun(fun(Q19987,bool),fun(list(Q19987),bool)),all0),s(fun(Q19987,bool),i(s(fun(Q19988,fun(Q19987,bool)),P0),s(Q19988,X))))),s(list(Q19987),L))))))))) # label(aFORALLu_ALL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 69 (all Q47779 all Q47768 all F0 all S0 all T0 ((all X all Y (s(Q47779,i(s(fun(Q47768,Q47779),F0),s(Q47768,Y))) = s(Q47779,i(s(fun(Q47768,Q47779),F0),s(Q47768,X))) -> s(Q47768,Y) = s(Q47768,X))) -> s(fun(Q47779,bool),i(s(fun(fun(Q47779,bool),fun(Q47779,bool)),i(s(fun(fun(Q47779,bool),fun(fun(Q47779,bool),fun(Q47779,bool))),inter),s(fun(Q47779,bool),i(s(fun(fun(Q47768,bool),fun(Q47779,bool)),i(s(fun(fun(Q47768,Q47779),fun(fun(Q47768,bool),fun(Q47779,bool))),image),s(fun(Q47768,Q47779),F0))),s(fun(Q47768,bool),S0))))),s(fun(Q47779,bool),i(s(fun(fun(Q47768,bool),fun(Q47779,bool)),i(s(fun(fun(Q47768,Q47779),fun(fun(Q47768,bool),fun(Q47779,bool))),image),s(fun(Q47768,Q47779),F0))),s(fun(Q47768,bool),T0))))) = s(fun(Q47779,bool),i(s(fun(fun(Q47768,bool),fun(Q47779,bool)),i(s(fun(fun(Q47768,Q47779),fun(fun(Q47768,bool),fun(Q47779,bool))),image),s(fun(Q47768,Q47779),F0))),s(fun(Q47768,bool),i(s(fun(fun(Q47768,bool),fun(Q47768,bool)),i(s(fun(fun(Q47768,bool),fun(fun(Q47768,bool),fun(Q47768,bool))),inter),s(fun(Q47768,bool),S0))),s(fun(Q47768,bool),T0))))))) # label(aIMAGEu_INTERu_INJ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 70 (all A all S0 all T0 all U (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,bool),U)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),S0))),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),T0))),s(fun(A,bool),U)))))) # label(aDISJOINTu_UNION) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 71 (all N0 s(bool,i(s(fun(num,bool),odd),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(bool,t)) # label(aARITHu_ODDu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 72 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))) # label(aREALu_LTu_ADDL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 73 (all U_0 ((all U s(bool,i(s(fun(nadd,bool),U_0),s(nadd,U))) = s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,m))))),s(nadd,U)))) -> s(hreal,i(s(fun(fun(nadd,bool),hreal),mku_hreal),s(fun(nadd,bool),U_0))) = s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,m))))) # label(ahrealu_ofu_num) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 74 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0)))))) # label(aARITHu_LTu_conjunct9) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 75 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_neg),s(real,X)))))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) | s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,X))) # label(aREALu_LTu_NEGTOTAL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 76 (all A all S0 all T0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),T0))),s(fun(A,bool),S0))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) # label(aUNIONu_COMM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 77 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(real,real),realu_inv),s(real,X)))))))) # label(aREALu_INVu_1u_LT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 78 (all Q49460 all U_0 ((all S0 all GENR_PVARR_43 ((exists T0 p(s(bool,i(s(fun(fun(Q49460,bool),bool),i(s(fun(bool,fun(fun(Q49460,bool),bool)),i(s(fun(fun(Q49460,bool),fun(bool,fun(fun(Q49460,bool),bool))),setspec),s(fun(Q49460,bool),GENR_PVARR_43))),s(bool,i(s(fun(fun(fun(Q49460,bool),bool),bool),i(s(fun(fun(Q49460,bool),fun(fun(fun(Q49460,bool),bool),bool)),in),s(fun(Q49460,bool),T0))),s(fun(fun(Q49460,bool),bool),S0))))),s(fun(Q49460,bool),i(s(fun(fun(Q49460,bool),fun(Q49460,bool)),i(s(fun(fun(Q49460,bool),fun(fun(Q49460,bool),fun(Q49460,bool))),diff),s(fun(Q49460,bool),univ))),s(fun(Q49460,bool),T0))))))) <-> p(s(bool,i(s(fun(fun(Q49460,bool),bool),i(s(fun(fun(fun(Q49460,bool),bool),fun(fun(Q49460,bool),bool)),U_0),s(fun(fun(Q49460,bool),bool),S0))),s(fun(Q49460,bool),GENR_PVARR_43)))))) -> (all S0 s(fun(Q49460,bool),i(s(fun(fun(fun(Q49460,bool),bool),fun(Q49460,bool)),unions),s(fun(fun(Q49460,bool),bool),S0))) = s(fun(Q49460,bool),i(s(fun(fun(Q49460,bool),fun(Q49460,bool)),i(s(fun(fun(Q49460,bool),fun(fun(Q49460,bool),fun(Q49460,bool))),diff),s(fun(Q49460,bool),univ))),s(fun(Q49460,bool),i(s(fun(fun(fun(Q49460,bool),bool),fun(Q49460,bool)),inters),s(fun(fun(Q49460,bool),bool),i(s(fun(fun(fun(Q49460,bool),bool),fun(fun(Q49460,bool),bool)),gspec),s(fun(fun(Q49460,bool),bool),i(s(fun(fun(fun(Q49460,bool),bool),fun(fun(Q49460,bool),bool)),U_0),s(fun(fun(Q49460,bool),bool),S0)))))))))))) # label(aUNIONSu_INTERS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 79 (all U_0 ((all F0 all P0 all I0 s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,I0))),s(num,P0))))) = s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(num,real),fun(num,fun(num,real))),U_0),s(fun(num,real),F0))),s(num,P0))),s(num,I0)))) -> (all P0 all F0 all M0 all N0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))),s(fun(num,real),F0))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(num,real),fun(num,fun(num,real))),U_0),s(fun(num,real),F0))),s(num,P0)))))))) # label(aSUMu_OFFSET) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 80 (all X s(int,X) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aINTu_SUBu_RZERO) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 81 (all M0 all N0 (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))))) # label(aSUBu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 82 (exists R0 ((all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(hreal,real),R0),s(hreal,Y))))),s(real,i(s(fun(hreal,real),R0),s(hreal,Z0))))) = s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,Y))),s(hreal,Z0)))) & (all X ((exists Y s(real,X) = s(real,i(s(fun(hreal,real),R0),s(hreal,Y)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))))))) # label(aREALu_HREALu_LEMMA1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 83 (all Q88408 all Q88409 all S0 all T0 (p(s(bool,i(s(fun(fun(Q88409,bool),bool),i(s(fun(fun(Q88408,bool),fun(fun(Q88409,bool),bool)),l_u_c),s(fun(Q88408,bool),S0))),s(fun(Q88409,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q88409,bool),bool),i(s(fun(fun(Q88408,bool),fun(fun(Q88409,bool),bool)),l_a_u_c),s(fun(Q88408,bool),S0))),s(fun(Q88409,bool),T0)))))) # label(aCARDu_LTu_IMPu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 84 (all A all F0 all U all V (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),U))),s(fun(A,bool),V)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V)))) & -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) -> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(A,num),F0),s(A,X))))) -> s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),V))),s(fun(A,num),F0))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),U))),s(fun(A,num),F0))))) # label(aNSUMu_SUPERSET) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 85 (all A all P0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),poset),s(fun(prod(A,A),bool),P0)))) -> (exists T0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),toset),s(fun(prod(A,A),bool),T0)))) & p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),subset),s(fun(prod(A,A),bool),P0))),s(fun(prod(A,A),bool),T0)))) & s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),T0))) = s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),P0))))))) # label(aOEP) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 86 (all X (s(real,X) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,i(s(fun(real,real),realu_inv),s(real,X))))))) # label(aREALu_MULu_RINV) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 87 (all M0 all N0 p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,M0))))),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,N0))))))),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))))) # label(aTREALu_OFu_NUMu_ADD) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 88 (all A all C all P all B all U_0 ((all CLAUSES all C0 all F0 ((all S0 all T0 exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(P,A),fun(C,fun(P,B))),bool),F0),s(prod(fun(P,A),fun(C,fun(P,B))),i(s(fun(fun(C,fun(P,B)),prod(fun(P,A),fun(C,fun(P,B)))),i(s(fun(fun(P,A),fun(fun(C,fun(P,B)),prod(fun(P,A),fun(C,fun(P,B))))),c_),s(fun(P,A),S0))),s(fun(C,fun(P,B)),T0))))))),s(bool,V)))) & (p(s(bool,V)) <-> (all X s(B,i(s(fun(P,B),i(s(fun(C,fun(P,B)),T0),s(C,C0))),s(P,X))) = s(B,i(s(fun(A,B),i(s(fun(C,fun(A,B)),i(s(fun(list(prod(fun(P,A),fun(C,fun(P,B)))),fun(C,fun(A,B))),casewise),s(list(prod(fun(P,A),fun(C,fun(P,B)))),CLAUSES))),s(C,C0))),s(A,i(s(fun(P,A),S0),s(P,X))))))))) <-> p(s(bool,i(s(fun(fun(prod(fun(P,A),fun(C,fun(P,B))),bool),bool),i(s(fun(C,fun(fun(prod(fun(P,A),fun(C,fun(P,B))),bool),bool)),i(s(fun(list(prod(fun(P,A),fun(C,fun(P,B)))),fun(C,fun(fun(prod(fun(P,A),fun(C,fun(P,B))),bool),bool))),U_0),s(list(prod(fun(P,A),fun(C,fun(P,B)))),CLAUSES))),s(C,C0))),s(fun(prod(fun(P,A),fun(C,fun(P,B))),bool),F0)))))) -> (all CLAUSES all C0 ((all S0 all T0 all SI_ all TI_ all X all Y (p(s(bool,i(s(fun(list(prod(fun(P,A),fun(C,fun(P,B)))),bool),i(s(fun(prod(fun(P,A),fun(C,fun(P,B))),fun(list(prod(fun(P,A),fun(C,fun(P,B)))),bool)),mem),s(prod(fun(P,A),fun(C,fun(P,B))),i(s(fun(fun(C,fun(P,B)),prod(fun(P,A),fun(C,fun(P,B)))),i(s(fun(fun(P,A),fun(fun(C,fun(P,B)),prod(fun(P,A),fun(C,fun(P,B))))),c_),s(fun(P,A),S0))),s(fun(C,fun(P,B)),T0))))),s(list(prod(fun(P,A),fun(C,fun(P,B)))),CLAUSES)))) & s(A,i(s(fun(P,A),SI_),s(P,Y))) = s(A,i(s(fun(P,A),S0),s(P,X))) & p(s(bool,i(s(fun(list(prod(fun(P,A),fun(C,fun(P,B)))),bool),i(s(fun(prod(fun(P,A),fun(C,fun(P,B))),fun(list(prod(fun(P,A),fun(C,fun(P,B)))),bool)),mem),s(prod(fun(P,A),fun(C,fun(P,B))),i(s(fun(fun(C,fun(P,B)),prod(fun(P,A),fun(C,fun(P,B)))),i(s(fun(fun(P,A),fun(fun(C,fun(P,B)),prod(fun(P,A),fun(C,fun(P,B))))),c_),s(fun(P,A),SI_))),s(fun(C,fun(P,B)),TI_))))),s(list(prod(fun(P,A),fun(C,fun(P,B)))),CLAUSES)))) -> s(B,i(s(fun(P,B),i(s(fun(C,fun(P,B)),T0),s(C,C0))),s(P,X))) = s(B,i(s(fun(P,B),i(s(fun(C,fun(P,B)),TI_),s(C,C0))),s(P,Y))))) -> p(s(bool,i(s(fun(list(prod(fun(P,A),fun(C,fun(P,B)))),bool),i(s(fun(fun(prod(fun(P,A),fun(C,fun(P,B))),bool),fun(list(prod(fun(P,A),fun(C,fun(P,B)))),bool)),all0),s(fun(prod(fun(P,A),fun(C,fun(P,B))),bool),i(s(fun(fun(fun(prod(fun(P,A),fun(C,fun(P,B))),bool),bool),fun(prod(fun(P,A),fun(C,fun(P,B))),bool)),gabs),s(fun(fun(prod(fun(P,A),fun(C,fun(P,B))),bool),bool),i(s(fun(C,fun(fun(prod(fun(P,A),fun(C,fun(P,B))),bool),bool)),i(s(fun(list(prod(fun(P,A),fun(C,fun(P,B)))),fun(C,fun(fun(prod(fun(P,A),fun(C,fun(P,B))),bool),bool))),U_0),s(list(prod(fun(P,A),fun(C,fun(P,B)))),CLAUSES))),s(C,C0))))))),s(list(prod(fun(P,A),fun(C,fun(P,B)))),CLAUSES)))))))) # label(aCASEWISEu_WORKS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 89 (all P0 all Q0 all R0 ((p(s(bool,Q0)) | p(s(bool,P0))) & p(s(bool,R0)) <-> p(s(bool,P0)) & p(s(bool,R0)) | p(s(bool,Q0)) & p(s(bool,R0)))) # label(aRIGHTu_ORu_DISTRIB) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 90 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))) # label(aREALu_LEu_ADDR) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 91 (all D all A all B all P all C all U_1 ((all G0 all Y all F0 all X s(D,i(s(fun(P,D),i(s(fun(fun(A,B),fun(P,D)),i(s(fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D))),i(s(fun(fun(P,fun(C,D)),fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D)))),U_1),s(fun(P,fun(C,D)),G0))),s(fun(fun(A,B),fun(P,C)),Y))),s(fun(A,B),F0))),s(P,X))) = s(D,i(s(fun(C,D),i(s(fun(P,fun(C,D)),G0),s(P,X))),s(C,i(s(fun(P,C),i(s(fun(fun(A,B),fun(P,C)),Y),s(fun(A,B),F0))),s(P,X)))))) -> (all U_0 ((all G0 all Y all F0 s(fun(P,D),i(s(fun(fun(A,B),fun(P,D)),i(s(fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D))),i(s(fun(fun(P,fun(C,D)),fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D)))),U_1),s(fun(P,fun(C,D)),G0))),s(fun(fun(A,B),fun(P,C)),Y))),s(fun(A,B),F0))) = s(fun(P,D),i(s(fun(fun(A,B),fun(P,D)),i(s(fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D))),i(s(fun(fun(P,fun(C,D)),fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D)))),U_0),s(fun(P,fun(C,D)),G0))),s(fun(fun(A,B),fun(P,C)),Y))),s(fun(A,B),F0)))) -> (all L_L_ all P0 all S0 all G0 all Y (p(s(bool,i(s(fun(fun(fun(A,B),fun(P,C)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,C)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,C)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,C)),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,C)),Y)))) -> p(s(bool,i(s(fun(fun(fun(A,B),fun(P,D)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,D)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,D)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,D)),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,D)),i(s(fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D))),i(s(fun(fun(P,fun(C,D)),fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D)))),U_0),s(fun(P,fun(C,D)),G0))),s(fun(fun(A,B),fun(P,C)),Y)))))))))))) # label(aADMISSIBLEu_RAND) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 92 (all A5 all B0 ((exists X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,A5))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,B0)))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,A5))),s(real,B0)))))) # label(aREALu_LTu_BETWEEN) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 93 (all X s(int,i(s(fun(int,int),intu_neg),s(int,X))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(int,X)))) # label(aINTu_NEGu_MINUS1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 94 (all X all Y all Z0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Y))),s(int,Z0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))),s(int,Z0)))) # label(aINTu_ADDu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 95 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (exists N0 all M0 all N1 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,N1)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N1))))))),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,N1))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N1))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,M0))))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N1))))),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N1))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N1))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,M0))))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N1))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N1)))))))))))))) # label(aNADDu_MULu_LINVu_LEMMA4) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 96 (all A all X all S0 all T0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),i(s(fun(bool,fun(fun(A,bool),fun(fun(A,bool),fun(A,bool)))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))),s(fun(A,bool),T0)))) # label(aINSERTu_UNION) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 97 (all A ((all P0 ((all X ((all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Y))),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))))) -> p(s(bool,i(s(fun(A,bool),P0),s(A,X)))))) -> (all X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) <-> p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))))) # label(aWFu_IND) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 98 (all Q18890 s(list(Q18890),i(s(fun(list(Q18890),list(Q18890)),i(s(fun(fun(Q18890,bool),fun(list(Q18890),list(Q18890))),filter0),s(fun(Q18890,bool),p0))),s(list(Q18890),i(s(fun(list(Q18890),list(Q18890)),i(s(fun(Q18890,fun(list(Q18890),list(Q18890))),cons),s(Q18890,h0))),s(list(Q18890),t0))))) = s(list(Q18890),i(s(fun(list(Q18890),list(Q18890)),i(s(fun(list(Q18890),fun(list(Q18890),list(Q18890))),i(s(fun(bool,fun(list(Q18890),fun(list(Q18890),list(Q18890)))),cond),s(bool,i(s(fun(Q18890,bool),p0),s(Q18890,h0))))),s(list(Q18890),i(s(fun(list(Q18890),list(Q18890)),i(s(fun(Q18890,fun(list(Q18890),list(Q18890))),cons),s(Q18890,h0))),s(list(Q18890),i(s(fun(list(Q18890),list(Q18890)),i(s(fun(fun(Q18890,bool),fun(list(Q18890),list(Q18890))),filter0),s(fun(Q18890,bool),p0))),s(list(Q18890),t0))))))),s(list(Q18890),i(s(fun(list(Q18890),list(Q18890)),i(s(fun(fun(Q18890,bool),fun(list(Q18890),list(Q18890))),filter0),s(fun(Q18890,bool),p0))),s(list(Q18890),t0)))))) # label(aFILTERu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 99 (all Q4857 all Q4856 all Q4855 all U_0 ((all P0 all F0 (p(s(bool,i(s(fun(fun(prod(Q4857,prod(Q4856,Q4855)),bool),bool),i(s(fun(fun(Q4857,fun(Q4856,fun(Q4855,bool))),fun(fun(prod(Q4857,prod(Q4856,Q4855)),bool),bool)),U_0),s(fun(Q4857,fun(Q4856,fun(Q4855,bool))),P0))),s(fun(prod(Q4857,prod(Q4856,Q4855)),bool),F0)))) <-> (all X all Y all Z0 p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(Q4857,prod(Q4856,Q4855)),bool),F0),s(prod(Q4857,prod(Q4856,Q4855)),i(s(fun(prod(Q4856,Q4855),prod(Q4857,prod(Q4856,Q4855))),i(s(fun(Q4857,fun(prod(Q4856,Q4855),prod(Q4857,prod(Q4856,Q4855)))),c_),s(Q4857,X))),s(prod(Q4856,Q4855),i(s(fun(Q4855,prod(Q4856,Q4855)),i(s(fun(Q4856,fun(Q4855,prod(Q4856,Q4855))),c_),s(Q4856,Y))),s(Q4855,Z0))))))))),s(bool,i(s(fun(Q4855,bool),i(s(fun(Q4856,fun(Q4855,bool)),i(s(fun(Q4857,fun(Q4856,fun(Q4855,bool))),P0),s(Q4857,X))),s(Q4856,Y))),s(Q4855,Z0))))))))) -> (all P0 ((all X all Y all Z0 p(s(bool,i(s(fun(Q4855,bool),i(s(fun(Q4856,fun(Q4855,bool)),i(s(fun(Q4857,fun(Q4856,fun(Q4855,bool))),P0),s(Q4857,X))),s(Q4856,Y))),s(Q4855,Z0))))) <-> p(s(bool,i(s(fun(fun(prod(Q4857,prod(Q4856,Q4855)),bool),bool),e_),s(fun(prod(Q4857,prod(Q4856,Q4855)),bool),i(s(fun(fun(fun(prod(Q4857,prod(Q4856,Q4855)),bool),bool),fun(prod(Q4857,prod(Q4856,Q4855)),bool)),gabs),s(fun(fun(prod(Q4857,prod(Q4856,Q4855)),bool),bool),i(s(fun(fun(Q4857,fun(Q4856,fun(Q4855,bool))),fun(fun(prod(Q4857,prod(Q4856,Q4855)),bool),bool)),U_0),s(fun(Q4857,fun(Q4856,fun(Q4855,bool))),P0)))))))))))) # label(aFORALLu_TRIPLEDu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 100 s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(real,y1) & s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(real,y2) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x1))),s(real,y2))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x2))),s(real,y1))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_inv),s(real,y1))))),s(real,i(s(fun(real,real),realu_inv),s(real,y2))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,x1))),s(real,y1))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,x2))),s(real,y2))))) # label(aRATu_LEMMA1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 101 (all M0 all N0 all P0 (s(hreal,P0) = s(hreal,N0) <-> s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,M0))),s(hreal,P0))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,M0))),s(hreal,N0))))) # label(aHREALu_EQu_ADDu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 102 (all C all A all B all P0 ((all X1 all Y1 all X2 all Y2 (s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),P0),s(A,X2))),s(B,Y2))) = s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),P0),s(A,X1))),s(B,Y1))) <-> s(A,X2) = s(A,X1) & s(B,Y1) = s(B,Y2))) -> (exists X exists Y all X0 all Y0 (s(A,X0) = s(A,i(s(fun(C,A),X),s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),P0),s(A,X0))),s(B,Y0))))) & s(B,i(s(fun(C,B),Y),s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),P0),s(A,X0))),s(B,Y0))))) = s(B,Y0))))) # label(aINJu_INVERSE2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 103 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,u_0))),s(num,i(s(fun(num,num),bit0),s(num,N0))))) = s(num,i(s(fun(num,num),bit0),s(num,N0)))) # label(aARITHu_ADDu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 104 (all Q67015 all F0 all S0 s(num,i(s(fun(fun(Q67015,num),num),i(s(fun(fun(Q67015,bool),fun(fun(Q67015,num),num)),nsum),s(fun(Q67015,bool),i(s(fun(fun(Q67015,bool),fun(Q67015,bool)),i(s(fun(fun(Q67015,num),fun(fun(Q67015,bool),fun(Q67015,bool))),i(s(fun(fun(num,fun(num,num)),fun(fun(Q67015,num),fun(fun(Q67015,bool),fun(Q67015,bool)))),support),s(fun(num,fun(num,num)),p_))),s(fun(Q67015,num),F0))),s(fun(Q67015,bool),S0))))),s(fun(Q67015,num),F0))) = s(num,i(s(fun(fun(Q67015,num),num),i(s(fun(fun(Q67015,bool),fun(fun(Q67015,num),num)),nsum),s(fun(Q67015,bool),S0))),s(fun(Q67015,num),F0)))) # label(aNSUMu_SUPPORT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 105 (all X all Y s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,X))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,Y))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),numpair),s(num,X))),s(num,Y)))) # label(aNUMPAIR) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 106 (all A all B all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(B,bool),fun(num,bool)),hasu_size),s(fun(B,bool),univ))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),univ))),s(num,M0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(fun(A,B),bool),fun(num,bool)),hasu_size),s(fun(fun(A,B),bool),univ))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,N0))),s(num,M0)))))))) # label(aHASu_SIZEu_FUNSPACEu_UNIV) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 107 (all X all Y all Z0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))),s(real,Z0)))) # label(aREALu_ADDu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 108 (all X all Y all Z0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))),s(int,Z0))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Z0))),s(int,Y)))))) # label(aINTu_LTu_ADDu_SUB) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 109 (all X all Y all Z0 p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Y))))),s(nadd,Z0))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Z0))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,Y))),s(nadd,Z0))))))))) # label(aNADDu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 110 (all A all B all A5 s(prod(A,B),i(s(fun(fun(A,fun(B,bool)),prod(A,B)),absu_prod),s(fun(A,fun(B,bool)),i(s(fun(prod(A,B),fun(A,fun(B,bool))),repu_prod),s(prod(A,B),A5))))) = s(prod(A,B),A5)) # label(aprodu_tybiju_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 111 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X))))))))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,Y))))),s(real,Z0)))))) # label(aREALu_ABSu_TRIANGLEu_LT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 112 (all X all Y (s(real,X) = s(real,i(s(fun(real,real),realu_neg),s(real,Y))) <-> s(real,Y) = s(real,i(s(fun(real,real),realu_neg),s(real,X))))) # label(aREALu_NEGu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 113 (all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))) = s(real,X)) # label(aREALu_ADDu_LID) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 114 (all Q47649 all U_0 ((all X s(Q47649,i(s(fun(Q47649,Q47649),U_0),s(Q47649,X))) = s(Q47649,X)) -> (all S0 s(fun(Q47649,bool),S0) = s(fun(Q47649,bool),i(s(fun(fun(Q47649,bool),fun(Q47649,bool)),i(s(fun(fun(Q47649,Q47649),fun(fun(Q47649,bool),fun(Q47649,bool))),image),s(fun(Q47649,Q47649),U_0))),s(fun(Q47649,bool),S0)))))) # label(aIMAGEu_ID) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 115 (all Q47492 all Q47481 ((all X (p(s(bool,i(s(fun(fun(Q47481,bool),bool),i(s(fun(Q47481,fun(fun(Q47481,bool),bool)),in),s(Q47481,X))),s(fun(Q47481,bool),s0)))) -> p(s(bool,i(s(fun(fun(Q47492,bool),bool),i(s(fun(fun(Q47492,bool),fun(fun(Q47492,bool),bool)),subset),s(fun(Q47492,bool),i(s(fun(Q47481,fun(Q47492,bool)),f),s(Q47481,X))))),s(fun(Q47492,bool),i(s(fun(Q47481,fun(Q47492,bool)),g),s(Q47481,X)))))))) -> p(s(bool,i(s(fun(fun(Q47492,bool),bool),i(s(fun(fun(Q47492,bool),fun(fun(Q47492,bool),bool)),subset),s(fun(Q47492,bool),i(s(fun(fun(fun(Q47492,bool),bool),fun(Q47492,bool)),unions),s(fun(fun(Q47492,bool),bool),i(s(fun(fun(Q47481,bool),fun(fun(Q47492,bool),bool)),i(s(fun(fun(Q47481,fun(Q47492,bool)),fun(fun(Q47481,bool),fun(fun(Q47492,bool),bool))),image),s(fun(Q47481,fun(Q47492,bool)),f))),s(fun(Q47481,bool),s0))))))),s(fun(Q47492,bool),i(s(fun(fun(fun(Q47492,bool),bool),fun(Q47492,bool)),unions),s(fun(fun(Q47492,bool),bool),i(s(fun(fun(Q47481,bool),fun(fun(Q47492,bool),bool)),i(s(fun(fun(Q47481,fun(Q47492,bool)),fun(fun(Q47481,bool),fun(fun(Q47492,bool),bool))),image),s(fun(Q47481,fun(Q47492,bool)),g))),s(fun(Q47481,bool),s0)))))))))) # label(aUNIONSu_MONOu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 116 (all M0 all N0 s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(fun(num,bool),fun(fun(num,bool),fun(num,bool))),i(s(fun(bool,fun(fun(num,bool),fun(fun(num,bool),fun(num,bool)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(num,fun(fun(num,bool),fun(num,bool))),insert),s(num,i(s(fun(num,num),suc),s(num,N0))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))) = s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aNUMSEGu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 117 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))))) # label(aREALu_LTu_RCANCELu_IMP) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 118 (all M0 all N0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(fun(num,real),f))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),f))))),s(real,i(s(fun(num,real),f),s(num,i(s(fun(num,num),suc),s(num,N0))))))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),f)))))) # label(aSUMu_CLAUSESu_NUMSEGu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 119 (all A all B all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all U all V ((all X (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V)))) -> s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(fun(B,fun(B,B)),B),neutral),s(fun(B,fun(B,B)),OP))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),U))),s(fun(A,bool),V)))) -> s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),V))),s(fun(A,B),F0))) = s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),U))),s(fun(A,B),F0))))))) # label(aITERATEu_SUPERSET) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 120 (all M0 all N0 (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))) = s(num,N0) <-> s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aEQu_ADDu_RCANCELu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 121 (all X s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X))) = s(int,i(s(fun(int,int),intu_neg),s(int,X)))) # label(aINTu_SUBu_LZERO) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 122 (all A all S0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),empty))),s(fun(A,bool),S0))))) # label(aEMPTYu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 13.83/13.84 123 (all U_0 ((all A5 all B0 all GENR_PVARR_126 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),i(s(fun(real,fun(real,fun(real,bool))),U_0),s(real,A5))),s(real,B0))),s(real,GENR_PVARR_126)))) <-> (exists X exists V (p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_126))),s(bool,V))),s(real,X)))) & (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,B0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,A5))),s(real,X)))) <-> p(s(bool,V))))))) -> (all A5 all B0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,A5))) = s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(real,fun(real,bool)),i(s(fun(real,fun(real,fun(real,bool))),U_0),s(real,A5))),s(real,B0)))))))))) # label(aFINITEu_REALu_INTERVALu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 124 (all Q46638 s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),p1))),s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),p1))),s(fun(Q46638,bool),q))))) = s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),p1))),s(fun(Q46638,bool),q)))) # label(aINTERu_ACIu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 125 (p(s(bool,c0)) -> p(s(bool,d0))) & (p(s(bool,a)) -> p(s(bool,b))) -> (p(s(bool,c0)) & p(s(bool,a)) -> p(s(bool,b)) & p(s(bool,d0))) # label(aMONOu_AND) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 126 (all A all C all B all D all S0 all SI_ all T0 all TI_ (p(s(bool,i(s(fun(fun(D,bool),bool),i(s(fun(fun(C,bool),fun(fun(D,bool),bool)),a_u_c),s(fun(C,bool),T0))),s(fun(D,bool),TI_)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),SI_)))) -> s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(A,bool),fun(fun(C,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(C,bool),T0))) = s(bool,i(s(fun(fun(D,bool),bool),i(s(fun(fun(B,bool),fun(fun(D,bool),bool)),a_u_c),s(fun(B,bool),SI_))),s(fun(D,bool),TI_))))) # label(aCARDu_EQu_CONG) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 127 (all N0 -p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,u_0))),s(num,i(s(fun(num,num),bit0),s(num,N0))))))) # label(aARITHu_GTu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 128 (all Q78499 all Q78498 all Q78500 ((exists X exists Y p(s(bool,i(s(fun(cart(Q78498,finite_sum(Q78499,Q78500)),bool),p0),s(cart(Q78498,finite_sum(Q78499,Q78500)),i(s(fun(cart(Q78498,Q78500),cart(Q78498,finite_sum(Q78499,Q78500))),i(s(fun(cart(Q78498,Q78499),fun(cart(Q78498,Q78500),cart(Q78498,finite_sum(Q78499,Q78500)))),pastecart),s(cart(Q78498,Q78499),X))),s(cart(Q78498,Q78500),Y))))))) <-> (exists P0 p(s(bool,i(s(fun(cart(Q78498,finite_sum(Q78499,Q78500)),bool),p0),s(cart(Q78498,finite_sum(Q78499,Q78500)),P0))))))) # label(aEXISTSu_PASTECART) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 129 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,i(s(fun(int,int),intu_neg),s(int,Y))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y))),s(int,X)))) # label(aINTu_SUBu_NEG2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 130 (exists F0 exists Z0 ((all X s(ind0,Z0) != s(ind0,i(s(fun(ind0,ind0),F0),s(ind0,X)))) & (all X1 all X2 (s(ind0,i(s(fun(ind0,ind0),F0),s(ind0,X1))) = s(ind0,i(s(fun(ind0,ind0),F0),s(ind0,X2))) <-> s(ind0,X1) = s(ind0,X2))))) # label(aINDu_SUCu_0u_EXISTS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 131 (all A all K0 (p(s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),K0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(A,bool),bool)),a_u_c),s(fun(prod(A,A),bool),i(s(fun(fun(A,bool),fun(prod(A,A),bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(prod(A,A),bool))),t_u_c),s(fun(A,bool),K0))),s(fun(A,bool),K0))))),s(fun(A,bool),K0)))))) # label(aCARDu_SQUAREu_INFINITE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 132 (all U_2 ((all A5 all J0 all Y all K0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(num,fun(real,fun(num,real))),i(s(fun(fun(num,real),fun(num,fun(real,fun(num,real)))),U_2),s(fun(num,real),A5))),s(num,J0))),s(real,Y))),s(num,K0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),A5),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,J0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,K0)))))) -> (all U_1 ((all N0 all A5 all Y all J0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,J0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(num,fun(real,fun(num,real))),i(s(fun(fun(num,real),fun(num,fun(real,fun(num,real)))),U_2),s(fun(num,real),A5))),s(num,J0))),s(real,Y))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),i(s(fun(num,fun(fun(num,real),fun(real,fun(num,real)))),U_1),s(num,N0))),s(fun(num,real),A5))),s(real,Y))),s(num,J0)))) -> (all U_0 ((all A5 all X all I0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),A5),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),A5))),s(real,X))),s(num,I0)))) -> (all A5 all X all Y all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),A5))),s(real,X))))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),A5))),s(real,Y))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),i(s(fun(num,fun(fun(num,real),fun(real,fun(num,real)))),U_1),s(num,N0))),s(fun(num,real),A5))),s(real,Y))))),s(real,X))))))))))))))) # label(aREALu_SUBu_POLYFUNu_ALT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 133 (all A all B all U_2 ((all X all F0 ((all I0 all J0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),geq),s(num,i(s(fun(prod(A,B),num),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,I0))),s(B,J0))))))),s(num,i(s(fun(B,num),i(s(fun(A,fun(B,num)),X),s(A,I0))),s(B,J0))))))) <-> p(s(bool,i(s(fun(fun(prod(A,B),num),bool),i(s(fun(fun(A,fun(B,num)),fun(fun(prod(A,B),num),bool)),U_2),s(fun(A,fun(B,num)),X))),s(fun(prod(A,B),num),F0)))))) -> (all U_1 ((all S0 all T0 all GENR_PVARR_169 (p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(prod(A,B),GENR_PVARR_169)))) <-> (exists I0 exists J0 exists V (p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(bool,fun(prod(A,B),bool)),i(s(fun(prod(A,B),fun(bool,fun(prod(A,B),bool))),setspec),s(prod(A,B),GENR_PVARR_169))),s(bool,V))),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,I0))),s(B,J0)))))) & (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0)))))) <-> p(s(bool,V))))))) -> (all U_0 ((all T0 all X all I0 s(num,i(s(fun(A,num),i(s(fun(fun(A,fun(B,num)),fun(A,num)),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,num)),fun(A,num))),U_0),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,num)),X))),s(A,I0))) = s(num,i(s(fun(fun(B,num),num),i(s(fun(fun(B,bool),fun(fun(B,num),num)),nsum),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0))))),s(fun(B,num),i(s(fun(A,fun(B,num)),X),s(A,I0)))))) -> (all S0 all T0 all X (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all I0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0)))))))) -> s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(fun(A,fun(B,num)),fun(A,num)),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,num)),fun(A,num))),U_0),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,num)),X))))) = s(num,i(s(fun(fun(prod(A,B),num),num),i(s(fun(fun(prod(A,B),bool),fun(fun(prod(A,B),num),num)),nsum),s(fun(prod(A,B),bool),i(s(fun(fun(prod(A,B),bool),fun(prod(A,B),bool)),gspec),s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))))))),s(fun(prod(A,B),num),i(s(fun(fun(fun(prod(A,B),num),bool),fun(prod(A,B),num)),gabs),s(fun(fun(prod(A,B),num),bool),i(s(fun(fun(A,fun(B,num)),fun(fun(prod(A,B),num),bool)),U_2),s(fun(A,fun(B,num)),X))))))))))))))) # label(aNSUMu_NSUMu_PRODUCT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 134 (all A all S0 ((exists X -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),univ)))))) # label(aPSUBSETu_UNIV) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 135 (all Q20083 all P0 all L1 all L2 s(list(Q20083),i(s(fun(list(Q20083),list(Q20083)),i(s(fun(list(Q20083),fun(list(Q20083),list(Q20083))),append),s(list(Q20083),i(s(fun(list(Q20083),list(Q20083)),i(s(fun(fun(Q20083,bool),fun(list(Q20083),list(Q20083))),filter0),s(fun(Q20083,bool),P0))),s(list(Q20083),L1))))),s(list(Q20083),i(s(fun(list(Q20083),list(Q20083)),i(s(fun(fun(Q20083,bool),fun(list(Q20083),list(Q20083))),filter0),s(fun(Q20083,bool),P0))),s(list(Q20083),L2))))) = s(list(Q20083),i(s(fun(list(Q20083),list(Q20083)),i(s(fun(fun(Q20083,bool),fun(list(Q20083),list(Q20083))),filter0),s(fun(Q20083,bool),P0))),s(list(Q20083),i(s(fun(list(Q20083),list(Q20083)),i(s(fun(list(Q20083),fun(list(Q20083),list(Q20083))),append),s(list(Q20083),L1))),s(list(Q20083),L2)))))) # label(aFILTERu_APPEND) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 136 p(s(bool,i(s(fun(num,bool),p0),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,x))),s(num,y)))))))) <-> (all D0 ((s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,x))),s(num,D0))) = s(num,y) -> p(s(bool,i(s(fun(num,bool),p0),s(num,D0))))) & (s(num,x) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,y))),s(num,D0))) -> p(s(bool,i(s(fun(num,bool),p0),s(num,D0))))))) # label(aDISTu_ELIMu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 137 (all A all P0 all Q0 ((all X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) & (all X p(s(bool,i(s(fun(A,bool),Q0),s(A,X))))) <-> (all X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) & p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))))) # label(aFORALLu_ANDu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 138 (all C all B all A all F0 all G0 all X s(C,i(s(fun(B,C),F0),s(B,i(s(fun(A,B),G0),s(A,X))))) = s(C,i(s(fun(A,C),i(s(fun(fun(A,B),fun(A,C)),i(s(fun(fun(B,C),fun(fun(A,B),fun(A,C))),o),s(fun(B,C),F0))),s(fun(A,B),G0))),s(A,X)))) # label(aou_DEF) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 139 p(s(bool,q)) & p(s(bool,p1)) & p(s(bool,r0)) <-> p(s(bool,q)) & p(s(bool,r0)) & p(s(bool,p1)) # label(aCONJu_ACIu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 140 (all Q69603 all F0 all P0 all S0 ((all X (p(s(bool,i(s(fun(fun(Q69603,bool),bool),i(s(fun(Q69603,fun(fun(Q69603,bool),bool)),in),s(Q69603,X))),s(fun(Q69603,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q69603,bool),bool),i(s(fun(Q69603,fun(fun(Q69603,bool),bool)),in),s(Q69603,i(s(fun(Q69603,Q69603),P0),s(Q69603,X))))),s(fun(Q69603,bool),S0)))))) & (all X all Y (p(s(bool,i(s(fun(fun(Q69603,bool),bool),i(s(fun(Q69603,fun(fun(Q69603,bool),bool)),in),s(Q69603,Y))),s(fun(Q69603,bool),S0)))) & s(Q69603,i(s(fun(Q69603,Q69603),P0),s(Q69603,Y))) = s(Q69603,i(s(fun(Q69603,Q69603),P0),s(Q69603,X))) & p(s(bool,i(s(fun(fun(Q69603,bool),bool),i(s(fun(Q69603,fun(fun(Q69603,bool),bool)),in),s(Q69603,X))),s(fun(Q69603,bool),S0)))) -> s(Q69603,X) = s(Q69603,Y))) & p(s(bool,i(s(fun(fun(Q69603,bool),bool),finite),s(fun(Q69603,bool),S0)))) -> s(num,i(s(fun(fun(Q69603,num),num),i(s(fun(fun(Q69603,bool),fun(fun(Q69603,num),num)),nsum),s(fun(Q69603,bool),S0))),s(fun(Q69603,num),i(s(fun(fun(Q69603,Q69603),fun(Q69603,num)),i(s(fun(fun(Q69603,num),fun(fun(Q69603,Q69603),fun(Q69603,num))),o),s(fun(Q69603,num),F0))),s(fun(Q69603,Q69603),P0))))) = s(num,i(s(fun(fun(Q69603,num),num),i(s(fun(fun(Q69603,bool),fun(fun(Q69603,num),num)),nsum),s(fun(Q69603,bool),S0))),s(fun(Q69603,num),F0))))) # label(aNSUMu_INJECTION) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 141 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,Z0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Z0)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y))))),s(int,Z0)))))) # label(aINTu_MAXu_LT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 142 (all Q83929 all P0 all Q0 (p(s(bool,i(s(fun(fun(Q83929,bool),bool),i(s(fun(fun(Q83929,bool),fun(fun(Q83929,bool),bool)),subset),s(fun(Q83929,bool),P0))),s(fun(Q83929,bool),Q0)))) <-> (all X (p(s(bool,i(s(fun(Q83929,bool),P0),s(Q83929,X)))) -> p(s(bool,i(s(fun(Q83929,bool),Q0),s(Q83929,X)))))))) # label(aSUBSETu_PRED) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 143 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) -> s(real,Y) != s(real,X))) # label(aREALu_LTu_IMPu_NE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 144 (all A all F0 all U all V (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),U))),s(fun(A,bool),V)))) & (all X (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V)))) -> s(real,i(s(fun(A,real),F0),s(A,X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) -> s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),V))),s(fun(A,real),F0))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),U))),s(fun(A,real),F0))))) # label(aSUMu_SUPERSET) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 145 (all A all S0 all F0 all B0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,B0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,B0)))))))) # label(aNSUMu_BOUND) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 146 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),poset),s(fun(prod(A,A),bool),L)))) -> (all X (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,X)))))))))) # label(aPOSETu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 147 (all A all U_0 ((all X all X0 all XI_ all XI_I_ (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(bool,fun(A,fun(A,bool))),i(s(fun(A,fun(bool,fun(A,fun(A,bool)))),U_0),s(A,X))),s(bool,X0))),s(A,XI_))),s(A,XI_I_)))) <-> (s(bool,X0) = s(bool,f0) -> s(A,XI_I_) = s(A,XI_)) & (s(bool,t) = s(bool,X0) -> s(A,XI_I_) = s(A,X)))) -> (all X all X0 all XI_ s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),i(s(fun(bool,fun(A,fun(A,A))),cond),s(bool,X))),s(A,X0))),s(A,XI_))) = s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(bool,fun(A,fun(A,bool))),i(s(fun(A,fun(bool,fun(A,fun(A,bool)))),U_0),s(A,X0))),s(bool,X))),s(A,XI_)))))))) # label(aCONDu_DEF) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 148 (all A5 all B0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,A5) -> s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,B0))),s(num,A5))))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,B0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) # label(aLEu_LDIVu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 149 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all X all Y all Z0 (p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,Z0)))))) -> p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Z0)))))))))) # label(aWOSETu_TRANSu_LESS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 150 (all X all XI_ (p(s(bool,X)) & p(s(bool,XI_)) <-> (all X0 s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),X0),s(bool,t))),s(bool,t))) = s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),X0),s(bool,X))),s(bool,XI_)))))) # label(aANDu_DEF) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 151 (all A all X all S0 all T0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))),s(fun(A,bool),T0)))) # label(aINSERTu_UNIONu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 152 (all M0 all N0 -(p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))))) # label(aLTEu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 153 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,N0)))) # label(aMULTu_2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 154 (all X all Y -(p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,X)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))))) # label(aINTu_LTEu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 155 (all Q87963 all Q87964 ((all X (p(s(bool,i(s(fun(fun(Q87964,bool),bool),i(s(fun(Q87964,fun(fun(Q87964,bool),bool)),in),s(Q87964,X))),s(fun(Q87964,bool),s0)))) -> p(s(bool,i(s(fun(fun(Q87963,bool),bool),i(s(fun(Q87963,fun(fun(Q87963,bool),bool)),in),s(Q87963,i(s(fun(Q87964,Q87963),f),s(Q87964,X))))),s(fun(Q87963,bool),t0)))))) & (all Y (p(s(bool,i(s(fun(fun(Q87963,bool),bool),i(s(fun(Q87963,fun(fun(Q87963,bool),bool)),in),s(Q87963,Y))),s(fun(Q87963,bool),t0)))) -> (all X all XI_ (p(s(bool,i(s(fun(fun(Q87964,bool),bool),i(s(fun(Q87964,fun(fun(Q87964,bool),bool)),in),s(Q87964,X))),s(fun(Q87964,bool),s0)))) & s(Q87963,i(s(fun(Q87964,Q87963),f),s(Q87964,X))) = s(Q87963,Y) & s(Q87963,Y) = s(Q87963,i(s(fun(Q87964,Q87963),f),s(Q87964,XI_))) & p(s(bool,i(s(fun(fun(Q87964,bool),bool),i(s(fun(Q87964,fun(fun(Q87964,bool),bool)),in),s(Q87964,XI_))),s(fun(Q87964,bool),s0)))) -> s(Q87964,X) = s(Q87964,XI_))) & (exists X (p(s(bool,i(s(fun(fun(Q87964,bool),bool),i(s(fun(Q87964,fun(fun(Q87964,bool),bool)),in),s(Q87964,X))),s(fun(Q87964,bool),s0)))) & s(Q87963,i(s(fun(Q87964,Q87963),f),s(Q87964,X))) = s(Q87963,Y))))) <-> (all X (p(s(bool,i(s(fun(fun(Q87964,bool),bool),i(s(fun(Q87964,fun(fun(Q87964,bool),bool)),in),s(Q87964,X))),s(fun(Q87964,bool),s0)))) -> p(s(bool,i(s(fun(fun(Q87963,bool),bool),i(s(fun(Q87963,fun(fun(Q87963,bool),bool)),in),s(Q87963,i(s(fun(Q87964,Q87963),f),s(Q87964,X))))),s(fun(Q87963,bool),t0)))))) & (exists G0 ((all Y (p(s(bool,i(s(fun(fun(Q87963,bool),bool),i(s(fun(Q87963,fun(fun(Q87963,bool),bool)),in),s(Q87963,Y))),s(fun(Q87963,bool),t0)))) -> s(Q87963,Y) = s(Q87963,i(s(fun(Q87964,Q87963),f),s(Q87964,i(s(fun(Q87963,Q87964),G0),s(Q87963,Y))))))) & (all X (p(s(bool,i(s(fun(fun(Q87964,bool),bool),i(s(fun(Q87964,fun(fun(Q87964,bool),bool)),in),s(Q87964,X))),s(fun(Q87964,bool),s0)))) -> s(Q87964,i(s(fun(Q87963,Q87964),G0),s(Q87963,i(s(fun(Q87964,Q87963),f),s(Q87964,X))))) = s(Q87964,X))) & (all Y (p(s(bool,i(s(fun(fun(Q87963,bool),bool),i(s(fun(Q87963,fun(fun(Q87963,bool),bool)),in),s(Q87963,Y))),s(fun(Q87963,bool),t0)))) -> p(s(bool,i(s(fun(fun(Q87964,bool),bool),i(s(fun(Q87964,fun(fun(Q87964,bool),bool)),in),s(Q87964,i(s(fun(Q87963,Q87964),G0),s(Q87963,Y))))),s(fun(Q87964,bool),s0)))))))))) # label(aBIJECTIVEu_INVERSES) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 156 (all M0 all N0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))) # label(aMODu_MODu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 157 (all P0 ((exists X p(s(bool,i(s(fun(nadd,bool),P0),s(nadd,X))))) & (exists M0 all X (p(s(bool,i(s(fun(nadd,bool),P0),s(nadd,X)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,M0)))))) -> (exists M0 ((all X (p(s(bool,i(s(fun(nadd,bool),P0),s(nadd,X)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,M0)))))) & (all MI_ ((all X (p(s(bool,i(s(fun(nadd,bool),P0),s(nadd,X)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,MI_)))))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,M0))),s(nadd,MI_)))))))))) # label(aNADDu_COMPLETE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 158 (all A all P0 all S0 all T0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),fun(A,bool))),hull),s(fun(fun(A,bool),bool),P0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),fun(A,bool))),hull),s(fun(fun(A,bool),bool),P0))),s(fun(A,bool),S0))))),s(fun(A,bool),T0))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),fun(A,bool))),hull),s(fun(fun(A,bool),bool),P0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aHULLu_UNIONu_LEFT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 159 (all Q60081 all Q60084 all S0 all T0 ((exists F0 all Y (p(s(bool,i(s(fun(fun(Q60081,bool),bool),i(s(fun(Q60081,fun(fun(Q60081,bool),bool)),in),s(Q60081,Y))),s(fun(Q60081,bool),T0)))) -> (exists X (p(s(bool,i(s(fun(fun(Q60084,bool),bool),i(s(fun(Q60084,fun(fun(Q60084,bool),bool)),in),s(Q60084,X))),s(fun(Q60084,bool),S0)))) & s(Q60081,Y) = s(Q60081,i(s(fun(Q60084,Q60081),F0),s(Q60084,X))))))) <-> p(s(bool,i(s(fun(fun(Q60081,bool),bool),i(s(fun(fun(Q60084,bool),fun(fun(Q60081,bool),bool)),g_a_u_c),s(fun(Q60084,bool),S0))),s(fun(Q60081,bool),T0)))))) # label(aGEu_C) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 160 (all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,u_0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,N0))),s(num,u_0)))) # label(aARITHu_GTu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 161 (all U_0 ((all F0 all I0 s(real,i(s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),U_0),s(fun(num,real),F0))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))))),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) -> (all F0 all M0 all N0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),U_0),s(fun(num,real),F0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),F0)))))) # label(aSUMu_PAIR) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 162 (all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,X))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,X)))) # label(aREALu_MULu_2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.85 163 (all X all Y (s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))) = s(int,Y) <-> s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,X))) # label(aINTu_EQu_ADDu_RCANCELu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 164 (all I0 exists N0 (s(real,i(s(fun(int,real),realu_ofu_int),s(int,I0))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))) | s(real,i(s(fun(int,real),realu_ofu_int),s(int,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))) # label(adestu_intu_rep) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 165 (all M0 all P0 all N0 s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))) = s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,M0))),s(num,N0)))))) # label(aDISTu_RADD) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 166 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,i(s(fun(num,num),bit1),s(num,N0))))),s(num,i(s(fun(num,num),bit0),s(num,M0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,N0))),s(num,M0)))) # label(aARITHu_GEu_conjunct7) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 167 (all A all P0 all Q0 ((exists X (p(s(bool,P0)) & p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))) <-> (exists X p(s(bool,i(s(fun(A,bool),Q0),s(A,X))))) & p(s(bool,P0)))) # label(aRIGHTu_ANDu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 168 (all Q46638 s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),q))),s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),p1))),s(fun(Q46638,bool),r0))))) = s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),p1))),s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),q))),s(fun(Q46638,bool),r0)))))) # label(aINTERu_ACIu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 169 (all Q67448 all F0 all G0 all S0 ((all X (p(s(bool,i(s(fun(fun(Q67448,bool),bool),i(s(fun(Q67448,fun(fun(Q67448,bool),bool)),in),s(Q67448,X))),s(fun(Q67448,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(Q67448,num),F0),s(Q67448,X))))),s(num,i(s(fun(Q67448,num),G0),s(Q67448,X)))))))) & s(fun(Q67448,bool),empty) != s(fun(Q67448,bool),S0) & p(s(bool,i(s(fun(fun(Q67448,bool),bool),finite),s(fun(Q67448,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(Q67448,num),num),i(s(fun(fun(Q67448,bool),fun(fun(Q67448,num),num)),nsum),s(fun(Q67448,bool),S0))),s(fun(Q67448,num),F0))))),s(num,i(s(fun(fun(Q67448,num),num),i(s(fun(fun(Q67448,bool),fun(fun(Q67448,num),num)),nsum),s(fun(Q67448,bool),S0))),s(fun(Q67448,num),G0)))))))) # label(aNSUMu_LTu_ALL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 170 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,X)))))) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(real,X))) # label(aREALu_LTu_SQUARE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 171 (all A5 all B0 all C0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,A5))),s(num,B0)))) <-> (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,N0))))),s(num,C0))))))))) # label(aBOUNDSu_LINEAR) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 172 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> (s(real,Y) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))) <-> s(real,X) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,Y))),s(real,Z0)))))) # label(aREALu_EQu_RDIVu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 173 (all Q18547 s(list(Q18547),i(s(fun(list(Q18547),list(Q18547)),butlast),s(list(Q18547),nil))) = s(list(Q18547),nil)) # label(aBUTLASTu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 174 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Z0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Y))),s(real,Z0)))))))) # label(aTRIANGLEu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 175 (all X all Y (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,Y))),s(nadd,X)))) | p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y)))))) # label(aNADDu_LEu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 176 (all Q72277 all F0 all S0 all A5 (p(s(bool,i(s(fun(fun(Q72277,bool),bool),finite),s(fun(Q72277,bool),S0)))) & p(s(bool,i(s(fun(fun(Q72277,bool),bool),i(s(fun(Q72277,fun(fun(Q72277,bool),bool)),in),s(Q72277,A5))),s(fun(Q72277,bool),S0)))) -> s(real,i(s(fun(fun(Q72277,real),real),i(s(fun(fun(Q72277,bool),fun(fun(Q72277,real),real)),sum),s(fun(Q72277,bool),i(s(fun(Q72277,fun(Q72277,bool)),i(s(fun(fun(Q72277,bool),fun(Q72277,fun(Q72277,bool))),delete),s(fun(Q72277,bool),S0))),s(Q72277,A5))))),s(fun(Q72277,real),F0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(fun(Q72277,real),real),i(s(fun(fun(Q72277,bool),fun(fun(Q72277,real),real)),sum),s(fun(Q72277,bool),S0))),s(fun(Q72277,real),F0))))),s(real,i(s(fun(Q72277,real),F0),s(Q72277,A5))))))) # label(aSUMu_DELETE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 177 (all M0 (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,M0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) & s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(num,M0))) # label(aSUBu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 178 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) <-> s(num,N0) = s(num,M0) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))))) # label(aLTu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 179 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,N0))))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0)))))) # label(aARITHu_EXPu_conjunct9) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 180 (all M0 all N0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))) = s(num,M0))) # label(aDIVISIONu_SIMPu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 181 (all A all X all S0 all T0 s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(fun(A,bool),T0))) = s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),T0)))))) # label(aSUBSETu_INSERTu_DELETE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 182 (all M0 all N0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_ge),s(real,i(s(fun(num,real),realu_ofu_num),s(num,M0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,M0))),s(num,N0)))) # label(aREALu_OFu_NUMu_GE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 183 (all F0 all G0 all M0 all N0 ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,N0)))) -> s(num,i(s(fun(num,num),G0),s(num,I0))) = s(num,i(s(fun(num,num),F0),s(num,I0))))) -> s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),G0))) = s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),F0))))) # label(aNSUMu_EQu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 184 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Y))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) # label(aREALu_LTu_ADD1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 185 (exists F0 (p(s(bool,i(s(fun(fun(ind0,ind0),bool),oneu_one),s(fun(ind0,ind0),F0)))) & -p(s(bool,i(s(fun(fun(ind0,ind0),bool),onto),s(fun(ind0,ind0),F0)))))) # label(aINFINITYu_AX) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 186 (all M all A all N all U_0 ((all F0 all G0 all I0 s(A,i(s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),i(s(fun(cart(A,M),fun(cart(A,N),fun(num,A))),U_0),s(cart(A,M),F0))),s(cart(A,N),G0))),s(num,I0))) = s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),i(s(fun(bool,fun(A,fun(A,A))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))))),s(A,i(s(fun(num,A),i(s(fun(cart(A,M),fun(num,A)),d_),s(cart(A,M),F0))),s(num,I0))))),s(A,i(s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),d_),s(cart(A,N),G0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))))))) -> (all F0 all G0 s(cart(A,finite_sum(M,N)),i(s(fun(fun(num,A),cart(A,finite_sum(M,N))),lambda),s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),i(s(fun(cart(A,M),fun(cart(A,N),fun(num,A))),U_0),s(cart(A,M),F0))),s(cart(A,N),G0))))) = s(cart(A,finite_sum(M,N)),i(s(fun(cart(A,N),cart(A,finite_sum(M,N))),i(s(fun(cart(A,M),fun(cart(A,N),cart(A,finite_sum(M,N)))),pastecart),s(cart(A,M),F0))),s(cart(A,N),G0)))))) # label(apastecart) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 187 (all Q20771 all L (s(list(Q20771),L) != s(list(Q20771),nil) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(list(Q20771),num),length),s(list(Q20771),L))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(num,i(s(fun(list(Q20771),num),length),s(list(Q20771),i(s(fun(list(Q20771),list(Q20771)),tl),s(list(Q20771),L))))))) # label(aLENGTHu_TL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 188 (all U_0 ((all U (p(s(bool,i(s(fun(bool,bool),U_0),s(bool,U)))) <-> (exists X exists Y (s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y))) = s(bool,U) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(hreal,fun(nadd,bool)),destu_hreal),s(hreal,y))),s(nadd,Y)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(hreal,fun(nadd,bool)),destu_hreal),s(hreal,x))),s(nadd,X)))))))) -> s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,x))),s(hreal,y))) = s(bool,i(s(fun(fun(bool,bool),bool),h_),s(fun(bool,bool),U_0))))) # label(ahrealu_le) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 189 (all Q55109 all Q55114 all F0 all S0 all N0 ((all X all Y (p(s(bool,i(s(fun(fun(Q55114,bool),bool),i(s(fun(Q55114,fun(fun(Q55114,bool),bool)),in),s(Q55114,Y))),s(fun(Q55114,bool),S0)))) & s(Q55109,i(s(fun(Q55114,Q55109),F0),s(Q55114,X))) = s(Q55109,i(s(fun(Q55114,Q55109),F0),s(Q55114,Y))) & p(s(bool,i(s(fun(fun(Q55114,bool),bool),i(s(fun(Q55114,fun(fun(Q55114,bool),bool)),in),s(Q55114,X))),s(fun(Q55114,bool),S0)))) -> s(Q55114,X) = s(Q55114,Y))) -> s(bool,i(s(fun(num,bool),i(s(fun(fun(Q55114,bool),fun(num,bool)),hasu_size),s(fun(Q55114,bool),S0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(fun(Q55109,bool),fun(num,bool)),hasu_size),s(fun(Q55109,bool),i(s(fun(fun(Q55114,bool),fun(Q55109,bool)),i(s(fun(fun(Q55114,Q55109),fun(fun(Q55114,bool),fun(Q55109,bool))),image),s(fun(Q55114,Q55109),F0))),s(fun(Q55114,bool),S0))))),s(num,N0))))) # label(aHASu_SIZEu_IMAGEu_INJu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 190 (all A5 all B0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_divides),s(int,i(s(fun(num,int),intu_ofu_num),s(num,A5))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,B0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),numu_divides),s(num,A5))),s(num,B0)))) # label(anumu_divides) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 191 (all A all P0 all L ((all X all Y (p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))) | p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(A,bool),bool)),chain),s(fun(prod(A,A),bool),L))),s(fun(A,bool),P0)))))) # label(achain) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 192 (all A all L all M0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),M0)))) & p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),L)))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),M0))),s(fun(prod(A,A),bool),L)))) | p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),L))),s(fun(prod(A,A),bool),M0)))))) # label(aORDINALu_CHAINED) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 193 (all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,X)))) # label(aREALu_SUBu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 194 (all Q67683 all F0 all X s(num,i(s(fun(Q67683,num),F0),s(Q67683,X))) = s(num,i(s(fun(fun(Q67683,num),num),i(s(fun(fun(Q67683,bool),fun(fun(Q67683,num),num)),nsum),s(fun(Q67683,bool),i(s(fun(fun(Q67683,bool),fun(Q67683,bool)),i(s(fun(Q67683,fun(fun(Q67683,bool),fun(Q67683,bool))),insert),s(Q67683,X))),s(fun(Q67683,bool),empty))))),s(fun(Q67683,num),F0)))) # label(aNSUMu_SING) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 195 (all N0 all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,N0)))))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))))) # label(aINTu_POWu_LT2u_REV) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 196 (all M0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(bool,f0)) # label(aLTu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 197 (all X all Y (s(int,X) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & s(int,Y) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) # label(aINTu_SOSu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 198 (all A all I0 all J0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> (s(finite_image(A),i(s(fun(num,finite_image(A)),finiteu_index),s(num,J0))) = s(finite_image(A),i(s(fun(num,finite_image(A)),finiteu_index),s(num,I0))) <-> s(num,J0) = s(num,I0)))) # label(aFINITEu_INDEXu_INJ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 199 (all X all Y all Z0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,Z0)))) # label(aINTu_LEu_LADD) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 200 (all X all Y p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(int,int),intu_abs),s(int,X))))),s(int,i(s(fun(int,int),intu_abs),s(int,Y))))))))),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))))))) # label(aINTu_ABSu_SUBu_ABS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 201 (all X exists N0 p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,N0))))))) # label(aHREALu_ARCH) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 202 (all Q20423 all Q20422 all Q20424 all Q20425 all U_1 ((all X all Y s(bool,i(s(fun(Q20422,bool),i(s(fun(Q20423,fun(Q20422,bool)),p0),s(Q20423,i(s(fun(Q20424,Q20423),f),s(Q20424,X))))),s(Q20422,i(s(fun(Q20425,Q20422),g),s(Q20425,Y))))) = s(bool,i(s(fun(Q20425,bool),i(s(fun(Q20424,fun(Q20425,bool)),U_1),s(Q20424,X))),s(Q20425,Y)))) -> (all U_0 ((all X s(fun(Q20425,bool),i(s(fun(Q20424,fun(Q20425,bool)),U_0),s(Q20424,X))) = s(fun(Q20425,bool),i(s(fun(Q20424,fun(Q20425,bool)),U_1),s(Q20424,X)))) -> (all L all M0 s(bool,i(s(fun(list(Q20425),bool),i(s(fun(list(Q20424),fun(list(Q20425),bool)),i(s(fun(fun(Q20424,fun(Q20425,bool)),fun(list(Q20424),fun(list(Q20425),bool))),all2),s(fun(Q20424,fun(Q20425,bool)),U_0))),s(list(Q20424),L))),s(list(Q20425),M0))) = s(bool,i(s(fun(list(Q20422),bool),i(s(fun(list(Q20423),fun(list(Q20422),bool)),i(s(fun(fun(Q20423,fun(Q20422,bool)),fun(list(Q20423),fun(list(Q20422),bool))),all2),s(fun(Q20423,fun(Q20422,bool)),p0))),s(list(Q20423),i(s(fun(list(Q20424),list(Q20423)),i(s(fun(fun(Q20424,Q20423),fun(list(Q20424),list(Q20423))),map0),s(fun(Q20424,Q20423),f))),s(list(Q20424),L))))),s(list(Q20422),i(s(fun(list(Q20425),list(Q20422)),i(s(fun(fun(Q20425,Q20422),fun(list(Q20425),list(Q20422))),map0),s(fun(Q20425,Q20422),g))),s(list(Q20425),M0)))))))))) # label(aALL2u_MAP2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 203 (all Q65977 all Q65978 all U_0 ((all OP all F0 all G0 all X s(Q65978,i(s(fun(Q65977,Q65978),i(s(fun(fun(Q65977,Q65978),fun(Q65977,Q65978)),i(s(fun(fun(Q65977,Q65978),fun(fun(Q65977,Q65978),fun(Q65977,Q65978))),i(s(fun(fun(Q65978,fun(Q65978,Q65978)),fun(fun(Q65977,Q65978),fun(fun(Q65977,Q65978),fun(Q65977,Q65978)))),U_0),s(fun(Q65978,fun(Q65978,Q65978)),OP))),s(fun(Q65977,Q65978),F0))),s(fun(Q65977,Q65978),G0))),s(Q65977,X))) = s(Q65978,i(s(fun(Q65978,Q65978),i(s(fun(Q65978,fun(Q65978,Q65978)),OP),s(Q65978,i(s(fun(Q65977,Q65978),F0),s(Q65977,X))))),s(Q65978,i(s(fun(Q65977,Q65978),G0),s(Q65977,X)))))) -> (all OP (p(s(bool,i(s(fun(fun(Q65978,fun(Q65978,Q65978)),bool),monoidal),s(fun(Q65978,fun(Q65978,Q65978)),OP)))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q65977,bool),bool),finite),s(fun(Q65977,bool),S0)))) -> s(Q65978,i(s(fun(fun(Q65977,Q65978),Q65978),i(s(fun(fun(Q65977,bool),fun(fun(Q65977,Q65978),Q65978)),i(s(fun(fun(Q65978,fun(Q65978,Q65978)),fun(fun(Q65977,bool),fun(fun(Q65977,Q65978),Q65978))),iterate),s(fun(Q65978,fun(Q65978,Q65978)),OP))),s(fun(Q65977,bool),S0))),s(fun(Q65977,Q65978),i(s(fun(fun(Q65977,Q65978),fun(Q65977,Q65978)),i(s(fun(fun(Q65977,Q65978),fun(fun(Q65977,Q65978),fun(Q65977,Q65978))),i(s(fun(fun(Q65978,fun(Q65978,Q65978)),fun(fun(Q65977,Q65978),fun(fun(Q65977,Q65978),fun(Q65977,Q65978)))),U_0),s(fun(Q65978,fun(Q65978,Q65978)),OP))),s(fun(Q65977,Q65978),F0))),s(fun(Q65977,Q65978),G0))))) = s(Q65978,i(s(fun(Q65978,Q65978),i(s(fun(Q65978,fun(Q65978,Q65978)),OP),s(Q65978,i(s(fun(fun(Q65977,Q65978),Q65978),i(s(fun(fun(Q65977,bool),fun(fun(Q65977,Q65978),Q65978)),i(s(fun(fun(Q65978,fun(Q65978,Q65978)),fun(fun(Q65977,bool),fun(fun(Q65977,Q65978),Q65978))),iterate),s(fun(Q65978,fun(Q65978,Q65978)),OP))),s(fun(Q65977,bool),S0))),s(fun(Q65977,Q65978),F0))))),s(Q65978,i(s(fun(fun(Q65977,Q65978),Q65978),i(s(fun(fun(Q65977,bool),fun(fun(Q65977,Q65978),Q65978)),i(s(fun(fun(Q65978,fun(Q65978,Q65978)),fun(fun(Q65977,bool),fun(fun(Q65977,Q65978),Q65978))),iterate),s(fun(Q65978,fun(Q65978,Q65978)),OP))),s(fun(Q65977,bool),S0))),s(fun(Q65977,Q65978),G0))))))))))) # label(aITERATEu_OP) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 204 (all S0 (s(fun(real,bool),S0) != s(fun(real,bool),empty) & (exists B0 all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,X)))))) -> (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))),s(real,X)))))) & (all B0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,X)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0)))))))))) # label(aINF) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 205 (all B all A all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0)))))))) # label(aFINITEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 206 (all Q47117 s(fun(Q47117,bool),s0) = s(fun(Q47117,bool),i(s(fun(fun(fun(Q47117,bool),bool),fun(Q47117,bool)),unions),s(fun(fun(Q47117,bool),bool),i(s(fun(fun(fun(Q47117,bool),bool),fun(fun(Q47117,bool),bool)),i(s(fun(fun(Q47117,bool),fun(fun(fun(Q47117,bool),bool),fun(fun(Q47117,bool),bool))),insert),s(fun(Q47117,bool),s0))),s(fun(fun(Q47117,bool),bool),empty)))))) # label(aUNIONSu_1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 207 (all Q72690 all U_0 ((all S0 all F0 all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(fun(Q72690,bool),bool),i(s(fun(Q72690,fun(fun(Q72690,bool),bool)),in),s(Q72690,X))),s(fun(Q72690,bool),S0))))),s(real,i(s(fun(Q72690,real),F0),s(Q72690,X))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(Q72690,real),i(s(fun(fun(Q72690,real),fun(Q72690,real)),i(s(fun(fun(Q72690,bool),fun(fun(Q72690,real),fun(Q72690,real))),U_0),s(fun(Q72690,bool),S0))),s(fun(Q72690,real),F0))),s(Q72690,X)))) -> (all F0 all S0 (p(s(bool,i(s(fun(fun(Q72690,bool),bool),finite),s(fun(Q72690,bool),S0)))) -> s(real,i(s(fun(fun(Q72690,real),real),i(s(fun(fun(Q72690,bool),fun(fun(Q72690,real),real)),sum),s(fun(Q72690,bool),S0))),s(fun(Q72690,real),i(s(fun(fun(Q72690,real),fun(Q72690,real)),i(s(fun(fun(Q72690,bool),fun(fun(Q72690,real),fun(Q72690,real))),U_0),s(fun(Q72690,bool),S0))),s(fun(Q72690,real),F0))))) = s(real,i(s(fun(fun(Q72690,real),real),i(s(fun(fun(Q72690,bool),fun(fun(Q72690,real),real)),sum),s(fun(Q72690,bool),S0))),s(fun(Q72690,real),F0))))))) # label(aSUMu_RESTRICT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 208 (all A all U_0 ((all S0 all X all GENR_PVARR_6 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),U_0),s(fun(A,bool),S0))),s(A,X))),s(A,GENR_PVARR_6)))) <-> (exists Y exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_6))),s(bool,V))),s(A,Y)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(A,X) != s(A,Y)))))) -> (all S0 all X s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),U_0),s(fun(A,bool),S0))),s(A,X)))))))) # label(aDELETE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 209 (all X p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,X))))) # label(aHREALu_LEu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 210 (all M0 all N0 p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,M0))))),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,N0))))))),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))))))) # label(aTREALu_OFu_NUMu_MUL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 211 (all X (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),intu_neg),s(int,X)))))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) | s(int,X) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aINTu_LTu_NEGTOTAL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 212 (all A all P0 (-(all X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) <-> (exists X -p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) # label(aEXISTSu_NOTu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 213 (all I0 s(int,i(s(fun(real,int),intu_ofu_real),s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(int,real),realu_ofu_int),s(int,I0))))))) = s(int,i(s(fun(int,int),intu_neg),s(int,I0)))) # label(aintu_neg) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 214 (all Q96826 all P0 all S0 ((all F0 ((all S0 (p(s(bool,i(s(fun(fun(fun(Q96826,bool),bool),bool),i(s(fun(fun(Q96826,bool),fun(fun(fun(Q96826,bool),bool),bool)),in),s(fun(Q96826,bool),S0))),s(fun(fun(Q96826,bool),bool),F0)))) -> p(s(bool,i(s(fun(fun(Q96826,bool),bool),P0),s(fun(Q96826,bool),S0)))))) -> p(s(bool,i(s(fun(fun(Q96826,bool),bool),P0),s(fun(Q96826,bool),i(s(fun(fun(fun(Q96826,bool),bool),fun(Q96826,bool)),inters),s(fun(fun(Q96826,bool),bool),F0)))))))) -> (s(fun(Q96826,bool),S0) = s(fun(Q96826,bool),i(s(fun(fun(Q96826,bool),fun(Q96826,bool)),i(s(fun(fun(fun(Q96826,bool),bool),fun(fun(Q96826,bool),fun(Q96826,bool))),hull),s(fun(fun(Q96826,bool),bool),P0))),s(fun(Q96826,bool),S0))) <-> p(s(bool,i(s(fun(fun(Q96826,bool),bool),P0),s(fun(Q96826,bool),S0))))))) # label(aHULLu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 215 (all B all A all F0 all U ((all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),U)))) & s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) -> s(A,Y) = s(A,X))) <-> (all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),U)))) & s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))) = s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),T0))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),U)))) -> s(fun(A,bool),T0) = s(fun(A,bool),S0))))) # label(aINJECTIVEu_ONu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 216 (all A all P0 all F0 all S0 (p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) & (all X all Y (p(s(bool,i(s(fun(num,bool),P0),s(num,Y)))) & p(s(bool,i(s(fun(num,bool),P0),s(num,X)))) -> p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,X))),s(num,Y)))))))) & (all A5 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,A5))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(A,num),F0),s(A,A5)))))))) -> p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0)))))))) # label(aNSUMu_CLOSED) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 217 (all A all X all S0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))))) # label(aCOMPONENT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 218 (all Q78455 all Q78445 all Q78456 all X all Y (s(cart(Q78455,finite_sum(Q78445,Q78456)),X) = s(cart(Q78455,finite_sum(Q78445,Q78456)),Y) <-> s(cart(Q78455,Q78445),i(s(fun(cart(Q78455,finite_sum(Q78445,Q78456)),cart(Q78455,Q78445)),fstcart),s(cart(Q78455,finite_sum(Q78445,Q78456)),X))) = s(cart(Q78455,Q78445),i(s(fun(cart(Q78455,finite_sum(Q78445,Q78456)),cart(Q78455,Q78445)),fstcart),s(cart(Q78455,finite_sum(Q78445,Q78456)),Y))) & s(cart(Q78455,Q78456),i(s(fun(cart(Q78455,finite_sum(Q78445,Q78456)),cart(Q78455,Q78456)),sndcart),s(cart(Q78455,finite_sum(Q78445,Q78456)),Y))) = s(cart(Q78455,Q78456),i(s(fun(cart(Q78455,finite_sum(Q78445,Q78456)),cart(Q78455,Q78456)),sndcart),s(cart(Q78455,finite_sum(Q78445,Q78456)),X))))) # label(aPASTECARTu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 219 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,X)))))) # label(aINTu_LETu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 220 (all A all S0 -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),univ))),s(fun(A,bool),S0))))) # label(aNOTu_UNIVu_PSUBSET) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 221 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,i(s(fun(real,real),realu_neg),s(real,Y))))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y)))))) # label(aREALu_NEGu_RMUL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 222 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))))) # label(aLEu_CASES) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 223 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))))) # label(aFINITEu_UNION) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 224 (all D0 all E0 ((all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,N0))),s(num,m)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),E0),s(num,N0))))),s(real,i(s(fun(num,real),E0),s(num,m)))))))) & (all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,N0))),s(num,m)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),D0),s(num,N0))))),s(real,i(s(fun(num,real),E0),s(num,N0)))))))) -> (all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,N0))),s(num,m)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),D0),s(num,N0))))),s(real,i(s(fun(num,real),E0),s(num,m)))))))))) # label(aSEQu_MONOu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 225 (all A all S0 all T0 (s(fun(A,bool),empty) = s(fun(A,bool),T0) & s(fun(A,bool),empty) = s(fun(A,bool),S0) <-> s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))) = s(fun(A,bool),empty))) # label(aEMPTYu_UNION) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 226 (all U_0 ((all N0 all GENR_PVARR_111 ((exists M0 p(s(bool,i(s(fun(num,bool),i(s(fun(bool,fun(num,bool)),i(s(fun(num,fun(bool,fun(num,bool))),setspec),s(num,GENR_PVARR_111))),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(num,M0))))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))),s(num,GENR_PVARR_111)))))) -> (all N0 p(s(bool,i(s(fun(fun(num,bool),bool),finite),s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),gspec),s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))))))))))) # label(aFINITEu_NUMSEGu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 227 (all X s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),realu_neg),s(real,X))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aREALu_LEu_NEGR) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 228 (all U_0 ((all X all I0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))),s(num,I0)))) -> (all X all M0 all N0 exists V (s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))),s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,M0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),suc),s(num,N0))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X))))))))) & (s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) <-> p(s(bool,V))))))) # label(aSUMu_GPu_OFFSET) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 229 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))) -> -p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,X)))))) # label(aINTu_LTu_GT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 230 (all N0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))))) # label(aREALu_POS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 231 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,N0))) = s(num,M0)) # label(aADDu_SUB) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 232 (all N0 s(bool,f0) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),bit1),s(num,N0))))),s(num,u_0)))) # label(aARITHu_LTu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 233 (all M0 all N0 all P0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))),s(num,P0))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,P0))))),s(num,N0))))) # label(aMODu_EXPu_MOD) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 234 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,N0))),s(num,M0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,i(s(fun(num,num),bit1),s(num,N0))))),s(num,i(s(fun(num,num),bit0),s(num,M0)))))) # label(aARITHu_GTu_conjunct7) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 235 (all N0 (s(num,u_0) = s(num,i(s(fun(num,num),bit0),s(num,N0))) <-> s(num,u_0) = s(num,N0))) # label(aARITHu_EQu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 236 (all A all L_L_ ((all X all Y all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,X))),s(A,Y)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,Z0)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,X))),s(A,Z0)))))) & (all X all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,X))),s(A,Y)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,X)))) -> s(A,X) = s(A,Y))) -> (all N0 all S0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,N0)))) -> (exists F0 (s(fun(A,bool),i(s(fun(fun(num,bool),fun(A,bool)),i(s(fun(fun(num,A),fun(fun(num,bool),fun(A,bool))),image),s(fun(num,A),F0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0))))) = s(fun(A,bool),S0) & (all J0 all K0 (p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,J0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))))) & p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,K0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,J0))),s(num,K0)))) -> -p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,i(s(fun(num,A),F0),s(num,K0))))),s(A,i(s(fun(num,A),F0),s(num,J0)))))))))))))) # label(aTOPOLOGICALu_SORT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 237 (all X s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,X)))) # label(aINTu_ADDu_LINV) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 238 (all U_0 ((all U ((exists X1 exists Y1 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(real,fun(prod(hreal,hreal),bool)),destu_real),s(real,y1))),s(prod(hreal,hreal),Y1)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(real,fun(prod(hreal,hreal),bool)),destu_real),s(real,x1))),s(prod(hreal,hreal),X1)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),Y1))))),s(prod(hreal,hreal),U)))))) <-> p(s(bool,i(s(fun(prod(hreal,hreal),bool),U_0),s(prod(hreal,hreal),U)))))) -> s(real,i(s(fun(fun(prod(hreal,hreal),bool),real),mku_real),s(fun(prod(hreal,hreal),bool),U_0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x1))),s(real,y1))))) # label(arealu_mul) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 239 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Z0)))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,Z0)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y))))),s(int,Z0)))))) # label(aINTu_MINu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 240 (all B all A all X all Y s(A,X) = s(A,i(s(fun(prod(A,B),A),fst),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))) # label(aFST) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 241 (all A all B all A5 all AI_ s(sum0(A,B),i(s(fun(A,sum0(A,B)),inl),s(A,A5))) != s(sum0(A,B),i(s(fun(B,sum0(A,B)),inr),s(B,AI_)))) # label(asumu_DISTINCT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 242 (all A all S0 p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(A,bool),fun(fun(prod(A,A),bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(prod(A,A),bool),i(s(fun(fun(A,bool),fun(prod(A,A),bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(prod(A,A),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(A,bool),S0))))))) # label(aCARDu_LEu_SQUARE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 243 (all A all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(A,real),F0),s(A,X))))))),s(real,i(s(fun(A,real),G0),s(A,X)))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))))),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),G0)))))))) # label(aSUMu_ABSu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 244 (all A all S0 all T0 (s(fun(A,bool),S0) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aSUBSETu_INTERu_ABSORPTION) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 245 (all A all B all AP all BP (p(s(bool,i(s(fun(fun(AP,bool),bool),i(s(fun(fun(A,bool),fun(fun(AP,bool),bool)),l_a_u_c),s(fun(A,bool),univ))),s(fun(AP,bool),univ)))) & p(s(bool,i(s(fun(fun(BP,bool),bool),i(s(fun(fun(B,bool),fun(fun(BP,bool),bool)),l_a_u_c),s(fun(B,bool),univ))),s(fun(BP,bool),univ)))) -> p(s(bool,i(s(fun(fun(fun(AP,BP),bool),bool),i(s(fun(fun(fun(A,B),bool),fun(fun(fun(AP,BP),bool),bool)),l_a_u_c),s(fun(fun(A,B),bool),univ))),s(fun(fun(AP,BP),bool),univ)))))) # label(aCARDu_FUNSPACEu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.86 246 (all Q96917 all P0 all Q0 all S0 (p(s(bool,i(s(fun(fun(fun(Q96917,bool),bool),bool),i(s(fun(fun(fun(Q96917,bool),bool),fun(fun(fun(Q96917,bool),bool),bool)),subset),s(fun(fun(Q96917,bool),bool),P0))),s(fun(fun(Q96917,bool),bool),Q0)))) -> p(s(bool,i(s(fun(fun(Q96917,bool),bool),i(s(fun(fun(Q96917,bool),fun(fun(Q96917,bool),bool)),subset),s(fun(Q96917,bool),i(s(fun(fun(Q96917,bool),fun(Q96917,bool)),i(s(fun(fun(fun(Q96917,bool),bool),fun(fun(Q96917,bool),fun(Q96917,bool))),hull),s(fun(fun(Q96917,bool),bool),Q0))),s(fun(Q96917,bool),S0))))),s(fun(Q96917,bool),i(s(fun(fun(Q96917,bool),fun(Q96917,bool)),i(s(fun(fun(fun(Q96917,bool),bool),fun(fun(Q96917,bool),fun(Q96917,bool))),hull),s(fun(fun(Q96917,bool),bool),P0))),s(fun(Q96917,bool),S0)))))))) # label(aHULLu_ANTIMONO) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 247 (all B all A all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))) <-> (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,i(s(fun(A,B),F0),s(A,X))) -> s(A,Y) = s(A,X)))))) # label(aCARDu_IMAGEu_EQu_INJ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 248 (all M0 all N0 all P0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,P0)))) # label(aLEu_ADDu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 249 (all X all Y s(real,i(s(fun(real,real),realu_sgn),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),realu_sgn),s(real,X))))),s(real,i(s(fun(real,real),realu_sgn),s(real,Y)))))) # label(aREALu_SGNu_DIV) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 250 (all S0 all A5 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) & s(fun(real,bool),empty) != s(fun(real,bool),S0) -> (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0)))))) <-> (exists X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X))))))))) # label(aREALu_LEu_SUPu_FINITE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 251 (all A5 all B0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,A5))),s(num,B0))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,A5))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,B0))),s(num,N0))))) <-> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,A5))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,B0))),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,A5))),s(num,B0))))),s(num,N0)))))) # label(aDIVu_ADDu_MOD) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 252 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> (exists N0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,Y))))))) # label(aREALu_ARCHu_POWu_INV) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 253 (all B all A all S0 all T0 p(s(bool,i(s(fun(fun(prod(B,A),bool),bool),i(s(fun(fun(prod(A,B),bool),fun(fun(prod(B,A),bool),bool)),a_u_c),s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(prod(B,A),bool),i(s(fun(fun(A,bool),fun(prod(B,A),bool)),i(s(fun(fun(B,bool),fun(fun(A,bool),fun(prod(B,A),bool))),t_u_c),s(fun(B,bool),T0))),s(fun(A,bool),S0))))))) # label(aCARDu_MULu_SYM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 254 (all X all Y all D0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X))))))),s(real,D0)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,D0))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,D0)))))))) # label(aREALu_ABSu_BETWEEN) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 255 (all U_0 ((all N0 all GENR_PVARR_136 ((exists X p(s(bool,i(s(fun(num,bool),i(s(fun(bool,fun(num,bool)),i(s(fun(num,fun(bool,fun(num,bool))),setspec),s(num,GENR_PVARR_136))),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,X))),s(num,N0))))),s(num,X))))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))),s(num,GENR_PVARR_136)))))) -> (all N0 s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),gspec),s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))))) = s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))))) # label(aNUMSEGu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 256 (all X (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),intu_neg),s(int,X)))))))) # label(aINTu_LEu_NEGTOTAL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 257 (all M0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,u_0))) = s(num,i(s(fun(num,num),bit1),s(num,u_0)))) # label(aARITHu_EXPu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 258 (all X s(real,i(s(fun(real,real),realu_abs),s(real,X))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))),s(real,X))),s(real,i(s(fun(real,real),realu_neg),s(real,X)))))) # label(arealu_abs) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 259 (all X s(int,i(s(fun(int,int),intu_sgn),s(int,i(s(fun(int,int),intu_abs),s(int,X))))) = s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),intu_sgn),s(int,X)))))) # label(aINTu_ABSu_SGN) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 260 (all Q58415 all R0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q58415,bool),bool),i(s(fun(fun(Q58415,fun(Q58415,bool)),fun(fun(Q58415,bool),bool)),pairwise),s(fun(Q58415,fun(Q58415,bool)),R0))),s(fun(Q58415,bool),S0)))) & p(s(bool,i(s(fun(fun(Q58415,bool),bool),i(s(fun(fun(Q58415,bool),fun(fun(Q58415,bool),bool)),subset),s(fun(Q58415,bool),T0))),s(fun(Q58415,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q58415,bool),bool),i(s(fun(fun(Q58415,fun(Q58415,bool)),fun(fun(Q58415,bool),bool)),pairwise),s(fun(Q58415,fun(Q58415,bool)),R0))),s(fun(Q58415,bool),T0)))))) # label(aPAIRWISEu_MONO) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 261 (all A all X all L ((exists L1 exists L2 s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),L1))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),L2))))) = s(list(A),L)) <-> p(s(bool,i(s(fun(list(A),bool),i(s(fun(A,fun(list(A),bool)),mem),s(A,X))),s(list(A),L)))))) # label(aMEMu_APPENDu_DECOMPOSE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 262 (all M0 all N0 all P0 (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))) <-> s(num,P0) = s(num,N0) | s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aEQu_MULTu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 263 (all Q53377 all S0 (p(s(bool,i(s(fun(fun(Q53377,bool),bool),finite),s(fun(Q53377,bool),S0)))) -> (s(fun(Q53377,bool),empty) = s(fun(Q53377,bool),S0) <-> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(fun(Q53377,bool),num),card),s(fun(Q53377,bool),S0)))))) # label(aCARDu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 264 (all A all P0 all Q0 ((exists X p(s(bool,Q0))) & (exists X p(s(bool,P0))) <-> (exists X (p(s(bool,Q0)) & p(s(bool,P0)))))) # label(aTRIVu_ANDu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 265 (all A all P0 all X s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),P0))) = s(bool,i(s(fun(A,bool),P0),s(A,X)))) # label(aIN) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 266 (all B all A all S0 all T0 (-p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(B,bool),fun(fun(A,bool),bool)),l_a_u_c),s(fun(B,bool),T0))),s(fun(A,bool),S0)))))) # label(aCARDu_NOTu_LT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 267 (all A all A5 s(finite_image(A),A5) = s(finite_image(A),i(s(fun(num,finite_image(A)),finiteu_index),s(num,i(s(fun(finite_image(A),num),destu_finiteu_image),s(finite_image(A),A5)))))) # label(afiniteu_imageu_tybiju_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 268 (all Q96267 all P0 all F0 ((exists D0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D0)))) & (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(Q96267,real),F0),s(Q96267,X))))),s(real,D0)))) -> p(s(bool,i(s(fun(Q96267,bool),P0),s(Q96267,X)))))))) <-> (exists D0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D0)))) & (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(Q96267,real),F0),s(Q96267,X))))),s(real,D0)))) -> p(s(bool,i(s(fun(Q96267,bool),P0),s(Q96267,X)))))))))) # label(aAPPROACHABLEu_LTu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 269 (all X -p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,X))))) # label(aREALu_LTu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 270 (all X all Y all Z0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))),s(real,Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0)))))) # label(aREALu_SUBu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 271 (all Q92953 all S0 all T0 (p(s(bool,i(s(fun(fun(Q92953,bool),bool),countable),s(fun(Q92953,bool),S0)))) | p(s(bool,i(s(fun(fun(Q92953,bool),bool),countable),s(fun(Q92953,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q92953,bool),bool),countable),s(fun(Q92953,bool),i(s(fun(fun(Q92953,bool),fun(Q92953,bool)),i(s(fun(fun(Q92953,bool),fun(fun(Q92953,bool),fun(Q92953,bool))),inter),s(fun(Q92953,bool),S0))),s(fun(Q92953,bool),T0)))))))) # label(aCOUNTABLEu_INTER) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 272 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_inv),s(real,X)))))))) # label(aREALu_LEu_INV) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 273 (all S0 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) & s(fun(real,bool),S0) != s(fun(real,bool),empty) -> (s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))) = s(real,a0) <-> p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,a0))),s(fun(real,bool),S0)))) & (all Y (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,Y))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,a0))))))))) # label(aSUPu_UNIQUEu_FINITE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 274 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0)))))))) # label(aREALu_LEu_RMUL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 275 (all X all Y s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),X))) = s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))) # label(aTREALu_MULu_SYMu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 276 (all X all Y all Z0 p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,Y))),s(nadd,Z0))))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Y))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Z0))))))))) # label(aNADDu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 277 (all A all S0 s(fun(A,bool),empty) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),empty)))) # label(aINTERu_EMPTYu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 278 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y)))))) # label(aintu_lt) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 279 (all Q63859 all Q63745 all F0 all S0 all T0 s(fun(Q63745,bool),i(s(fun(fun(Q63745,bool),fun(Q63745,bool)),i(s(fun(fun(Q63745,bool),fun(fun(Q63745,bool),fun(Q63745,bool))),union),s(fun(Q63745,bool),i(s(fun(fun(Q63745,bool),fun(Q63745,bool)),i(s(fun(fun(Q63745,Q63859),fun(fun(Q63745,bool),fun(Q63745,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63745,Q63859),fun(fun(Q63745,bool),fun(Q63745,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63745,Q63859),F0))),s(fun(Q63745,bool),S0))))),s(fun(Q63745,bool),i(s(fun(fun(Q63745,bool),fun(Q63745,bool)),i(s(fun(fun(Q63745,Q63859),fun(fun(Q63745,bool),fun(Q63745,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63745,Q63859),fun(fun(Q63745,bool),fun(Q63745,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63745,Q63859),F0))),s(fun(Q63745,bool),T0))))) = s(fun(Q63745,bool),i(s(fun(fun(Q63745,bool),fun(Q63745,bool)),i(s(fun(fun(Q63745,Q63859),fun(fun(Q63745,bool),fun(Q63745,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63745,Q63859),fun(fun(Q63745,bool),fun(Q63745,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63745,Q63859),F0))),s(fun(Q63745,bool),i(s(fun(fun(Q63745,bool),fun(Q63745,bool)),i(s(fun(fun(Q63745,bool),fun(fun(Q63745,bool),fun(Q63745,bool))),union),s(fun(Q63745,bool),S0))),s(fun(Q63745,bool),T0)))))) # label(aSUPPORTu_CLAUSESu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 280 (all Q67486 all F0 all G0 all S0 ((all X (p(s(bool,i(s(fun(fun(Q67486,bool),bool),i(s(fun(Q67486,fun(fun(Q67486,bool),bool)),in),s(Q67486,X))),s(fun(Q67486,bool),S0)))) -> s(num,i(s(fun(Q67486,num),G0),s(Q67486,X))) = s(num,i(s(fun(Q67486,num),F0),s(Q67486,X))))) -> s(num,i(s(fun(fun(Q67486,num),num),i(s(fun(fun(Q67486,bool),fun(fun(Q67486,num),num)),nsum),s(fun(Q67486,bool),S0))),s(fun(Q67486,num),F0))) = s(num,i(s(fun(fun(Q67486,num),num),i(s(fun(fun(Q67486,bool),fun(fun(Q67486,num),num)),nsum),s(fun(Q67486,bool),S0))),s(fun(Q67486,num),G0))))) # label(aNSUMu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 281 (all U_0 ((all N0 all GENR_PVARR_109 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))),s(num,GENR_PVARR_109)))) <-> (exists M0 p(s(bool,i(s(fun(num,bool),i(s(fun(bool,fun(num,bool)),i(s(fun(num,fun(bool,fun(num,bool))),setspec),s(num,GENR_PVARR_109))),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0))))),s(num,M0))))))) -> (all N0 p(s(bool,i(s(fun(fun(num,bool),bool),finite),s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),gspec),s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))))))))))) # label(aFINITEu_NUMSEGu_LT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 282 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))))) # label(aLTu_IMPu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 283 (all Q51738 all Q51718 all P0 all F0 all S0 ((exists T0 (p(s(bool,i(s(fun(fun(Q51718,bool),bool),finite),s(fun(Q51718,bool),T0)))) & p(s(bool,i(s(fun(fun(Q51738,bool),bool),P0),s(fun(Q51738,bool),i(s(fun(fun(Q51718,bool),fun(Q51738,bool)),i(s(fun(fun(Q51718,Q51738),fun(fun(Q51718,bool),fun(Q51738,bool))),image),s(fun(Q51718,Q51738),F0))),s(fun(Q51718,bool),T0)))))) & p(s(bool,i(s(fun(fun(Q51718,bool),bool),i(s(fun(fun(Q51718,bool),fun(fun(Q51718,bool),bool)),subset),s(fun(Q51718,bool),T0))),s(fun(Q51718,bool),S0)))))) <-> (exists T0 (p(s(bool,i(s(fun(fun(Q51738,bool),bool),i(s(fun(fun(Q51738,bool),fun(fun(Q51738,bool),bool)),subset),s(fun(Q51738,bool),T0))),s(fun(Q51738,bool),i(s(fun(fun(Q51718,bool),fun(Q51738,bool)),i(s(fun(fun(Q51718,Q51738),fun(fun(Q51718,bool),fun(Q51738,bool))),image),s(fun(Q51718,Q51738),F0))),s(fun(Q51718,bool),S0)))))) & p(s(bool,i(s(fun(fun(Q51738,bool),bool),P0),s(fun(Q51738,bool),T0)))) & p(s(bool,i(s(fun(fun(Q51738,bool),bool),finite),s(fun(Q51738,bool),T0)))))))) # label(aEXISTSu_FINITEu_SUBSETu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 284 (all X p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),X))))) # label(aTREALu_LEu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 285 (all Q47409 all S0 all T0 s(fun(Q47409,bool),i(s(fun(fun(Q47409,bool),fun(Q47409,bool)),i(s(fun(fun(Q47409,bool),fun(fun(Q47409,bool),fun(Q47409,bool))),union),s(fun(Q47409,bool),i(s(fun(fun(fun(Q47409,bool),bool),fun(Q47409,bool)),unions),s(fun(fun(Q47409,bool),bool),S0))))),s(fun(Q47409,bool),i(s(fun(fun(fun(Q47409,bool),bool),fun(Q47409,bool)),unions),s(fun(fun(Q47409,bool),bool),T0))))) = s(fun(Q47409,bool),i(s(fun(fun(fun(Q47409,bool),bool),fun(Q47409,bool)),unions),s(fun(fun(Q47409,bool),bool),i(s(fun(fun(fun(Q47409,bool),bool),fun(fun(Q47409,bool),bool)),i(s(fun(fun(fun(Q47409,bool),bool),fun(fun(fun(Q47409,bool),bool),fun(fun(Q47409,bool),bool))),union),s(fun(fun(Q47409,bool),bool),S0))),s(fun(fun(Q47409,bool),bool),T0)))))) # label(aUNIONSu_UNION) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 286 (all X all D0 (s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(int,D0) -> (exists C0 p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,C0))),s(int,D0))))))))) # label(aINTu_ARCH) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 287 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,P0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,P0)))) <-> p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,P0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0)))))))) # label(aINu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 288 (all A all B all X all Y all XI_ all X0 (s(B,Y) = s(B,X0) & s(A,XI_) = s(A,X) <-> p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),i(s(fun(B,fun(A,fun(B,bool))),i(s(fun(A,fun(B,fun(A,fun(B,bool)))),mku_pair),s(A,X))),s(B,Y))),s(A,XI_))),s(B,X0)))))) # label(amku_pairu_def) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 289 (all M0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(num,M0)) # label(aADDu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 290 (all Q73037 all S0 all T0 all U (p(s(bool,i(s(fun(fun(Q73037,bool),bool),finite),s(fun(Q73037,bool),U)))) & s(fun(Q73037,bool),i(s(fun(fun(Q73037,bool),fun(Q73037,bool)),i(s(fun(fun(Q73037,bool),fun(fun(Q73037,bool),fun(Q73037,bool))),inter),s(fun(Q73037,bool),S0))),s(fun(Q73037,bool),T0))) = s(fun(Q73037,bool),empty) & s(fun(Q73037,bool),U) = s(fun(Q73037,bool),i(s(fun(fun(Q73037,bool),fun(Q73037,bool)),i(s(fun(fun(Q73037,bool),fun(fun(Q73037,bool),fun(Q73037,bool))),union),s(fun(Q73037,bool),S0))),s(fun(Q73037,bool),T0))) -> s(real,i(s(fun(fun(Q73037,real),real),i(s(fun(fun(Q73037,bool),fun(fun(Q73037,real),real)),sum),s(fun(Q73037,bool),U))),s(fun(Q73037,real),f))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(Q73037,real),real),i(s(fun(fun(Q73037,bool),fun(fun(Q73037,real),real)),sum),s(fun(Q73037,bool),S0))),s(fun(Q73037,real),f))))),s(real,i(s(fun(fun(Q73037,real),real),i(s(fun(fun(Q73037,bool),fun(fun(Q73037,real),real)),sum),s(fun(Q73037,bool),T0))),s(fun(Q73037,real),f))))))) # label(aSUMu_UNIONu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 291 (all A all S0 all T0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),T0))),s(fun(A,bool),S0))))),s(fun(A,bool),S0))))) # label(aINTERu_SUBSETu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 292 (all X1 all Y2 all X2 all Y1 s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,X1))),s(hreal,Y1))))),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,X2))),s(hreal,Y2))))) = s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X1))),s(hreal,Y2))))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X2))),s(hreal,Y1)))))) # label(atrealu_le) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 293 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))) = s(num,i(s(fun(fun(num,bool),num),card),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0)))))) # label(aCARDu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 294 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),suc),s(num,N0))))),s(num,i(s(fun(num,num),fact),s(num,N0))))) = s(num,i(s(fun(num,num),fact),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aFACTu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 295 (all P0 (p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) & (all N0 (p(s(bool,i(s(fun(num,bool),P0),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),suc),s(num,N0)))))))) -> (all N0 p(s(bool,i(s(fun(num,bool),P0),s(num,N0))))))) # label(anumu_INDUCTION) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 296 (all S0 all A5 all B0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))) & s(fun(real,bool),empty) != s(fun(real,bool),S0) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0)))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))))),s(real,B0)))))) # label(aREALu_SUPu_BOUNDS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 297 p(s(bool,p1)) | p(s(bool,q)) <-> p(s(bool,p1)) | p(s(bool,p1)) | p(s(bool,q)) # label(aDISJu_ACIu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 298 (all A all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (all X s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))) = s(bool,i(s(fun(list(A),bool),i(s(fun(A,fun(list(A),bool)),mem),s(A,X))),s(list(A),i(s(fun(fun(A,bool),list(A)),listu_ofu_set),s(fun(A,bool),S0)))))))) # label(aMEMu_LISTu_OFu_SET) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 299 (all B0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),s0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,X)))))) & s(fun(real,bool),s0) != s(fun(real,bool),empty) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),s0)))))))) # label(aREALu_LEu_INF) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 300 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,i(s(fun(num,num),bit1),s(num,N0))))),s(num,i(s(fun(num,num),bit1),s(num,M0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,N0))),s(num,M0)))) # label(aARITHu_GEu_conjunct9) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 301 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),infinite),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(sum0(A,B),bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(sum0(A,B),bool),i(s(fun(fun(B,bool),fun(sum0(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(sum0(A,B),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(B,bool),T0)))))) # label(aCARDu_ADDu_ABSORBu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 302 (all A all B all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,bool),fun(A,bool)))),support),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,bool),S0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,bool),fun(A,bool)))),support),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,bool),T0))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,bool),fun(A,bool)))),support),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,bool),S0)))))) -> s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))) = s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),OP),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,B),F0))))),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),T0))),s(fun(A,B),F0))))))))) # label(aITERATEu_DIFFu_GEN) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 303 (all Q93018 all X p(s(bool,i(s(fun(fun(Q93018,bool),bool),countable),s(fun(Q93018,bool),i(s(fun(fun(Q93018,bool),fun(Q93018,bool)),i(s(fun(Q93018,fun(fun(Q93018,bool),fun(Q93018,bool))),insert),s(Q93018,X))),s(fun(Q93018,bool),empty))))))) # label(aCOUNTABLEu_SING) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 304 (all U_0 ((all A5 all B0 all GENR_PVARR_128 ((exists X exists V (p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_128))),s(bool,V))),s(real,X)))) & (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,A5))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),i(s(fun(real,fun(real,fun(real,bool))),U_0),s(real,A5))),s(real,B0))),s(real,GENR_PVARR_128)))))) -> (all A5 all B0 s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(real,fun(real,bool)),i(s(fun(real,fun(real,fun(real,bool))),U_0),s(real,A5))),s(real,B0))))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,A5)))))) # label(aFINITEu_REALu_INTERVALu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 305 (all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))))) # label(aLTu_NZ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 306 (all X s(int,i(s(fun(real,int),intu_ofu_real),s(real,i(s(fun(real,real),realu_sgn),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))))) = s(int,i(s(fun(int,int),intu_sgn),s(int,X)))) # label(aintu_sgn) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 307 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,P0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,P0)))))) # label(aLTu_TRANS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 308 (all N0 (-p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))) <-> p(s(bool,i(s(fun(num,bool),even),s(num,N0)))))) # label(aNOTu_ODD) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 309 (all A all S0 all T0 (s(fun(A,bool),T0) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aSUBSETu_UNIONu_ABSORPTION) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 310 (all X s(real,i(s(fun(real,real),realu_sgn),s(real,X))) = s(real,i(s(fun(real,real),realu_sgn),s(real,i(s(fun(real,real),realu_inv),s(real,X)))))) # label(aREALu_SGNu_INV) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 311 (all A all X s(bool,t) = s(bool,i(s(fun(A,bool),univ),s(A,X)))) # label(aUNIV) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 312 (all X (s(int,i(s(fun(int,int),intu_abs),s(int,X))) = s(int,X) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))))) # label(aINTu_ABSu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 313 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y)))))) # label(aINTu_LTu_ADDR) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 314 (all Q19896 all N0 all X s(num,i(s(fun(list(Q19896),num),length),s(list(Q19896),i(s(fun(Q19896,list(Q19896)),i(s(fun(num,fun(Q19896,list(Q19896))),replicate),s(num,N0))),s(Q19896,X))))) = s(num,N0)) # label(aLENGTHu_REPLICATE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 315 (all B all A all C all S0 all T0 all U p(s(bool,i(s(fun(fun(sum0(prod(A,B),prod(A,C)),bool),bool),i(s(fun(fun(prod(A,sum0(B,C)),bool),fun(fun(sum0(prod(A,B),prod(A,C)),bool),bool)),a_u_c),s(fun(prod(A,sum0(B,C)),bool),i(s(fun(fun(sum0(B,C),bool),fun(prod(A,sum0(B,C)),bool)),i(s(fun(fun(A,bool),fun(fun(sum0(B,C),bool),fun(prod(A,sum0(B,C)),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(sum0(B,C),bool),i(s(fun(fun(C,bool),fun(sum0(B,C),bool)),i(s(fun(fun(B,bool),fun(fun(C,bool),fun(sum0(B,C),bool))),p_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U))))))),s(fun(sum0(prod(A,B),prod(A,C)),bool),i(s(fun(fun(prod(A,C),bool),fun(sum0(prod(A,B),prod(A,C)),bool)),i(s(fun(fun(prod(A,B),bool),fun(fun(prod(A,C),bool),fun(sum0(prod(A,B),prod(A,C)),bool))),p_u_c),s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(prod(A,C),bool),i(s(fun(fun(C,bool),fun(prod(A,C),bool)),i(s(fun(fun(A,bool),fun(fun(C,bool),fun(prod(A,C),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(C,bool),U))))))))) # label(aCARDu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 316 (all S0 all A5 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,A5)))))) & s(fun(real,bool),empty) != s(fun(real,bool),S0) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))))))),s(real,A5)))))) # label(aREALu_ABSu_SUPu_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 317 (all A all B all F0 ((all P0 ((exists Y p(s(bool,i(s(fun(B,bool),P0),s(B,Y))))) <-> (exists X p(s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(A,B),F0),s(A,X))))))))) <-> (all Y exists X s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y)))) # label(aSURJECTIVEu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 318 (all Q4903 all Q4902 all Q4901 all U_0 ((all P0 all F0 ((all X all Y all Z0 p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(Q4903,prod(Q4902,Q4901)),bool),F0),s(prod(Q4903,prod(Q4902,Q4901)),i(s(fun(prod(Q4902,Q4901),prod(Q4903,prod(Q4902,Q4901))),i(s(fun(Q4903,fun(prod(Q4902,Q4901),prod(Q4903,prod(Q4902,Q4901)))),c_),s(Q4903,X))),s(prod(Q4902,Q4901),i(s(fun(Q4901,prod(Q4902,Q4901)),i(s(fun(Q4902,fun(Q4901,prod(Q4902,Q4901))),c_),s(Q4902,Y))),s(Q4901,Z0))))))))),s(bool,i(s(fun(Q4901,bool),i(s(fun(Q4902,fun(Q4901,bool)),i(s(fun(Q4903,fun(Q4902,fun(Q4901,bool))),P0),s(Q4903,X))),s(Q4902,Y))),s(Q4901,Z0))))))) <-> p(s(bool,i(s(fun(fun(prod(Q4903,prod(Q4902,Q4901)),bool),bool),i(s(fun(fun(Q4903,fun(Q4902,fun(Q4901,bool))),fun(fun(prod(Q4903,prod(Q4902,Q4901)),bool),bool)),U_0),s(fun(Q4903,fun(Q4902,fun(Q4901,bool))),P0))),s(fun(prod(Q4903,prod(Q4902,Q4901)),bool),F0)))))) -> (all P0 (p(s(bool,i(s(fun(fun(prod(Q4903,prod(Q4902,Q4901)),bool),bool),q_),s(fun(prod(Q4903,prod(Q4902,Q4901)),bool),i(s(fun(fun(fun(prod(Q4903,prod(Q4902,Q4901)),bool),bool),fun(prod(Q4903,prod(Q4902,Q4901)),bool)),gabs),s(fun(fun(prod(Q4903,prod(Q4902,Q4901)),bool),bool),i(s(fun(fun(Q4903,fun(Q4902,fun(Q4901,bool))),fun(fun(prod(Q4903,prod(Q4902,Q4901)),bool),bool)),U_0),s(fun(Q4903,fun(Q4902,fun(Q4901,bool))),P0)))))))) <-> (exists X exists Y exists Z0 p(s(bool,i(s(fun(Q4901,bool),i(s(fun(Q4902,fun(Q4901,bool)),i(s(fun(Q4903,fun(Q4902,fun(Q4901,bool))),P0),s(Q4903,X))),s(Q4902,Y))),s(Q4901,Z0))))))))) # label(aEXISTSu_TRIPLEDu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 319 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,u_0))),s(num,i(s(fun(num,num),bit0),s(num,N0))))) = s(num,u_0)) # label(aARITHu_SUBu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 320 (all X all N0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,X))))),s(num,N0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0)))))) # label(aREALu_OFu_NUMu_POW) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 321 (all A all B all F0 ((all P0 ((all Y p(s(bool,i(s(fun(B,bool),P0),s(B,Y))))) <-> (all X p(s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(A,B),F0),s(A,X))))))))) <-> (all Y exists X s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X)))))) # label(aSURJECTIVEu_FORALLu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 322 (all A all A5 all B0 (s(A,B0) = s(A,A5) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),geq),s(A,A5))),s(A,B0)))))) # label(aGEQu_DEF) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 323 (all A all C all B all D all S0 all SI_ all T0 all TI_ (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),SI_)))) & p(s(bool,i(s(fun(fun(D,bool),bool),i(s(fun(fun(C,bool),fun(fun(D,bool),bool)),a_u_c),s(fun(C,bool),T0))),s(fun(D,bool),TI_)))) -> p(s(bool,i(s(fun(fun(sum0(B,D),bool),bool),i(s(fun(fun(sum0(A,C),bool),fun(fun(sum0(B,D),bool),bool)),a_u_c),s(fun(sum0(A,C),bool),i(s(fun(fun(C,bool),fun(sum0(A,C),bool)),i(s(fun(fun(A,bool),fun(fun(C,bool),fun(sum0(A,C),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(C,bool),T0))))),s(fun(sum0(B,D),bool),i(s(fun(fun(D,bool),fun(sum0(B,D),bool)),i(s(fun(fun(B,bool),fun(fun(D,bool),fun(sum0(B,D),bool))),p_u_c),s(fun(B,bool),SI_))),s(fun(D,bool),TI_)))))))) # label(aCARDu_ADDu_CONG) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 324 (all A all B0 all T0 s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),i(s(fun(bool,fun(A,fun(A,A))),cond),s(bool,B0))),s(A,T0))),s(A,T0))) = s(A,T0)) # label(aCONDu_ID) # label(axiom) # label(non_clause). [assumption]. 13.83/13.87 325 (all A all B all U_0 ((all S0 all T0 all GENR_PVARR_70 ((exists X p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(bool,fun(fun(B,bool),bool)),i(s(fun(fun(B,bool),fun(bool,fun(fun(B,bool),bool))),setspec),s(fun(B,bool),GENR_PVARR_70))),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X))))))) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(fun(B,bool),GENR_PVARR_70)))))) -> (all S0 all T0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,M0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(B,bool),fun(num,bool)),hasu_size),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X))))),s(num,N0)))))) & (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(A,X) != s(A,Y) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),disjoint),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X))))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,Y)))))))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(B,bool),fun(num,bool)),hasu_size),s(fun(B,bool),i(s(fun(fun(fun(B,bool),bool),fun(B,bool)),unions),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),gspec),s(fun(fun(B,bool),bool),i(s(fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))))))) # label(aHASu_SIZEu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 326 p(s(bool,t)) <-> s(num,u_0) = s(num,u_0) # label(aARITHu_EQu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 327 (all Q97175 all P0 all A5 all S0 (p(s(bool,i(s(fun(fun(Q97175,bool),bool),i(s(fun(Q97175,fun(fun(Q97175,bool),bool)),in),s(Q97175,A5))),s(fun(Q97175,bool),i(s(fun(fun(Q97175,bool),fun(Q97175,bool)),i(s(fun(fun(fun(Q97175,bool),bool),fun(fun(Q97175,bool),fun(Q97175,bool))),hull),s(fun(fun(Q97175,bool),bool),P0))),s(fun(Q97175,bool),S0)))))) <-> s(fun(Q97175,bool),i(s(fun(fun(Q97175,bool),fun(Q97175,bool)),i(s(fun(fun(fun(Q97175,bool),bool),fun(fun(Q97175,bool),fun(Q97175,bool))),hull),s(fun(fun(Q97175,bool),bool),P0))),s(fun(Q97175,bool),S0))) = s(fun(Q97175,bool),i(s(fun(fun(Q97175,bool),fun(Q97175,bool)),i(s(fun(fun(fun(Q97175,bool),bool),fun(fun(Q97175,bool),fun(Q97175,bool))),hull),s(fun(fun(Q97175,bool),bool),P0))),s(fun(Q97175,bool),i(s(fun(fun(Q97175,bool),fun(Q97175,bool)),i(s(fun(Q97175,fun(fun(Q97175,bool),fun(Q97175,bool))),insert),s(Q97175,A5))),s(fun(Q97175,bool),S0))))))) # label(aHULLu_REDUNDANTu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 328 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))) # label(aSUBu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 329 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) | s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,P0) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0)))))))) # label(aLEu_MULTu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 330 (all A all B all X all Y ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(B,bool),num),dimindex),s(fun(B,bool),univ)))))) -> s(A,i(s(fun(num,A),i(s(fun(cart(A,B),fun(num,A)),d_),s(cart(A,B),X))),s(num,I0))) = s(A,i(s(fun(num,A),i(s(fun(cart(A,B),fun(num,A)),d_),s(cart(A,B),Y))),s(num,I0))))) <-> s(cart(A,B),X) = s(cart(A,B),Y))) # label(aCARTu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 331 (all X all Y all Z0 (s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Y))),s(int,Z0))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0))) <-> s(int,Y) = s(int,X))) # label(aINTu_EQu_ADDu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 332 (all A all X all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))),s(fun(A,bool),T0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))))) # label(aINSERTu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 333 (all A ((all X (p(s(bool,i(s(fun(A,bool),p0),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),q0),s(A,X)))))) -> ((all X p(s(bool,i(s(fun(A,bool),p0),s(A,X))))) -> (all X p(s(bool,i(s(fun(A,bool),q0),s(A,X)))))))) # label(aMONOu_FORALL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 334 (all I0 (p(s(bool,i(s(fun(ind0,bool),numu_rep),s(ind0,I0)))) -> p(s(bool,i(s(fun(ind0,bool),numu_rep),s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,I0)))))))) # label(aNUMu_REPu_RULESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 335 (all X all Y all N0 ((exists D0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,N0))),s(int,D0)))) <-> p(s(bool,i(s(fun(fun(int,fun(int,bool)),bool),i(s(fun(int,fun(fun(int,fun(int,bool)),bool)),i(s(fun(int,fun(int,fun(fun(int,fun(int,bool)),bool))),a_a_),s(int,X))),s(int,Y))),s(fun(int,fun(int,bool)),i(s(fun(int,fun(int,fun(int,bool))),intu_mod),s(int,N0)))))))) # label(aintu_congruent) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 336 (all A5 all B0 exists D0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_divides),s(int,D0))),s(int,A5)))) & (exists X exists Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,A5))),s(int,X))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,B0))),s(int,Y))))) = s(int,D0)) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_divides),s(int,D0))),s(int,B0)))))) # label(aINTu_GCDu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 337 (all N0 p(s(bool,i(s(fun(fun(num,bool),bool),infinite),s(fun(num,bool),i(s(fun(num,fun(num,bool)),from),s(num,N0))))))) # label(aINFINITEu_FROM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 338 (all N0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,x))),s(num,N0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,x))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(arealu_powu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 339 (all X (s(real,i(s(fun(real,real),realu_sgn),s(real,X))) = s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))))) # label(aINTu_SGNu_EQu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 340 (all A all B all U_1 ((all P0 all GENR_PVARR_53 (p(s(bool,i(s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),U_1),s(fun(B,bool),P0))),s(B,GENR_PVARR_53)))) <-> (exists X p(s(bool,i(s(fun(B,bool),i(s(fun(bool,fun(B,bool)),i(s(fun(B,fun(bool,fun(B,bool))),setspec),s(B,GENR_PVARR_53))),s(bool,i(s(fun(B,bool),P0),s(B,X))))),s(B,X))))))) -> (all U_0 ((all P0 all F0 all GENR_PVARR_52 ((exists X p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_52))),s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(A,B),F0),s(A,X))))))),s(A,X))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),i(s(fun(fun(B,bool),fun(fun(A,B),fun(A,bool))),U_0),s(fun(B,bool),P0))),s(fun(A,B),F0))),s(A,GENR_PVARR_52)))))) -> (all F0 ((all P0 s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),gspec),s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),U_1),s(fun(B,bool),P0))))) = s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),i(s(fun(fun(B,bool),fun(fun(A,B),fun(A,bool))),U_0),s(fun(B,bool),P0))),s(fun(A,B),F0)))))))) <-> (all Y exists X s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X)))))))))) # label(aSURJECTIVEu_IMAGEu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 341 (all N0 (p(s(bool,f0)) <-> s(num,i(s(fun(num,num),bit1),s(num,N0))) = s(num,u_0))) # label(aARITHu_EQu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 342 (all Q55049 all Q55042 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q55049,bool),bool),i(s(fun(fun(Q55049,bool),fun(fun(Q55049,bool),bool)),subset),s(fun(Q55049,bool),S0))),s(fun(Q55049,bool),i(s(fun(fun(Q55042,bool),fun(Q55049,bool)),i(s(fun(fun(Q55042,Q55049),fun(fun(Q55042,bool),fun(Q55049,bool))),image),s(fun(Q55042,Q55049),F0))),s(fun(Q55042,bool),T0)))))) & p(s(bool,i(s(fun(fun(Q55042,bool),bool),finite),s(fun(Q55042,bool),T0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(Q55049,bool),num),card),s(fun(Q55049,bool),S0))))),s(num,i(s(fun(fun(Q55042,bool),num),card),s(fun(Q55042,bool),T0)))))))) # label(aCARDu_SUBSETu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 343 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),i(s(fun(bool,fun(int,fun(int,int))),cond),s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y))))),s(int,X))),s(int,Y))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y)))) # label(aINTu_MIN) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 344 (all M all N all X all Y all W all Z0 (s(cart(real,N),Z0) = s(cart(real,N),Y) & s(cart(real,M),X) = s(cart(real,M),W) <-> s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X))),s(cart(real,N),Y))) = s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),W))),s(cart(real,N),Z0))))) # label(aPASTECARTu_INJ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 345 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))))),s(int,i(s(fun(int,int),intu_abs),s(int,Y)))))) -> s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(int,X))) # label(aINTu_ABSu_STILLNZ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 346 (all T1 all T2 (p(s(bool,T2)) | p(s(bool,T1)) <-> p(s(bool,T2)) | p(s(bool,T1)))) # label(aDISJu_SYM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 347 (all B all A all C all S0 all T0 all U (p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(B,bool),fun(fun(C,bool),bool)),a_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(A,bool),fun(fun(C,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(C,bool),U)))))) # label(aCARDu_EQu_TRANS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 348 (all A all S0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(A,bool),univ))))) # label(aCARDu_LEu_UNIV) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 349 (all X all Y all X0 s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,Y))),s(num,X0))))) = s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Y))))),s(num,X0)))) # label(aNADDu_MUL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 350 (all Q71474 all U_0 ((all F0 all X s(real,i(s(fun(Q71474,real),i(s(fun(fun(Q71474,real),fun(Q71474,real)),U_0),s(fun(Q71474,real),F0))),s(Q71474,X))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(Q71474,real),F0),s(Q71474,X)))))) -> (all F0 all S0 s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(fun(Q71474,real),real),i(s(fun(fun(Q71474,bool),fun(fun(Q71474,real),real)),sum),s(fun(Q71474,bool),S0))),s(fun(Q71474,real),F0))))) = s(real,i(s(fun(fun(Q71474,real),real),i(s(fun(fun(Q71474,bool),fun(fun(Q71474,real),real)),sum),s(fun(Q71474,bool),S0))),s(fun(Q71474,real),i(s(fun(fun(Q71474,real),fun(Q71474,real)),U_0),s(fun(Q71474,real),F0)))))))) # label(aSUMu_NEG) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 351 (all A all B all P all L_L_ all S0 all P0 all T0 (p(s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),tailadmissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),T0)))) <-> (exists P1 exists G0 exists H0 ((all F0 all G1 all A5 ((all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Z0))),s(A,i(s(fun(P,A),S0),s(P,A5)))))) -> s(B,i(s(fun(A,B),F0),s(A,Z0))) = s(B,i(s(fun(A,B),G1),s(A,Z0))))) -> s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P1),s(fun(A,B),G1))),s(P,A5))) = s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P1),s(fun(A,B),F0))),s(P,A5))) & s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),H0),s(fun(A,B),G1))),s(P,A5))) = s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),H0),s(fun(A,B),F0))),s(P,A5))) & s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),G0),s(fun(A,B),G1))),s(P,A5))) = s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),G0),s(fun(A,B),F0))),s(P,A5))))) & (all F0 all A5 (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,A5)))) -> s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),T0),s(fun(A,B),F0))),s(P,A5))) = s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P1),s(fun(A,B),F0))),s(P,A5))))),s(B,i(s(fun(A,B),F0),s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),G0),s(fun(A,B),F0))),s(P,A5))))))),s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),H0),s(fun(A,B),F0))),s(P,A5))))))) & (all F0 all A5 all Y (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P1),s(fun(A,B),F0))),s(P,A5)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),G0),s(fun(A,B),F0))),s(P,A5)))))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,i(s(fun(P,A),S0),s(P,A5)))))))))))) # label(atailadmissible) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 352 (all Q59081 all P0 all A5 all S0 ((exists X (p(s(bool,i(s(fun(Q59081,bool),P0),s(Q59081,X)))) & p(s(bool,i(s(fun(fun(Q59081,bool),bool),i(s(fun(Q59081,fun(fun(Q59081,bool),bool)),in),s(Q59081,X))),s(fun(Q59081,bool),S0)))))) | p(s(bool,i(s(fun(Q59081,bool),P0),s(Q59081,A5)))) <-> (exists X (p(s(bool,i(s(fun(fun(Q59081,bool),bool),i(s(fun(Q59081,fun(fun(Q59081,bool),bool)),in),s(Q59081,X))),s(fun(Q59081,bool),i(s(fun(fun(Q59081,bool),fun(Q59081,bool)),i(s(fun(Q59081,fun(fun(Q59081,bool),fun(Q59081,bool))),insert),s(Q59081,A5))),s(fun(Q59081,bool),S0)))))) & p(s(bool,i(s(fun(Q59081,bool),P0),s(Q59081,X)))))))) # label(aEXISTSu_INu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 353 (all M0 all N0 all P0 all Q0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,P0))),s(num,Q0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,Q0)))))))) # label(aLEu_MULT2) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 354 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_inv),s(real,X))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aREALu_INVu_LTu_1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 355 (all Q53282 all S0 all T0 all U (s(fun(Q53282,bool),i(s(fun(fun(Q53282,bool),fun(Q53282,bool)),i(s(fun(fun(Q53282,bool),fun(fun(Q53282,bool),fun(Q53282,bool))),inter),s(fun(Q53282,bool),S0))),s(fun(Q53282,bool),T0))) = s(fun(Q53282,bool),empty) & s(fun(Q53282,bool),U) = s(fun(Q53282,bool),i(s(fun(fun(Q53282,bool),fun(Q53282,bool)),i(s(fun(fun(Q53282,bool),fun(fun(Q53282,bool),fun(Q53282,bool))),union),s(fun(Q53282,bool),S0))),s(fun(Q53282,bool),T0))) & p(s(bool,i(s(fun(fun(Q53282,bool),bool),finite),s(fun(Q53282,bool),U)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(Q53282,bool),num),card),s(fun(Q53282,bool),S0))))),s(num,i(s(fun(fun(Q53282,bool),num),card),s(fun(Q53282,bool),T0))))) = s(num,i(s(fun(fun(Q53282,bool),num),card),s(fun(Q53282,bool),U))))) # label(aCARDu_UNIONu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 356 (all A all S0 all T0 all U (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),T0))),s(fun(A,bool),U)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),U)))))) # label(aSUBSETu_PSUBSETu_TRANS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 357 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,X)))) <-> s(real,X) != s(real,Y))) # label(aREALu_NOTu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 358 (all X s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(int,int),intu_abs),s(int,X))))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X)))))) # label(aintu_absu_th) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 359 (all Q19647 all U_0 ((all F0 all X (s(Q19647,i(s(fun(Q19647,Q19647),F0),s(Q19647,X))) = s(Q19647,X) <-> p(s(bool,i(s(fun(Q19647,bool),i(s(fun(fun(Q19647,Q19647),fun(Q19647,bool)),U_0),s(fun(Q19647,Q19647),F0))),s(Q19647,X)))))) -> (all L all F0 (p(s(bool,i(s(fun(list(Q19647),bool),i(s(fun(fun(Q19647,bool),fun(list(Q19647),bool)),all0),s(fun(Q19647,bool),i(s(fun(fun(Q19647,Q19647),fun(Q19647,bool)),U_0),s(fun(Q19647,Q19647),F0))))),s(list(Q19647),L)))) -> s(list(Q19647),i(s(fun(list(Q19647),list(Q19647)),i(s(fun(fun(Q19647,Q19647),fun(list(Q19647),list(Q19647))),map0),s(fun(Q19647,Q19647),F0))),s(list(Q19647),L))) = s(list(Q19647),L))))) # label(aMAPu_EQu_DEGEN) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 360 (all A all B s(fun(finite_sum(A,B),bool),univ) = s(fun(finite_sum(A,B),bool),i(s(fun(fun(num,bool),fun(finite_sum(A,B),bool)),i(s(fun(fun(num,finite_sum(A,B)),fun(fun(num,bool),fun(finite_sum(A,B),bool))),image),s(fun(num,finite_sum(A,B)),mku_finiteu_sum))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),univ))))),s(num,i(s(fun(fun(B,bool),num),dimindex),s(fun(B,bool),univ)))))))))) # label(aFINITEu_SUMu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 361 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,N0))))))) # label(aLEu_SQUAREu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 362 (all Q71183 all U_0 ((all F0 all G0 all X s(real,i(s(fun(Q71183,real),i(s(fun(fun(Q71183,real),fun(Q71183,real)),i(s(fun(fun(Q71183,real),fun(fun(Q71183,real),fun(Q71183,real))),U_0),s(fun(Q71183,real),F0))),s(fun(Q71183,real),G0))),s(Q71183,X))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(Q71183,real),F0),s(Q71183,X))))),s(real,i(s(fun(Q71183,real),G0),s(Q71183,X)))))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q71183,bool),bool),finite),s(fun(Q71183,bool),S0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(Q71183,real),real),i(s(fun(fun(Q71183,bool),fun(fun(Q71183,real),real)),sum),s(fun(Q71183,bool),S0))),s(fun(Q71183,real),F0))))),s(real,i(s(fun(fun(Q71183,real),real),i(s(fun(fun(Q71183,bool),fun(fun(Q71183,real),real)),sum),s(fun(Q71183,bool),S0))),s(fun(Q71183,real),G0))))) = s(real,i(s(fun(fun(Q71183,real),real),i(s(fun(fun(Q71183,bool),fun(fun(Q71183,real),real)),sum),s(fun(Q71183,bool),S0))),s(fun(Q71183,real),i(s(fun(fun(Q71183,real),fun(Q71183,real)),i(s(fun(fun(Q71183,real),fun(fun(Q71183,real),fun(Q71183,real))),U_0),s(fun(Q71183,real),F0))),s(fun(Q71183,real),G0))))))))) # label(aSUMu_ADD) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 363 (all N0 (-p(s(bool,i(s(fun(num,bool),even),s(num,N0)))) <-> p(s(bool,i(s(fun(num,bool),even),s(num,i(s(fun(num,num),suc),s(num,N0)))))))) # label(aEVENu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 364 (all Q48465 all Q48464 all U_0 ((all P0 all GENR_PVARR_18 ((exists X exists Y p(s(bool,i(s(fun(prod(Q48465,Q48464),bool),i(s(fun(bool,fun(prod(Q48465,Q48464),bool)),i(s(fun(prod(Q48465,Q48464),fun(bool,fun(prod(Q48465,Q48464),bool))),setspec),s(prod(Q48465,Q48464),GENR_PVARR_18))),s(bool,i(s(fun(Q48464,bool),i(s(fun(Q48465,fun(Q48464,bool)),P0),s(Q48465,X))),s(Q48464,Y))))),s(prod(Q48465,Q48464),i(s(fun(Q48464,prod(Q48465,Q48464)),i(s(fun(Q48465,fun(Q48464,prod(Q48465,Q48464))),c_),s(Q48465,X))),s(Q48464,Y))))))) <-> p(s(bool,i(s(fun(prod(Q48465,Q48464),bool),i(s(fun(fun(Q48465,fun(Q48464,bool)),fun(prod(Q48465,Q48464),bool)),U_0),s(fun(Q48465,fun(Q48464,bool)),P0))),s(prod(Q48465,Q48464),GENR_PVARR_18)))))) -> (all P0 all A5 all B0 s(bool,i(s(fun(fun(prod(Q48465,Q48464),bool),bool),i(s(fun(prod(Q48465,Q48464),fun(fun(prod(Q48465,Q48464),bool),bool)),in),s(prod(Q48465,Q48464),i(s(fun(Q48464,prod(Q48465,Q48464)),i(s(fun(Q48465,fun(Q48464,prod(Q48465,Q48464))),c_),s(Q48465,A5))),s(Q48464,B0))))),s(fun(prod(Q48465,Q48464),bool),i(s(fun(fun(prod(Q48465,Q48464),bool),fun(prod(Q48465,Q48464),bool)),gspec),s(fun(prod(Q48465,Q48464),bool),i(s(fun(fun(Q48465,fun(Q48464,bool)),fun(prod(Q48465,Q48464),bool)),U_0),s(fun(Q48465,fun(Q48464,bool)),P0))))))) = s(bool,i(s(fun(Q48464,bool),i(s(fun(Q48465,fun(Q48464,bool)),P0),s(Q48465,A5))),s(Q48464,B0)))))) # label(aINu_ELIMu_PAIRu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 365 (all A all X s(A,i(s(fun(A,A),i1),s(A,X))) = s(A,X)) # label(aIu_DEF) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 366 (all N0 all X (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aINTu_POWu_1u_LE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 367 (all A all B all P0 ((all A5 p(s(bool,i(s(fun(sum0(A,B),bool),P0),s(sum0(A,B),i(s(fun(A,sum0(A,B)),inl),s(A,A5))))))) & (all A5 p(s(bool,i(s(fun(sum0(A,B),bool),P0),s(sum0(A,B),i(s(fun(B,sum0(A,B)),inr),s(B,A5))))))) -> (all X p(s(bool,i(s(fun(sum0(A,B),bool),P0),s(sum0(A,B),X))))))) # label(asumu_INDUCT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 368 (all Q19562 all U_0 ((all X s(bool,t) = s(bool,i(s(fun(Q19562,bool),U_0),s(Q19562,X)))) -> (all L p(s(bool,i(s(fun(list(Q19562),bool),i(s(fun(fun(Q19562,bool),fun(list(Q19562),bool)),all0),s(fun(Q19562,bool),U_0))),s(list(Q19562),L))))))) # label(aALLu_T) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 369 (all A all N0 all S0 ((p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))))) -> (exists T0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),T0))),s(num,N0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0)))))))) # label(aCHOOSEu_SUBSETu_STRONG) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 370 (all A all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (exists A5 all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,i(s(fun(A,real),F0),s(A,X)))))))))) # label(aLOWERu_BOUNDu_FINITEu_SETu_REAL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 371 (all X1 all Y2 all X2 all Y1 (s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X2))),s(hreal,Y1))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X1))),s(hreal,Y2))) <-> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,X1))),s(hreal,Y1))))),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,X2))),s(hreal,Y2)))))))) # label(atrealu_eq) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 372 (all A all F0 all S0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(real,i(s(fun(A,real),F0),s(A,X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))) # label(aSUMu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 373 (all M0 all N0 (s(num,M0) = s(num,N0) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,M0))))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,N0)))))))) # label(aNADDu_OFu_NUMu_WELLDEF) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 374 (all F0 all M0 all N0 ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,I0)))) -> s(num,i(s(fun(num,num),F0),s(num,I0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),F0))))) # label(aNSUMu_EQu_0u_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 375 (all Q19791 all U_0 ((all P0 all Q0 all X (p(s(bool,i(s(fun(Q19791,bool),i(s(fun(fun(Q19791,bool),fun(Q19791,bool)),i(s(fun(fun(Q19791,bool),fun(fun(Q19791,bool),fun(Q19791,bool))),U_0),s(fun(Q19791,bool),P0))),s(fun(Q19791,bool),Q0))),s(Q19791,X)))) <-> (p(s(bool,i(s(fun(Q19791,bool),P0),s(Q19791,X)))) -> p(s(bool,i(s(fun(Q19791,bool),Q0),s(Q19791,X))))))) -> (all P0 all Q0 all L (p(s(bool,i(s(fun(list(Q19791),bool),i(s(fun(fun(Q19791,bool),fun(list(Q19791),bool)),all0),s(fun(Q19791,bool),i(s(fun(fun(Q19791,bool),fun(Q19791,bool)),i(s(fun(fun(Q19791,bool),fun(fun(Q19791,bool),fun(Q19791,bool))),U_0),s(fun(Q19791,bool),P0))),s(fun(Q19791,bool),Q0))))),s(list(Q19791),L)))) & p(s(bool,i(s(fun(list(Q19791),bool),i(s(fun(fun(Q19791,bool),fun(list(Q19791),bool)),all0),s(fun(Q19791,bool),P0))),s(list(Q19791),L)))) -> p(s(bool,i(s(fun(list(Q19791),bool),i(s(fun(fun(Q19791,bool),fun(list(Q19791),bool)),all0),s(fun(Q19791,bool),Q0))),s(list(Q19791),L)))))))) # label(aALLu_MP) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 376 (all M0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(num,i(s(fun(num,num),suc),s(num,M0)))) # label(aADD1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 377 (all Q64259 all Q64274 all OP (p(s(bool,i(s(fun(fun(Q64274,fun(Q64274,Q64274)),bool),monoidal),s(fun(Q64274,fun(Q64274,Q64274)),OP)))) -> (all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q64259,bool),bool),finite),s(fun(Q64259,bool),S0)))) & p(s(bool,i(s(fun(fun(Q64259,bool),bool),finite),s(fun(Q64259,bool),T0)))) & p(s(bool,i(s(fun(fun(Q64259,bool),bool),i(s(fun(fun(Q64259,bool),fun(fun(Q64259,bool),bool)),disjoint),s(fun(Q64259,bool),S0))),s(fun(Q64259,bool),T0)))) -> s(Q64274,i(s(fun(Q64274,Q64274),i(s(fun(Q64274,fun(Q64274,Q64274)),OP),s(Q64274,i(s(fun(fun(Q64259,Q64274),Q64274),i(s(fun(fun(Q64259,bool),fun(fun(Q64259,Q64274),Q64274)),i(s(fun(fun(Q64274,fun(Q64274,Q64274)),fun(fun(Q64259,bool),fun(fun(Q64259,Q64274),Q64274))),iterate),s(fun(Q64274,fun(Q64274,Q64274)),OP))),s(fun(Q64259,bool),S0))),s(fun(Q64259,Q64274),F0))))),s(Q64274,i(s(fun(fun(Q64259,Q64274),Q64274),i(s(fun(fun(Q64259,bool),fun(fun(Q64259,Q64274),Q64274)),i(s(fun(fun(Q64274,fun(Q64274,Q64274)),fun(fun(Q64259,bool),fun(fun(Q64259,Q64274),Q64274))),iterate),s(fun(Q64274,fun(Q64274,Q64274)),OP))),s(fun(Q64259,bool),T0))),s(fun(Q64259,Q64274),F0))))) = s(Q64274,i(s(fun(fun(Q64259,Q64274),Q64274),i(s(fun(fun(Q64259,bool),fun(fun(Q64259,Q64274),Q64274)),i(s(fun(fun(Q64274,fun(Q64274,Q64274)),fun(fun(Q64259,bool),fun(fun(Q64259,Q64274),Q64274))),iterate),s(fun(Q64274,fun(Q64274,Q64274)),OP))),s(fun(Q64259,bool),i(s(fun(fun(Q64259,bool),fun(Q64259,bool)),i(s(fun(fun(Q64259,bool),fun(fun(Q64259,bool),fun(Q64259,bool))),union),s(fun(Q64259,bool),S0))),s(fun(Q64259,bool),T0))))),s(fun(Q64259,Q64274),F0))))))) # label(aITERATEu_UNION) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 378 (all A all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (exists A5 all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,A5)))))))) # label(aUPPERu_BOUNDu_FINITEu_SETu_REAL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 379 (all X all XI_ all Y all YI_ (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,XI_)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,Y))),s(nadd,YI_)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Y))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,XI_))),s(nadd,YI_)))))))) # label(aNADDu_ADDu_WELLDEF) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 380 (all A all L all P0 all Q0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),Q0))),s(fun(A,bool),P0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(A,bool),bool)),chain),s(fun(prod(A,A),bool),L))),s(fun(A,bool),P0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(A,bool),bool)),chain),s(fun(prod(A,A),bool),L))),s(fun(A,bool),Q0)))))) # label(aCHAINu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 381 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Z0))),s(int,X)))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Z0))),s(int,Y)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Z0))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y)))))))) # label(aINTu_LTu_MAX) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 382 (all S0 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) & s(fun(real,bool),S0) != s(fun(real,bool),empty) -> p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))),s(fun(real,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))),s(real,X)))))))) # label(aINFu_FINITE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 383 (all Q4590 all Q4594 all Q4593 all Q4578 all U_0 ((all F0 all FI_ ((all X all Y all Z0 p(s(bool,i(s(fun(Q4578,bool),i(s(fun(Q4578,fun(Q4578,bool)),geq),s(Q4578,i(s(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),FI_),s(prod(Q4590,prod(Q4594,Q4593)),i(s(fun(prod(Q4594,Q4593),prod(Q4590,prod(Q4594,Q4593))),i(s(fun(Q4590,fun(prod(Q4594,Q4593),prod(Q4590,prod(Q4594,Q4593)))),c_),s(Q4590,X))),s(prod(Q4594,Q4593),i(s(fun(Q4593,prod(Q4594,Q4593)),i(s(fun(Q4594,fun(Q4593,prod(Q4594,Q4593))),c_),s(Q4594,Y))),s(Q4593,Z0))))))))),s(Q4578,i(s(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),F0),s(prod(Q4590,prod(Q4594,Q4593)),i(s(fun(prod(Q4594,Q4593),prod(Q4590,prod(Q4594,Q4593))),i(s(fun(Q4590,fun(prod(Q4594,Q4593),prod(Q4590,prod(Q4594,Q4593)))),c_),s(Q4590,X))),s(prod(Q4594,Q4593),i(s(fun(Q4593,prod(Q4594,Q4593)),i(s(fun(Q4594,fun(Q4593,prod(Q4594,Q4593))),c_),s(Q4594,Y))),s(Q4593,Z0))))))))))) <-> p(s(bool,i(s(fun(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),bool),i(s(fun(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),fun(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),bool)),U_0),s(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),F0))),s(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),FI_)))))) -> (all F0 s(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),F0) = s(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),i(s(fun(fun(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),bool),fun(prod(Q4590,prod(Q4594,Q4593)),Q4578)),gabs),s(fun(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),bool),i(s(fun(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),fun(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),bool)),U_0),s(fun(prod(Q4590,prod(Q4594,Q4593)),Q4578),F0)))))))) # label(aPAIREDu_ETAu_THMu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 384 (all X s(real,X) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_sgn),s(real,X))))),s(real,i(s(fun(real,real),realu_abs),s(real,X)))))) # label(aREALu_SGNu_ABS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 385 (all X all N0 (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,X) & s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))) # label(aREALu_POWu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.88 386 (all Q44102 all U_2 ((all P0 all X all T0 (s(Q44102,X) = s(Q44102,T0) & p(s(bool,P0)) <-> p(s(bool,i(s(fun(Q44102,bool),i(s(fun(Q44102,fun(Q44102,bool)),i(s(fun(bool,fun(Q44102,fun(Q44102,bool))),U_2),s(bool,P0))),s(Q44102,X))),s(Q44102,T0)))))) -> (all U_1 ((all X all P0 s(fun(Q44102,bool),i(s(fun(bool,fun(Q44102,bool)),i(s(fun(Q44102,fun(bool,fun(Q44102,bool))),U_1),s(Q44102,X))),s(bool,P0))) = s(fun(Q44102,bool),i(s(fun(Q44102,fun(Q44102,bool)),i(s(fun(bool,fun(Q44102,fun(Q44102,bool))),U_2),s(bool,P0))),s(Q44102,X)))) -> (all U_0 ((all P0 all V s(bool,i(s(fun(fun(bool,fun(Q44102,bool)),bool),P0),s(fun(bool,fun(Q44102,bool)),i(s(fun(Q44102,fun(bool,fun(Q44102,bool))),setspec),s(Q44102,V))))) = s(bool,i(s(fun(Q44102,bool),i(s(fun(fun(fun(bool,fun(Q44102,bool)),bool),fun(Q44102,bool)),U_0),s(fun(fun(bool,fun(Q44102,bool)),bool),P0))),s(Q44102,V)))) -> (all P0 all X s(bool,i(s(fun(fun(bool,fun(Q44102,bool)),bool),P0),s(fun(bool,fun(Q44102,bool)),i(s(fun(Q44102,fun(bool,fun(Q44102,bool))),U_1),s(Q44102,X))))) = s(bool,i(s(fun(fun(Q44102,bool),bool),i(s(fun(Q44102,fun(fun(Q44102,bool),bool)),in),s(Q44102,X))),s(fun(Q44102,bool),i(s(fun(fun(Q44102,bool),fun(Q44102,bool)),gspec),s(fun(Q44102,bool),i(s(fun(fun(fun(bool,fun(Q44102,bool)),bool),fun(Q44102,bool)),U_0),s(fun(fun(bool,fun(Q44102,bool)),bool),P0)))))))))))))) # label(aINu_ELIMu_THMu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 387 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) # label(aINTu_LTu_ADDL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 388 (all X all K0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_abs),s(int,X))))),s(int,K0)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,K0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_neg),s(int,K0))))),s(int,X)))))) # label(aINTu_BOUNDSu_LT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 389 (all X all N0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),realu_inv),s(real,X))))),s(num,N0))) = s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0)))))) # label(aREALu_INVu_POW) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 390 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Z0))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Z0))),s(real,X)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Z0))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,Y)))))))) # label(aREALu_LTu_MIN) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 391 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),odd),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))) <-> p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),odd),s(num,M0)))))) # label(aODDu_MULT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 392 (exists B0 p(s(bool,B0))) # label(aEXISTSu_ONEu_REP) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 393 (all X all Y (p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,Y)))) -> (exists D0 s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X))),s(hreal,D0))) = s(hreal,Y)))) # label(aHREALu_LEu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 394 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,P0)))) & s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,M0) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0)))))))) # label(aLTu_LMULT) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 395 (all A all B all U_1 ((all R0 all R1 all S0 all S1 all F0 ((all R2 all S2 exists V ((p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),R0),s(A,R1))),s(A,R2)))) | p(s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),S0),s(B,S1))),s(B,S2)))) & s(A,R1) = s(A,R2) <-> p(s(bool,V))) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(A,B),bool),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,R2))),s(B,S2))))))),s(bool,V)))))) <-> p(s(bool,i(s(fun(fun(prod(A,B),bool),bool),i(s(fun(B,fun(fun(prod(A,B),bool),bool)),i(s(fun(fun(B,fun(B,bool)),fun(B,fun(fun(prod(A,B),bool),bool))),i(s(fun(A,fun(fun(B,fun(B,bool)),fun(B,fun(fun(prod(A,B),bool),bool)))),i(s(fun(fun(A,fun(A,bool)),fun(A,fun(fun(B,fun(B,bool)),fun(B,fun(fun(prod(A,B),bool),bool))))),U_1),s(fun(A,fun(A,bool)),R0))),s(A,R1))),s(fun(B,fun(B,bool)),S0))),s(B,S1))),s(fun(prod(A,B),bool),F0)))))) -> (all U_0 ((all R0 all S0 all F0 ((all R1 all S1 p(s(bool,i(s(fun(fun(prod(A,B),bool),bool),i(s(fun(fun(prod(A,B),bool),fun(fun(prod(A,B),bool),bool)),geq),s(fun(prod(A,B),bool),i(s(fun(prod(A,B),fun(prod(A,B),bool)),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,R1))),s(B,S1))))))),s(fun(prod(A,B),bool),i(s(fun(fun(fun(prod(A,B),bool),bool),fun(prod(A,B),bool)),gabs),s(fun(fun(prod(A,B),bool),bool),i(s(fun(B,fun(fun(prod(A,B),bool),bool)),i(s(fun(fun(B,fun(B,bool)),fun(B,fun(fun(prod(A,B),bool),bool))),i(s(fun(A,fun(fun(B,fun(B,bool)),fun(B,fun(fun(prod(A,B),bool),bool)))),i(s(fun(fun(A,fun(A,bool)),fun(A,fun(fun(B,fun(B,bool)),fun(B,fun(fun(prod(A,B),bool),bool))))),U_1),s(fun(A,fun(A,bool)),R0))),s(A,R1))),s(fun(B,fun(B,bool)),S0))),s(B,S1))))))))) <-> p(s(bool,i(s(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),i(s(fun(fun(B,fun(B,bool)),fun(fun(prod(A,B),fun(prod(A,B),bool)),bool)),i(s(fun(fun(A,fun(A,bool)),fun(fun(B,fun(B,bool)),fun(fun(prod(A,B),fun(prod(A,B),bool)),bool))),U_0),s(fun(A,fun(A,bool)),R0))),s(fun(B,fun(B,bool)),S0))),s(fun(prod(A,B),fun(prod(A,B),bool)),F0)))))) -> (all R0 all S0 (p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),R0)))) & p(s(bool,i(s(fun(fun(B,fun(B,bool)),bool),wf),s(fun(B,fun(B,bool)),S0)))) -> p(s(bool,i(s(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),wf),s(fun(prod(A,B),fun(prod(A,B),bool)),i(s(fun(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),fun(prod(A,B),fun(prod(A,B),bool))),gabs),s(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),i(s(fun(fun(B,fun(B,bool)),fun(fun(prod(A,B),fun(prod(A,B),bool)),bool)),i(s(fun(fun(A,fun(A,bool)),fun(fun(B,fun(B,bool)),fun(fun(prod(A,B),fun(prod(A,B),bool)),bool))),U_0),s(fun(A,fun(A,bool)),R0))),s(fun(B,fun(B,bool)),S0)))))))))))))) # label(aWFu_LEX) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 396 (all X all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,Z0)))) # label(aREALu_LEu_LADD) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 397 (all X all Y (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,Y)))) <-> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,Y))),s(nadd,X)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y)))))) # label(aNADDu_LEu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 398 (all A all P0 all Q0 ((exists X p(s(bool,i(s(fun(A,bool),Q0),s(A,X))))) | (exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) <-> (exists X (p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))) | p(s(bool,i(s(fun(A,bool),P0),s(A,X)))))))) # label(aEXISTSu_ORu_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 399 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all P0 ((exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) & (all X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))))) -> (exists Y (p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))) & (all Z0 (p(s(bool,i(s(fun(A,bool),P0),s(A,Z0)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,Z0)))))))))))))) # label(aWOSETu_WELL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 400 (all Q92028 all Q92030 all S0 all T0 (p(s(bool,i(s(fun(fun(Q92030,bool),bool),finite),s(fun(Q92030,bool),T0)))) & p(s(bool,i(s(fun(fun(Q92028,bool),bool),finite),s(fun(Q92028,bool),S0)))) -> p(s(bool,i(s(fun(fun(sum0(Q92028,Q92030),bool),bool),finite),s(fun(sum0(Q92028,Q92030),bool),i(s(fun(fun(Q92030,bool),fun(sum0(Q92028,Q92030),bool)),i(s(fun(fun(Q92028,bool),fun(fun(Q92030,bool),fun(sum0(Q92028,Q92030),bool))),p_u_c),s(fun(Q92028,bool),S0))),s(fun(Q92030,bool),T0)))))))) # label(aCARDu_ADDu_FINITE) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 401 (all X ((exists B0 all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),X),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,i(s(fun(num,num),X),s(num,M0))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))))) <-> p(s(bool,i(s(fun(fun(num,num),bool),isu_nadd),s(fun(num,num),X)))))) # label(aisu_nadd) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 402 (all S0 (s(fun(real,bool),S0) != s(fun(real,bool),empty) & (exists B0 all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,B0)))))) -> (s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))) = s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))) <-> (exists A5 s(fun(real,bool),S0) = s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),i(s(fun(real,fun(fun(real,bool),fun(real,bool))),insert),s(real,A5))),s(fun(real,bool),empty))))))) # label(aREALu_SUPu_EQu_INF) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 403 (all X all Y (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,X) | s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,Y))) # label(aREALu_DIVu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 404 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,M0))),s(num,N0))))))),s(num,P0))) = s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0)))))))) # label(aDISTu_RMUL) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 405 (all B all A all F0 all S0 ((all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) -> s(A,X) = s(A,Y))) -> s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))) = s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))))) # label(aFINITEu_IMAGEu_INJu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 406 (all N0 s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),numeral),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,N0)))))) # label(aBIT0u_THM) # label(axiom) # label(non_clause). [assumption]. 13.83/13.89 407 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (all N0 exists A5 exists B0 all M0 all N1 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,N1))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N1))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,M0))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,N1))))),s(num,B0)))))))))) # label(aNADDu_MULu_LINVu_LEMMA7a) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 408 p(s(bool,i(s(fun(bool,bool),p0),s(bool,f0)))) & p(s(bool,i(s(fun(bool,bool),p0),s(bool,t)))) <-> (all B0 p(s(bool,i(s(fun(bool,bool),p0),s(bool,B0))))) # label(aFORALLu_BOOLu_THM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 409 (all A all U_0 ((all Q0 all GENR_PVARR_269 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_0),s(fun(A,bool),Q0))),s(A,GENR_PVARR_269)))) <-> (exists X p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_269))),s(bool,i(s(fun(A,bool),Q0),s(A,X))))),s(A,X))))))) -> (all P0 all Q0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_0),s(fun(A,bool),Q0)))))))) & (all X (p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))) -> (exists D0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D0)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(real,fun(A,bool)),P0),s(real,D0))),s(A,X)))))))) & (all D0 all E0 all X (p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,E0))),s(real,D0)))) -> (p(s(bool,i(s(fun(A,bool),i(s(fun(real,fun(A,bool)),P0),s(real,D0))),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(real,fun(A,bool)),P0),s(real,E0))),s(A,X))))))) -> (exists D0 ((all X (p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(real,fun(A,bool)),P0),s(real,D0))),s(A,X)))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D0)))))))))) # label(aEPSILONu_DELTAu_MINIMAL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 410 (all X all Y (s(real,X) = s(real,Y) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))))) # label(aREALu_EQu_IMPu_LE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 411 (all N0 s(num,i(s(fun(num,num),pre),s(num,i(s(fun(num,num),suc),s(num,N0))))) = s(num,N0)) # label(aPREu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 412 (all Q20804 all K0 all L all M0 s(Q20804,i(s(fun(list(Q20804),Q20804),i(s(fun(num,fun(list(Q20804),Q20804)),el),s(num,K0))),s(list(Q20804),i(s(fun(list(Q20804),list(Q20804)),i(s(fun(list(Q20804),fun(list(Q20804),list(Q20804))),append),s(list(Q20804),L))),s(list(Q20804),M0))))) = s(Q20804,i(s(fun(Q20804,Q20804),i(s(fun(Q20804,fun(Q20804,Q20804)),i(s(fun(bool,fun(Q20804,fun(Q20804,Q20804))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,K0))),s(num,i(s(fun(list(Q20804),num),length),s(list(Q20804),L))))))),s(Q20804,i(s(fun(list(Q20804),Q20804),i(s(fun(num,fun(list(Q20804),Q20804)),el),s(num,K0))),s(list(Q20804),L))))),s(Q20804,i(s(fun(list(Q20804),Q20804),i(s(fun(num,fun(list(Q20804),Q20804)),el),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,K0))),s(num,i(s(fun(list(Q20804),num),length),s(list(Q20804),L))))))),s(list(Q20804),M0)))))) # label(aELu_APPEND) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 413 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),infinite),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))))) # label(aCARDu_LTu_FINITEu_INFINITE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 414 (all A all Q63442 all U_1 ((all OP all F0 all X all A5 s(Q63442,i(s(fun(Q63442,Q63442),i(s(fun(Q63442,fun(Q63442,Q63442)),OP),s(Q63442,i(s(fun(A,Q63442),F0),s(A,X))))),s(Q63442,A5))) = s(Q63442,i(s(fun(Q63442,Q63442),i(s(fun(A,fun(Q63442,Q63442)),i(s(fun(fun(A,Q63442),fun(A,fun(Q63442,Q63442))),i(s(fun(fun(Q63442,fun(Q63442,Q63442)),fun(fun(A,Q63442),fun(A,fun(Q63442,Q63442)))),U_1),s(fun(Q63442,fun(Q63442,Q63442)),OP))),s(fun(A,Q63442),F0))),s(A,X))),s(Q63442,A5)))) -> (all U_0 ((all OP all F0 all X s(fun(Q63442,Q63442),i(s(fun(A,fun(Q63442,Q63442)),i(s(fun(fun(A,Q63442),fun(A,fun(Q63442,Q63442))),i(s(fun(fun(Q63442,fun(Q63442,Q63442)),fun(fun(A,Q63442),fun(A,fun(Q63442,Q63442)))),U_0),s(fun(Q63442,fun(Q63442,Q63442)),OP))),s(fun(A,Q63442),F0))),s(A,X))) = s(fun(Q63442,Q63442),i(s(fun(A,fun(Q63442,Q63442)),i(s(fun(fun(A,Q63442),fun(A,fun(Q63442,Q63442))),i(s(fun(fun(Q63442,fun(Q63442,Q63442)),fun(fun(A,Q63442),fun(A,fun(Q63442,Q63442)))),U_1),s(fun(Q63442,fun(Q63442,Q63442)),OP))),s(fun(A,Q63442),F0))),s(A,X)))) -> (all F0 all S0 all OP s(Q63442,i(s(fun(Q63442,Q63442),i(s(fun(Q63442,fun(Q63442,Q63442)),i(s(fun(bool,fun(Q63442,fun(Q63442,Q63442))),cond),s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,Q63442),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(Q63442,fun(Q63442,Q63442)),fun(fun(A,Q63442),fun(fun(A,bool),fun(A,bool)))),support),s(fun(Q63442,fun(Q63442,Q63442)),OP))),s(fun(A,Q63442),F0))),s(fun(A,bool),S0))))))),s(Q63442,i(s(fun(Q63442,Q63442),i(s(fun(fun(A,bool),fun(Q63442,Q63442)),i(s(fun(fun(A,fun(Q63442,Q63442)),fun(fun(A,bool),fun(Q63442,Q63442))),itset),s(fun(A,fun(Q63442,Q63442)),i(s(fun(fun(A,Q63442),fun(A,fun(Q63442,Q63442))),i(s(fun(fun(Q63442,fun(Q63442,Q63442)),fun(fun(A,Q63442),fun(A,fun(Q63442,Q63442)))),U_0),s(fun(Q63442,fun(Q63442,Q63442)),OP))),s(fun(A,Q63442),F0))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,Q63442),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(Q63442,fun(Q63442,Q63442)),fun(fun(A,Q63442),fun(fun(A,bool),fun(A,bool)))),support),s(fun(Q63442,fun(Q63442,Q63442)),OP))),s(fun(A,Q63442),F0))),s(fun(A,bool),S0))))),s(Q63442,i(s(fun(fun(Q63442,fun(Q63442,Q63442)),Q63442),neutral),s(fun(Q63442,fun(Q63442,Q63442)),OP))))))),s(Q63442,i(s(fun(fun(Q63442,fun(Q63442,Q63442)),Q63442),neutral),s(fun(Q63442,fun(Q63442,Q63442)),OP))))) = s(Q63442,i(s(fun(fun(A,Q63442),Q63442),i(s(fun(fun(A,bool),fun(fun(A,Q63442),Q63442)),i(s(fun(fun(Q63442,fun(Q63442,Q63442)),fun(fun(A,bool),fun(fun(A,Q63442),Q63442))),iterate),s(fun(Q63442,fun(Q63442,Q63442)),OP))),s(fun(A,bool),S0))),s(fun(A,Q63442),F0)))))))) # label(aiterate) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 415 (all N0 exists V (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,V))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,N0) <-> p(s(bool,V))))) # label(aEXPu_ZERO) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 416 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,i(s(fun(real,real),realu_neg),s(real,Y))))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y)))))) # label(aREALu_MULu_RNEG) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 417 (all A all P0 all F0 all S0 ((all X all Y (p(s(bool,i(s(fun(real,bool),P0),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),P0),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),P0),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))))) & (all A5 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,A5))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),P0),s(real,i(s(fun(A,real),F0),s(A,A5)))))))) & p(s(bool,i(s(fun(real,bool),P0),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> p(s(bool,i(s(fun(real,bool),P0),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0)))))))) # label(aSUMu_CLOSED) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 418 (all X1 all X2 all Y1 all Y2 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),Y1))),s(prod(hreal,hreal),Y2)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),X2)))) -> s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),Y1))) = s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),X2))),s(prod(hreal,hreal),Y2))))) # label(aTREALu_LEu_WELLDEF) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 419 (all Q4757 all Q4756 all Q4750 all U_0 ((all F0 all F1 ((all A5 all B0 p(s(bool,i(s(fun(Q4750,bool),i(s(fun(Q4750,fun(Q4750,bool)),geq),s(Q4750,i(s(fun(prod(Q4757,Q4756),Q4750),F1),s(prod(Q4757,Q4756),i(s(fun(Q4756,prod(Q4757,Q4756)),i(s(fun(Q4757,fun(Q4756,prod(Q4757,Q4756))),c_),s(Q4757,A5))),s(Q4756,B0))))))),s(Q4750,i(s(fun(Q4756,Q4750),i(s(fun(Q4757,fun(Q4756,Q4750)),F0),s(Q4757,A5))),s(Q4756,B0))))))) <-> p(s(bool,i(s(fun(fun(prod(Q4757,Q4756),Q4750),bool),i(s(fun(fun(Q4757,fun(Q4756,Q4750)),fun(fun(prod(Q4757,Q4756),Q4750),bool)),U_0),s(fun(Q4757,fun(Q4756,Q4750)),F0))),s(fun(prod(Q4757,Q4756),Q4750),F1)))))) -> (all P0 ((all F0 p(s(bool,i(s(fun(fun(prod(Q4757,Q4756),Q4750),bool),P0),s(fun(prod(Q4757,Q4756),Q4750),i(s(fun(fun(fun(prod(Q4757,Q4756),Q4750),bool),fun(prod(Q4757,Q4756),Q4750)),gabs),s(fun(fun(prod(Q4757,Q4756),Q4750),bool),i(s(fun(fun(Q4757,fun(Q4756,Q4750)),fun(fun(prod(Q4757,Q4756),Q4750),bool)),U_0),s(fun(Q4757,fun(Q4756,Q4750)),F0))))))))) <-> (all F0 p(s(bool,i(s(fun(fun(prod(Q4757,Q4756),Q4750),bool),P0),s(fun(prod(Q4757,Q4756),Q4750),F0))))))))) # label(aFORALLu_CURRY) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 420 (all S0 all A5 (s(fun(real,bool),S0) != s(fun(real,bool),empty) & p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) -> ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,A5)))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))))),s(real,A5))))))) # label(aREALu_SUPu_LEu_FINITE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 421 (all X all Y all Z0 (s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Z0))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))) <-> s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,X) | s(int,Y) = s(int,Z0))) # label(aINTu_EQu_MULu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 422 (all X all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,N0))))))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0)))))))) # label(aNADDu_MULu_LINVu_LEMMA1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 423 (all X s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),realu_abs),s(real,X))))) = s(real,i(s(fun(real,real),realu_abs),s(real,X)))) # label(aREALu_ABSu_ABS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 424 (all Q56069 all Q56068 all U_0 ((all S0 all T0 all GENR_PVARR_88 ((exists X exists Y exists V ((p(s(bool,i(s(fun(fun(Q56069,bool),bool),i(s(fun(Q56069,fun(fun(Q56069,bool),bool)),in),s(Q56069,X))),s(fun(Q56069,bool),S0)))) & p(s(bool,i(s(fun(fun(Q56068,bool),bool),i(s(fun(Q56068,fun(fun(Q56068,bool),bool)),in),s(Q56068,Y))),s(fun(Q56068,bool),T0)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(prod(Q56069,Q56068),bool),i(s(fun(bool,fun(prod(Q56069,Q56068),bool)),i(s(fun(prod(Q56069,Q56068),fun(bool,fun(prod(Q56069,Q56068),bool))),setspec),s(prod(Q56069,Q56068),GENR_PVARR_88))),s(bool,V))),s(prod(Q56069,Q56068),i(s(fun(Q56068,prod(Q56069,Q56068)),i(s(fun(Q56069,fun(Q56068,prod(Q56069,Q56068))),c_),s(Q56069,X))),s(Q56068,Y)))))))) <-> p(s(bool,i(s(fun(prod(Q56069,Q56068),bool),i(s(fun(fun(Q56068,bool),fun(prod(Q56069,Q56068),bool)),i(s(fun(fun(Q56069,bool),fun(fun(Q56068,bool),fun(prod(Q56069,Q56068),bool))),U_0),s(fun(Q56069,bool),S0))),s(fun(Q56068,bool),T0))),s(prod(Q56069,Q56068),GENR_PVARR_88)))))) -> (all S0 all T0 s(fun(prod(Q56069,Q56068),bool),i(s(fun(fun(Q56068,bool),fun(prod(Q56069,Q56068),bool)),i(s(fun(fun(Q56069,bool),fun(fun(Q56068,bool),fun(prod(Q56069,Q56068),bool))),cross0),s(fun(Q56069,bool),S0))),s(fun(Q56068,bool),T0))) = s(fun(prod(Q56069,Q56068),bool),i(s(fun(fun(prod(Q56069,Q56068),bool),fun(prod(Q56069,Q56068),bool)),gspec),s(fun(prod(Q56069,Q56068),bool),i(s(fun(fun(Q56068,bool),fun(prod(Q56069,Q56068),bool)),i(s(fun(fun(Q56069,bool),fun(fun(Q56068,bool),fun(prod(Q56069,Q56068),bool))),U_0),s(fun(Q56069,bool),S0))),s(fun(Q56068,bool),T0)))))))) # label(aCROSS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 425 (all X all N0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(num,bool),even),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(num,N0)))) # label(aREALu_POWu_NEG) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 426 (all U_0 ((all C0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),U_0),s(num,C0))),s(num,N0))) = s(num,C0)) -> (all C0 all M0 all N0 s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),i(s(fun(num,fun(num,num)),U_0),s(num,C0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))),s(num,C0)))))) # label(aNSUMu_CONSTu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 427 (all X s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,X)))))) # label(aINTu_LEu_DOUBLE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 428 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,P0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,P0)))))) # label(aLTEu_TRANS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 429 (all A all U_0 ((all P0 all GENR_PVARR_272 ((exists X p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_272))),s(bool,i(s(fun(A,bool),P0),s(A,X))))),s(A,X))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_0),s(fun(A,bool),P0))),s(A,GENR_PVARR_272)))))) -> (all P0 all P1 all S0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(A,bool),P1),s(A,X)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_0),s(fun(A,bool),P1)))))))) -> (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),fun(A,bool))),hull),s(fun(fun(A,bool),bool),P0))),s(fun(A,bool),S0)))))) -> p(s(bool,i(s(fun(A,bool),P1),s(A,X)))))))))) # label(aHULLu_INDUCT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 430 (all N0 s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))) # label(aintu_ofu_numu_th) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 431 (all Q49390 all U_0 ((all S0 all U all GENR_PVARR_41 (p(s(bool,i(s(fun(fun(Q49390,bool),bool),i(s(fun(fun(Q49390,bool),fun(fun(Q49390,bool),bool)),i(s(fun(fun(fun(Q49390,bool),bool),fun(fun(Q49390,bool),fun(fun(Q49390,bool),bool))),U_0),s(fun(fun(Q49390,bool),bool),S0))),s(fun(Q49390,bool),U))),s(fun(Q49390,bool),GENR_PVARR_41)))) <-> (exists T0 p(s(bool,i(s(fun(fun(Q49390,bool),bool),i(s(fun(bool,fun(fun(Q49390,bool),bool)),i(s(fun(fun(Q49390,bool),fun(bool,fun(fun(Q49390,bool),bool))),setspec),s(fun(Q49390,bool),GENR_PVARR_41))),s(bool,i(s(fun(fun(fun(Q49390,bool),bool),bool),i(s(fun(fun(Q49390,bool),fun(fun(fun(Q49390,bool),bool),bool)),in),s(fun(Q49390,bool),T0))),s(fun(fun(Q49390,bool),bool),S0))))),s(fun(Q49390,bool),i(s(fun(fun(Q49390,bool),fun(Q49390,bool)),i(s(fun(fun(Q49390,bool),fun(fun(Q49390,bool),fun(Q49390,bool))),diff),s(fun(Q49390,bool),U))),s(fun(Q49390,bool),T0))))))))) -> (all U all S0 s(fun(Q49390,bool),i(s(fun(fun(fun(Q49390,bool),bool),fun(Q49390,bool)),unions),s(fun(fun(Q49390,bool),bool),i(s(fun(fun(fun(Q49390,bool),bool),fun(fun(Q49390,bool),bool)),gspec),s(fun(fun(Q49390,bool),bool),i(s(fun(fun(Q49390,bool),fun(fun(Q49390,bool),bool)),i(s(fun(fun(fun(Q49390,bool),bool),fun(fun(Q49390,bool),fun(fun(Q49390,bool),bool))),U_0),s(fun(fun(Q49390,bool),bool),S0))),s(fun(Q49390,bool),U))))))) = s(fun(Q49390,bool),i(s(fun(fun(Q49390,bool),fun(Q49390,bool)),i(s(fun(fun(Q49390,bool),fun(fun(Q49390,bool),fun(Q49390,bool))),diff),s(fun(Q49390,bool),U))),s(fun(Q49390,bool),i(s(fun(fun(fun(Q49390,bool),bool),fun(Q49390,bool)),inters),s(fun(fun(Q49390,bool),bool),S0)))))))) # label(aDIFFu_INTERS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 432 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,P0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0)))))) # label(aEXPu_ADD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 433 (all A (p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_l_)))) & (all X all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,X))),s(A,Y)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_l_),s(A,X))),s(A,Y)))))) -> p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))))) # label(aWFu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 13.89/13.89 434 (all X all Y p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),intu_abs),s(int,X))))),s(int,i(s(fun(int,int),intu_abs),s(int,Y))))))))) # label(aINTu_ABSu_TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.90 435 (all N0 p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))))) # label(aINTu_POS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.90 436 (all Q58342 all S0 all R0 (p(s(bool,i(s(fun(fun(Q58342,bool),bool),i(s(fun(fun(Q58342,fun(Q58342,bool)),fun(fun(Q58342,bool),bool)),pairwise),s(fun(Q58342,fun(Q58342,bool)),R0))),s(fun(Q58342,bool),S0)))) <-> (all X all Y (p(s(bool,i(s(fun(fun(Q58342,bool),bool),i(s(fun(Q58342,fun(fun(Q58342,bool),bool)),in),s(Q58342,Y))),s(fun(Q58342,bool),S0)))) & s(Q58342,Y) != s(Q58342,X) & p(s(bool,i(s(fun(fun(Q58342,bool),bool),i(s(fun(Q58342,fun(fun(Q58342,bool),bool)),in),s(Q58342,X))),s(fun(Q58342,bool),S0)))) -> p(s(bool,i(s(fun(Q58342,bool),i(s(fun(Q58342,fun(Q58342,bool)),R0),s(Q58342,X))),s(Q58342,Y)))))))) # label(apairwise) # label(axiom) # label(non_clause). [assumption]. 13.89/13.90 437 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0)))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,Z0)))))) # label(aREALu_LEu_LCANCELu_IMP) # label(axiom) # label(non_clause). [assumption]. 13.89/13.90 438 (all A all B all F0 all B0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (exists A5 exists N0 p(s(bool,i(s(fun(num,bool),i(s(fun(B,fun(num,bool)),i(s(fun(fun(A,bool),fun(B,fun(num,bool))),i(s(fun(B,fun(fun(A,bool),fun(B,fun(num,bool)))),i(s(fun(fun(A,fun(B,B)),fun(B,fun(fun(A,bool),fun(B,fun(num,bool))))),finrec),s(fun(A,fun(B,B)),F0))),s(B,B0))),s(fun(A,bool),S0))),s(B,A5))),s(num,N0))))))) # label(aFINRECu_EXISTSu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 13.89/13.90 439 (all A all B all C all P all U_6 ((all A5 all B0 all H0 all F0 all X s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(P,num),A5),s(P,X))))),s(num,i(s(fun(P,num),B0),s(P,X))))))),s(fun(num,real),i(s(fun(P,fun(num,real)),i(s(fun(fun(B,C),fun(P,fun(num,real))),H0),s(fun(B,C),F0))),s(P,X))))) = s(real,i(s(fun(P,real),i(s(fun(fun(B,C),fun(P,real)),i(s(fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real))))),U_6),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,fun(num,real))),H0))),s(fun(B,C),F0))),s(P,X)))) -> (all U_5 ((all A5 all B0 all H0 all F0 s(fun(P,real),i(s(fun(fun(B,C),fun(P,real)),i(s(fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real))))),U_6),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,fun(num,real))),H0))),s(fun(B,C),F0))) = s(fun(P,real),i(s(fun(fun(B,C),fun(P,real)),i(s(fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real))))),U_5),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,fun(num,real))),H0))),s(fun(B,C),F0)))) -> (all U_4 ((all H0 all F0 all F1 ((all K0 all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),geq),s(real,i(s(fun(prod(num,P),real),F1),s(prod(num,P),i(s(fun(P,prod(num,P)),i(s(fun(num,fun(P,prod(num,P))),c_),s(num,K0))),s(P,X))))))),s(real,i(s(fun(num,real),i(s(fun(P,fun(num,real)),i(s(fun(fun(B,C),fun(P,fun(num,real))),H0),s(fun(B,C),F0))),s(P,X))),s(num,K0))))))) <-> p(s(bool,i(s(fun(fun(prod(num,P),real),bool),i(s(fun(fun(B,C),fun(fun(prod(num,P),real),bool)),i(s(fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(fun(prod(num,P),real),bool))),U_4),s(fun(fun(B,C),fun(P,fun(num,real))),H0))),s(fun(B,C),F0))),s(fun(prod(num,P),real),F1)))))) -> (all U_3 ((all H0 all F0 s(fun(prod(num,P),real),i(s(fun(fun(fun(prod(num,P),real),bool),fun(prod(num,P),real)),gabs),s(fun(fun(prod(num,P),real),bool),i(s(fun(fun(B,C),fun(fun(prod(num,P),real),bool)),i(s(fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(fun(prod(num,P),real),bool))),U_4),s(fun(fun(B,C),fun(P,fun(num,real))),H0))),s(fun(B,C),F0))))) = s(fun(prod(num,P),real),i(s(fun(fun(B,C),fun(prod(num,P),real)),i(s(fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(prod(num,P),real))),U_3),s(fun(fun(B,C),fun(P,fun(num,real))),H0))),s(fun(B,C),F0)))) -> (all U_2 ((all S0 all F0 ((all K0 all X p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),geq),s(A,i(s(fun(prod(num,P),A),F0),s(prod(num,P),i(s(fun(P,prod(num,P)),i(s(fun(num,fun(P,prod(num,P))),c_),s(num,K0))),s(P,X))))))),s(A,i(s(fun(P,A),S0),s(P,X))))))) <-> p(s(bool,i(s(fun(fun(prod(num,P),A),bool),i(s(fun(fun(P,A),fun(fun(prod(num,P),A),bool)),U_2),s(fun(P,A),S0))),s(fun(prod(num,P),A),F0)))))) -> (all U_1 ((all A5 all B0 all P0 all F0 all F1 ((all K0 all X exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(num,P),bool),F1),s(prod(num,P),i(s(fun(P,prod(num,P)),i(s(fun(num,fun(P,prod(num,P))),c_),s(num,K0))),s(P,X))))))),s(bool,V)))) & (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(P,num),A5),s(P,X))))),s(num,K0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(P,num),B0),s(P,X)))))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(B,C),fun(P,bool)),P0),s(fun(B,C),F0))),s(P,X)))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(fun(prod(num,P),bool),bool),i(s(fun(fun(B,C),fun(fun(prod(num,P),bool),bool)),i(s(fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool))))),U_1),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,bool)),P0))),s(fun(B,C),F0))),s(fun(prod(num,P),bool),F1)))))) -> (all U_0 ((all A5 all B0 all P0 all F0 s(fun(prod(num,P),bool),i(s(fun(fun(B,C),fun(prod(num,P),bool)),i(s(fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool))))),U_0),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,bool)),P0))),s(fun(B,C),F0))) = s(fun(prod(num,P),bool),i(s(fun(fun(fun(prod(num,P),bool),bool),fun(prod(num,P),bool)),gabs),s(fun(fun(prod(num,P),bool),bool),i(s(fun(fun(B,C),fun(fun(prod(num,P),bool),bool)),i(s(fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool))))),U_1),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,bool)),P0))),s(fun(B,C),F0)))))) -> (all L_L_ all P0 all S0 all H0 all A5 all B0 (p(s(bool,i(s(fun(fun(fun(B,C),fun(prod(num,P),real)),bool),i(s(fun(fun(prod(num,P),A),fun(fun(fun(B,C),fun(prod(num,P),real)),bool)),i(s(fun(fun(fun(B,C),fun(prod(num,P),bool)),fun(fun(prod(num,P),A),fun(fun(fun(B,C),fun(prod(num,P),real)),bool))),i(s(fun(fun(B,fun(A,bool)),fun(fun(fun(B,C),fun(prod(num,P),bool)),fun(fun(prod(num,P),A),fun(fun(fun(B,C),fun(prod(num,P),real)),bool)))),admissible),s(fun(B,fun(A,bool)),L_L_))),s(fun(fun(B,C),fun(prod(num,P),bool)),i(s(fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool))))),U_0),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,bool)),P0))))),s(fun(prod(num,P),A),i(s(fun(fun(fun(prod(num,P),A),bool),fun(prod(num,P),A)),gabs),s(fun(fun(prod(num,P),A),bool),i(s(fun(fun(P,A),fun(fun(prod(num,P),A),bool)),U_2),s(fun(P,A),S0))))))),s(fun(fun(B,C),fun(prod(num,P),real)),i(s(fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(prod(num,P),real))),U_3),s(fun(fun(B,C),fun(P,fun(num,real))),H0)))))) -> p(s(bool,i(s(fun(fun(fun(B,C),fun(P,real)),bool),i(s(fun(fun(P,A),fun(fun(fun(B,C),fun(P,real)),bool)),i(s(fun(fun(fun(B,C),fun(P,bool)),fun(fun(P,A),fun(fun(fun(B,C),fun(P,real)),bool))),i(s(fun(fun(B,fun(A,bool)),fun(fun(fun(B,C),fun(P,bool)),fun(fun(P,A),fun(fun(fun(B,C),fun(P,real)),bool)))),admissible),s(fun(B,fun(A,bool)),L_L_))),s(fun(fun(B,C),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(B,C),fun(P,real)),i(s(fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,real))),fun(fun(B,C),fun(P,real))))),U_5),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,fun(num,real))),H0)))))))))))))))))))))) # label(aADMISSIBLEu_SUM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.90 440 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (exists N0 all N1 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,N1)))) -> s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N1))))))) # label(aNADDu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 13.89/13.90 441 (all A all B all U_1 ((all X1 all Y1 all F0 ((all X2 all Y2 exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(A,B),bool),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X2))),s(B,Y2))))))),s(bool,V)))) & (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,X1))),s(A,X2)))) & p(s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),l_l_l_),s(B,Y1))),s(B,Y2)))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(fun(prod(A,B),bool),bool),i(s(fun(B,fun(fun(prod(A,B),bool),bool)),i(s(fun(A,fun(B,fun(fun(prod(A,B),bool),bool))),U_1),s(A,X1))),s(B,Y1))),s(fun(prod(A,B),bool),F0)))))) -> (all U_0 ((all F0 (p(s(bool,i(s(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),U_0),s(fun(prod(A,B),fun(prod(A,B),bool)),F0)))) <-> (all X1 all Y1 p(s(bool,i(s(fun(fun(prod(A,B),bool),bool),i(s(fun(fun(prod(A,B),bool),fun(fun(prod(A,B),bool),bool)),geq),s(fun(prod(A,B),bool),i(s(fun(prod(A,B),fun(prod(A,B),bool)),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X1))),s(B,Y1))))))),s(fun(prod(A,B),bool),i(s(fun(fun(fun(prod(A,B),bool),bool),fun(prod(A,B),bool)),gabs),s(fun(fun(prod(A,B),bool),bool),i(s(fun(B,fun(fun(prod(A,B),bool),bool)),i(s(fun(A,fun(B,fun(fun(prod(A,B),bool),bool))),U_1),s(A,X1))),s(B,Y1))))))))))) -> (p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))) & p(s(bool,i(s(fun(fun(B,fun(B,bool)),bool),wf),s(fun(B,fun(B,bool)),l_l_l_)))) -> p(s(bool,i(s(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),wf),s(fun(prod(A,B),fun(prod(A,B),bool)),i(s(fun(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),fun(prod(A,B),fun(prod(A,B),bool))),gabs),s(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),U_0))))))))))) # label(aWFu_POINTWISE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.90 442 (all X (-p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),trealu_inv),s(prod(hreal,hreal),X))))),s(prod(hreal,hreal),X))))),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aTREALu_MULu_LINV) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 443 (all W all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,Z0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,W))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,W))),s(int,Y))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0)))))))) # label(aINTu_LETu_ADD2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 444 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,Y))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y)))))) # label(aREALu_NEGu_LMUL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 445 (all Q66768 s(fun(fun(Q66768,bool),fun(fun(Q66768,num),num)),nsum) = s(fun(fun(Q66768,bool),fun(fun(Q66768,num),num)),i(s(fun(fun(num,fun(num,num)),fun(fun(Q66768,bool),fun(fun(Q66768,num),num))),iterate),s(fun(num,fun(num,num)),p_)))) # label(ansum) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 446 (all Q53515 all S0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53515,bool),fun(num,bool)),hasu_size),s(fun(Q53515,bool),S0))),s(num,N0)))) -> s(num,i(s(fun(fun(Q53515,bool),num),card),s(fun(Q53515,bool),S0))) = s(num,N0))) # label(aHASu_SIZEu_CARD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 447 (all A all P all B all U_3 ((all F0 all F1 (p(s(bool,i(s(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool),i(s(fun(fun(A,B),fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool)),U_3),s(fun(A,B),F0))),s(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),F1)))) <-> (all S0 all T0 exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),F1),s(prod(fun(P,A),fun(fun(A,B),fun(P,B))),i(s(fun(fun(fun(A,B),fun(P,B)),prod(fun(P,A),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),prod(fun(P,A),fun(fun(A,B),fun(P,B))))),c_),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),T0))))))),s(bool,V)))) & ((all X s(B,i(s(fun(A,B),F0),s(A,i(s(fun(P,A),S0),s(P,X))))) = s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),T0),s(fun(A,B),F0))),s(P,X)))) <-> p(s(bool,V))))))) -> (all U_2 ((all A5 s(bool,i(s(fun(P,bool),U_2),s(P,A5))) = s(bool,t)) -> (all U_1 ((all F0 s(fun(P,bool),U_2) = s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),U_1),s(fun(A,B),F0)))) -> (all U_0 ((all L_L_ all F0 (p(s(bool,i(s(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool),i(s(fun(fun(A,fun(A,bool)),fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool)),U_0),s(fun(A,fun(A,bool)),L_L_))),s(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),F0)))) <-> (all S0 all T0 p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),F0),s(prod(fun(P,A),fun(fun(A,B),fun(P,B))),i(s(fun(fun(fun(A,B),fun(P,B)),prod(fun(P,A),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),prod(fun(P,A),fun(fun(A,B),fun(P,B))))),c_),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),T0))))))),s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),tailadmissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),U_1))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),T0))))))))) -> (all CLAUSES ((exists L_L_ (p(s(bool,i(s(fun(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),bool),i(s(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),fun(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),bool)),all0),s(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),i(s(fun(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool),fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool)),gabs),s(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool),i(s(fun(fun(A,fun(A,bool)),fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool)),U_0),s(fun(A,fun(A,bool)),L_L_))))))),s(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),CLAUSES)))) & p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),L_L_)))))) & (all S0 all T0 all SI_ all TI_ all F0 all X all Y (p(s(bool,i(s(fun(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),bool),i(s(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),fun(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),bool)),mem),s(prod(fun(P,A),fun(fun(A,B),fun(P,B))),i(s(fun(fun(fun(A,B),fun(P,B)),prod(fun(P,A),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),prod(fun(P,A),fun(fun(A,B),fun(P,B))))),c_),s(fun(P,A),SI_))),s(fun(fun(A,B),fun(P,B)),TI_))))),s(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),CLAUSES)))) & p(s(bool,i(s(fun(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),bool),i(s(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),fun(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),bool)),mem),s(prod(fun(P,A),fun(fun(A,B),fun(P,B))),i(s(fun(fun(fun(A,B),fun(P,B)),prod(fun(P,A),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),prod(fun(P,A),fun(fun(A,B),fun(P,B))))),c_),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),T0))))),s(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),CLAUSES)))) -> (s(A,i(s(fun(P,A),S0),s(P,X))) = s(A,i(s(fun(P,A),SI_),s(P,Y))) -> s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),T0),s(fun(A,B),F0))),s(P,X))) = s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),TI_),s(fun(A,B),F0))),s(P,Y)))))) -> (exists F0 p(s(bool,i(s(fun(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),bool),i(s(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),fun(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),bool)),all0),s(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),i(s(fun(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool),fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool)),gabs),s(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool),i(s(fun(fun(A,B),fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool)),U_3),s(fun(A,B),F0))))))),s(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),CLAUSES))))))))))))))) # label(aRECURSIONu_CASEWISE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 448 (all B all A all F0 all S0 ((all X all Y (s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,i(s(fun(A,B),F0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,Y) = s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))) # label(aCARDu_IMAGEu_INJ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 449 (all A all S0 all T0 s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),T0))),s(fun(A,bool),S0))) = s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) # label(aDISJOINTu_SYM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 450 (all Q89903 all Q89902 all U_1 ((all T0 all GENR_PVARR_217 (p(s(bool,i(s(fun(sum0(Q89903,Q89902),bool),i(s(fun(fun(Q89902,bool),fun(sum0(Q89903,Q89902),bool)),U_1),s(fun(Q89902,bool),T0))),s(sum0(Q89903,Q89902),GENR_PVARR_217)))) <-> (exists Y p(s(bool,i(s(fun(sum0(Q89903,Q89902),bool),i(s(fun(bool,fun(sum0(Q89903,Q89902),bool)),i(s(fun(sum0(Q89903,Q89902),fun(bool,fun(sum0(Q89903,Q89902),bool))),setspec),s(sum0(Q89903,Q89902),GENR_PVARR_217))),s(bool,i(s(fun(fun(Q89902,bool),bool),i(s(fun(Q89902,fun(fun(Q89902,bool),bool)),in),s(Q89902,Y))),s(fun(Q89902,bool),T0))))),s(sum0(Q89903,Q89902),i(s(fun(Q89902,sum0(Q89903,Q89902)),inr),s(Q89902,Y))))))))) -> (all U_0 ((all S0 all GENR_PVARR_216 (p(s(bool,i(s(fun(sum0(Q89903,Q89902),bool),i(s(fun(fun(Q89903,bool),fun(sum0(Q89903,Q89902),bool)),U_0),s(fun(Q89903,bool),S0))),s(sum0(Q89903,Q89902),GENR_PVARR_216)))) <-> (exists X p(s(bool,i(s(fun(sum0(Q89903,Q89902),bool),i(s(fun(bool,fun(sum0(Q89903,Q89902),bool)),i(s(fun(sum0(Q89903,Q89902),fun(bool,fun(sum0(Q89903,Q89902),bool))),setspec),s(sum0(Q89903,Q89902),GENR_PVARR_216))),s(bool,i(s(fun(fun(Q89903,bool),bool),i(s(fun(Q89903,fun(fun(Q89903,bool),bool)),in),s(Q89903,X))),s(fun(Q89903,bool),S0))))),s(sum0(Q89903,Q89902),i(s(fun(Q89903,sum0(Q89903,Q89902)),inl),s(Q89903,X))))))))) -> (all S0 all T0 s(fun(sum0(Q89903,Q89902),bool),i(s(fun(fun(sum0(Q89903,Q89902),bool),fun(sum0(Q89903,Q89902),bool)),i(s(fun(fun(sum0(Q89903,Q89902),bool),fun(fun(sum0(Q89903,Q89902),bool),fun(sum0(Q89903,Q89902),bool))),union),s(fun(sum0(Q89903,Q89902),bool),i(s(fun(fun(sum0(Q89903,Q89902),bool),fun(sum0(Q89903,Q89902),bool)),gspec),s(fun(sum0(Q89903,Q89902),bool),i(s(fun(fun(Q89903,bool),fun(sum0(Q89903,Q89902),bool)),U_0),s(fun(Q89903,bool),S0))))))),s(fun(sum0(Q89903,Q89902),bool),i(s(fun(fun(sum0(Q89903,Q89902),bool),fun(sum0(Q89903,Q89902),bool)),gspec),s(fun(sum0(Q89903,Q89902),bool),i(s(fun(fun(Q89902,bool),fun(sum0(Q89903,Q89902),bool)),U_1),s(fun(Q89902,bool),T0))))))) = s(fun(sum0(Q89903,Q89902),bool),i(s(fun(fun(Q89902,bool),fun(sum0(Q89903,Q89902),bool)),i(s(fun(fun(Q89903,bool),fun(fun(Q89902,bool),fun(sum0(Q89903,Q89902),bool))),p_u_c),s(fun(Q89903,bool),S0))),s(fun(Q89902,bool),T0)))))))) # label(aaddu_c) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 451 (all A all X p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),univ))))) # label(aINu_UNIV) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 452 (all A all B all X all Y all A5 all B0 (s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y))) = s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,A5))),s(B,B0))) <-> s(B,B0) = s(B,Y) & s(A,X) = s(A,A5))) # label(aPAIRu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 453 (all M0 all N0 all P0 all Q0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,Q0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,P0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,P0))),s(num,Q0)))))))) # label(aLTEu_ADD2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 454 (all X all Y s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y)))))) # label(aintu_addu_th) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 455 (all X all Y all Z0 (s(int,X) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Z0))),s(int,Y))) <-> s(int,Z0) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))) # label(aINTu_EQu_SUBu_RADD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 456 (all A ((all H0 ((all F0 all G0 all X ((all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Z0))),s(A,X)))) -> s(bool,i(s(fun(A,bool),F0),s(A,Z0))) = s(bool,i(s(fun(A,bool),G0),s(A,Z0))))) -> s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),H0),s(fun(A,bool),F0))),s(A,X))) = s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),H0),s(fun(A,bool),G0))),s(A,X))))) -> (all F0 all G0 ((all X s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),H0),s(fun(A,bool),G0))),s(A,X))) = s(bool,i(s(fun(A,bool),G0),s(A,X)))) & (all X s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),H0),s(fun(A,bool),F0))),s(A,X))) = s(bool,i(s(fun(A,bool),F0),s(A,X)))) -> s(fun(A,bool),F0) = s(fun(A,bool),G0))))) -> p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))))) # label(aWFu_URECu_WF) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 457 (all Q4341 all Q4340 all P0 ((all X all Y p(s(bool,i(s(fun(prod(Q4341,Q4340),bool),P0),s(prod(Q4341,Q4340),i(s(fun(Q4340,prod(Q4341,Q4340)),i(s(fun(Q4341,fun(Q4340,prod(Q4341,Q4340))),c_),s(Q4341,X))),s(Q4340,Y))))))) -> (all P1 p(s(bool,i(s(fun(prod(Q4341,Q4340),bool),P0),s(prod(Q4341,Q4340),P1))))))) # label(apairu_cases) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 458 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) <-> p(s(bool,i(s(fun(fun(sum0(A,B),bool),bool),finite),s(fun(sum0(A,B),bool),i(s(fun(fun(B,bool),fun(sum0(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(sum0(A,B),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))))))) # label(aCARDu_ADDu_FINITEu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 459 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))) = s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))))) # label(aCARDu_EQu_CARDu_IMP) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 460 (all X s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aREALu_NEGu_LT0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 461 (all A all U_0 ((all C0 all F0 all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(A,real),F0),s(A,X))))) = s(real,i(s(fun(A,real),i(s(fun(fun(A,real),fun(A,real)),i(s(fun(real,fun(fun(A,real),fun(A,real))),U_0),s(real,C0))),s(fun(A,real),F0))),s(A,X)))) -> (all F0 all C0 all S0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(fun(A,real),fun(A,real)),i(s(fun(real,fun(fun(A,real),fun(A,real))),U_0),s(real,C0))),s(fun(A,real),F0)))))))) # label(aSUMu_LMUL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 462 (all A all B all U_1 ((all T0 all GENR_PVARR_257 ((exists V p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(bool,fun(fun(B,bool),bool)),i(s(fun(fun(B,bool),fun(bool,fun(fun(B,bool),bool))),setspec),s(fun(B,bool),GENR_PVARR_257))),s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),V))),s(fun(B,bool),T0))))),s(fun(B,bool),V))))) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),U_1),s(fun(B,bool),T0))),s(fun(B,bool),GENR_PVARR_257)))))) -> (all U_0 ((all S0 all GENR_PVARR_256 ((exists U p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_256))),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),U))),s(fun(A,bool),S0))))),s(fun(A,bool),U))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))),s(fun(A,bool),GENR_PVARR_256)))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(fun(B,bool),bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(fun(B,bool),bool),bool)),l_a_u_c),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))))))),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),gspec),s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),U_1),s(fun(B,bool),T0)))))))))))))) # label(aCARDu_LEu_POWERSET) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 463 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))) # label(aLEu_0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 464 (all Q19442 all Q19431 all U_0 ((all F0 all G0 all X (p(s(bool,i(s(fun(Q19431,bool),i(s(fun(fun(Q19431,Q19442),fun(Q19431,bool)),i(s(fun(fun(Q19431,Q19442),fun(fun(Q19431,Q19442),fun(Q19431,bool))),U_0),s(fun(Q19431,Q19442),F0))),s(fun(Q19431,Q19442),G0))),s(Q19431,X)))) <-> s(Q19442,i(s(fun(Q19431,Q19442),F0),s(Q19431,X))) = s(Q19442,i(s(fun(Q19431,Q19442),G0),s(Q19431,X))))) -> (all F0 all G0 all L (p(s(bool,i(s(fun(list(Q19431),bool),i(s(fun(fun(Q19431,bool),fun(list(Q19431),bool)),all0),s(fun(Q19431,bool),i(s(fun(fun(Q19431,Q19442),fun(Q19431,bool)),i(s(fun(fun(Q19431,Q19442),fun(fun(Q19431,Q19442),fun(Q19431,bool))),U_0),s(fun(Q19431,Q19442),F0))),s(fun(Q19431,Q19442),G0))))),s(list(Q19431),L)))) -> s(list(Q19442),i(s(fun(list(Q19431),list(Q19442)),i(s(fun(fun(Q19431,Q19442),fun(list(Q19431),list(Q19442))),map0),s(fun(Q19431,Q19442),G0))),s(list(Q19431),L))) = s(list(Q19442),i(s(fun(list(Q19431),list(Q19442)),i(s(fun(fun(Q19431,Q19442),fun(list(Q19431),list(Q19442))),map0),s(fun(Q19431,Q19442),F0))),s(list(Q19431),L))))))) # label(aMAPu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 465 (all X all N0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0)))))))) # label(aINTu_POWu_LT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 466 (all Q58224 all L p(s(bool,i(s(fun(fun(Q58224,bool),bool),finite),s(fun(Q58224,bool),i(s(fun(list(Q58224),fun(Q58224,bool)),setu_ofu_list),s(list(Q58224),L))))))) # label(aFINITEu_SETu_OFu_LIST) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 467 (all M0 all N0 all Q0 all R0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,R0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,R0))),s(int,i(s(fun(int,int),intu_abs),s(int,N0)))))) & s(int,M0) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Q0))),s(int,N0))))),s(int,R0))) -> s(int,Q0) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),div0),s(int,M0))),s(int,N0))) & s(int,R0) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),rem),s(int,M0))),s(int,N0))))) # label(aINTu_DIVMODu_UNIQ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 468 (all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,i(s(fun(real,real),realu_abs),s(real,Y))))))))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))))))) # label(aREALu_ABSu_SUBu_ABS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 469 (all A all B all U_0 ((all F0 all A5 all GENR_PVARR_228 ((exists X p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_228))),s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),A5))))),s(A,X))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),U_0),s(fun(A,B),F0))),s(fun(B,bool),A5))),s(A,GENR_PVARR_228)))))) -> (all F0 all A5 ((all X all Y (s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) -> s(A,X) = s(A,Y))) & p(s(bool,i(s(fun(fun(B,bool),bool),countable),s(fun(B,bool),A5)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),U_0),s(fun(A,B),F0))),s(fun(B,bool),A5)))))))))))) # label(aCOUNTABLEu_IMAGEu_INJ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 470 (all A all P0 all Q0 (p(s(bool,P0)) & (exists X p(s(bool,i(s(fun(A,bool),Q0),s(A,X))))) <-> (exists X (p(s(bool,P0)) & p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))))) # label(aRIGHTu_EXISTSu_ANDu_THM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 471 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) -> s(num,M0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))))),s(num,N0))))) # label(aSUBu_ADD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 472 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),suc),s(num,M0))))),s(num,i(s(fun(num,num),suc),s(num,N0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) # label(aLTu_SUC) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 473 (all X all N0 s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,i(s(fun(int,int),intu_abs),s(int,X))))),s(num,N0))) = s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0)))))) # label(aINTu_ABSu_POW) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 474 (all A all L all A5 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),i(s(fun(A,fun(prod(A,A),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(prod(A,A),bool))),linseg),s(fun(prod(A,A),bool),L))),s(A,A5)))))))) # label(aLINSEGu_WOSET) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 475 (all A all P0 all Q0 (p(s(bool,P0)) | (exists X p(s(bool,i(s(fun(A,bool),Q0),s(A,X))))) <-> (exists X (p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))) | p(s(bool,P0)))))) # label(aRIGHTu_ORu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 476 (all Q48254 all Q48245 all F0 all S0 s(fun(Q48254,bool),i(s(fun(fun(Q48245,bool),fun(Q48254,bool)),i(s(fun(fun(Q48245,Q48254),fun(fun(Q48245,bool),fun(Q48254,bool))),image),s(fun(Q48245,Q48254),F0))),s(fun(Q48245,bool),i(s(fun(fun(fun(Q48245,bool),bool),fun(Q48245,bool)),unions),s(fun(fun(Q48245,bool),bool),S0))))) = s(fun(Q48254,bool),i(s(fun(fun(fun(Q48254,bool),bool),fun(Q48254,bool)),unions),s(fun(fun(Q48254,bool),bool),i(s(fun(fun(fun(Q48245,bool),bool),fun(fun(Q48254,bool),bool)),i(s(fun(fun(fun(Q48245,bool),fun(Q48254,bool)),fun(fun(fun(Q48245,bool),bool),fun(fun(Q48254,bool),bool))),image),s(fun(fun(Q48245,bool),fun(Q48254,bool)),i(s(fun(fun(Q48245,Q48254),fun(fun(Q48245,bool),fun(Q48254,bool))),image),s(fun(Q48245,Q48254),F0))))),s(fun(fun(Q48245,bool),bool),S0)))))) # label(aIMAGEu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 477 (all A ((all P0 ((exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) <-> (exists X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) & (all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Y))),s(A,X)))) -> -p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))))))))) <-> p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))))) # label(aWFu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 478 (all A all U_0 ((all L all A5 all F0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(A,fun(fun(prod(A,A),bool),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(fun(prod(A,A),bool),bool))),U_0),s(fun(prod(A,A),bool),L))),s(A,A5))),s(fun(prod(A,A),bool),F0)))) <-> (all X all Y exists V ((p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,A5)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(A,A),bool),F0),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y))))))),s(bool,V)))))))) -> (all L all A5 s(fun(prod(A,A),bool),i(s(fun(A,fun(prod(A,A),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(prod(A,A),bool))),linseg),s(fun(prod(A,A),bool),L))),s(A,A5))) = s(fun(prod(A,A),bool),i(s(fun(fun(fun(prod(A,A),bool),bool),fun(prod(A,A),bool)),gabs),s(fun(fun(prod(A,A),bool),bool),i(s(fun(A,fun(fun(prod(A,A),bool),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(fun(prod(A,A),bool),bool))),U_0),s(fun(prod(A,A),bool),L))),s(A,A5)))))))) # label(alinseg) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 479 (all Q74742 all U_0 ((all A5 all X exists V ((p(s(bool,V)) <-> s(Q74742,X) = s(Q74742,A5)) & s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,y))),s(real,i(s(fun(Q74742,real),f),s(Q74742,X))))) = s(real,i(s(fun(Q74742,real),i(s(fun(Q74742,fun(Q74742,real)),U_0),s(Q74742,A5))),s(Q74742,X))))) -> (all S0 all A5 (p(s(bool,i(s(fun(fun(Q74742,bool),bool),finite),s(fun(Q74742,bool),S0)))) & p(s(bool,i(s(fun(fun(Q74742,bool),bool),i(s(fun(Q74742,fun(fun(Q74742,bool),bool)),in),s(Q74742,A5))),s(fun(Q74742,bool),S0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(Q74742,real),real),i(s(fun(fun(Q74742,bool),fun(fun(Q74742,real),real)),sum),s(fun(Q74742,bool),S0))),s(fun(Q74742,real),f))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,y))),s(real,i(s(fun(Q74742,real),f),s(Q74742,A5))))))) = s(real,i(s(fun(fun(Q74742,real),real),i(s(fun(fun(Q74742,bool),fun(fun(Q74742,real),real)),sum),s(fun(Q74742,bool),S0))),s(fun(Q74742,real),i(s(fun(Q74742,fun(Q74742,real)),U_0),s(Q74742,A5))))))))) # label(aSUMu_CASESu_1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 480 (all A all S0 s(fun(A,bool),S0) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),S0)))) # label(aUNIONu_IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 481 (all Q92074 all Q92076 all S0 all T0 (p(s(bool,i(s(fun(fun(Q92076,bool),bool),finite),s(fun(Q92076,bool),T0)))) & p(s(bool,i(s(fun(fun(Q92074,bool),bool),finite),s(fun(Q92074,bool),S0)))) -> p(s(bool,i(s(fun(fun(prod(Q92074,Q92076),bool),bool),finite),s(fun(prod(Q92074,Q92076),bool),i(s(fun(fun(Q92076,bool),fun(prod(Q92074,Q92076),bool)),i(s(fun(fun(Q92074,bool),fun(fun(Q92076,bool),fun(prod(Q92074,Q92076),bool))),t_u_c),s(fun(Q92074,bool),S0))),s(fun(Q92076,bool),T0)))))))) # label(aCARDu_MULu_FINITE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 482 (all A all S0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(A,bool),S0))))) # label(aCARDu_EQu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 483 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))))) # label(aREALu_LTEu_ADD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 484 (all A all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),empty))) = s(fun(A,bool),S0)) # label(aUNIONu_EMPTYu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 485 (all Q47544 s(fun(Q47544,bool),i(s(fun(fun(fun(Q47544,bool),bool),fun(Q47544,bool)),inters),s(fun(fun(Q47544,bool),bool),i(s(fun(fun(fun(Q47544,bool),bool),fun(fun(Q47544,bool),bool)),i(s(fun(fun(Q47544,bool),fun(fun(fun(Q47544,bool),bool),fun(fun(Q47544,bool),bool))),insert),s(fun(Q47544,bool),s0))),s(fun(fun(Q47544,bool),bool),u))))) = s(fun(Q47544,bool),i(s(fun(fun(Q47544,bool),fun(Q47544,bool)),i(s(fun(fun(Q47544,bool),fun(fun(Q47544,bool),fun(Q47544,bool))),inter),s(fun(Q47544,bool),s0))),s(fun(Q47544,bool),i(s(fun(fun(fun(Q47544,bool),bool),fun(Q47544,bool)),inters),s(fun(fun(Q47544,bool),bool),u)))))) # label(aINTERSu_INSERT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 486 (all X all Y all Z0 (s(real,Z0) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))) <-> s(real,X) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Z0))),s(real,Y))))) # label(aREALu_EQu_SUBu_RADD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 487 (all A5 all B0 all C0 all D0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,A5))),s(int,B0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,C0))),s(int,D0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,A5))),s(int,C0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,B0))),s(int,D0)))))) # label(aINTu_ADD2u_SUB2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 488 (all N0 all X (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,X) | s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0)))))))) # label(aEXPu_LTu_0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 489 (all A all X all L (p(s(bool,i(s(fun(list(A),bool),i(s(fun(A,fun(list(A),bool)),mem),s(A,X))),s(list(A),L)))) <-> (exists L1 exists L2 (s(list(A),L) = s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),L1))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),L2))))) & -p(s(bool,i(s(fun(list(A),bool),i(s(fun(A,fun(list(A),bool)),mem),s(A,X))),s(list(A),L1)))))))) # label(aMEMu_APPENDu_DECOMPOSEu_LEFT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 490 (all A all B all C all S0 all T0 all U (p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(B,bool),fun(fun(C,bool),bool)),l_a_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U)))) & p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(A,bool),fun(fun(C,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(C,bool),U)))) & p(s(bool,i(s(fun(fun(C,bool),bool),infinite),s(fun(C,bool),U)))) -> p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(prod(A,B),bool),fun(fun(C,bool),bool)),l_a_u_c),s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(C,bool),U)))))) # label(aCARDu_MUL2u_ABSORBu_LE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 491 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,u_0))),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(num,u_0)) # label(aARITHu_MULTu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 492 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,X)))) <-> -p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))))) # label(aINTu_NOTu_LE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 493 (all A all B all U_0 ((all S0 all T0 all GENR_PVARR_76 ((exists X p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(bool,fun(fun(B,bool),bool)),i(s(fun(fun(B,bool),fun(bool,fun(fun(B,bool),bool))),setspec),s(fun(B,bool),GENR_PVARR_76))),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X))))))) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(fun(B,bool),GENR_PVARR_76)))))) -> (all S0 all T0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,M0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X))))))),s(num,N0)))))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),i(s(fun(fun(fun(B,bool),bool),fun(B,bool)),unions),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),gspec),s(fun(fun(B,bool),bool),i(s(fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))))))) # label(aCARDu_UNIONSu_LE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 494 (all M0 all N0 s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,M0))))),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,N0))))) = s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))) # label(aHREALu_OFu_NUMu_ADD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 495 (all X all Y (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,Y)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),naddu_inv),s(nadd,X))))),s(nadd,i(s(fun(nadd,nadd),naddu_inv),s(nadd,Y)))))))) # label(aNADDu_INVu_WELLDEF) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 496 (all U_0 ((all U ((exists X1 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),trealu_neg),s(prod(hreal,hreal),X1))))),s(prod(hreal,hreal),U)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(real,fun(prod(hreal,hreal),bool)),destu_real),s(real,x1))),s(prod(hreal,hreal),X1)))))) <-> p(s(bool,i(s(fun(prod(hreal,hreal),bool),U_0),s(prod(hreal,hreal),U)))))) -> s(real,i(s(fun(fun(prod(hreal,hreal),bool),real),mku_real),s(fun(prod(hreal,hreal),bool),U_0))) = s(real,i(s(fun(real,real),realu_neg),s(real,x1))))) # label(arealu_neg) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 497 (all A all A10 all A20 (s(fun(num,fun(A,bool)),i(s(fun(A,fun(num,fun(A,bool))),inja),s(A,A10))) = s(fun(num,fun(A,bool)),i(s(fun(A,fun(num,fun(A,bool))),inja),s(A,A20))) <-> s(A,A20) = s(A,A10))) # label(aINJAu_INJ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 498 (all A p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),l_u_c),s(fun(A,bool),univ))),s(fun(fun(A,bool),bool),univ))))) # label(aCANTORu_THMu_UNIV) # label(axiom) # label(non_clause). [assumption]. 13.89/13.91 499 (all A all S0 all F0 all B0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,B0)))))) & (exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,B0)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))))),s(real,B0)))))))) # label(aSUMu_BOUNDu_LT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.92 500 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Z0))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,Y)))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Z0))),s(real,X)))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Z0))),s(real,Y)))))) # label(aREALu_LEu_MAX) # label(axiom) # label(non_clause). [assumption]. 13.89/13.92 501 (all Q47433 all S0 all T0 s(fun(Q47433,bool),i(s(fun(fun(fun(Q47433,bool),bool),fun(Q47433,bool)),inters),s(fun(fun(Q47433,bool),bool),i(s(fun(fun(fun(Q47433,bool),bool),fun(fun(Q47433,bool),bool)),i(s(fun(fun(fun(Q47433,bool),bool),fun(fun(fun(Q47433,bool),bool),fun(fun(Q47433,bool),bool))),union),s(fun(fun(Q47433,bool),bool),S0))),s(fun(fun(Q47433,bool),bool),T0))))) = s(fun(Q47433,bool),i(s(fun(fun(Q47433,bool),fun(Q47433,bool)),i(s(fun(fun(Q47433,bool),fun(fun(Q47433,bool),fun(Q47433,bool))),inter),s(fun(Q47433,bool),i(s(fun(fun(fun(Q47433,bool),bool),fun(Q47433,bool)),inters),s(fun(fun(Q47433,bool),bool),S0))))),s(fun(Q47433,bool),i(s(fun(fun(fun(Q47433,bool),bool),fun(Q47433,bool)),inters),s(fun(fun(Q47433,bool),bool),T0)))))) # label(aINTERSu_UNION) # label(axiom) # label(non_clause). [assumption]. 13.89/13.92 502 (all U_0 ((all F0 all N0 all I0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(fun(num,num),fun(num,fun(num,num))),U_0),s(fun(num,num),F0))),s(num,N0))),s(num,I0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),F0),s(num,I0))))),s(num,N0)))) -> (all F0 all A5 all B0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,A5))),s(num,B0))))),s(fun(num,num),F0))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,A5))),s(num,B0))))),s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(fun(num,num),fun(num,fun(num,num))),U_0),s(fun(num,num),F0))),s(num,N0))))))),s(num,N0))))))) # label(aMODu_NSUMu_MODu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 13.89/13.92 503 (all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aMODu_0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.92 504 (all B all D all P all Q all A all U_3 ((all PAT all U all Q0 all F0 all ARG all X all V ((exists T0 p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),u_guardedu_pattern),s(bool,i(s(fun(D,bool),i(s(fun(D,fun(D,bool)),geq),s(D,i(s(fun(Q,D),PAT),s(Q,T0))))),s(D,U))))),s(bool,i(s(fun(Q,bool),i(s(fun(P,fun(Q,bool)),Q0),s(P,X))),s(Q,T0))))),s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),geq),s(B,i(s(fun(A,B),F0),s(A,i(s(fun(Q,A),i(s(fun(P,fun(Q,A)),ARG),s(P,X))),s(Q,T0))))))),s(B,V))))))) <-> p(s(bool,i(s(fun(B,bool),i(s(fun(P,fun(B,bool)),i(s(fun(fun(P,fun(Q,A)),fun(P,fun(B,bool))),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool)))),i(s(fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool))))),i(s(fun(D,fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool)))))),i(s(fun(fun(Q,D),fun(D,fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool))))))),U_3),s(fun(Q,D),PAT))),s(D,U))),s(fun(P,fun(Q,bool)),Q0))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG))),s(P,X))),s(B,V)))))) -> (all U_2 ((all PAT all Q0 all F0 all ARG all X all U s(fun(B,bool),i(s(fun(D,fun(B,bool)),i(s(fun(P,fun(D,fun(B,bool))),i(s(fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool)))),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool))))),i(s(fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool)))))),i(s(fun(fun(Q,D),fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool))))))),U_2),s(fun(Q,D),PAT))),s(fun(P,fun(Q,bool)),Q0))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG))),s(P,X))),s(D,U))) = s(fun(B,bool),i(s(fun(P,fun(B,bool)),i(s(fun(fun(P,fun(Q,A)),fun(P,fun(B,bool))),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool)))),i(s(fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool))))),i(s(fun(D,fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool)))))),i(s(fun(fun(Q,D),fun(D,fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool))))))),U_3),s(fun(Q,D),PAT))),s(D,U))),s(fun(P,fun(Q,bool)),Q0))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG))),s(P,X)))) -> (all U_1 ((all E0 all PAT all Q0 all F0 all ARG all X s(B,i(s(fun(P,B),i(s(fun(fun(P,fun(Q,A)),fun(P,B)),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B))),i(s(fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B)))),i(s(fun(fun(Q,D),fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B))))),i(s(fun(fun(P,D),fun(fun(Q,D),fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B)))))),U_1),s(fun(P,D),E0))),s(fun(Q,D),PAT))),s(fun(P,fun(Q,bool)),Q0))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG))),s(P,X))) = s(B,i(s(fun(fun(D,fun(B,bool)),B),i(s(fun(D,fun(fun(D,fun(B,bool)),B)),u_match),s(D,i(s(fun(P,D),E0),s(P,X))))),s(fun(D,fun(B,bool)),i(s(fun(P,fun(D,fun(B,bool))),i(s(fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool)))),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool))))),i(s(fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool)))))),i(s(fun(fun(Q,D),fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool))))))),U_2),s(fun(Q,D),PAT))),s(fun(P,fun(Q,bool)),Q0))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG))),s(P,X)))))) -> (all U_0 ((all E0 all PAT all Q0 all ARG all F0 s(fun(P,B),i(s(fun(fun(P,fun(Q,A)),fun(P,B)),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B))),i(s(fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B)))),i(s(fun(fun(Q,D),fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B))))),i(s(fun(fun(P,D),fun(fun(Q,D),fun(fun(P,fun(Q,bool)),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B)))))),U_1),s(fun(P,D),E0))),s(fun(Q,D),PAT))),s(fun(P,fun(Q,bool)),Q0))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG))) = s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B))),i(s(fun(fun(P,fun(Q,bool)),fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(Q,D),fun(fun(P,fun(Q,bool)),fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B))))),i(s(fun(fun(P,D),fun(fun(Q,D),fun(fun(P,fun(Q,bool)),fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B)))))),U_0),s(fun(P,D),E0))),s(fun(Q,D),PAT))),s(fun(P,fun(Q,bool)),Q0))),s(fun(P,fun(Q,A)),ARG))),s(fun(A,B),F0)))) -> (all L_L_ all P0 all S0 all E0 all PAT all Q0 all ARG ((all F0 all A5 all T0 (p(s(bool,i(s(fun(Q,bool),i(s(fun(P,fun(Q,bool)),Q0),s(P,A5))),s(Q,T0)))) & s(D,i(s(fun(P,D),E0),s(P,A5))) = s(D,i(s(fun(Q,D),PAT),s(Q,T0))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,A5)))) -> (all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,i(s(fun(Q,A),i(s(fun(P,fun(Q,A)),ARG),s(P,A5))),s(Q,T0)))))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,i(s(fun(P,A),S0),s(P,A5)))))))))) & (all F0 all A5 all T0 all U (p(s(bool,i(s(fun(Q,bool),i(s(fun(P,fun(Q,bool)),Q0),s(P,A5))),s(Q,U)))) & s(D,i(s(fun(P,D),E0),s(P,A5))) = s(D,i(s(fun(Q,D),PAT),s(Q,U))) & p(s(bool,i(s(fun(Q,bool),i(s(fun(P,fun(Q,bool)),Q0),s(P,A5))),s(Q,T0)))) & s(D,i(s(fun(Q,D),PAT),s(Q,T0))) = s(D,i(s(fun(P,D),E0),s(P,A5))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,A5)))) -> s(A,i(s(fun(Q,A),i(s(fun(P,fun(Q,A)),ARG),s(P,A5))),s(Q,U))) = s(A,i(s(fun(Q,A),i(s(fun(P,fun(Q,A)),ARG),s(P,A5))),s(Q,T0))))) -> p(s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),superadmissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B))),i(s(fun(fun(P,fun(Q,bool)),fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(Q,D),fun(fun(P,fun(Q,bool)),fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B))))),i(s(fun(fun(P,D),fun(fun(Q,D),fun(fun(P,fun(Q,bool)),fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B)))))),U_0),s(fun(P,D),E0))),s(fun(Q,D),PAT))),s(fun(P,fun(Q,bool)),Q0))),s(fun(P,fun(Q,A)),ARG)))))))))))))))) # label(aSUPERADMISSIBLEu_MATCHu_GUARDEDu_PATTERN) # label(axiom) # label(non_clause). [assumption]. 13.89/13.92 505 (all T1 all T2 ((-p(s(bool,T1)) -> -p(s(bool,T2))) <-> (p(s(bool,T2)) -> p(s(bool,T1))))) # label(aCONTRAPOSu_THM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.92 506 (all U_0 ((all A5 all GENR_PVARR_122 ((exists X p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_122))),s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,A5))),s(real,X))))),s(real,X))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),U_0),s(real,A5))),s(real,GENR_PVARR_122)))))) -> (all A5 -p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(real,fun(real,bool)),U_0),s(real,A5))))))))))) # label(aFINITEu_REALu_INTERVALu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.92 507 (all A all X all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))))) # label(aCARDu_DELETE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.92 508 (all Q49537 all U_0 ((all S0 all U all GENR_PVARR_45 ((exists T0 p(s(bool,i(s(fun(fun(Q49537,bool),bool),i(s(fun(bool,fun(fun(Q49537,bool),bool)),i(s(fun(fun(Q49537,bool),fun(bool,fun(fun(Q49537,bool),bool))),setspec),s(fun(Q49537,bool),GENR_PVARR_45))),s(bool,i(s(fun(fun(fun(Q49537,bool),bool),bool),i(s(fun(fun(Q49537,bool),fun(fun(fun(Q49537,bool),bool),bool)),in),s(fun(Q49537,bool),T0))),s(fun(fun(Q49537,bool),bool),S0))))),s(fun(Q49537,bool),i(s(fun(fun(Q49537,bool),fun(Q49537,bool)),i(s(fun(fun(Q49537,bool),fun(fun(Q49537,bool),fun(Q49537,bool))),diff),s(fun(Q49537,bool),U))),s(fun(Q49537,bool),T0))))))) <-> p(s(bool,i(s(fun(fun(Q49537,bool),bool),i(s(fun(fun(Q49537,bool),fun(fun(Q49537,bool),bool)),i(s(fun(fun(fun(Q49537,bool),bool),fun(fun(Q49537,bool),fun(fun(Q49537,bool),bool))),U_0),s(fun(fun(Q49537,bool),bool),S0))),s(fun(Q49537,bool),U))),s(fun(Q49537,bool),GENR_PVARR_45)))))) -> (all U all S0 s(fun(Q49537,bool),i(s(fun(fun(Q49537,bool),fun(Q49537,bool)),i(s(fun(fun(Q49537,bool),fun(fun(Q49537,bool),fun(Q49537,bool))),diff),s(fun(Q49537,bool),U))),s(fun(Q49537,bool),i(s(fun(fun(fun(Q49537,bool),bool),fun(Q49537,bool)),unions),s(fun(fun(Q49537,bool),bool),S0))))) = s(fun(Q49537,bool),i(s(fun(fun(Q49537,bool),fun(Q49537,bool)),i(s(fun(fun(Q49537,bool),fun(fun(Q49537,bool),fun(Q49537,bool))),inter),s(fun(Q49537,bool),U))),s(fun(Q49537,bool),i(s(fun(fun(fun(Q49537,bool),bool),fun(Q49537,bool)),inters),s(fun(fun(Q49537,bool),bool),i(s(fun(fun(fun(Q49537,bool),bool),fun(fun(Q49537,bool),bool)),gspec),s(fun(fun(Q49537,bool),bool),i(s(fun(fun(Q49537,bool),fun(fun(Q49537,bool),bool)),i(s(fun(fun(fun(Q49537,bool),bool),fun(fun(Q49537,bool),fun(fun(Q49537,bool),bool))),U_0),s(fun(fun(Q49537,bool),bool),S0))),s(fun(Q49537,bool),U)))))))))))) # label(aDIFFu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.93 509 (all M0 all N0 all F0 ((all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,P0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,P0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(num,real),F0),s(num,P0)))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0)))))))) # label(aSUMu_POSu_LEu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 13.89/13.93 510 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(int,Y)))) # label(aINTu_LTu_DISCRETE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.93 511 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) | s(num,i(s(fun(num,num),suc),s(num,N0))) = s(num,M0) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0)))))))) # label(aLEu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.93 512 (all Q80486 all Q80567 all Q80487 all Q80534 all P all Q80574 all U_3 ((all PAT all E0 all T0 all Y all F0 all X s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80487,Q80534),fun(P,bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool)))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool))))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool)))))),U_3),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0))),s(fun(fun(Q80487,Q80534),fun(P,Q80574)),T0))),s(fun(fun(Q80487,Q80534),fun(P,Q80574)),Y))),s(fun(Q80487,Q80534),F0))),s(P,X))) = s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),u_unguardedu_pattern),s(bool,i(s(fun(Q80567,bool),i(s(fun(Q80567,fun(Q80567,bool)),geq),s(Q80567,i(s(fun(P,Q80567),i(s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT),s(fun(Q80487,Q80534),F0))),s(P,X))))),s(Q80567,i(s(fun(P,Q80567),i(s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0),s(fun(Q80487,Q80534),F0))),s(P,X))))))),s(bool,i(s(fun(Q80574,bool),i(s(fun(Q80574,fun(Q80574,bool)),geq),s(Q80574,i(s(fun(P,Q80574),i(s(fun(fun(Q80487,Q80534),fun(P,Q80574)),T0),s(fun(Q80487,Q80534),F0))),s(P,X))))),s(Q80574,i(s(fun(P,Q80574),i(s(fun(fun(Q80487,Q80534),fun(P,Q80574)),Y),s(fun(Q80487,Q80534),F0))),s(P,X)))))))) -> (all U_2 ((all PAT all E0 all T0 all Y all F0 s(fun(P,bool),i(s(fun(fun(Q80487,Q80534),fun(P,bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool)))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool))))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool)))))),U_2),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0))),s(fun(fun(Q80487,Q80534),fun(P,Q80574)),T0))),s(fun(fun(Q80487,Q80534),fun(P,Q80574)),Y))),s(fun(Q80487,Q80534),F0))) = s(fun(P,bool),i(s(fun(fun(Q80487,Q80534),fun(P,bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool)))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool))))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool)))))),U_3),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0))),s(fun(fun(Q80487,Q80534),fun(P,Q80574)),T0))),s(fun(fun(Q80487,Q80534),fun(P,Q80574)),Y))),s(fun(Q80487,Q80534),F0)))) -> (all U_1 ((all P0 all PAT all E0 all F0 all X (s(Q80567,i(s(fun(P,Q80567),i(s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT),s(fun(Q80487,Q80534),F0))),s(P,X))) = s(Q80567,i(s(fun(P,Q80567),i(s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0),s(fun(Q80487,Q80534),F0))),s(P,X))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80487,Q80534),fun(P,bool)),P0),s(fun(Q80487,Q80534),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80487,Q80534),fun(P,bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool)))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool))))),U_1),s(fun(fun(Q80487,Q80534),fun(P,bool)),P0))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0))),s(fun(Q80487,Q80534),F0))),s(P,X)))))) -> (all U_0 ((all P0 all PAT all E0 all F0 s(fun(P,bool),i(s(fun(fun(Q80487,Q80534),fun(P,bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool)))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool))))),U_1),s(fun(fun(Q80487,Q80534),fun(P,bool)),P0))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0))),s(fun(Q80487,Q80534),F0))) = s(fun(P,bool),i(s(fun(fun(Q80487,Q80534),fun(P,bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool)))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool))))),U_0),s(fun(fun(Q80487,Q80534),fun(P,bool)),P0))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0))),s(fun(Q80487,Q80534),F0)))) -> (all L_L_ all P0 all S0 all PAT all E0 all T0 all Y (p(s(bool,i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),bool),i(s(fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),bool))),i(s(fun(fun(Q80487,fun(Q80486,bool)),fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),bool)))),admissible),s(fun(Q80487,fun(Q80486,bool)),L_L_))),s(fun(fun(Q80487,Q80534),fun(P,bool)),P0))),s(fun(P,Q80486),S0))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT)))) & p(s(bool,i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),bool),i(s(fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),bool))),i(s(fun(fun(Q80487,fun(Q80486,bool)),fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),bool)))),admissible),s(fun(Q80487,fun(Q80486,bool)),L_L_))),s(fun(fun(Q80487,Q80534),fun(P,bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool)))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool))))),U_0),s(fun(fun(Q80487,Q80534),fun(P,bool)),P0))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0))))),s(fun(P,Q80486),S0))),s(fun(fun(Q80487,Q80534),fun(P,Q80574)),Y)))) & p(s(bool,i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),bool),i(s(fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),bool))),i(s(fun(fun(Q80487,fun(Q80486,bool)),fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),bool)))),admissible),s(fun(Q80487,fun(Q80486,bool)),L_L_))),s(fun(fun(Q80487,Q80534),fun(P,bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool)))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(Q80487,Q80534),fun(P,bool))))),U_0),s(fun(fun(Q80487,Q80534),fun(P,bool)),P0))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0))))),s(fun(P,Q80486),S0))),s(fun(fun(Q80487,Q80534),fun(P,Q80574)),T0)))) & p(s(bool,i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),bool),i(s(fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),bool))),i(s(fun(fun(Q80487,fun(Q80486,bool)),fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),bool)))),admissible),s(fun(Q80487,fun(Q80486,bool)),L_L_))),s(fun(fun(Q80487,Q80534),fun(P,bool)),P0))),s(fun(P,Q80486),S0))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0)))) -> p(s(bool,i(s(fun(fun(fun(Q80487,Q80534),fun(P,bool)),bool),i(s(fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,bool)),bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,bool)),bool))),i(s(fun(fun(Q80487,fun(Q80486,bool)),fun(fun(fun(Q80487,Q80534),fun(P,bool)),fun(fun(P,Q80486),fun(fun(fun(Q80487,Q80534),fun(P,bool)),bool)))),admissible),s(fun(Q80487,fun(Q80486,bool)),L_L_))),s(fun(fun(Q80487,Q80534),fun(P,bool)),P0))),s(fun(P,Q80486),S0))),s(fun(fun(Q80487,Q80534),fun(P,bool)),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool)))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool))))),i(s(fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80567)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(fun(Q80487,Q80534),fun(P,Q80574)),fun(fun(Q80487,Q80534),fun(P,bool)))))),U_2),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),PAT))),s(fun(fun(Q80487,Q80534),fun(P,Q80567)),E0))),s(fun(fun(Q80487,Q80534),fun(P,Q80574)),T0))),s(fun(fun(Q80487,Q80534),fun(P,Q80574)),Y)))))))))))))))) # label(aADMISSIBLEu_UNGUARDEDu_PATTERN) # label(axiom) # label(non_clause). [assumption]. 13.89/13.93 513 (all A all B all U_3 ((all K0 all I0 s(real,i(s(fun(B,real),i(s(fun(fun(B,num),fun(B,real)),U_3),s(fun(B,num),K0))),s(B,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(B,num),K0),s(B,I0)))))) -> (all U_2 ((all T0 all R0 all I0 all GENR_PVARR_181 ((exists J0 exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),R0),s(A,I0))),s(B,J0))))) & p(s(bool,i(s(fun(B,bool),i(s(fun(bool,fun(B,bool)),i(s(fun(B,fun(bool,fun(B,bool))),setspec),s(B,GENR_PVARR_181))),s(bool,V))),s(B,J0)))))) <-> p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),i(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,fun(B,bool)))),U_2),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0))),s(B,GENR_PVARR_181)))))) -> (all U_1 ((all T0 all R0 all I0 s(real,i(s(fun(A,real),i(s(fun(fun(A,fun(B,bool)),fun(A,real)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,real))),U_1),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),gspec),s(fun(B,bool),i(s(fun(A,fun(B,bool)),i(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,fun(B,bool)))),U_2),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0)))))))))) -> (all U_0 ((all S0 all R0 all J0 all GENR_PVARR_180 ((exists I0 exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),R0),s(A,I0))),s(B,J0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_180))),s(bool,V))),s(A,I0)))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,fun(B,bool)),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(B,fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),R0))),s(B,J0))),s(A,GENR_PVARR_180)))))) -> (all R0 all S0 all T0 all K0 ((all J0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),T0)))) -> s(num,i(s(fun(B,num),K0),s(B,J0))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,fun(B,bool)),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(B,fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),R0))),s(B,J0))))))))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(real,i(s(fun(fun(B,real),real),i(s(fun(fun(B,bool),fun(fun(B,real),real)),sum),s(fun(B,bool),T0))),s(fun(B,real),i(s(fun(fun(B,num),fun(B,real)),U_3),s(fun(B,num),K0))))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(fun(A,fun(B,bool)),fun(A,real)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,real))),U_1),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))))))))))))))) # label(aSUMu_MULTICOUNTu_GEN) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 514 (all Q50439 all Q50443 all Q50444 all P0 all F0 all G0 ((exists H0 all X (p(s(bool,i(s(fun(Q50444,bool),P0),s(Q50444,X)))) -> s(Q50439,i(s(fun(Q50443,Q50439),G0),s(Q50443,i(s(fun(Q50444,Q50443),H0),s(Q50444,X))))) = s(Q50439,i(s(fun(Q50444,Q50439),F0),s(Q50444,X))))) <-> (all X (p(s(bool,i(s(fun(Q50444,bool),P0),s(Q50444,X)))) -> (exists Y s(Q50439,i(s(fun(Q50443,Q50439),G0),s(Q50443,Y))) = s(Q50439,i(s(fun(Q50444,Q50439),F0),s(Q50444,X)))))))) # label(aFUNCTIONu_FACTORSu_RIGHTu_GEN) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 515 (all A5 all B0 s(bool,i(s(fun(prod(int,int),bool),intu_coprime),s(prod(int,int),i(s(fun(int,prod(int,int)),i(s(fun(int,fun(int,prod(int,int))),c_),s(int,i(s(fun(num,int),intu_ofu_num),s(num,A5))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,B0))))))) = s(bool,i(s(fun(prod(num,num),bool),numu_coprime),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,A5))),s(num,B0)))))) # label(anumu_coprime) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 516 (all X all Y all Z0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Y))),s(int,Z0)))))) # label(aINTu_LTu_RADD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 517 (all A (p(s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),univ)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(list(A),bool),fun(fun(A,bool),bool)),a_u_c),s(fun(list(A),bool),univ))),s(fun(A,bool),univ)))))) # label(aCARDu_EQu_LIST) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 518 (all A5 all B0 all N0 (s(num,A5) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,B0))),s(num,A5))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,N0))))),s(num,B0))))) # label(aLEu_RDIVu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 519 (all N0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(num,N0))))))) # label(aREALu_LTu_POW2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 520 (all A all L all A5 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),i(s(fun(A,fun(prod(A,A),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(prod(A,A),bool))),linseg),s(fun(prod(A,A),bool),L))),s(A,A5))))),s(fun(prod(A,A),bool),L)))))) # label(aLINSEGu_INSEG) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 521 (all C all A all B all OP (p(s(bool,i(s(fun(fun(C,fun(C,C)),bool),monoidal),s(fun(C,fun(C,C)),OP)))) -> (all G0 all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,i(s(fun(A,B),F0),s(A,X))) & s(A,X) != s(A,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(C,i(s(fun(B,C),G0),s(B,i(s(fun(A,B),F0),s(A,X))))) = s(C,i(s(fun(fun(C,fun(C,C)),C),neutral),s(fun(C,fun(C,C)),OP))))) -> s(C,i(s(fun(fun(A,C),C),i(s(fun(fun(A,bool),fun(fun(A,C),C)),i(s(fun(fun(C,fun(C,C)),fun(fun(A,bool),fun(fun(A,C),C))),iterate),s(fun(C,fun(C,C)),OP))),s(fun(A,bool),S0))),s(fun(A,C),i(s(fun(fun(A,B),fun(A,C)),i(s(fun(fun(B,C),fun(fun(A,B),fun(A,C))),o),s(fun(B,C),G0))),s(fun(A,B),F0))))) = s(C,i(s(fun(fun(B,C),C),i(s(fun(fun(B,bool),fun(fun(B,C),C)),i(s(fun(fun(C,fun(C,C)),fun(fun(B,bool),fun(fun(B,C),C))),iterate),s(fun(C,fun(C,C)),OP))),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,C),G0))))))) # label(aITERATEu_IMAGEu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 522 (all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,i(s(fun(real,real),realu_abs),s(real,Y))))))))) # label(aREALu_ABSu_TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 523 (all Q20694 all U_0 ((all X s(Q20694,i(s(fun(Q20694,Q20694),U_0),s(Q20694,X))) = s(Q20694,X)) -> (all L s(list(Q20694),L) = s(list(Q20694),i(s(fun(list(Q20694),list(Q20694)),i(s(fun(fun(Q20694,Q20694),fun(list(Q20694),list(Q20694))),map0),s(fun(Q20694,Q20694),U_0))),s(list(Q20694),L)))))) # label(aMAPu_ID) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 524 (all X s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) # label(aREALu_NEGu_LE0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 525 (all A all A5 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),A5)))) <-> s(fun(A,bool),A5) = s(fun(A,bool),empty) | (exists X exists S0 (s(fun(A,bool),A5) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))))))) # label(aFINITEu_CASES) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 526 (all X all Y -(p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,X)))))) # label(aREALu_LTEu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 527 (all X s(int,i(s(fun(int,int),intu_abs),s(int,X))) = s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),intu_abs),s(int,X)))))) # label(aINTu_ABSu_ABS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 528 (all A all U all S0 (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),U))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (exists J0 exists K0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,K0))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_gt),s(real,i(s(fun(A,real),U),s(A,K0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(A,real),U),s(A,J0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,J0))),s(fun(A,bool),S0)))))) | (all I0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(A,real),U),s(A,I0))))))) # label(aSUMu_ZEROu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 529 (all Q20016 all X all L1 all L2 (p(s(bool,i(s(fun(list(Q20016),bool),i(s(fun(Q20016,fun(list(Q20016),bool)),mem),s(Q20016,X))),s(list(Q20016),i(s(fun(list(Q20016),list(Q20016)),i(s(fun(list(Q20016),fun(list(Q20016),list(Q20016))),append),s(list(Q20016),L1))),s(list(Q20016),L2)))))) <-> p(s(bool,i(s(fun(list(Q20016),bool),i(s(fun(Q20016,fun(list(Q20016),bool)),mem),s(Q20016,X))),s(list(Q20016),L1)))) | p(s(bool,i(s(fun(list(Q20016),bool),i(s(fun(Q20016,fun(list(Q20016),bool)),mem),s(Q20016,X))),s(list(Q20016),L2)))))) # label(aMEMu_APPEND) # label(axiom) # label(non_clause). [assumption]. 13.89/13.94 530 (all Q73298 all Q73297 all U_5 ((all F0 all Y all X s(real,i(s(fun(Q73297,real),i(s(fun(Q73298,fun(Q73297,real)),F0),s(Q73298,X))),s(Q73297,Y))) = s(real,i(s(fun(Q73298,real),i(s(fun(Q73297,fun(Q73298,real)),i(s(fun(fun(Q73298,fun(Q73297,real)),fun(Q73297,fun(Q73298,real))),U_5),s(fun(Q73298,fun(Q73297,real)),F0))),s(Q73297,Y))),s(Q73298,X)))) -> (all U_4 ((all S0 all R0 all Y all GENR_PVARR_178 (p(s(bool,i(s(fun(Q73298,bool),i(s(fun(Q73297,fun(Q73298,bool)),i(s(fun(fun(Q73298,fun(Q73297,bool)),fun(Q73297,fun(Q73298,bool))),i(s(fun(fun(Q73298,bool),fun(fun(Q73298,fun(Q73297,bool)),fun(Q73297,fun(Q73298,bool)))),U_4),s(fun(Q73298,bool),S0))),s(fun(Q73298,fun(Q73297,bool)),R0))),s(Q73297,Y))),s(Q73298,GENR_PVARR_178)))) <-> (exists X exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(Q73298,bool),bool),i(s(fun(Q73298,fun(fun(Q73298,bool),bool)),in),s(Q73298,X))),s(fun(Q73298,bool),S0)))) & p(s(bool,i(s(fun(Q73297,bool),i(s(fun(Q73298,fun(Q73297,bool)),R0),s(Q73298,X))),s(Q73297,Y))))) & p(s(bool,i(s(fun(Q73298,bool),i(s(fun(bool,fun(Q73298,bool)),i(s(fun(Q73298,fun(bool,fun(Q73298,bool))),setspec),s(Q73298,GENR_PVARR_178))),s(bool,V))),s(Q73298,X)))))))) -> (all U_3 ((all S0 all R0 all F0 all Y s(real,i(s(fun(Q73297,real),i(s(fun(fun(Q73298,fun(Q73297,real)),fun(Q73297,real)),i(s(fun(fun(Q73298,fun(Q73297,bool)),fun(fun(Q73298,fun(Q73297,real)),fun(Q73297,real))),i(s(fun(fun(Q73298,bool),fun(fun(Q73298,fun(Q73297,bool)),fun(fun(Q73298,fun(Q73297,real)),fun(Q73297,real)))),U_3),s(fun(Q73298,bool),S0))),s(fun(Q73298,fun(Q73297,bool)),R0))),s(fun(Q73298,fun(Q73297,real)),F0))),s(Q73297,Y))) = s(real,i(s(fun(fun(Q73298,real),real),i(s(fun(fun(Q73298,bool),fun(fun(Q73298,real),real)),sum),s(fun(Q73298,bool),i(s(fun(fun(Q73298,bool),fun(Q73298,bool)),gspec),s(fun(Q73298,bool),i(s(fun(Q73297,fun(Q73298,bool)),i(s(fun(fun(Q73298,fun(Q73297,bool)),fun(Q73297,fun(Q73298,bool))),i(s(fun(fun(Q73298,bool),fun(fun(Q73298,fun(Q73297,bool)),fun(Q73297,fun(Q73298,bool)))),U_4),s(fun(Q73298,bool),S0))),s(fun(Q73298,fun(Q73297,bool)),R0))),s(Q73297,Y))))))),s(fun(Q73298,real),i(s(fun(Q73297,fun(Q73298,real)),i(s(fun(fun(Q73298,fun(Q73297,real)),fun(Q73297,fun(Q73298,real))),U_5),s(fun(Q73298,fun(Q73297,real)),F0))),s(Q73297,Y)))))) -> (all U_2 ((all F0 all X all Y s(real,i(s(fun(Q73297,real),i(s(fun(Q73298,fun(Q73297,real)),i(s(fun(fun(Q73298,fun(Q73297,real)),fun(Q73298,fun(Q73297,real))),U_2),s(fun(Q73298,fun(Q73297,real)),F0))),s(Q73298,X))),s(Q73297,Y))) = s(real,i(s(fun(Q73297,real),i(s(fun(Q73298,fun(Q73297,real)),F0),s(Q73298,X))),s(Q73297,Y)))) -> (all U_1 ((all T0 all R0 all X all GENR_PVARR_177 ((exists Y exists V (p(s(bool,i(s(fun(Q73297,bool),i(s(fun(bool,fun(Q73297,bool)),i(s(fun(Q73297,fun(bool,fun(Q73297,bool))),setspec),s(Q73297,GENR_PVARR_177))),s(bool,V))),s(Q73297,Y)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(Q73297,bool),bool),i(s(fun(Q73297,fun(fun(Q73297,bool),bool)),in),s(Q73297,Y))),s(fun(Q73297,bool),T0)))) & p(s(bool,i(s(fun(Q73297,bool),i(s(fun(Q73298,fun(Q73297,bool)),R0),s(Q73298,X))),s(Q73297,Y))))))) <-> p(s(bool,i(s(fun(Q73297,bool),i(s(fun(Q73298,fun(Q73297,bool)),i(s(fun(fun(Q73298,fun(Q73297,bool)),fun(Q73298,fun(Q73297,bool))),i(s(fun(fun(Q73297,bool),fun(fun(Q73298,fun(Q73297,bool)),fun(Q73298,fun(Q73297,bool)))),U_1),s(fun(Q73297,bool),T0))),s(fun(Q73298,fun(Q73297,bool)),R0))),s(Q73298,X))),s(Q73297,GENR_PVARR_177)))))) -> (all U_0 ((all T0 all R0 all F0 all X s(real,i(s(fun(fun(Q73297,real),real),i(s(fun(fun(Q73297,bool),fun(fun(Q73297,real),real)),sum),s(fun(Q73297,bool),i(s(fun(fun(Q73297,bool),fun(Q73297,bool)),gspec),s(fun(Q73297,bool),i(s(fun(Q73298,fun(Q73297,bool)),i(s(fun(fun(Q73298,fun(Q73297,bool)),fun(Q73298,fun(Q73297,bool))),i(s(fun(fun(Q73297,bool),fun(fun(Q73298,fun(Q73297,bool)),fun(Q73298,fun(Q73297,bool)))),U_1),s(fun(Q73297,bool),T0))),s(fun(Q73298,fun(Q73297,bool)),R0))),s(Q73298,X))))))),s(fun(Q73297,real),i(s(fun(Q73298,fun(Q73297,real)),i(s(fun(fun(Q73298,fun(Q73297,real)),fun(Q73298,fun(Q73297,real))),U_2),s(fun(Q73298,fun(Q73297,real)),F0))),s(Q73298,X))))) = s(real,i(s(fun(Q73298,real),i(s(fun(fun(Q73298,fun(Q73297,real)),fun(Q73298,real)),i(s(fun(fun(Q73298,fun(Q73297,bool)),fun(fun(Q73298,fun(Q73297,real)),fun(Q73298,real))),i(s(fun(fun(Q73297,bool),fun(fun(Q73298,fun(Q73297,bool)),fun(fun(Q73298,fun(Q73297,real)),fun(Q73298,real)))),U_0),s(fun(Q73297,bool),T0))),s(fun(Q73298,fun(Q73297,bool)),R0))),s(fun(Q73298,fun(Q73297,real)),F0))),s(Q73298,X)))) -> (all R0 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q73297,bool),bool),finite),s(fun(Q73297,bool),T0)))) & p(s(bool,i(s(fun(fun(Q73298,bool),bool),finite),s(fun(Q73298,bool),S0)))) -> s(real,i(s(fun(fun(Q73297,real),real),i(s(fun(fun(Q73297,bool),fun(fun(Q73297,real),real)),sum),s(fun(Q73297,bool),T0))),s(fun(Q73297,real),i(s(fun(fun(Q73298,fun(Q73297,real)),fun(Q73297,real)),i(s(fun(fun(Q73298,fun(Q73297,bool)),fun(fun(Q73298,fun(Q73297,real)),fun(Q73297,real))),i(s(fun(fun(Q73298,bool),fun(fun(Q73298,fun(Q73297,bool)),fun(fun(Q73298,fun(Q73297,real)),fun(Q73297,real)))),U_3),s(fun(Q73298,bool),S0))),s(fun(Q73298,fun(Q73297,bool)),R0))),s(fun(Q73298,fun(Q73297,real)),F0))))) = s(real,i(s(fun(fun(Q73298,real),real),i(s(fun(fun(Q73298,bool),fun(fun(Q73298,real),real)),sum),s(fun(Q73298,bool),S0))),s(fun(Q73298,real),i(s(fun(fun(Q73298,fun(Q73297,real)),fun(Q73298,real)),i(s(fun(fun(Q73298,fun(Q73297,bool)),fun(fun(Q73298,fun(Q73297,real)),fun(Q73298,real))),i(s(fun(fun(Q73297,bool),fun(fun(Q73298,fun(Q73297,bool)),fun(fun(Q73298,fun(Q73297,real)),fun(Q73298,real)))),U_0),s(fun(Q73297,bool),T0))),s(fun(Q73298,fun(Q73297,bool)),R0))),s(fun(Q73298,fun(Q73297,real)),F0))))))))))))))))))) # label(aSUMu_SUMu_RESTRICT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 531 (all N0 s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),suc),s(num,N0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aINTu_OFu_NUMu_SUC) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 532 (all Q47899 all Q47903 all F0 all S0 (s(fun(Q47903,bool),empty) = s(fun(Q47903,bool),S0) <-> s(fun(Q47899,bool),empty) = s(fun(Q47899,bool),i(s(fun(fun(Q47903,bool),fun(Q47899,bool)),i(s(fun(fun(Q47903,Q47899),fun(fun(Q47903,bool),fun(Q47899,bool))),image),s(fun(Q47903,Q47899),F0))),s(fun(Q47903,bool),S0))))) # label(aIMAGEu_EQu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 533 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(num,fun(fun(num,bool),fun(num,bool))),insert),s(num,N0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))) # label(aNUMSEGu_RREC) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 534 (all T0 (p(s(bool,T0)) | -p(s(bool,T0)))) # label(aEXCLUDEDu_MIDDLE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 535 (all Q81078 all Q81087 all A all B all P all Q81093 all U_6 ((all H0 all L all F0 all X s(list(Q81087),i(s(fun(P,list(Q81087)),i(s(fun(fun(A,B),fun(P,list(Q81087))),i(s(fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(P,list(Q81087)))),i(s(fun(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(P,list(Q81087))))),U_6),s(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),H0))),s(fun(fun(A,B),fun(P,list(Q81093))),L))),s(fun(A,B),F0))),s(P,X))) = s(list(Q81087),i(s(fun(list(Q81093),list(Q81087)),i(s(fun(fun(Q81093,Q81087),fun(list(Q81093),list(Q81087))),map0),s(fun(Q81093,Q81087),i(s(fun(P,fun(Q81093,Q81087)),i(s(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),H0),s(fun(A,B),F0))),s(P,X))))),s(list(Q81093),i(s(fun(P,list(Q81093)),i(s(fun(fun(A,B),fun(P,list(Q81093))),L),s(fun(A,B),F0))),s(P,X)))))) -> (all U_5 ((all H0 all L all F0 s(fun(P,list(Q81087)),i(s(fun(fun(A,B),fun(P,list(Q81087))),i(s(fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(P,list(Q81087)))),i(s(fun(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(P,list(Q81087))))),U_5),s(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),H0))),s(fun(fun(A,B),fun(P,list(Q81093))),L))),s(fun(A,B),F0))) = s(fun(P,list(Q81087)),i(s(fun(fun(A,B),fun(P,list(Q81087))),i(s(fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(P,list(Q81087)))),i(s(fun(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(P,list(Q81087))))),U_6),s(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),H0))),s(fun(fun(A,B),fun(P,list(Q81093))),L))),s(fun(A,B),F0)))) -> (all U_4 ((all H0 all F0 all F1 ((all Y all X p(s(bool,i(s(fun(Q81087,bool),i(s(fun(Q81087,fun(Q81087,bool)),geq),s(Q81087,i(s(fun(prod(Q81093,P),Q81087),F1),s(prod(Q81093,P),i(s(fun(P,prod(Q81093,P)),i(s(fun(Q81093,fun(P,prod(Q81093,P))),c_),s(Q81093,Y))),s(P,X))))))),s(Q81087,i(s(fun(Q81093,Q81087),i(s(fun(P,fun(Q81093,Q81087)),i(s(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),H0),s(fun(A,B),F0))),s(P,X))),s(Q81093,Y))))))) <-> p(s(bool,i(s(fun(fun(prod(Q81093,P),Q81087),bool),i(s(fun(fun(A,B),fun(fun(prod(Q81093,P),Q81087),bool)),i(s(fun(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),fun(fun(A,B),fun(fun(prod(Q81093,P),Q81087),bool))),U_4),s(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),H0))),s(fun(A,B),F0))),s(fun(prod(Q81093,P),Q81087),F1)))))) -> (all U_3 ((all H0 all F0 s(fun(prod(Q81093,P),Q81087),i(s(fun(fun(A,B),fun(prod(Q81093,P),Q81087)),i(s(fun(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),fun(fun(A,B),fun(prod(Q81093,P),Q81087))),U_3),s(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),H0))),s(fun(A,B),F0))) = s(fun(prod(Q81093,P),Q81087),i(s(fun(fun(fun(prod(Q81093,P),Q81087),bool),fun(prod(Q81093,P),Q81087)),gabs),s(fun(fun(prod(Q81093,P),Q81087),bool),i(s(fun(fun(A,B),fun(fun(prod(Q81093,P),Q81087),bool)),i(s(fun(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),fun(fun(A,B),fun(fun(prod(Q81093,P),Q81087),bool))),U_4),s(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),H0))),s(fun(A,B),F0)))))) -> (all U_2 ((all S0 all F0 ((all Y all X p(s(bool,i(s(fun(Q81078,bool),i(s(fun(Q81078,fun(Q81078,bool)),geq),s(Q81078,i(s(fun(prod(Q81093,P),Q81078),F0),s(prod(Q81093,P),i(s(fun(P,prod(Q81093,P)),i(s(fun(Q81093,fun(P,prod(Q81093,P))),c_),s(Q81093,Y))),s(P,X))))))),s(Q81078,i(s(fun(P,Q81078),S0),s(P,X))))))) <-> p(s(bool,i(s(fun(fun(prod(Q81093,P),Q81078),bool),i(s(fun(fun(P,Q81078),fun(fun(prod(Q81093,P),Q81078),bool)),U_2),s(fun(P,Q81078),S0))),s(fun(prod(Q81093,P),Q81078),F0)))))) -> (all U_1 ((all P0 all L all F0 all F1 ((all Y all X exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(Q81093,P),bool),F1),s(prod(Q81093,P),i(s(fun(P,prod(Q81093,P)),i(s(fun(Q81093,fun(P,prod(Q81093,P))),c_),s(Q81093,Y))),s(P,X))))))),s(bool,V)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(list(Q81093),bool),i(s(fun(Q81093,fun(list(Q81093),bool)),mem),s(Q81093,Y))),s(list(Q81093),i(s(fun(P,list(Q81093)),i(s(fun(fun(A,B),fun(P,list(Q81093))),L),s(fun(A,B),F0))),s(P,X)))))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,X))))))) <-> p(s(bool,i(s(fun(fun(prod(Q81093,P),bool),bool),i(s(fun(fun(A,B),fun(fun(prod(Q81093,P),bool),bool)),i(s(fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(fun(prod(Q81093,P),bool),bool))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(fun(prod(Q81093,P),bool),bool)))),U_1),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,list(Q81093))),L))),s(fun(A,B),F0))),s(fun(prod(Q81093,P),bool),F1)))))) -> (all U_0 ((all P0 all L all F0 s(fun(prod(Q81093,P),bool),i(s(fun(fun(A,B),fun(prod(Q81093,P),bool)),i(s(fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(prod(Q81093,P),bool))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(prod(Q81093,P),bool)))),U_0),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,list(Q81093))),L))),s(fun(A,B),F0))) = s(fun(prod(Q81093,P),bool),i(s(fun(fun(fun(prod(Q81093,P),bool),bool),fun(prod(Q81093,P),bool)),gabs),s(fun(fun(prod(Q81093,P),bool),bool),i(s(fun(fun(A,B),fun(fun(prod(Q81093,P),bool),bool)),i(s(fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(fun(prod(Q81093,P),bool),bool))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(fun(prod(Q81093,P),bool),bool)))),U_1),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,list(Q81093))),L))),s(fun(A,B),F0)))))) -> (all L_L_ all P0 all S0 all H0 all L (p(s(bool,i(s(fun(fun(fun(A,B),fun(prod(Q81093,P),Q81087)),bool),i(s(fun(fun(prod(Q81093,P),Q81078),fun(fun(fun(A,B),fun(prod(Q81093,P),Q81087)),bool)),i(s(fun(fun(fun(A,B),fun(prod(Q81093,P),bool)),fun(fun(prod(Q81093,P),Q81078),fun(fun(fun(A,B),fun(prod(Q81093,P),Q81087)),bool))),i(s(fun(fun(A,fun(Q81078,bool)),fun(fun(fun(A,B),fun(prod(Q81093,P),bool)),fun(fun(prod(Q81093,P),Q81078),fun(fun(fun(A,B),fun(prod(Q81093,P),Q81087)),bool)))),admissible),s(fun(A,fun(Q81078,bool)),L_L_))),s(fun(fun(A,B),fun(prod(Q81093,P),bool)),i(s(fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(prod(Q81093,P),bool))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(prod(Q81093,P),bool)))),U_0),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,list(Q81093))),L))))),s(fun(prod(Q81093,P),Q81078),i(s(fun(fun(fun(prod(Q81093,P),Q81078),bool),fun(prod(Q81093,P),Q81078)),gabs),s(fun(fun(prod(Q81093,P),Q81078),bool),i(s(fun(fun(P,Q81078),fun(fun(prod(Q81093,P),Q81078),bool)),U_2),s(fun(P,Q81078),S0))))))),s(fun(fun(A,B),fun(prod(Q81093,P),Q81087)),i(s(fun(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),fun(fun(A,B),fun(prod(Q81093,P),Q81087))),U_3),s(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),H0)))))) & p(s(bool,i(s(fun(fun(fun(A,B),fun(P,list(Q81093))),bool),i(s(fun(fun(P,Q81078),fun(fun(fun(A,B),fun(P,list(Q81093))),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,Q81078),fun(fun(fun(A,B),fun(P,list(Q81093))),bool))),i(s(fun(fun(A,fun(Q81078,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,Q81078),fun(fun(fun(A,B),fun(P,list(Q81093))),bool)))),admissible),s(fun(A,fun(Q81078,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,Q81078),S0))),s(fun(fun(A,B),fun(P,list(Q81093))),L)))) -> p(s(bool,i(s(fun(fun(fun(A,B),fun(P,list(Q81087))),bool),i(s(fun(fun(P,Q81078),fun(fun(fun(A,B),fun(P,list(Q81087))),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,Q81078),fun(fun(fun(A,B),fun(P,list(Q81087))),bool))),i(s(fun(fun(A,fun(Q81078,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,Q81078),fun(fun(fun(A,B),fun(P,list(Q81087))),bool)))),admissible),s(fun(A,fun(Q81078,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,Q81078),S0))),s(fun(fun(A,B),fun(P,list(Q81087))),i(s(fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(P,list(Q81087)))),i(s(fun(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),fun(fun(fun(A,B),fun(P,list(Q81093))),fun(fun(A,B),fun(P,list(Q81087))))),U_5),s(fun(fun(A,B),fun(P,fun(Q81093,Q81087))),H0))),s(fun(fun(A,B),fun(P,list(Q81093))),L)))))))))))))))))))))) # label(aADMISSIBLEu_MAP) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 536 (all X all N0 (s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) <-> s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) | (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> p(s(bool,i(s(fun(num,bool),even),s(num,N0))))) & s(real,i(s(fun(real,real),realu_abs),s(real,X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) # label(aREALu_POWu_EQu_1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 537 (all X all Y s(int,Y) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))),s(int,X)))) # label(aINTu_ADDu_SUB) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 538 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all P0 ((all X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))))) & (exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) -> (exists Y (p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))) & (all Z0 (p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Z0))),s(A,Y)))))) -> -p(s(bool,i(s(fun(A,bool),P0),s(A,Z0)))))))))))) # label(aWOSETu_WELLu_CONTRAPOS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 539 (all S0 ((exists A5 all X (p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,X))),s(fun(num,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,X))),s(num,A5)))))) <-> p(s(bool,i(s(fun(fun(num,bool),bool),finite),s(fun(num,bool),S0)))))) # label(anumu_FINITE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 540 (all A all X all S0 s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0))) = s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X)))))) # label(aCOUNTABLEu_DELETE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 541 (all B all A all U_1 ((all S0 all F0 all Y all GENR_PVARR_168 (p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))),s(A,GENR_PVARR_168)))) <-> (exists X exists V ((p(s(bool,V)) <-> s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_168))),s(bool,V))),s(A,X)))))))) -> (all U_0 ((all S0 all F0 all G0 all Y s(num,i(s(fun(B,num),i(s(fun(fun(A,num),fun(B,num)),i(s(fun(fun(A,B),fun(fun(A,num),fun(B,num))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,num),fun(B,num)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,num),G0))),s(B,Y))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))))))),s(fun(A,num),G0)))) -> (all F0 all G0 all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),G0))) = s(num,i(s(fun(fun(B,num),num),i(s(fun(fun(B,bool),fun(fun(B,num),num)),nsum),s(fun(B,bool),T0))),s(fun(B,num),i(s(fun(fun(A,num),fun(B,num)),i(s(fun(fun(A,B),fun(fun(A,num),fun(B,num))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,num),fun(B,num)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,num),G0))))))))))) # label(aNSUMu_GROUP) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 542 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y)))))))) # label(aREALu_LTu_MUL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 543 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_gt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(real,real),realu_sgn),s(real,X))))) # label(aREALu_SGNu_EQu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 544 (all C all A all B all F0 all X all Y s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),F0),s(A,X))),s(B,Y))) = s(C,i(s(fun(prod(A,B),C),i(s(fun(fun(A,fun(B,C)),fun(prod(A,B),C)),uncurry),s(fun(A,fun(B,C)),F0))),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))) # label(aUNCURRYu_DEF) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 545 (all Q18705 all Q18712 (p(s(bool,i(s(fun(list(Q18712),bool),i(s(fun(list(Q18705),fun(list(Q18712),bool)),i(s(fun(fun(Q18705,fun(Q18712,bool)),fun(list(Q18705),fun(list(Q18712),bool))),all2),s(fun(Q18705,fun(Q18712,bool)),p0))),s(list(Q18705),nil))),s(list(Q18712),l2)))) <-> s(list(Q18712),nil) = s(list(Q18712),l2))) # label(aALL2u_DEFu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 546 (all A s(A,h0) = s(A,i(s(fun(list(A),A),last0),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,h0))),s(list(A),nil)))))) # label(aLASTu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 547 (all Q20306 all L all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,i(s(fun(list(Q20306),num),length),s(list(Q20306),L)))))) -> p(s(bool,i(s(fun(list(Q20306),bool),i(s(fun(Q20306,fun(list(Q20306),bool)),mem),s(Q20306,i(s(fun(list(Q20306),Q20306),i(s(fun(num,fun(list(Q20306),Q20306)),el),s(num,N0))),s(list(Q20306),L))))),s(list(Q20306),L)))))) # label(aMEMu_EL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 548 (all M0 all N0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,i(s(fun(num,int),intu_ofu_num),s(num,M0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),min),s(num,M0))),s(num,N0)))))) # label(aINTu_OFu_NUMu_MIN) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 549 (all A all B exists X exists A5 exists B0 s(fun(A,fun(B,bool)),X) = s(fun(A,fun(B,bool)),i(s(fun(B,fun(A,fun(B,bool))),i(s(fun(A,fun(B,fun(A,fun(B,bool)))),mku_pair),s(A,A5))),s(B,B0)))) # label(aPAIRu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 550 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (exists N0 all N1 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,N1)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N1))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,N1))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N1))),s(num,N1))))))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N1)))))))))) # label(aNADDu_MULu_LINVu_LEMMA2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 551 (all X (s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,X) <-> s(int,i(s(fun(int,int),intu_neg),s(int,X))) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aINTu_NEGu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 552 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,M0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,M0))))))) # label(aINTu_OFu_NUMu_SUB) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 553 (all Q56600 all Q56603 all U_0 ((all T0 all S0 all GENR_PVARR_94 ((exists F0 exists V (((all X (-p(s(bool,i(s(fun(fun(Q56603,bool),bool),i(s(fun(Q56603,fun(fun(Q56603,bool),bool)),in),s(Q56603,X))),s(fun(Q56603,bool),S0)))) -> s(Q56600,i(s(fun(Q56603,Q56600),F0),s(Q56603,X))) = s(Q56600,d))) & (all X (p(s(bool,i(s(fun(fun(Q56603,bool),bool),i(s(fun(Q56603,fun(fun(Q56603,bool),bool)),in),s(Q56603,X))),s(fun(Q56603,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q56600,bool),bool),i(s(fun(Q56600,fun(fun(Q56600,bool),bool)),in),s(Q56600,i(s(fun(Q56603,Q56600),F0),s(Q56603,X))))),s(fun(Q56600,bool),T0)))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(fun(Q56603,Q56600),bool),i(s(fun(bool,fun(fun(Q56603,Q56600),bool)),i(s(fun(fun(Q56603,Q56600),fun(bool,fun(fun(Q56603,Q56600),bool))),setspec),s(fun(Q56603,Q56600),GENR_PVARR_94))),s(bool,V))),s(fun(Q56603,Q56600),F0)))))) <-> p(s(bool,i(s(fun(fun(Q56603,Q56600),bool),i(s(fun(fun(Q56603,bool),fun(fun(Q56603,Q56600),bool)),i(s(fun(fun(Q56600,bool),fun(fun(Q56603,bool),fun(fun(Q56603,Q56600),bool))),U_0),s(fun(Q56600,bool),T0))),s(fun(Q56603,bool),S0))),s(fun(Q56603,Q56600),GENR_PVARR_94)))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(Q56600,bool),bool),finite),s(fun(Q56600,bool),T0)))) & p(s(bool,i(s(fun(fun(Q56603,bool),bool),finite),s(fun(Q56603,bool),S0)))) -> p(s(bool,i(s(fun(fun(fun(Q56603,Q56600),bool),bool),finite),s(fun(fun(Q56603,Q56600),bool),i(s(fun(fun(fun(Q56603,Q56600),bool),fun(fun(Q56603,Q56600),bool)),gspec),s(fun(fun(Q56603,Q56600),bool),i(s(fun(fun(Q56603,bool),fun(fun(Q56603,Q56600),bool)),i(s(fun(fun(Q56600,bool),fun(fun(Q56603,bool),fun(fun(Q56603,Q56600),bool))),U_0),s(fun(Q56600,bool),T0))),s(fun(Q56603,bool),S0)))))))))))) # label(aFINITEu_FUNSPACE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 554 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),fact),s(num,M0))))),s(num,i(s(fun(num,num),fact),s(num,N0)))))))) # label(aFACTu_MONO) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 555 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),fact),s(num,N0))))))) # label(aFACTu_LT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 556 (all A all S0 ((exists X s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),empty))) = s(fun(A,bool),S0)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),sing),s(fun(A,bool),S0)))))) # label(aSING) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 557 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) & s(num,M0) != s(num,N0) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))))) # label(aLTu_LE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 558 (all N0 all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,N0)))))))) # label(aINTu_POWu_LE2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 559 (all P0 ((all D0 all E0 (p(s(bool,i(s(fun(real,bool),P0),s(real,D0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,D0))),s(real,E0)))) -> p(s(bool,i(s(fun(real,bool),P0),s(real,E0)))))) & (all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> p(s(bool,i(s(fun(real,bool),P0),s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))))))))) -> (all E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) -> p(s(bool,i(s(fun(real,bool),P0),s(real,E0)))))))) # label(aFORALLu_POSu_MONO) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 560 (all R0 ((all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,N0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))) & (all X all Y all Z0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,Y))),s(num,Z0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,X))),s(num,Y)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,X))),s(num,Z0)))))) -> (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,M0))),s(num,N0)))))))) # label(aTRANSITIVEu_STEPWISEu_LT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 561 (all N0 all X (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0)))))))) # label(aINTu_POWu_LTu_1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 562 (all B all A all S0 all T0 p(s(bool,i(s(fun(fun(sum0(B,A),bool),bool),i(s(fun(fun(sum0(A,B),bool),fun(fun(sum0(B,A),bool),bool)),a_u_c),s(fun(sum0(A,B),bool),i(s(fun(fun(B,bool),fun(sum0(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(sum0(A,B),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(sum0(B,A),bool),i(s(fun(fun(A,bool),fun(sum0(B,A),bool)),i(s(fun(fun(B,bool),fun(fun(A,bool),fun(sum0(B,A),bool))),p_u_c),s(fun(B,bool),T0))),s(fun(A,bool),S0))))))) # label(aCARDu_ADDu_SYM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 563 (all N0 s(num,N0) = s(num,i(s(fun(int,num),numu_ofu_int),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0)))))) # label(aNUMu_OFu_INTu_OFu_NUM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 564 (all N0 s(num,N0) = s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))))) # label(aDISTu_LZERO) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 565 (all B0 all X s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,B0))),s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,X))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,X))))) = s(num,i(s(fun(num,num),i(s(fun(bool,fun(num,num)),numsum),s(bool,B0))),s(num,X)))) # label(aNUMSUM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 566 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))) = s(num,M0))) # label(aMODu_LT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 567 (all Q20262 all Q20246 all L all X s(bool,i(s(fun(list(prod(Q20262,Q20246)),bool),i(s(fun(prod(Q20262,Q20246),fun(list(prod(Q20262,Q20246)),bool)),mem),s(prod(Q20262,Q20246),i(s(fun(Q20246,prod(Q20262,Q20246)),i(s(fun(Q20262,fun(Q20246,prod(Q20262,Q20246))),c_),s(Q20262,X))),s(Q20246,i(s(fun(list(prod(Q20262,Q20246)),Q20246),i(s(fun(Q20262,fun(list(prod(Q20262,Q20246)),Q20246)),assoc),s(Q20262,X))),s(list(prod(Q20262,Q20246)),L))))))),s(list(prod(Q20262,Q20246)),L))) = s(bool,i(s(fun(list(Q20262),bool),i(s(fun(Q20262,fun(list(Q20262),bool)),mem),s(Q20262,X))),s(list(Q20262),i(s(fun(list(prod(Q20262,Q20246)),list(Q20262)),i(s(fun(fun(prod(Q20262,Q20246),Q20262),fun(list(prod(Q20262,Q20246)),list(Q20262))),map0),s(fun(prod(Q20262,Q20246),Q20262),fst))),s(list(prod(Q20262,Q20246)),L)))))) # label(aMEMu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 568 (all Q71888 all F0 all S0 (p(s(bool,i(s(fun(fun(Q71888,bool),bool),finite),s(fun(Q71888,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(Q71888,bool),bool),i(s(fun(Q71888,fun(fun(Q71888,bool),bool)),in),s(Q71888,X))),s(fun(Q71888,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(Q71888,real),F0),s(Q71888,X)))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(fun(Q71888,real),real),i(s(fun(fun(Q71888,bool),fun(fun(Q71888,real),real)),sum),s(fun(Q71888,bool),S0))),s(fun(Q71888,real),F0)))))))) # label(aSUMu_POSu_LE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 569 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_abs),s(int,X))))),s(int,i(s(fun(int,int),intu_abs),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aINTu_LTu_SQUAREu_ABS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 570 (all X (s(real,i(s(fun(real,real),realu_sgn),s(real,X))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) # label(aREALu_SGNu_EQu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 571 (all X all Y s(real,Y) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y)))))) # label(aREALu_SUBu_SUB2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 572 (all A all P0 all Q0 ((all X p(s(bool,i(s(fun(A,bool),Q0),s(A,X))))) | p(s(bool,P0)) <-> (all X (p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))) | p(s(bool,P0)))))) # label(aRIGHTu_FORALLu_ORu_THM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 573 (all X all Y all Z0 s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Z0))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,Y))),s(nadd,Z0))))) = s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y)))) # label(aNADDu_LEu_RADD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.95 574 (all M all A all N all X all Y s(cart(A,N),Y) = s(cart(A,N),i(s(fun(cart(A,finite_sum(M,N)),cart(A,N)),sndcart),s(cart(A,finite_sum(M,N)),i(s(fun(cart(A,N),cart(A,finite_sum(M,N))),i(s(fun(cart(A,M),fun(cart(A,N),cart(A,finite_sum(M,N)))),pastecart),s(cart(A,M),X))),s(cart(A,N),Y)))))) # label(aSNDCARTu_PASTECART) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 575 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all X (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,X)))))))))) # label(aWOSETu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 576 (all X all Y all Z0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))),s(int,Z0))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Z0))),s(int,Y)))))) # label(aINTu_LTu_SUBu_RADD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 577 (all X s(real,X) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aREALu_MULu_RID) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 578 (all Y all X s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_ge),s(real,X))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,X)))) # label(arealu_ge) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 579 (all Q77980 all Q77984 all U_0 ((all G0 all I0 s(Q77980,i(s(fun(num,Q77980),i(s(fun(cart(Q77980,Q77984),fun(num,Q77980)),d_),s(cart(Q77980,Q77984),G0))),s(num,I0))) = s(Q77980,i(s(fun(num,Q77980),i(s(fun(cart(Q77980,Q77984),fun(num,Q77980)),U_0),s(cart(Q77980,Q77984),G0))),s(num,I0)))) -> (all G0 s(cart(Q77980,Q77984),i(s(fun(fun(num,Q77980),cart(Q77980,Q77984)),lambda),s(fun(num,Q77980),i(s(fun(cart(Q77980,Q77984),fun(num,Q77980)),U_0),s(cart(Q77980,Q77984),G0))))) = s(cart(Q77980,Q77984),G0)))) # label(aLAMBDAu_ETA) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 580 (all Q72330 all F0 all S0 all A5 (p(s(bool,i(s(fun(fun(Q72330,bool),bool),finite),s(fun(Q72330,bool),S0)))) -> s(real,i(s(fun(fun(Q72330,real),real),i(s(fun(fun(Q72330,bool),fun(fun(Q72330,real),real)),sum),s(fun(Q72330,bool),i(s(fun(Q72330,fun(Q72330,bool)),i(s(fun(fun(Q72330,bool),fun(Q72330,fun(Q72330,bool))),delete),s(fun(Q72330,bool),S0))),s(Q72330,A5))))),s(fun(Q72330,real),F0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(fun(Q72330,bool),bool),i(s(fun(Q72330,fun(fun(Q72330,bool),bool)),in),s(Q72330,A5))),s(fun(Q72330,bool),S0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(fun(Q72330,real),real),i(s(fun(fun(Q72330,bool),fun(fun(Q72330,real),real)),sum),s(fun(Q72330,bool),S0))),s(fun(Q72330,real),F0))))),s(real,i(s(fun(Q72330,real),F0),s(Q72330,A5))))))),s(real,i(s(fun(fun(Q72330,real),real),i(s(fun(fun(Q72330,bool),fun(fun(Q72330,real),real)),sum),s(fun(Q72330,bool),S0))),s(fun(Q72330,real),F0))))))) # label(aSUMu_DELETEu_CASES) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 581 (all B all A all F0 all B0 ((all X all Y all S0 (s(A,Y) != s(A,X) -> s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,S0))))) = s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,S0))))))) -> (exists G0 ((all X all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(B,i(s(fun(fun(A,bool),B),G0),s(fun(A,bool),S0))))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,i(s(fun(fun(A,bool),B),G0),s(fun(A,bool),S0))))))) = s(B,i(s(fun(fun(A,bool),B),G0),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))))) & s(B,i(s(fun(fun(A,bool),B),G0),s(fun(A,bool),empty))) = s(B,B0))))) # label(aSETu_RECURSIONu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 582 (all N0 ((exists M0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))) = s(num,N0)) <-> p(s(bool,i(s(fun(num,bool),even),s(num,N0)))))) # label(aEVENu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 583 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))))) # label(aCARDu_EQu_CARD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 584 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),bit1),s(num,N0))))),s(num,u_0))) = s(num,i(s(fun(num,num),bit1),s(num,N0)))) # label(aARITHu_SUBu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 585 (all A all B all F0 ((all Y exists X s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X)))) <-> (all M0 exists L s(list(B),M0) = s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),L)))))) # label(aSURJECTIVEu_MAP) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 586 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Z0))),s(real,Y)))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Z0))),s(real,X)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Z0))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,Y)))))))) # label(aREALu_LTu_MAX) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 587 (all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))) -> s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aLEu_1u_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 588 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))))))))) # label(aARITHu_MULTu_conjunct9) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 589 (all S0 all A5 all B0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))) & s(fun(real,bool),empty) != s(fun(real,bool),S0) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))),s(real,B0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0)))))))) # label(aREALu_INFu_BOUNDS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 590 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,Y))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,Y))))),s(real,Y)))))) # label(aREALu_MINu_MIN) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 591 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,i(s(fun(real,real),realu_neg),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))) # label(aREALu_SUBu_RNEG) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 592 (all X all Y (s(real,Y) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(real,X) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y))))))) # label(aREALu_DIVu_LMUL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 593 (all X all Y all Z0 p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),Z0))))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Z0))))))))) # label(aTREALu_ADDu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 594 (all U_0 ((all X all I0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))),s(num,I0)))) -> (all X all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))))))))))) # label(aREALu_SUBu_POWu_L1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 595 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y))))) = s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y)))))) # label(aintu_minu_th) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 596 (all A all B all U_2 ((all P0 all X (-p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_2),s(fun(A,bool),P0))),s(A,X)))))) -> (all U_1 ((all S0 all P0 all GENR_PVARR_149 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),P0))),s(A,GENR_PVARR_149)))) <-> (exists X exists V ((p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_149))),s(bool,V))),s(A,X)))))))) -> (all U_0 ((all P0 all F0 all G0 all X s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,i(s(fun(A,bool),P0),s(A,X))))),s(B,i(s(fun(A,B),F0),s(A,X))))),s(B,i(s(fun(A,B),G0),s(A,X))))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),i(s(fun(fun(A,B),fun(fun(A,B),fun(A,B))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,B),fun(A,B)))),U_0),s(fun(A,bool),P0))),s(fun(A,B),F0))),s(fun(A,B),G0))),s(A,X)))) -> (all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all S0 all P0 all F0 all G0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),i(s(fun(fun(A,B),fun(fun(A,B),fun(A,B))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,B),fun(A,B)))),U_0),s(fun(A,bool),P0))),s(fun(A,B),F0))),s(fun(A,B),G0))))) = s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),OP),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),P0))))))),s(fun(A,B),F0))))),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_2),s(fun(A,bool),P0))))))))),s(fun(A,B),G0))))))))))))))) # label(aITERATEu_CASES) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 597 (all X exists N0 p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,N0))))))) # label(aNADDu_ARCH) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 598 (all A all S0 s(fun(A,bool),S0) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),empty)))) # label(aDIFFu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 599 (all A all U_0 ((all R0 all N0 s(fun(num,fun(A,bool)),i(s(fun(num,fun(num,fun(A,bool))),i(s(fun(fun(num,recspace(A)),fun(num,fun(num,fun(A,bool)))),U_0),s(fun(num,recspace(A)),R0))),s(num,N0))) = s(fun(num,fun(A,bool)),i(s(fun(recspace(A),fun(num,fun(A,bool))),u_destu_rec),s(recspace(A),i(s(fun(num,recspace(A)),R0),s(num,N0)))))) -> (all C0 all I0 all R0 s(recspace(A),i(s(fun(fun(num,recspace(A)),recspace(A)),i(s(fun(A,fun(fun(num,recspace(A)),recspace(A))),i(s(fun(num,fun(A,fun(fun(num,recspace(A)),recspace(A)))),constr),s(num,C0))),s(A,I0))),s(fun(num,recspace(A)),R0))) = s(recspace(A),i(s(fun(fun(num,fun(A,bool)),recspace(A)),u_mku_rec),s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))),i(s(fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool)))),i(s(fun(num,fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))))),zconstr),s(num,C0))),s(A,I0))),s(fun(num,fun(num,fun(A,bool))),i(s(fun(fun(num,recspace(A)),fun(num,fun(num,fun(A,bool)))),U_0),s(fun(num,recspace(A)),R0)))))))))) # label(aCONSTR) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 600 (all Q96736 all U_0 ((all P0 all S0 all GENR_PVARR_270 (p(s(bool,i(s(fun(fun(Q96736,bool),bool),i(s(fun(fun(Q96736,bool),fun(fun(Q96736,bool),bool)),i(s(fun(fun(fun(Q96736,bool),bool),fun(fun(Q96736,bool),fun(fun(Q96736,bool),bool))),U_0),s(fun(fun(Q96736,bool),bool),P0))),s(fun(Q96736,bool),S0))),s(fun(Q96736,bool),GENR_PVARR_270)))) <-> (exists T0 exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(Q96736,bool),bool),i(s(fun(fun(Q96736,bool),fun(fun(Q96736,bool),bool)),subset),s(fun(Q96736,bool),S0))),s(fun(Q96736,bool),T0)))) & p(s(bool,i(s(fun(fun(Q96736,bool),bool),P0),s(fun(Q96736,bool),T0))))) & p(s(bool,i(s(fun(fun(Q96736,bool),bool),i(s(fun(bool,fun(fun(Q96736,bool),bool)),i(s(fun(fun(Q96736,bool),fun(bool,fun(fun(Q96736,bool),bool))),setspec),s(fun(Q96736,bool),GENR_PVARR_270))),s(bool,V))),s(fun(Q96736,bool),T0)))))))) -> (all P0 all S0 s(fun(Q96736,bool),i(s(fun(fun(Q96736,bool),fun(Q96736,bool)),i(s(fun(fun(fun(Q96736,bool),bool),fun(fun(Q96736,bool),fun(Q96736,bool))),hull),s(fun(fun(Q96736,bool),bool),P0))),s(fun(Q96736,bool),S0))) = s(fun(Q96736,bool),i(s(fun(fun(fun(Q96736,bool),bool),fun(Q96736,bool)),inters),s(fun(fun(Q96736,bool),bool),i(s(fun(fun(fun(Q96736,bool),bool),fun(fun(Q96736,bool),bool)),gspec),s(fun(fun(Q96736,bool),bool),i(s(fun(fun(Q96736,bool),fun(fun(Q96736,bool),bool)),i(s(fun(fun(fun(Q96736,bool),bool),fun(fun(Q96736,bool),fun(fun(Q96736,bool),bool))),U_0),s(fun(fun(Q96736,bool),bool),P0))),s(fun(Q96736,bool),S0)))))))))) # label(ahull) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 601 (all A all L all X (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),L)))) -> (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),i(s(fun(fun(fun(prod(A,A),bool),bool),fun(prod(A,A),bool)),unions),s(fun(fun(prod(A,A),bool),bool),ordinal))))),s(A,X))))))) # label(aORDINALu_UNIONu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 602 (all A all S0 all T0 all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))))) # label(aINu_INTER) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 603 (all A all U_0 ((all X s(bool,t) = s(bool,i(s(fun(A,bool),U_0),s(A,X)))) -> (all N0 s(A,i(s(fun(num,A),fnil),s(num,N0))) = s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),U_0)))))) # label(aFNIL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 604 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Z0)))))) # label(aREALu_LETu_TRANS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 605 (exists N0 (s(real,x) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))) | s(real,x) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))) <-> p(s(bool,i(s(fun(real,bool),integer),s(real,x)))) # label(aisu_int) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 606 (all B all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(B,bool),fun(fun(A,bool),bool)),l_a_u_c),s(fun(B,bool),T0))),s(fun(A,bool),S0)))) | p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))))) # label(aCARDu_LTEu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 607 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y))),s(int,X))) = s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y)))))) # label(aINTu_NEGu_SUB) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 608 (all A all T0 ((all X p(s(bool,T0))) <-> p(s(bool,T0)))) # label(aFORALLu_SIMP) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 609 (all A all P0 all Q0 ((exists X (p(s(bool,P0)) & p(s(bool,Q0)))) <-> (exists X p(s(bool,P0))) & (exists X p(s(bool,Q0))))) # label(aTRIVu_EXISTSu_ANDu_THM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 610 (all X all Y all N0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y))))),s(num,N0)))) # label(aREALu_POWu_DIV) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 611 (all X s(real,i(s(fun(real,real),realu_sgn),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))) = s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(int,int),intu_sgn),s(int,X)))))) # label(aintu_sgnu_th) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 612 (all X all Y s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,i(s(fun(int,int),intu_neg),s(int,Y)))))) # label(aINTu_NEGu_ADD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 613 (all U_0 ((all F0 all M0 all I0 s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(num,real),fun(num,fun(num,real))),U_0),s(fun(num,real),F0))),s(num,M0))),s(num,I0))) = s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,I0))),s(num,M0)))))) -> (all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,M0))))))),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(num,real),fun(num,fun(num,real))),U_0),s(fun(num,real),F0))),s(num,M0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))))))) # label(aSUMu_OFFSETu_0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 614 (all X all Y ((exists B0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,Y))),s(num,N0))))))))),s(num,B0))))) <-> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,Y)))))) # label(anaddu_eq) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 615 (all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,M0))),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))) # label(aDISTu_ADDBOUND) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 616 (all Q20861 all N0 all H0 all T0 exists V (s(Q20861,i(s(fun(list(Q20861),Q20861),i(s(fun(num,fun(list(Q20861),Q20861)),el),s(num,N0))),s(list(Q20861),i(s(fun(list(Q20861),list(Q20861)),i(s(fun(Q20861,fun(list(Q20861),list(Q20861))),cons),s(Q20861,H0))),s(list(Q20861),T0))))) = s(Q20861,i(s(fun(Q20861,Q20861),i(s(fun(Q20861,fun(Q20861,Q20861)),i(s(fun(bool,fun(Q20861,fun(Q20861,Q20861))),cond),s(bool,V))),s(Q20861,H0))),s(Q20861,i(s(fun(list(Q20861),Q20861),i(s(fun(num,fun(list(Q20861),Q20861)),el),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(list(Q20861),T0))))) & (p(s(bool,V)) <-> s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aELu_CONS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 617 (all Q65020 all Q65001 all U_0 ((all A5 all F0 all OP all X exists V (s(Q65001,i(s(fun(Q65001,Q65001),i(s(fun(Q65001,fun(Q65001,Q65001)),i(s(fun(bool,fun(Q65001,fun(Q65001,Q65001))),cond),s(bool,V))),s(Q65001,i(s(fun(Q65020,Q65001),F0),s(Q65020,X))))),s(Q65001,i(s(fun(fun(Q65001,fun(Q65001,Q65001)),Q65001),neutral),s(fun(Q65001,fun(Q65001,Q65001)),OP))))) = s(Q65001,i(s(fun(Q65020,Q65001),i(s(fun(fun(Q65001,fun(Q65001,Q65001)),fun(Q65020,Q65001)),i(s(fun(fun(Q65020,Q65001),fun(fun(Q65001,fun(Q65001,Q65001)),fun(Q65020,Q65001))),i(s(fun(Q65020,fun(fun(Q65020,Q65001),fun(fun(Q65001,fun(Q65001,Q65001)),fun(Q65020,Q65001)))),U_0),s(Q65020,A5))),s(fun(Q65020,Q65001),F0))),s(fun(Q65001,fun(Q65001,Q65001)),OP))),s(Q65020,X))) & (p(s(bool,V)) <-> s(Q65020,X) = s(Q65020,A5)))) -> (all OP (p(s(bool,i(s(fun(fun(Q65001,fun(Q65001,Q65001)),bool),monoidal),s(fun(Q65001,fun(Q65001,Q65001)),OP)))) -> (all F0 all A5 all S0 s(Q65001,i(s(fun(fun(Q65020,Q65001),Q65001),i(s(fun(fun(Q65020,bool),fun(fun(Q65020,Q65001),Q65001)),i(s(fun(fun(Q65001,fun(Q65001,Q65001)),fun(fun(Q65020,bool),fun(fun(Q65020,Q65001),Q65001))),iterate),s(fun(Q65001,fun(Q65001,Q65001)),OP))),s(fun(Q65020,bool),S0))),s(fun(Q65020,Q65001),i(s(fun(fun(Q65001,fun(Q65001,Q65001)),fun(Q65020,Q65001)),i(s(fun(fun(Q65020,Q65001),fun(fun(Q65001,fun(Q65001,Q65001)),fun(Q65020,Q65001))),i(s(fun(Q65020,fun(fun(Q65020,Q65001),fun(fun(Q65001,fun(Q65001,Q65001)),fun(Q65020,Q65001)))),U_0),s(Q65020,A5))),s(fun(Q65020,Q65001),F0))),s(fun(Q65001,fun(Q65001,Q65001)),OP))))) = s(Q65001,i(s(fun(Q65001,Q65001),i(s(fun(Q65001,fun(Q65001,Q65001)),i(s(fun(bool,fun(Q65001,fun(Q65001,Q65001))),cond),s(bool,i(s(fun(fun(Q65020,bool),bool),i(s(fun(Q65020,fun(fun(Q65020,bool),bool)),in),s(Q65020,A5))),s(fun(Q65020,bool),S0))))),s(Q65001,i(s(fun(Q65020,Q65001),F0),s(Q65020,A5))))),s(Q65001,i(s(fun(fun(Q65001,fun(Q65001,Q65001)),Q65001),neutral),s(fun(Q65001,fun(Q65001,Q65001)),OP)))))))))) # label(aITERATEu_DELTA) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 618 (all Q18672 all H0 all X all T0 ((p(s(bool,i(s(fun(list(Q18672),bool),i(s(fun(Q18672,fun(list(Q18672),bool)),mem),s(Q18672,X))),s(list(Q18672),i(s(fun(list(Q18672),list(Q18672)),i(s(fun(Q18672,fun(list(Q18672),list(Q18672))),cons),s(Q18672,H0))),s(list(Q18672),T0)))))) <-> s(Q18672,X) = s(Q18672,H0) | p(s(bool,i(s(fun(list(Q18672),bool),i(s(fun(Q18672,fun(list(Q18672),bool)),mem),s(Q18672,X))),s(list(Q18672),T0))))) & s(bool,f0) = s(bool,i(s(fun(list(Q18672),bool),i(s(fun(Q18672,fun(list(Q18672),bool)),mem),s(Q18672,X))),s(list(Q18672),nil))))) # label(aSeq2o_MEM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 619 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,P0))),s(num,M0)))) & s(num,P0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,N0))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,N0))),s(num,P0)))))))) # label(aDIVu_MONO2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 620 (all A all B all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all G0 all S0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),G0),s(A,X))))) -> s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))) = s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),G0))))))) # label(aITERATEu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 621 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,Z0)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Z0)))))) # label(aINTu_LTu_TRANS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 622 (all B all A all U_0 ((all R0 all GENR_PVARR_213 (p(s(bool,i(s(fun(B,bool),i(s(fun(fun(A,fun(B,bool)),fun(B,bool)),U_0),s(fun(A,fun(B,bool)),R0))),s(B,GENR_PVARR_213)))) <-> (exists Y exists V (p(s(bool,i(s(fun(B,bool),i(s(fun(bool,fun(B,bool)),i(s(fun(B,fun(bool,fun(B,bool))),setspec),s(B,GENR_PVARR_213))),s(bool,V))),s(B,Y)))) & (p(s(bool,V)) <-> (exists X (p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),R0),s(A,X))),s(B,Y)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),s0))))))))))) -> (all R0 ((all X all Y all YI_ (p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),R0),s(A,X))),s(B,YI_)))) & p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),R0),s(A,X))),s(B,Y)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),s0)))) -> s(B,YI_) = s(B,Y))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(B,bool),fun(fun(A,bool),bool)),l_a_u_c),s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),gspec),s(fun(B,bool),i(s(fun(fun(A,fun(B,bool)),fun(B,bool)),U_0),s(fun(A,fun(B,bool)),R0))))))),s(fun(A,bool),s0)))))))) # label(aCARDu_LEu_RELATIONAL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 623 (all X all Y all Z0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Z0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Y))),s(int,Z0)))))) # label(aINTu_ADDu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 624 (all Q50925 all A5 p(s(bool,i(s(fun(fun(Q50925,bool),bool),finite),s(fun(Q50925,bool),i(s(fun(fun(Q50925,bool),fun(Q50925,bool)),i(s(fun(Q50925,fun(fun(Q50925,bool),fun(Q50925,bool))),insert),s(Q50925,A5))),s(fun(Q50925,bool),empty))))))) # label(aFINITEu_SING) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 625 (all N0 all X (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aINTu_POWu_1u_LT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 626 (all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,X))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aREALu_POWu_2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 627 (all X s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,X)))) # label(aINTu_POWu_2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 628 (all P0 ((all N0 p(s(bool,i(s(fun(real,bool),P0),s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))))) & (all D0 all E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,D0))),s(real,E0)))) & p(s(bool,i(s(fun(real,bool),P0),s(real,D0)))) -> p(s(bool,i(s(fun(real,bool),P0),s(real,E0)))))) -> (all E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) -> p(s(bool,i(s(fun(real,bool),P0),s(real,E0)))))))) # label(aFORALLu_POSu_MONOu_1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 629 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,N0))))) # label(aLEu_REFL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 630 (all Q97352 all P0 all F0 all S0 (p(s(bool,i(s(fun(fun(Q97352,bool),bool),P0),s(fun(Q97352,bool),i(s(fun(fun(Q97352,bool),fun(Q97352,bool)),i(s(fun(fun(fun(Q97352,bool),bool),fun(fun(Q97352,bool),fun(Q97352,bool))),hull),s(fun(fun(Q97352,bool),bool),P0))),s(fun(Q97352,bool),S0)))))) & (all S0 (p(s(bool,i(s(fun(fun(Q97352,bool),bool),P0),s(fun(Q97352,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q97352,bool),bool),P0),s(fun(Q97352,bool),i(s(fun(fun(Q97352,bool),fun(Q97352,bool)),i(s(fun(fun(Q97352,Q97352),fun(fun(Q97352,bool),fun(Q97352,bool))),image),s(fun(Q97352,Q97352),F0))),s(fun(Q97352,bool),S0)))))))) -> p(s(bool,i(s(fun(fun(Q97352,bool),bool),i(s(fun(fun(Q97352,bool),fun(fun(Q97352,bool),bool)),subset),s(fun(Q97352,bool),i(s(fun(fun(Q97352,bool),fun(Q97352,bool)),i(s(fun(fun(fun(Q97352,bool),bool),fun(fun(Q97352,bool),fun(Q97352,bool))),hull),s(fun(fun(Q97352,bool),bool),P0))),s(fun(Q97352,bool),i(s(fun(fun(Q97352,bool),fun(Q97352,bool)),i(s(fun(fun(Q97352,Q97352),fun(fun(Q97352,bool),fun(Q97352,bool))),image),s(fun(Q97352,Q97352),F0))),s(fun(Q97352,bool),S0))))))),s(fun(Q97352,bool),i(s(fun(fun(Q97352,bool),fun(Q97352,bool)),i(s(fun(fun(Q97352,Q97352),fun(fun(Q97352,bool),fun(Q97352,bool))),image),s(fun(Q97352,Q97352),F0))),s(fun(Q97352,bool),i(s(fun(fun(Q97352,bool),fun(Q97352,bool)),i(s(fun(fun(fun(Q97352,bool),bool),fun(fun(Q97352,bool),fun(Q97352,bool))),hull),s(fun(fun(Q97352,bool),bool),P0))),s(fun(Q97352,bool),S0)))))))))) # label(aHULLu_IMAGEu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 631 (all X exists N0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))))) # label(aREALu_ARCHu_LT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 632 (all X all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))),s(real,Z0))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Z0))),s(real,Y)))))) # label(aREALu_LTu_SUBu_RADD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 633 (all Q19598 all Q19587 all U_1 ((all X all Y (p(s(bool,i(s(fun(Q19587,bool),i(s(fun(Q19587,fun(Q19587,bool)),U_1),s(Q19587,X))),s(Q19587,Y)))) <-> s(Q19598,i(s(fun(Q19587,Q19598),f),s(Q19587,X))) = s(Q19598,i(s(fun(Q19587,Q19598),f),s(Q19587,Y))))) -> (all U_0 ((all X s(fun(Q19587,bool),i(s(fun(Q19587,fun(Q19587,bool)),U_0),s(Q19587,X))) = s(fun(Q19587,bool),i(s(fun(Q19587,fun(Q19587,bool)),U_1),s(Q19587,X)))) -> (all L all M0 (p(s(bool,i(s(fun(list(Q19587),bool),i(s(fun(list(Q19587),fun(list(Q19587),bool)),i(s(fun(fun(Q19587,fun(Q19587,bool)),fun(list(Q19587),fun(list(Q19587),bool))),all2),s(fun(Q19587,fun(Q19587,bool)),U_0))),s(list(Q19587),L))),s(list(Q19587),M0)))) -> s(list(Q19598),i(s(fun(list(Q19587),list(Q19598)),i(s(fun(fun(Q19587,Q19598),fun(list(Q19587),list(Q19598))),map0),s(fun(Q19587,Q19598),f))),s(list(Q19587),L))) = s(list(Q19598),i(s(fun(list(Q19587),list(Q19598)),i(s(fun(fun(Q19587,Q19598),fun(list(Q19587),list(Q19598))),map0),s(fun(Q19587,Q19598),f))),s(list(Q19587),M0))))))))) # label(aMAPu_EQu_ALL2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 634 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,P0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,P0)))))) # label(aLETu_TRANS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 635 (all X all Y all Z0 (s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X))),s(hreal,Y))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X))),s(hreal,Z0))) -> s(hreal,Z0) = s(hreal,Y))) # label(aHREALu_ADDu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 636 (all Q63859 all Q63849 all Q63858 all F0 all G0 all S0 s(fun(Q63849,bool),i(s(fun(fun(Q63849,bool),fun(Q63849,bool)),i(s(fun(fun(Q63849,Q63859),fun(fun(Q63849,bool),fun(Q63849,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63849,Q63859),fun(fun(Q63849,bool),fun(Q63849,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63849,Q63859),G0))),s(fun(Q63849,bool),i(s(fun(fun(Q63858,bool),fun(Q63849,bool)),i(s(fun(fun(Q63858,Q63849),fun(fun(Q63858,bool),fun(Q63849,bool))),image),s(fun(Q63858,Q63849),F0))),s(fun(Q63858,bool),S0))))) = s(fun(Q63849,bool),i(s(fun(fun(Q63858,bool),fun(Q63849,bool)),i(s(fun(fun(Q63858,Q63849),fun(fun(Q63858,bool),fun(Q63849,bool))),image),s(fun(Q63858,Q63849),F0))),s(fun(Q63858,bool),i(s(fun(fun(Q63858,bool),fun(Q63858,bool)),i(s(fun(fun(Q63858,Q63859),fun(fun(Q63858,bool),fun(Q63858,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63858,Q63859),fun(fun(Q63858,bool),fun(Q63858,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63858,Q63859),i(s(fun(fun(Q63858,Q63849),fun(Q63858,Q63859)),i(s(fun(fun(Q63849,Q63859),fun(fun(Q63858,Q63849),fun(Q63858,Q63859))),o),s(fun(Q63849,Q63859),G0))),s(fun(Q63858,Q63849),F0))))),s(fun(Q63858,bool),S0)))))) # label(aSUPPORTu_CLAUSESu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 637 (all X all Y (s(num,i(s(fun(num,num),numright),s(num,i(s(fun(num,num),i(s(fun(bool,fun(num,num)),numsum),s(bool,X))),s(num,Y))))) = s(num,Y) & s(bool,X) = s(bool,i(s(fun(num,bool),numleft),s(num,i(s(fun(num,num),i(s(fun(bool,fun(num,num)),numsum),s(bool,X))),s(num,Y))))))) # label(aNUMSUMu_DEST) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 638 (all A all C0 all I0 all R0 ((all N0 p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),zrecspace),s(fun(num,fun(A,bool)),i(s(fun(num,fun(num,fun(A,bool))),R0),s(num,N0))))))) -> p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),zrecspace),s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))),i(s(fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool)))),i(s(fun(num,fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))))),zconstr),s(num,C0))),s(A,I0))),s(fun(num,fun(num,fun(A,bool))),R0)))))))) # label(aZRECSPACEu_RULESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 639 (all M0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))) # label(aEXPu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 640 (all X all Y -(p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))))) # label(aREALu_LTu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.96 641 (all M0 all N0 all P0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0))))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))) # label(aMODu_MOD) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 642 (all X all Y all Z0 p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,Y))),s(nadd,Z0))))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Y))))),s(nadd,Z0))))))) # label(aNADDu_MULu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 643 (all Q47193 all P0 all S0 ((all T0 all X (p(s(bool,i(s(fun(fun(Q47193,bool),bool),i(s(fun(Q47193,fun(fun(Q47193,bool),bool)),in),s(Q47193,X))),s(fun(Q47193,bool),T0)))) & p(s(bool,i(s(fun(fun(fun(Q47193,bool),bool),bool),i(s(fun(fun(Q47193,bool),fun(fun(fun(Q47193,bool),bool),bool)),in),s(fun(Q47193,bool),T0))),s(fun(fun(Q47193,bool),bool),S0)))) -> p(s(bool,i(s(fun(Q47193,bool),P0),s(Q47193,X)))))) <-> (all X (p(s(bool,i(s(fun(fun(Q47193,bool),bool),i(s(fun(Q47193,fun(fun(Q47193,bool),bool)),in),s(Q47193,X))),s(fun(Q47193,bool),i(s(fun(fun(fun(Q47193,bool),bool),fun(Q47193,bool)),unions),s(fun(fun(Q47193,bool),bool),S0)))))) -> p(s(bool,i(s(fun(Q47193,bool),P0),s(Q47193,X)))))))) # label(aFORALLu_INu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 644 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,M0))))),s(num,i(s(fun(num,num),numeral),s(num,N0)))))) # label(aARITHu_LEu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 645 (all A all S0 all T0 all U (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),U)))))) # label(aSUBSETu_TRANS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 646 (all A all OP ((all X all Y s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),OP),s(A,Y))),s(A,X))) = s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),OP),s(A,X))),s(A,Y)))) & (all X s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),OP),s(A,i(s(fun(fun(A,fun(A,A)),A),neutral),s(fun(A,fun(A,A)),OP))))),s(A,X))) = s(A,X)) & (all X all Y all Z0 s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),OP),s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),OP),s(A,X))),s(A,Y))))),s(A,Z0))) = s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),OP),s(A,X))),s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),OP),s(A,Y))),s(A,Z0)))))) <-> p(s(bool,i(s(fun(fun(A,fun(A,A)),bool),monoidal),s(fun(A,fun(A,A)),OP)))))) # label(amonoidal) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 647 (all Q18568 s(list(Q18568),i(s(fun(Q18568,list(Q18568)),i(s(fun(num,fun(Q18568,list(Q18568))),replicate),s(num,i(s(fun(num,num),suc),s(num,n))))),s(Q18568,x))) = s(list(Q18568),i(s(fun(list(Q18568),list(Q18568)),i(s(fun(Q18568,fun(list(Q18568),list(Q18568))),cons),s(Q18568,x))),s(list(Q18568),i(s(fun(Q18568,list(Q18568)),i(s(fun(num,fun(Q18568,list(Q18568))),replicate),s(num,n))),s(Q18568,x)))))) # label(aREPLICATEu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 648 (all A all S0 all T0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))))) # label(aSUBSETu_UNIONu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 649 (all A all X all Y all S0 exists V (s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),i(s(fun(bool,fun(fun(A,bool),fun(fun(A,bool),fun(A,bool)))),cond),s(bool,V))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,Y))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,Y))))))) = s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))),s(A,Y))) & (s(A,Y) = s(A,X) <-> p(s(bool,V))))) # label(aDELETEu_INSERT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 650 (all Q46115 all S0 all T0 p(s(bool,i(s(fun(fun(Q46115,bool),bool),i(s(fun(fun(Q46115,bool),fun(fun(Q46115,bool),bool)),subset),s(fun(Q46115,bool),i(s(fun(fun(Q46115,bool),fun(Q46115,bool)),i(s(fun(fun(Q46115,bool),fun(fun(Q46115,bool),fun(Q46115,bool))),diff),s(fun(Q46115,bool),S0))),s(fun(Q46115,bool),T0))))),s(fun(Q46115,bool),S0))))) # label(aSUBSETu_DIFF) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 651 (all M0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) <-> s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aLEu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 652 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,i(s(fun(real,real),realu_abs),s(real,Y)))))) # label(aREALu_LEu_SQUAREu_ABS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 653 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y)))))))) # label(aREALu_LEu_MUL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 654 (all A all N1 all N2 (s(fun(num,fun(A,bool)),i(s(fun(num,fun(num,fun(A,bool))),injn),s(num,N1))) = s(fun(num,fun(A,bool)),i(s(fun(num,fun(num,fun(A,bool))),injn),s(num,N2))) <-> s(num,N2) = s(num,N1))) # label(aINJNu_INJ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 655 (all S0 all A5 (s(fun(real,bool),empty) != s(fun(real,bool),S0) & p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) -> (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0)))))) <-> (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X))))))))) # label(aREALu_LEu_INFu_FINITE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 656 (all A all S0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),S0))))))) # label(aDIMINDEXu_GEu_1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 657 (all Q96968 all P0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q96968,bool),bool),P0),s(fun(Q96968,bool),T0)))) -> s(bool,i(s(fun(fun(Q96968,bool),bool),i(s(fun(fun(Q96968,bool),fun(fun(Q96968,bool),bool)),subset),s(fun(Q96968,bool),S0))),s(fun(Q96968,bool),T0))) = s(bool,i(s(fun(fun(Q96968,bool),bool),i(s(fun(fun(Q96968,bool),fun(fun(Q96968,bool),bool)),subset),s(fun(Q96968,bool),i(s(fun(fun(Q96968,bool),fun(Q96968,bool)),i(s(fun(fun(fun(Q96968,bool),bool),fun(fun(Q96968,bool),fun(Q96968,bool))),hull),s(fun(fun(Q96968,bool),bool),P0))),s(fun(Q96968,bool),S0))))),s(fun(Q96968,bool),T0))))) # label(aSUBSETu_HULL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 658 (all N0 p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(num,N0))))))) # label(aINTu_LEu_POW2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 659 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),realu_neg),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aREALu_LTu_RNEG) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 660 (all A all M all N all U_0 ((all F0 all I0 s(A,i(s(fun(num,A),i(s(fun(cart(A,finite_sum(M,N)),fun(num,A)),U_0),s(cart(A,finite_sum(M,N)),F0))),s(num,I0))) = s(A,i(s(fun(num,A),i(s(fun(cart(A,finite_sum(M,N)),fun(num,A)),d_),s(cart(A,finite_sum(M,N)),F0))),s(num,I0)))) -> (all F0 s(cart(A,M),i(s(fun(fun(num,A),cart(A,M)),lambda),s(fun(num,A),i(s(fun(cart(A,finite_sum(M,N)),fun(num,A)),U_0),s(cart(A,finite_sum(M,N)),F0))))) = s(cart(A,M),i(s(fun(cart(A,finite_sum(M,N)),cart(A,M)),fstcart),s(cart(A,finite_sum(M,N)),F0)))))) # label(afstcart) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 661 (all U_0 ((all N0 all GENR_PVARR_107 ((exists M0 p(s(bool,i(s(fun(num,bool),i(s(fun(bool,fun(num,bool)),i(s(fun(num,fun(bool,fun(num,bool))),setspec),s(num,GENR_PVARR_107))),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0))))),s(num,M0))))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))),s(num,GENR_PVARR_107)))))) -> (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),hasu_size),s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),gspec),s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))))))),s(num,N0))))))) # label(aHASu_SIZEu_NUMSEGu_LT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 662 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))))) # label(aINTu_LTu_IMPu_LE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 663 (all Q47530 s(fun(Q47530,bool),i(s(fun(fun(fun(Q47530,bool),bool),fun(Q47530,bool)),inters),s(fun(fun(Q47530,bool),bool),i(s(fun(fun(fun(Q47530,bool),bool),fun(fun(Q47530,bool),bool)),i(s(fun(fun(Q47530,bool),fun(fun(fun(Q47530,bool),bool),fun(fun(Q47530,bool),bool))),insert),s(fun(Q47530,bool),s0))),s(fun(fun(Q47530,bool),bool),i(s(fun(fun(fun(Q47530,bool),bool),fun(fun(Q47530,bool),bool)),i(s(fun(fun(Q47530,bool),fun(fun(fun(Q47530,bool),bool),fun(fun(Q47530,bool),bool))),insert),s(fun(Q47530,bool),t0))),s(fun(fun(Q47530,bool),bool),empty))))))) = s(fun(Q47530,bool),i(s(fun(fun(Q47530,bool),fun(Q47530,bool)),i(s(fun(fun(Q47530,bool),fun(fun(Q47530,bool),fun(Q47530,bool))),inter),s(fun(Q47530,bool),s0))),s(fun(Q47530,bool),t0)))) # label(aINTERSu_2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 664 (all A all A5 all F0 s(A,A5) = s(A,i(s(fun(num,A),i(s(fun(fun(num,A),fun(num,A)),i(s(fun(A,fun(fun(num,A),fun(num,A))),fcons),s(A,A5))),s(fun(num,A),F0))),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aFCONSu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 665 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Z0)))) -> s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Z0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Y))),s(int,Z0))))))) # label(aINTu_LTu_RMULu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 666 (all A all U_0 ((all S0 all GENR_PVARR_239 ((exists L exists V (p(s(bool,i(s(fun(list(A),bool),i(s(fun(bool,fun(list(A),bool)),i(s(fun(list(A),fun(bool,fun(list(A),bool))),setspec),s(list(A),GENR_PVARR_239))),s(bool,V))),s(list(A),L)))) & (p(s(bool,V)) <-> (all X (p(s(bool,i(s(fun(list(A),bool),i(s(fun(A,fun(list(A),bool)),mem),s(A,X))),s(list(A),L)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))))))) <-> p(s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,bool),fun(list(A),bool)),U_0),s(fun(A,bool),S0))),s(list(A),GENR_PVARR_239)))))) -> (all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(list(A),bool),fun(fun(A,bool),bool)),a_u_c),s(fun(list(A),bool),i(s(fun(fun(list(A),bool),fun(list(A),bool)),gspec),s(fun(list(A),bool),i(s(fun(fun(A,bool),fun(list(A),bool)),U_0),s(fun(A,bool),S0))))))),s(fun(A,bool),S0)))))))) # label(aCARDu_EQu_LISTu_GEN) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 667 (all Z all A all NILI_ all CONSI_ exists FN ((all A01 all A10 s(Z,i(s(fun(list(A),Z),FN),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,A01))),s(list(A),A10))))) = s(Z,i(s(fun(Z,Z),i(s(fun(list(A),fun(Z,Z)),i(s(fun(A,fun(list(A),fun(Z,Z))),CONSI_),s(A,A01))),s(list(A),A10))),s(Z,i(s(fun(list(A),Z),FN),s(list(A),A10)))))) & s(Z,i(s(fun(list(A),Z),FN),s(list(A),nil))) = s(Z,NILI_))) # label(alistu_RECURSION) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 668 (all A all B all U_0 ((all S0 all T0 all GENR_PVARR_86 ((exists X exists Y exists V (p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(bool,fun(prod(A,B),bool)),i(s(fun(prod(A,B),fun(bool,fun(prod(A,B),bool))),setspec),s(prod(A,B),GENR_PVARR_86))),s(bool,V))),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))) & (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),U_0),s(fun(A,bool),S0))),s(fun(B,bool),T0))),s(prod(A,B),GENR_PVARR_86)))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))))) = s(num,i(s(fun(fun(prod(A,B),bool),num),card),s(fun(prod(A,B),bool),i(s(fun(fun(prod(A,B),bool),fun(prod(A,B),bool)),gspec),s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),U_0),s(fun(A,bool),S0))),s(fun(B,bool),T0))))))))))) # label(aCARDu_PRODUCT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 669 (all B all A all F0 all S0 ((all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,X) = s(A,Y))) -> s(bool,i(s(fun(fun(B,bool),bool),countable),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))) = s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0))))) # label(aCOUNTABLEu_IMAGEu_INJu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 670 (all Q49024 all Q49010 all U_1 ((all P0 all F0 all GENR_PVARR_30 ((exists A5 exists V (((exists X (p(s(bool,i(s(fun(fun(Q49010,bool),bool),i(s(fun(Q49010,fun(fun(Q49010,bool),bool)),in),s(Q49010,A5))),s(fun(Q49010,bool),i(s(fun(Q49024,fun(Q49010,bool)),F0),s(Q49024,X)))))) & p(s(bool,i(s(fun(Q49024,bool),P0),s(Q49024,X)))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(Q49010,bool),i(s(fun(bool,fun(Q49010,bool)),i(s(fun(Q49010,fun(bool,fun(Q49010,bool))),setspec),s(Q49010,GENR_PVARR_30))),s(bool,V))),s(Q49010,A5)))))) <-> p(s(bool,i(s(fun(Q49010,bool),i(s(fun(fun(Q49024,fun(Q49010,bool)),fun(Q49010,bool)),i(s(fun(fun(Q49024,bool),fun(fun(Q49024,fun(Q49010,bool)),fun(Q49010,bool))),U_1),s(fun(Q49024,bool),P0))),s(fun(Q49024,fun(Q49010,bool)),F0))),s(Q49010,GENR_PVARR_30)))))) -> (all U_0 ((all P0 all F0 all GENR_PVARR_29 (p(s(bool,i(s(fun(fun(Q49010,bool),bool),i(s(fun(fun(Q49024,fun(Q49010,bool)),fun(fun(Q49010,bool),bool)),i(s(fun(fun(Q49024,bool),fun(fun(Q49024,fun(Q49010,bool)),fun(fun(Q49010,bool),bool))),U_0),s(fun(Q49024,bool),P0))),s(fun(Q49024,fun(Q49010,bool)),F0))),s(fun(Q49010,bool),GENR_PVARR_29)))) <-> (exists X p(s(bool,i(s(fun(fun(Q49010,bool),bool),i(s(fun(bool,fun(fun(Q49010,bool),bool)),i(s(fun(fun(Q49010,bool),fun(bool,fun(fun(Q49010,bool),bool))),setspec),s(fun(Q49010,bool),GENR_PVARR_29))),s(bool,i(s(fun(Q49024,bool),P0),s(Q49024,X))))),s(fun(Q49010,bool),i(s(fun(Q49024,fun(Q49010,bool)),F0),s(Q49024,X))))))))) -> (all P0 all F0 s(fun(Q49010,bool),i(s(fun(fun(Q49010,bool),fun(Q49010,bool)),gspec),s(fun(Q49010,bool),i(s(fun(fun(Q49024,fun(Q49010,bool)),fun(Q49010,bool)),i(s(fun(fun(Q49024,bool),fun(fun(Q49024,fun(Q49010,bool)),fun(Q49010,bool))),U_1),s(fun(Q49024,bool),P0))),s(fun(Q49024,fun(Q49010,bool)),F0))))) = s(fun(Q49010,bool),i(s(fun(fun(fun(Q49010,bool),bool),fun(Q49010,bool)),unions),s(fun(fun(Q49010,bool),bool),i(s(fun(fun(fun(Q49010,bool),bool),fun(fun(Q49010,bool),bool)),gspec),s(fun(fun(Q49010,bool),bool),i(s(fun(fun(Q49024,fun(Q49010,bool)),fun(fun(Q49010,bool),bool)),i(s(fun(fun(Q49024,bool),fun(fun(Q49024,fun(Q49010,bool)),fun(fun(Q49010,bool),bool))),U_0),s(fun(Q49024,bool),P0))),s(fun(Q49024,fun(Q49010,bool)),F0)))))))))))) # label(aUNIONSu_GSPECu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 671 (all A all X all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,i(s(fun(num,num),suc),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))))) # label(aCARDu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 672 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> (s(real,Y) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Z0))) <-> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0))) = s(real,X)))) # label(aREALu_EQu_LDIVu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 673 (all M0 all N0 all Q1 all R1 all Q2 all R2 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,R2))),s(num,N0)))) & s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,Q2))),s(num,N0))))),s(num,R2))) = s(num,M0) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,R1))),s(num,N0)))) & s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,Q1))),s(num,N0))))),s(num,R1))) = s(num,M0) -> s(num,Q2) = s(num,Q1) & s(num,R2) = s(num,R1))) # label(aDIVMODu_UNIQu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 674 (all Q17931 all Q17928 (p(s(bool,i(s(fun(fun(Q17928,Q17931),bool),i(s(fun(fun(Q17931,Q17928),fun(fun(Q17928,Q17931),bool)),iso0),s(fun(Q17931,Q17928),f))),s(fun(Q17928,Q17931),g)))) -> (all P0 ((all X p(s(bool,i(s(fun(Q17931,bool),P0),s(Q17931,X))))) <-> (all X p(s(bool,i(s(fun(Q17931,bool),P0),s(Q17931,i(s(fun(Q17928,Q17931),g),s(Q17928,X))))))))) & (all P0 ((exists X p(s(bool,i(s(fun(Q17931,bool),P0),s(Q17931,X))))) <-> (exists X p(s(bool,i(s(fun(Q17931,bool),P0),s(Q17931,i(s(fun(Q17928,Q17931),g),s(Q17928,X))))))))) & (all A5 all B0 (s(Q17931,A5) = s(Q17931,i(s(fun(Q17928,Q17931),g),s(Q17928,B0))) <-> s(Q17928,B0) = s(Q17928,i(s(fun(Q17931,Q17928),f),s(Q17931,A5))))))) # label(aISOu_USAGE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 675 (all A s(fun(A,bool),univ) = s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),inters),s(fun(fun(A,bool),bool),empty)))) # label(aINTERSu_0) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 676 (all W all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,W))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,W))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0)))))))) # label(aREALu_LTEu_ADD2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 677 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,X)))) | s(real,X) = s(real,Y))) # label(aREALu_LTu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 678 (all A all P0 ((all X -p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) <-> -(exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) # label(aFORALLu_NOTu_THM) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 679 (all X s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),realu_sgn),s(real,X))))) = s(real,i(s(fun(real,real),realu_sgn),s(real,i(s(fun(real,real),realu_abs),s(real,X)))))) # label(aREALu_ABSu_SGN) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 680 (all A all B all U_0 ((all F0 all A5 all GENR_PVARR_64 ((exists X p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_64))),s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),A5))))),s(A,X))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),U_0),s(fun(A,B),F0))),s(fun(B,bool),A5))),s(A,GENR_PVARR_64)))))) -> (all F0 all A5 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),A5)))) & (all X all Y (s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) -> s(A,Y) = s(A,X))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),U_0),s(fun(A,B),F0))),s(fun(B,bool),A5)))))))))))) # label(aFINITEu_IMAGEu_INJ) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 681 (all X all K0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,K0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_neg),s(real,K0))))),s(real,X)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,K0)))))) # label(aREALu_BOUNDSu_LT) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 682 (all X exists B0 all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,M0))))),s(num,B0))))))) # label(aNADDu_MULTIPLICATIVE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 683 (all X s(int,i(s(fun(int,int),intu_abs),s(int,X))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),i(s(fun(bool,fun(int,fun(int,int))),cond),s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X))))),s(int,X))),s(int,i(s(fun(int,int),intu_neg),s(int,X)))))) # label(aINTu_ABS) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 684 (all A all X all S0 (s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))) = s(fun(A,bool),S0) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))) # label(aABSORPTION) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 685 (all M0 all N0 all P0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,P0))),s(num,N0))))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))),s(num,N0))))) # label(aMODu_MULTu_MOD2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 686 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) & s(real,X) != s(real,Y) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))))) # label(aREALu_LTu_LE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 687 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0)))))))) # label(aREALu_LTu_LMUL) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 688 (all A all P0 ((exists X ((all Y (p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))) -> s(A,Y) = s(A,X))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X)))))) <-> (all X all XI_ (p(s(bool,i(s(fun(A,bool),P0),s(A,XI_)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> s(A,X) = s(A,XI_))) & (exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) # label(aEXISTSu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 689 (all M0 all N0 all P0 all Q0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,P0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,Q0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,P0))),s(num,Q0)))))))) # label(aLTu_ADD2) # label(axiom) # label(non_clause). [assumption]. 13.89/13.97 690 (all A5 all B0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(prod(int,int),int),intu_gcd),s(prod(int,int),i(s(fun(int,prod(int,int)),i(s(fun(int,fun(int,prod(int,int))),c_),s(int,A5))),s(int,B0)))))))) & (exists X exists Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,A5))),s(int,X))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,B0))),s(int,Y))))) = s(int,i(s(fun(prod(int,int),int),intu_gcd),s(prod(int,int),i(s(fun(int,prod(int,int)),i(s(fun(int,fun(int,prod(int,int))),c_),s(int,A5))),s(int,B0)))))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_divides),s(int,i(s(fun(prod(int,int),int),intu_gcd),s(prod(int,int),i(s(fun(int,prod(int,int)),i(s(fun(int,fun(int,prod(int,int))),c_),s(int,A5))),s(int,B0))))))),s(int,B0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_divides),s(int,i(s(fun(prod(int,int),int),intu_gcd),s(prod(int,int),i(s(fun(int,prod(int,int)),i(s(fun(int,fun(int,prod(int,int))),c_),s(int,A5))),s(int,B0))))))),s(int,A5)))))) # label(aintu_gcd) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 691 (all X all Y (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))) -> s(real,X) = s(real,i(s(fun(real,real),realu_inv),s(real,Y))))) # label(aREALu_MULu_LINVu_UNIQ) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 692 (all B all D all P all Q all A all U_3 ((all PAT all U all F0 all ARG all X all V (p(s(bool,i(s(fun(B,bool),i(s(fun(P,fun(B,bool)),i(s(fun(fun(P,fun(Q,A)),fun(P,fun(B,bool))),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool)))),i(s(fun(D,fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool))))),i(s(fun(fun(Q,D),fun(D,fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool)))))),U_3),s(fun(Q,D),PAT))),s(D,U))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG))),s(P,X))),s(B,V)))) <-> (exists T0 p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),u_unguardedu_pattern),s(bool,i(s(fun(D,bool),i(s(fun(D,fun(D,bool)),geq),s(D,i(s(fun(Q,D),PAT),s(Q,T0))))),s(D,U))))),s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),geq),s(B,i(s(fun(A,B),F0),s(A,i(s(fun(Q,A),i(s(fun(P,fun(Q,A)),ARG),s(P,X))),s(Q,T0))))))),s(B,V))))))))) -> (all U_2 ((all PAT all F0 all ARG all X all U s(fun(B,bool),i(s(fun(D,fun(B,bool)),i(s(fun(P,fun(D,fun(B,bool))),i(s(fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool)))),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool))))),i(s(fun(fun(Q,D),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool)))))),U_2),s(fun(Q,D),PAT))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG))),s(P,X))),s(D,U))) = s(fun(B,bool),i(s(fun(P,fun(B,bool)),i(s(fun(fun(P,fun(Q,A)),fun(P,fun(B,bool))),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool)))),i(s(fun(D,fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool))))),i(s(fun(fun(Q,D),fun(D,fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(B,bool)))))),U_3),s(fun(Q,D),PAT))),s(D,U))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG))),s(P,X)))) -> (all U_1 ((all E0 all PAT all F0 all ARG all X s(B,i(s(fun(fun(D,fun(B,bool)),B),i(s(fun(D,fun(fun(D,fun(B,bool)),B)),u_match),s(D,i(s(fun(P,D),E0),s(P,X))))),s(fun(D,fun(B,bool)),i(s(fun(P,fun(D,fun(B,bool))),i(s(fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool)))),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool))))),i(s(fun(fun(Q,D),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,fun(D,fun(B,bool)))))),U_2),s(fun(Q,D),PAT))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG))),s(P,X))))) = s(B,i(s(fun(P,B),i(s(fun(fun(P,fun(Q,A)),fun(P,B)),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B))),i(s(fun(fun(Q,D),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B)))),i(s(fun(fun(P,D),fun(fun(Q,D),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B))))),U_1),s(fun(P,D),E0))),s(fun(Q,D),PAT))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG))),s(P,X)))) -> (all U_0 ((all E0 all PAT all ARG all F0 s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B))),i(s(fun(fun(Q,D),fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(P,D),fun(fun(Q,D),fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B))))),U_0),s(fun(P,D),E0))),s(fun(Q,D),PAT))),s(fun(P,fun(Q,A)),ARG))),s(fun(A,B),F0))) = s(fun(P,B),i(s(fun(fun(P,fun(Q,A)),fun(P,B)),i(s(fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B))),i(s(fun(fun(Q,D),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B)))),i(s(fun(fun(P,D),fun(fun(Q,D),fun(fun(A,B),fun(fun(P,fun(Q,A)),fun(P,B))))),U_1),s(fun(P,D),E0))),s(fun(Q,D),PAT))),s(fun(A,B),F0))),s(fun(P,fun(Q,A)),ARG)))) -> (all L_L_ all P0 all S0 all E0 all PAT all ARG ((all F0 all A5 all T0 all U (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,A5)))) & s(D,i(s(fun(Q,D),PAT),s(Q,T0))) = s(D,i(s(fun(P,D),E0),s(P,A5))) & s(D,i(s(fun(P,D),E0),s(P,A5))) = s(D,i(s(fun(Q,D),PAT),s(Q,U))) -> s(A,i(s(fun(Q,A),i(s(fun(P,fun(Q,A)),ARG),s(P,A5))),s(Q,U))) = s(A,i(s(fun(Q,A),i(s(fun(P,fun(Q,A)),ARG),s(P,A5))),s(Q,T0))))) & (all F0 all A5 all T0 (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,A5)))) & s(D,i(s(fun(Q,D),PAT),s(Q,T0))) = s(D,i(s(fun(P,D),E0),s(P,A5))) -> (all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,i(s(fun(Q,A),i(s(fun(P,fun(Q,A)),ARG),s(P,A5))),s(Q,T0)))))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,i(s(fun(P,A),S0),s(P,A5)))))))))) -> p(s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),superadmissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B))),i(s(fun(fun(Q,D),fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(P,D),fun(fun(Q,D),fun(fun(P,fun(Q,A)),fun(fun(A,B),fun(P,B))))),U_0),s(fun(P,D),E0))),s(fun(Q,D),PAT))),s(fun(P,fun(Q,A)),ARG)))))))))))))))) # label(aSUPERADMISSIBLEu_MATCHu_UNGUARDEDu_PATTERN) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 693 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,i(s(fun(int,int),intu_neg),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aINTu_LEu_RNEG) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 694 (all A all F0 all X s(fun(A,bool),i(s(fun(num,fun(A,bool)),i(s(fun(num,fun(num,fun(A,bool))),F0),s(num,i(s(fun(num,num),numfst),s(num,X))))),s(num,i(s(fun(num,num),numsnd),s(num,X))))) = s(fun(A,bool),i(s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))),injf),s(fun(num,fun(num,fun(A,bool))),F0))),s(num,X)))) # label(aINJF) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 695 (all Q47663 all S0 s(fun(Q47663,bool),i(s(fun(fun(Q47663,bool),fun(Q47663,bool)),i(s(fun(fun(Q47663,Q47663),fun(fun(Q47663,bool),fun(Q47663,bool))),image),s(fun(Q47663,Q47663),i1))),s(fun(Q47663,bool),S0))) = s(fun(Q47663,bool),S0)) # label(aIMAGEu_I) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 696 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all X all Y all Z0 (p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,Z0)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) -> p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Z0)))))))))) # label(aWOSETu_TRANSu_LE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 697 (all X exists N0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))))) # label(aREALu_ARCHu_SIMPLE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 698 (all Q44161 all U_2 ((all P0 all X all T0 (p(s(bool,i(s(fun(Q44161,bool),i(s(fun(Q44161,fun(Q44161,bool)),i(s(fun(bool,fun(Q44161,fun(Q44161,bool))),U_2),s(bool,P0))),s(Q44161,X))),s(Q44161,T0)))) <-> p(s(bool,P0)) & s(Q44161,X) = s(Q44161,T0))) -> (all U_1 ((all X all P0 s(fun(Q44161,bool),i(s(fun(bool,fun(Q44161,bool)),i(s(fun(Q44161,fun(bool,fun(Q44161,bool))),U_1),s(Q44161,X))),s(bool,P0))) = s(fun(Q44161,bool),i(s(fun(Q44161,fun(Q44161,bool)),i(s(fun(bool,fun(Q44161,fun(Q44161,bool))),U_2),s(bool,P0))),s(Q44161,X)))) -> (all U_0 ((all P0 all V s(bool,i(s(fun(Q44161,bool),i(s(fun(fun(fun(bool,fun(Q44161,bool)),bool),fun(Q44161,bool)),U_0),s(fun(fun(bool,fun(Q44161,bool)),bool),P0))),s(Q44161,V))) = s(bool,i(s(fun(fun(bool,fun(Q44161,bool)),bool),P0),s(fun(bool,fun(Q44161,bool)),i(s(fun(Q44161,fun(bool,fun(Q44161,bool))),setspec),s(Q44161,V)))))) -> (all P0 all X s(bool,i(s(fun(Q44161,bool),i(s(fun(fun(Q44161,bool),fun(Q44161,bool)),gspec),s(fun(Q44161,bool),i(s(fun(fun(fun(bool,fun(Q44161,bool)),bool),fun(Q44161,bool)),U_0),s(fun(fun(bool,fun(Q44161,bool)),bool),P0))))),s(Q44161,X))) = s(bool,i(s(fun(fun(bool,fun(Q44161,bool)),bool),P0),s(fun(bool,fun(Q44161,bool)),i(s(fun(Q44161,fun(bool,fun(Q44161,bool))),U_1),s(Q44161,X)))))))))))) # label(aINu_ELIMu_THMu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 699 (all Q47725 all Q47714 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q47714,bool),bool),i(s(fun(fun(Q47714,bool),fun(fun(Q47714,bool),bool)),subset),s(fun(Q47714,bool),S0))),s(fun(Q47714,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q47725,bool),bool),i(s(fun(fun(Q47725,bool),fun(fun(Q47725,bool),bool)),subset),s(fun(Q47725,bool),i(s(fun(fun(Q47714,bool),fun(Q47725,bool)),i(s(fun(fun(Q47714,Q47725),fun(fun(Q47714,bool),fun(Q47725,bool))),image),s(fun(Q47714,Q47725),F0))),s(fun(Q47714,bool),S0))))),s(fun(Q47725,bool),i(s(fun(fun(Q47714,bool),fun(Q47725,bool)),i(s(fun(fun(Q47714,Q47725),fun(fun(Q47714,bool),fun(Q47725,bool))),image),s(fun(Q47714,Q47725),F0))),s(fun(Q47714,bool),T0)))))))) # label(aIMAGEu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 700 (all Q81350 all Q81351 all Q81352 all U_0 ((all C0 all F0 s(fun(Q81351,Q81352),i(s(fun(fun(Q81350,Q81352),fun(Q81351,Q81352)),i(s(fun(fun(Q81351,Q81352),fun(fun(Q81350,Q81352),fun(Q81351,Q81352))),U_0),s(fun(Q81351,Q81352),C0))),s(fun(Q81350,Q81352),F0))) = s(fun(Q81351,Q81352),C0)) -> (all P0 all S0 all C0 p(s(bool,i(s(fun(fun(fun(Q81350,Q81352),fun(Q81351,Q81352)),bool),i(s(fun(fun(Q81351,Q81350),fun(fun(fun(Q81350,Q81352),fun(Q81351,Q81352)),bool)),i(s(fun(fun(fun(Q81350,Q81352),fun(Q81351,bool)),fun(fun(Q81351,Q81350),fun(fun(fun(Q81350,Q81352),fun(Q81351,Q81352)),bool))),i(s(fun(fun(Q81350,fun(Q81350,bool)),fun(fun(fun(Q81350,Q81352),fun(Q81351,bool)),fun(fun(Q81351,Q81350),fun(fun(fun(Q81350,Q81352),fun(Q81351,Q81352)),bool)))),superadmissible),s(fun(Q81350,fun(Q81350,bool)),l_l_))),s(fun(fun(Q81350,Q81352),fun(Q81351,bool)),P0))),s(fun(Q81351,Q81350),S0))),s(fun(fun(Q81350,Q81352),fun(Q81351,Q81352)),i(s(fun(fun(Q81351,Q81352),fun(fun(Q81350,Q81352),fun(Q81351,Q81352))),U_0),s(fun(Q81351,Q81352),C0))))))))) # label(aSUPERADMISSIBLEu_CONST) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 701 (all X all Y (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) <-> s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & s(real,Y) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aREALu_SOSu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 702 (all A all S0 all T0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),T0))),s(fun(A,bool),S0)))) # label(aINTERu_COMM) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 703 (all A all B all U_1 ((all X all M0 all XI_ s(bool,i(s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),i(s(fun(A,fun(fun(A,B),fun(A,bool))),U_1),s(A,X))),s(fun(A,B),M0))),s(A,XI_))) = s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),l_l_),s(B,i(s(fun(A,B),M0),s(A,X))))),s(B,i(s(fun(A,B),M0),s(A,XI_)))))) -> (all U_0 ((all M0 all X s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),i(s(fun(A,fun(fun(A,B),fun(A,bool))),U_1),s(A,X))),s(fun(A,B),M0))) = s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,B),fun(A,fun(A,bool))),U_0),s(fun(A,B),M0))),s(A,X)))) -> (all M0 (p(s(bool,i(s(fun(fun(B,fun(B,bool)),bool),wf),s(fun(B,fun(B,bool)),l_l_)))) -> p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),i(s(fun(fun(A,B),fun(A,fun(A,bool))),U_0),s(fun(A,B),M0)))))))))))) # label(aWFu_MEASUREu_GEN) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 704 (all A all N ((exists X all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),p0),s(num,I0))),s(A,i(s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),d_),s(cart(A,N),X))),s(num,I0)))))))) <-> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> (exists X p(s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),p0),s(num,I0))),s(A,X))))))))) # label(aLAMBDAu_SKOLEM) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 705 (all N0 s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aARITHu_SUCu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 706 (all Q51804 all Q51784 all P0 all F0 all S0 ((all T0 (p(s(bool,i(s(fun(fun(Q51804,bool),bool),i(s(fun(fun(Q51804,bool),fun(fun(Q51804,bool),bool)),subset),s(fun(Q51804,bool),T0))),s(fun(Q51804,bool),i(s(fun(fun(Q51784,bool),fun(Q51804,bool)),i(s(fun(fun(Q51784,Q51804),fun(fun(Q51784,bool),fun(Q51804,bool))),image),s(fun(Q51784,Q51804),F0))),s(fun(Q51784,bool),S0)))))) & p(s(bool,i(s(fun(fun(Q51804,bool),bool),finite),s(fun(Q51804,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q51804,bool),bool),P0),s(fun(Q51804,bool),T0)))))) <-> (all T0 (p(s(bool,i(s(fun(fun(Q51784,bool),bool),i(s(fun(fun(Q51784,bool),fun(fun(Q51784,bool),bool)),subset),s(fun(Q51784,bool),T0))),s(fun(Q51784,bool),S0)))) & p(s(bool,i(s(fun(fun(Q51784,bool),bool),finite),s(fun(Q51784,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q51804,bool),bool),P0),s(fun(Q51804,bool),i(s(fun(fun(Q51784,bool),fun(Q51804,bool)),i(s(fun(fun(Q51784,Q51804),fun(fun(Q51784,bool),fun(Q51804,bool))),image),s(fun(Q51784,Q51804),F0))),s(fun(Q51784,bool),T0)))))))))) # label(aFORALLu_FINITEu_SUBSETu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 707 (all Q73784 all U_0 ((all F0 all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(Q73784,num),F0),s(Q73784,X))))) = s(real,i(s(fun(Q73784,real),i(s(fun(fun(Q73784,num),fun(Q73784,real)),U_0),s(fun(Q73784,num),F0))),s(Q73784,X)))) -> (all F0 all S0 (p(s(bool,i(s(fun(fun(Q73784,bool),bool),finite),s(fun(Q73784,bool),S0)))) -> s(real,i(s(fun(fun(Q73784,real),real),i(s(fun(fun(Q73784,bool),fun(fun(Q73784,real),real)),sum),s(fun(Q73784,bool),S0))),s(fun(Q73784,real),i(s(fun(fun(Q73784,num),fun(Q73784,real)),U_0),s(fun(Q73784,num),F0))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(Q73784,num),num),i(s(fun(fun(Q73784,bool),fun(fun(Q73784,num),num)),nsum),s(fun(Q73784,bool),S0))),s(fun(Q73784,num),F0))))))))) # label(aREALu_OFu_NUMu_SUM) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 708 (all A all S0 s(fun(A,bool),S0) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),univ))),s(fun(A,bool),S0)))) # label(aINTERu_UNIVu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 709 (all N0 s(num,i(s(fun(fun(num,bool),num),card),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0))))) = s(num,N0)) # label(aCARDu_NUMSEGu_1) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 710 (all A all S0 all T0 ((all X s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0))) = s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> s(fun(A,bool),S0) = s(fun(A,bool),T0))) # label(aEXTENSION) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 711 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,Y)))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,Y)))))))) # label(aREALu_MAXu_MAX) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 712 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aEXPu_2) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 713 (all A all B all U_0 ((all T0 all S0 all D0 all GENR_PVARR_92 (p(s(bool,i(s(fun(fun(A,B),bool),i(s(fun(B,fun(fun(A,B),bool)),i(s(fun(fun(A,bool),fun(B,fun(fun(A,B),bool))),i(s(fun(fun(B,bool),fun(fun(A,bool),fun(B,fun(fun(A,B),bool)))),U_0),s(fun(B,bool),T0))),s(fun(A,bool),S0))),s(B,D0))),s(fun(A,B),GENR_PVARR_92)))) <-> (exists F0 exists V ((p(s(bool,V)) <-> (all X (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(B,D0) = s(B,i(s(fun(A,B),F0),s(A,X))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0))))))) & p(s(bool,i(s(fun(fun(A,B),bool),i(s(fun(bool,fun(fun(A,B),bool)),i(s(fun(fun(A,B),fun(bool,fun(fun(A,B),bool))),setspec),s(fun(A,B),GENR_PVARR_92))),s(bool,V))),s(fun(A,B),F0)))))))) -> (all D0 all N0 all T0 all M0 all S0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,M0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(B,bool),fun(num,bool)),hasu_size),s(fun(B,bool),T0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(fun(A,B),bool),fun(num,bool)),hasu_size),s(fun(fun(A,B),bool),i(s(fun(fun(fun(A,B),bool),fun(fun(A,B),bool)),gspec),s(fun(fun(A,B),bool),i(s(fun(B,fun(fun(A,B),bool)),i(s(fun(fun(A,bool),fun(B,fun(fun(A,B),bool))),i(s(fun(fun(B,bool),fun(fun(A,bool),fun(B,fun(fun(A,B),bool)))),U_0),s(fun(B,bool),T0))),s(fun(A,bool),S0))),s(B,D0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,N0))),s(num,M0)))))))))) # label(aHASu_SIZEu_FUNSPACE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 714 (all X all M0 all N0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,M0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0)))))) # label(aREALu_POWu_ADD) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 715 (all X all Y all Z0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y))),s(int,Z0))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0))))),s(int,Y)))) # label(aINTu_LTu_SUBu_LADD) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 716 (all A all H0 all T0 s(num,i(s(fun(num,num),suc),s(num,i(s(fun(list(A),num),length),s(list(A),T0))))) = s(num,i(s(fun(list(A),num),length),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,H0))),s(list(A),T0)))))) # label(aLENGTHu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 717 (all Q48678 all Q48614 all Q48613 all U_0 ((all P0 all F0 all GENR_PVARR_22 ((exists X exists Y p(s(bool,i(s(fun(Q48678,bool),i(s(fun(bool,fun(Q48678,bool)),i(s(fun(Q48678,fun(bool,fun(Q48678,bool))),setspec),s(Q48678,GENR_PVARR_22))),s(bool,i(s(fun(Q48613,bool),i(s(fun(Q48614,fun(Q48613,bool)),P0),s(Q48614,X))),s(Q48613,Y))))),s(Q48678,i(s(fun(Q48613,Q48678),i(s(fun(Q48614,fun(Q48613,Q48678)),F0),s(Q48614,X))),s(Q48613,Y))))))) <-> p(s(bool,i(s(fun(Q48678,bool),i(s(fun(fun(Q48614,fun(Q48613,Q48678)),fun(Q48678,bool)),i(s(fun(fun(Q48614,fun(Q48613,bool)),fun(fun(Q48614,fun(Q48613,Q48678)),fun(Q48678,bool))),U_0),s(fun(Q48614,fun(Q48613,bool)),P0))),s(fun(Q48614,fun(Q48613,Q48678)),F0))),s(Q48678,GENR_PVARR_22)))))) -> (all P0 all F0 ((all Z0 (p(s(bool,i(s(fun(fun(Q48678,bool),bool),i(s(fun(Q48678,fun(fun(Q48678,bool),bool)),in),s(Q48678,Z0))),s(fun(Q48678,bool),i(s(fun(fun(Q48678,bool),fun(Q48678,bool)),gspec),s(fun(Q48678,bool),i(s(fun(fun(Q48614,fun(Q48613,Q48678)),fun(Q48678,bool)),i(s(fun(fun(Q48614,fun(Q48613,bool)),fun(fun(Q48614,fun(Q48613,Q48678)),fun(Q48678,bool))),U_0),s(fun(Q48614,fun(Q48613,bool)),P0))),s(fun(Q48614,fun(Q48613,Q48678)),F0)))))))) -> p(s(bool,i(s(fun(Q48678,bool),q0),s(Q48678,Z0)))))) <-> (all X all Y (p(s(bool,i(s(fun(Q48613,bool),i(s(fun(Q48614,fun(Q48613,bool)),P0),s(Q48614,X))),s(Q48613,Y)))) -> p(s(bool,i(s(fun(Q48678,bool),q0),s(Q48678,i(s(fun(Q48613,Q48678),i(s(fun(Q48614,fun(Q48613,Q48678)),F0),s(Q48614,X))),s(Q48613,Y)))))))))))) # label(aFORALLu_INu_GSPECu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 718 (all Z all E0 all F0 exists FN (s(Z,E0) = s(Z,i(s(fun(num,Z),FN),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & (all N0 s(Z,i(s(fun(Z,Z),i(s(fun(num,fun(Z,Z)),F0),s(num,N0))),s(Z,i(s(fun(num,Z),FN),s(num,N0))))) = s(Z,i(s(fun(num,Z),FN),s(num,i(s(fun(num,num),suc),s(num,N0)))))))) # label(anumu_RECURSIONu_STD) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 719 (all A all S0 (s(fun(A,bool),empty) = s(fun(A,bool),S0) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aHASu_SIZEu_0) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 720 (all M0 all N0 s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,M0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),from),s(num,N0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) # label(aINu_FROM) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 721 (all A all S0 (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),finite),s(fun(fun(A,bool),bool),S0)))) & (all T0 (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T0))),s(fun(fun(A,bool),bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))))) & (all T0 all U (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T0))),s(fun(fun(A,bool),bool),S0)))) & s(fun(A,bool),T0) != s(fun(A,bool),U) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),U))),s(fun(fun(A,bool),bool),S0)))) -> s(fun(A,bool),empty) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),T0))),s(fun(A,bool),U))))) -> s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),unions),s(fun(fun(A,bool),bool),S0))))) = s(num,i(s(fun(fun(fun(A,bool),num),num),i(s(fun(fun(fun(A,bool),bool),fun(fun(fun(A,bool),num),num)),nsum),s(fun(fun(A,bool),bool),S0))),s(fun(fun(A,bool),num),card))))) # label(aCARDu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 722 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0)))))) # label(aARITHu_SUBu_conjunct9) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 723 (all A all P0 all Q0 ((p(s(bool,P0)) -> (exists X p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))) <-> (exists X (p(s(bool,P0)) -> p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))))) # label(aRIGHTu_EXISTSu_IMPu_THM) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 724 (p(s(bool,c0)) -> p(s(bool,d0))) & (p(s(bool,a)) -> p(s(bool,b))) -> (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,b0))),s(bool,a))),s(bool,c0)))) -> p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,b0))),s(bool,b))),s(bool,d0))))) # label(aMONOu_COND) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 725 (all A all B all C all S0 all T0 all U (p(s(bool,i(s(fun(fun(C,bool),bool),infinite),s(fun(C,bool),U)))) & p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(A,bool),fun(fun(C,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(C,bool),U)))) & p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(B,bool),fun(fun(C,bool),bool)),l_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U)))) -> p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(sum0(A,B),bool),fun(fun(C,bool),bool)),l_u_c),s(fun(sum0(A,B),bool),i(s(fun(fun(B,bool),fun(sum0(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(sum0(A,B),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(C,bool),U)))))) # label(aCARDu_ADD2u_ABSORBu_LT) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 726 (all M0 all N0 all P0 (s(num,P0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,N0))),s(num,P0)))))))) # label(aDIVu_MONOu_LT) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 727 (all Q19015 all Q19023 s(list(prod(Q19015,Q19023)),nil) = s(list(prod(Q19015,Q19023)),i(s(fun(list(Q19023),list(prod(Q19015,Q19023))),i(s(fun(list(Q19015),fun(list(Q19023),list(prod(Q19015,Q19023)))),zip0),s(list(Q19015),nil))),s(list(Q19023),l2)))) # label(aZIPu_DEFu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 728 (all Q47151 s(fun(Q47151,bool),i(s(fun(fun(Q47151,bool),fun(Q47151,bool)),i(s(fun(fun(Q47151,bool),fun(fun(Q47151,bool),fun(Q47151,bool))),union),s(fun(Q47151,bool),s0))),s(fun(Q47151,bool),i(s(fun(fun(fun(Q47151,bool),bool),fun(Q47151,bool)),unions),s(fun(fun(Q47151,bool),bool),u))))) = s(fun(Q47151,bool),i(s(fun(fun(fun(Q47151,bool),bool),fun(Q47151,bool)),unions),s(fun(fun(Q47151,bool),bool),i(s(fun(fun(fun(Q47151,bool),bool),fun(fun(Q47151,bool),bool)),i(s(fun(fun(Q47151,bool),fun(fun(fun(Q47151,bool),bool),fun(fun(Q47151,bool),bool))),insert),s(fun(Q47151,bool),s0))),s(fun(fun(Q47151,bool),bool),u)))))) # label(aUNIONSu_INSERT) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 729 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,Y))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y)))))) # label(aREALu_MULu_LNEG) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 730 (all N0 (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) <-> p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))))) # label(aODDu_MOD) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 731 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))))) # label(aLETu_CASES) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 732 (all X all Y all Z0 (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Y))),s(real,Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0))) <-> s(real,Y) = s(real,X))) # label(aREALu_EQu_ADDu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 733 (all Q4566 all Q4565 all Q4558 all U_0 ((all F0 all FI_ (p(s(bool,i(s(fun(fun(prod(Q4566,Q4565),Q4558),bool),i(s(fun(fun(prod(Q4566,Q4565),Q4558),fun(fun(prod(Q4566,Q4565),Q4558),bool)),U_0),s(fun(prod(Q4566,Q4565),Q4558),F0))),s(fun(prod(Q4566,Q4565),Q4558),FI_)))) <-> (all X all Y p(s(bool,i(s(fun(Q4558,bool),i(s(fun(Q4558,fun(Q4558,bool)),geq),s(Q4558,i(s(fun(prod(Q4566,Q4565),Q4558),FI_),s(prod(Q4566,Q4565),i(s(fun(Q4565,prod(Q4566,Q4565)),i(s(fun(Q4566,fun(Q4565,prod(Q4566,Q4565))),c_),s(Q4566,X))),s(Q4565,Y))))))),s(Q4558,i(s(fun(prod(Q4566,Q4565),Q4558),F0),s(prod(Q4566,Q4565),i(s(fun(Q4565,prod(Q4566,Q4565)),i(s(fun(Q4566,fun(Q4565,prod(Q4566,Q4565))),c_),s(Q4566,X))),s(Q4565,Y))))))))))) -> (all F0 s(fun(prod(Q4566,Q4565),Q4558),i(s(fun(fun(fun(prod(Q4566,Q4565),Q4558),bool),fun(prod(Q4566,Q4565),Q4558)),gabs),s(fun(fun(prod(Q4566,Q4565),Q4558),bool),i(s(fun(fun(prod(Q4566,Q4565),Q4558),fun(fun(prod(Q4566,Q4565),Q4558),bool)),U_0),s(fun(prod(Q4566,Q4565),Q4558),F0))))) = s(fun(prod(Q4566,Q4565),Q4558),F0)))) # label(aPAIREDu_ETAu_THMu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 734 (all A all X all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))),s(fun(A,bool),T0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) & -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))))) # label(aDISJOINTu_INSERT) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 735 (all A all B all C all S0 all T0 all U p(s(bool,i(s(fun(fun(sum0(prod(A,C),prod(B,C)),bool),bool),i(s(fun(fun(prod(sum0(A,B),C),bool),fun(fun(sum0(prod(A,C),prod(B,C)),bool),bool)),a_u_c),s(fun(prod(sum0(A,B),C),bool),i(s(fun(fun(C,bool),fun(prod(sum0(A,B),C),bool)),i(s(fun(fun(sum0(A,B),bool),fun(fun(C,bool),fun(prod(sum0(A,B),C),bool))),t_u_c),s(fun(sum0(A,B),bool),i(s(fun(fun(B,bool),fun(sum0(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(sum0(A,B),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(C,bool),U))))),s(fun(sum0(prod(A,C),prod(B,C)),bool),i(s(fun(fun(prod(B,C),bool),fun(sum0(prod(A,C),prod(B,C)),bool)),i(s(fun(fun(prod(A,C),bool),fun(fun(prod(B,C),bool),fun(sum0(prod(A,C),prod(B,C)),bool))),p_u_c),s(fun(prod(A,C),bool),i(s(fun(fun(C,bool),fun(prod(A,C),bool)),i(s(fun(fun(A,bool),fun(fun(C,bool),fun(prod(A,C),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(C,bool),U))))),s(fun(prod(B,C),bool),i(s(fun(fun(C,bool),fun(prod(B,C),bool)),i(s(fun(fun(B,bool),fun(fun(C,bool),fun(prod(B,C),bool))),t_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U))))))))) # label(aCARDu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 736 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y)))))) # label(aREALu_DIFFSQ) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 737 (all Q18705 all Q18712 exists V ((exists VI_ (s(bool,i(s(fun(list(Q18712),bool),i(s(fun(list(Q18705),fun(list(Q18712),bool)),i(s(fun(fun(Q18705,fun(Q18712,bool)),fun(list(Q18705),fun(list(Q18712),bool))),all2),s(fun(Q18705,fun(Q18712,bool)),p0))),s(list(Q18705),i(s(fun(list(Q18705),list(Q18705)),i(s(fun(Q18705,fun(list(Q18705),list(Q18705))),cons),s(Q18705,h1))),s(list(Q18705),t1))))),s(list(Q18712),l2))) = s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,VI_))),s(bool,f0))),s(bool,V))) & (s(list(Q18712),l2) = s(list(Q18712),nil) <-> p(s(bool,VI_))))) & (p(s(bool,i(s(fun(list(Q18712),bool),i(s(fun(list(Q18705),fun(list(Q18712),bool)),i(s(fun(fun(Q18705,fun(Q18712,bool)),fun(list(Q18705),fun(list(Q18712),bool))),all2),s(fun(Q18705,fun(Q18712,bool)),p0))),s(list(Q18705),t1))),s(list(Q18712),i(s(fun(list(Q18712),list(Q18712)),tl),s(list(Q18712),l2)))))) & p(s(bool,i(s(fun(Q18712,bool),i(s(fun(Q18705,fun(Q18712,bool)),p0),s(Q18705,h1))),s(Q18712,i(s(fun(list(Q18712),Q18712),hd),s(list(Q18712),l2)))))) <-> p(s(bool,V))))) # label(aALL2u_DEFu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 738 (all N0 p(s(bool,i(s(fun(num,bool),odd),s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))))))) # label(aODDu_DOUBLE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 739 (all A all U all V all F0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),U)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),U))),s(fun(A,bool),V)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),V))),s(fun(A,bool),U)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(A,real),F0),s(A,X)))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),V)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),U))),s(fun(A,real),F0))))),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),V))),s(fun(A,real),F0)))))))) # label(aSUMu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 740 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,X))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y)))))) # label(aINTu_SUBu_LE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 741 (all Q63859 all Q63783 all F0 all S0 all T0 s(fun(Q63783,bool),i(s(fun(fun(Q63783,bool),fun(Q63783,bool)),i(s(fun(fun(Q63783,Q63859),fun(fun(Q63783,bool),fun(Q63783,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63783,Q63859),fun(fun(Q63783,bool),fun(Q63783,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63783,Q63859),F0))),s(fun(Q63783,bool),i(s(fun(fun(Q63783,bool),fun(Q63783,bool)),i(s(fun(fun(Q63783,bool),fun(fun(Q63783,bool),fun(Q63783,bool))),inter),s(fun(Q63783,bool),S0))),s(fun(Q63783,bool),T0))))) = s(fun(Q63783,bool),i(s(fun(fun(Q63783,bool),fun(Q63783,bool)),i(s(fun(fun(Q63783,bool),fun(fun(Q63783,bool),fun(Q63783,bool))),inter),s(fun(Q63783,bool),i(s(fun(fun(Q63783,bool),fun(Q63783,bool)),i(s(fun(fun(Q63783,Q63859),fun(fun(Q63783,bool),fun(Q63783,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63783,Q63859),fun(fun(Q63783,bool),fun(Q63783,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63783,Q63859),F0))),s(fun(Q63783,bool),S0))))),s(fun(Q63783,bool),i(s(fun(fun(Q63783,bool),fun(Q63783,bool)),i(s(fun(fun(Q63783,Q63859),fun(fun(Q63783,bool),fun(Q63783,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63783,Q63859),fun(fun(Q63783,bool),fun(Q63783,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63783,Q63859),F0))),s(fun(Q63783,bool),T0)))))) # label(aSUPPORTu_CLAUSESu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 742 (all Q53339 all S0 all T0 (p(s(bool,i(s(fun(fun(Q53339,bool),bool),i(s(fun(fun(Q53339,bool),fun(fun(Q53339,bool),bool)),subset),s(fun(Q53339,bool),T0))),s(fun(Q53339,bool),S0)))) & p(s(bool,i(s(fun(fun(Q53339,bool),bool),finite),s(fun(Q53339,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(fun(Q53339,bool),num),card),s(fun(Q53339,bool),S0))))),s(num,i(s(fun(fun(Q53339,bool),num),card),s(fun(Q53339,bool),T0))))) = s(num,i(s(fun(fun(Q53339,bool),num),card),s(fun(Q53339,bool),i(s(fun(fun(Q53339,bool),fun(Q53339,bool)),i(s(fun(fun(Q53339,bool),fun(fun(Q53339,bool),fun(Q53339,bool))),diff),s(fun(Q53339,bool),S0))),s(fun(Q53339,bool),T0))))))) # label(aCARDu_DIFF) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 743 (all A all S0 all X (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X)))))))) # label(aFINITEu_DELETEu_IMP) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 744 (all X all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Y))),s(real,Z0))))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,i(s(fun(real,real),realu_neg),s(real,Z0)))))))) # label(aREALu_LTu_ADDNEG) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 745 (all Q59021 all P0 all A5 all S0 ((all X (p(s(bool,i(s(fun(fun(Q59021,bool),bool),i(s(fun(Q59021,fun(fun(Q59021,bool),bool)),in),s(Q59021,X))),s(fun(Q59021,bool),S0)))) -> p(s(bool,i(s(fun(Q59021,bool),P0),s(Q59021,X)))))) & p(s(bool,i(s(fun(Q59021,bool),P0),s(Q59021,A5)))) <-> (all X (p(s(bool,i(s(fun(fun(Q59021,bool),bool),i(s(fun(Q59021,fun(fun(Q59021,bool),bool)),in),s(Q59021,X))),s(fun(Q59021,bool),i(s(fun(fun(Q59021,bool),fun(Q59021,bool)),i(s(fun(Q59021,fun(fun(Q59021,bool),fun(Q59021,bool))),insert),s(Q59021,A5))),s(fun(Q59021,bool),S0)))))) -> p(s(bool,i(s(fun(Q59021,bool),P0),s(Q59021,X)))))))) # label(aFORALLu_INu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 746 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (exists N0 all M0 all N1 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,N1)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N1))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,N1))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N1))),s(num,N1))))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N1)))))))))))))) # label(aNADDu_MULu_LINVu_LEMMA3) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 747 (all A all F0 s(fun(num,A),i(s(fun(fun(num,A),fun(num,A)),i(s(fun(A,fun(fun(num,A),fun(num,A))),fcons),s(A,i(s(fun(num,A),F0),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(num,A),i(s(fun(fun(num,num),fun(num,A)),i(s(fun(fun(num,A),fun(fun(num,num),fun(num,A))),o),s(fun(num,A),F0))),s(fun(num,num),suc))))) = s(fun(num,A),F0)) # label(aFCONSu_UNDO) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 748 (all Q19728 all Q19718 all F0 all A5 all L1 all L2 s(Q19718,i(s(fun(Q19718,Q19718),i(s(fun(list(Q19728),fun(Q19718,Q19718)),i(s(fun(fun(Q19728,fun(Q19718,Q19718)),fun(list(Q19728),fun(Q19718,Q19718))),itlist),s(fun(Q19728,fun(Q19718,Q19718)),F0))),s(list(Q19728),L1))),s(Q19718,i(s(fun(Q19718,Q19718),i(s(fun(list(Q19728),fun(Q19718,Q19718)),i(s(fun(fun(Q19728,fun(Q19718,Q19718)),fun(list(Q19728),fun(Q19718,Q19718))),itlist),s(fun(Q19728,fun(Q19718,Q19718)),F0))),s(list(Q19728),L2))),s(Q19718,A5))))) = s(Q19718,i(s(fun(Q19718,Q19718),i(s(fun(list(Q19728),fun(Q19718,Q19718)),i(s(fun(fun(Q19728,fun(Q19718,Q19718)),fun(list(Q19728),fun(Q19718,Q19718))),itlist),s(fun(Q19728,fun(Q19718,Q19718)),F0))),s(list(Q19728),i(s(fun(list(Q19728),list(Q19728)),i(s(fun(list(Q19728),fun(list(Q19728),list(Q19728))),append),s(list(Q19728),L1))),s(list(Q19728),L2))))),s(Q19718,A5)))) # label(aITLISTu_APPEND) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 749 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),suc),s(num,M0))))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aLEu_SUC) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 750 (all R0 ((all X all Y all Z0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,X))),s(num,Y)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,Y))),s(num,Z0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,X))),s(num,Z0)))))) -> ((all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,N0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))) <-> (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,M0))),s(num,N0))))))))) # label(aTRANSITIVEu_STEPWISEu_LTu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 751 (all M0 all N0 (s(num,i(s(fun(num,num),bit1),s(num,M0))) = s(num,i(s(fun(num,num),bit1),s(num,N0))) <-> s(num,N0) = s(num,M0))) # label(aARITHu_EQu_conjunct9) # label(axiom) # label(non_clause). [assumption]. 13.98/13.98 752 (all B all A all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all P0 all S0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(A,A),P0),s(A,X))))),s(fun(A,bool),S0)))))) & (all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) -> (exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(A,i(s(fun(A,A),P0),s(A,X))) = s(A,Y))) & (all X all XI_ (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0)))) & s(A,Y) = s(A,i(s(fun(A,A),P0),s(A,XI_))) & s(A,Y) = s(A,i(s(fun(A,A),P0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,X) = s(A,XI_))))) -> s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),i(s(fun(fun(A,A),fun(A,B)),i(s(fun(fun(A,B),fun(fun(A,A),fun(A,B))),o),s(fun(A,B),F0))),s(fun(A,A),P0))))) = s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))))))) # label(aITERATEu_BIJECTION) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 753 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,N0))),s(num,P0))))))) = s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0)))))))) # label(aDISTu_LMUL) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 754 (all X s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) # label(aINTu_NEGu_LT0) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 755 (all N0 s(num,i(s(fun(ind0,num),mku_num),s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,i(s(fun(num,ind0),destu_num),s(num,N0))))))) = s(num,i(s(fun(num,num),suc),s(num,N0)))) # label(aSUCu_DEF) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 756 (all X p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(nadd,X))))) # label(aNADDu_LEu_0) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 757 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,u_0))))) # label(aARITHu_GEu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 758 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_ge),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Y))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_gt),s(int,X))),s(int,Y)))) # label(aINTu_GTu_DISCRETE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 759 (all A all B all U_0 ((all S0 all F0 all GENR_PVARR_56 (p(s(bool,i(s(fun(B,bool),i(s(fun(fun(A,B),fun(B,bool)),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,GENR_PVARR_56)))) <-> (exists Y exists V (p(s(bool,i(s(fun(B,bool),i(s(fun(bool,fun(B,bool)),i(s(fun(B,fun(bool,fun(B,bool))),setspec),s(B,GENR_PVARR_56))),s(bool,V))),s(B,Y)))) & (p(s(bool,V)) <-> (exists X (s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))))))))) -> (all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),gspec),s(fun(B,bool),i(s(fun(fun(A,B),fun(B,bool)),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0)))))))))))) # label(aFINITEu_IMAGEu_EXPAND) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 760 (all Q67326 all F0 all G0 all S0 ((all X (p(s(bool,i(s(fun(fun(Q67326,bool),bool),i(s(fun(Q67326,fun(fun(Q67326,bool),bool)),in),s(Q67326,X))),s(fun(Q67326,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(Q67326,num),F0),s(Q67326,X))))),s(num,i(s(fun(Q67326,num),G0),s(Q67326,X)))))))) & p(s(bool,i(s(fun(fun(Q67326,bool),bool),finite),s(fun(Q67326,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(Q67326,num),num),i(s(fun(fun(Q67326,bool),fun(fun(Q67326,num),num)),nsum),s(fun(Q67326,bool),S0))),s(fun(Q67326,num),F0))))),s(num,i(s(fun(fun(Q67326,num),num),i(s(fun(fun(Q67326,bool),fun(fun(Q67326,num),num)),nsum),s(fun(Q67326,bool),S0))),s(fun(Q67326,num),G0)))))))) # label(aNSUMu_LE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 761 (all A all B all F0 all U all V ((all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),V)))) -> (exists X (s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))))))) <-> (all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),T0))),s(fun(B,bool),V)))) -> (exists S0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),U)))) & s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))) = s(fun(B,bool),T0))))))) # label(aSURJECTIVEu_ONu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 762 (all N ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> p(s(bool,i(s(fun(finite_image(N),bool),p0),s(finite_image(N),i(s(fun(num,finite_image(N)),finiteu_index),s(num,I0)))))))) <-> (all K0 p(s(bool,i(s(fun(finite_image(N),bool),p0),s(finite_image(N),K0))))))) # label(aFORALLu_FINITEu_INDEX) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 763 (all X all N0 s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0))))) = s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,i(s(fun(num,int),intu_ofu_num),s(num,X))))),s(num,N0)))) # label(aINTu_OFu_NUMu_POW) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 764 (all X all Y (s(real,Y) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(real,X) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y))))),s(real,Y))))) # label(aREALu_DIVu_RMUL) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 765 (all A all C all B all D all S0 all SI_ all T0 all TI_ (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),SI_)))) & p(s(bool,i(s(fun(fun(D,bool),bool),i(s(fun(fun(C,bool),fun(fun(D,bool),bool)),a_u_c),s(fun(C,bool),T0))),s(fun(D,bool),TI_)))) -> s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(A,bool),fun(fun(C,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(C,bool),T0))) = s(bool,i(s(fun(fun(D,bool),bool),i(s(fun(fun(B,bool),fun(fun(D,bool),bool)),l_u_c),s(fun(B,bool),SI_))),s(fun(D,bool),TI_))))) # label(aCARDu_LTu_CONG) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 766 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) <-> -(exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))))))) # label(aINu_DISJOINT) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 767 (all N0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,x))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,x))),s(num,N0))))) = s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,x))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aINTu_POWu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 768 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (exists A5 exists B0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,N0))))),s(num,B0))))))))) # label(aNADDu_MULu_LINVu_LEMMA0) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 769 (all A all B all C all U_0 ((all S0 all T0 all F0 all GENR_PVARR_231 ((exists X exists Y exists V (p(s(bool,i(s(fun(C,bool),i(s(fun(bool,fun(C,bool)),i(s(fun(C,fun(bool,fun(C,bool))),setspec),s(C,GENR_PVARR_231))),s(bool,V))),s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),F0),s(A,X))),s(B,Y)))))) & (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X)))))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(C,bool),i(s(fun(fun(A,fun(B,C)),fun(C,bool)),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(C,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(C,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,C)),F0))),s(C,GENR_PVARR_231)))))) -> (all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),countable),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X)))))))) -> p(s(bool,i(s(fun(fun(C,bool),bool),countable),s(fun(C,bool),i(s(fun(fun(C,bool),fun(C,bool)),gspec),s(fun(C,bool),i(s(fun(fun(A,fun(B,C)),fun(C,bool)),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(C,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(C,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,C)),F0)))))))))))) # label(aCOUNTABLEu_PRODUCTu_DEPENDENT) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 770 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,N0))),s(num,M0)))) & (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,M0))),s(num,N0)))))) -> (all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,M0))),s(num,N0))))) # label(aWLOGu_LE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 771 (all A all B all C all U_1 ((all F0 all A5 all B0 s(C,i(s(fun(prod(A,B),C),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,A5))),s(B,B0))))) = s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),i(s(fun(fun(prod(A,B),C),fun(A,fun(B,C))),U_1),s(fun(prod(A,B),C),F0))),s(A,A5))),s(B,B0)))) -> (all U_0 ((all F0 all A5 s(fun(B,C),i(s(fun(A,fun(B,C)),i(s(fun(fun(prod(A,B),C),fun(A,fun(B,C))),U_1),s(fun(prod(A,B),C),F0))),s(A,A5))) = s(fun(B,C),i(s(fun(A,fun(B,C)),i(s(fun(fun(prod(A,B),C),fun(A,fun(B,C))),U_0),s(fun(prod(A,B),C),F0))),s(A,A5)))) -> (all P0 ((exists F0 p(s(bool,i(s(fun(fun(A,fun(B,C)),bool),P0),s(fun(A,fun(B,C)),F0))))) <-> (exists F0 p(s(bool,i(s(fun(fun(A,fun(B,C)),bool),P0),s(fun(A,fun(B,C)),i(s(fun(fun(prod(A,B),C),fun(A,fun(B,C))),U_0),s(fun(prod(A,B),C),F0))))))))))))) # label(aEXISTSu_UNCURRY) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 772 (all U_0 ((all A5 all GENR_PVARR_123 ((exists X p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_123))),s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X))))),s(real,X))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),U_0),s(real,A5))),s(real,GENR_PVARR_123)))))) -> (all A5 -p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(real,fun(real,bool)),U_0),s(real,A5))))))))))) # label(aFINITEu_REALu_INTERVALu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 773 (all B all A all U_2 ((all S0 all G0 all GENR_PVARR_50 ((exists X p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(bool,fun(fun(B,bool),bool)),i(s(fun(fun(B,bool),fun(bool,fun(fun(B,bool),bool))),setspec),s(fun(B,bool),GENR_PVARR_50))),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),G0),s(A,X))))))) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool))),U_2),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),G0))),s(fun(B,bool),GENR_PVARR_50)))))) -> (all U_1 ((all F0 all S0 all GENR_PVARR_51 ((exists G0 exists V (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(bool,fun(fun(B,bool),bool)),i(s(fun(fun(B,bool),fun(bool,fun(fun(B,bool),bool))),setspec),s(fun(B,bool),GENR_PVARR_51))),s(bool,V))),s(fun(B,bool),i(s(fun(fun(fun(B,bool),bool),fun(B,bool)),inters),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),gspec),s(fun(fun(B,bool),bool),i(s(fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(fun(B,bool),bool))),U_2),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),G0)))))))))) & (p(s(bool,V)) <-> (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(fun(B,bool),bool),bool),i(s(fun(fun(B,bool),fun(fun(fun(B,bool),bool),bool)),in),s(fun(B,bool),i(s(fun(A,fun(B,bool)),G0),s(A,X))))),s(fun(fun(B,bool),bool),i(s(fun(A,fun(fun(B,bool),bool)),F0),s(A,X))))))))))) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),i(s(fun(fun(A,fun(fun(B,bool),bool)),fun(fun(A,bool),fun(fun(B,bool),bool))),U_1),s(fun(A,fun(fun(B,bool),bool)),F0))),s(fun(A,bool),S0))),s(fun(B,bool),GENR_PVARR_51)))))) -> (all U_0 ((all S0 all F0 all GENR_PVARR_47 ((exists X p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(bool,fun(fun(B,bool),bool)),i(s(fun(fun(B,bool),fun(bool,fun(fun(B,bool),bool))),setspec),s(fun(B,bool),GENR_PVARR_47))),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(fun(B,bool),i(s(fun(fun(fun(B,bool),bool),fun(B,bool)),unions),s(fun(fun(B,bool),bool),i(s(fun(A,fun(fun(B,bool),bool)),F0),s(A,X))))))))) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,fun(fun(B,bool),bool)),fun(fun(B,bool),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(fun(B,bool),bool)),fun(fun(B,bool),bool))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(fun(B,bool),bool)),F0))),s(fun(B,bool),GENR_PVARR_47)))))) -> (all F0 all S0 s(fun(B,bool),i(s(fun(fun(fun(B,bool),bool),fun(B,bool)),unions),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),gspec),s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),i(s(fun(fun(A,fun(fun(B,bool),bool)),fun(fun(A,bool),fun(fun(B,bool),bool))),U_1),s(fun(A,fun(fun(B,bool),bool)),F0))),s(fun(A,bool),S0))))))) = s(fun(B,bool),i(s(fun(fun(fun(B,bool),bool),fun(B,bool)),inters),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),gspec),s(fun(fun(B,bool),bool),i(s(fun(fun(A,fun(fun(B,bool),bool)),fun(fun(B,bool),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(fun(B,bool),bool)),fun(fun(B,bool),bool))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(fun(B,bool),bool)),F0)))))))))))))) # label(aINTERSu_OVERu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 774 (all X all Y all Z0 s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,X))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,Y))),s(hreal,Z0))))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,X))),s(hreal,Y))))),s(hreal,Z0)))) # label(aHREALu_MULu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 775 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Z0)))))) # label(aREALu_LTEu_TRANS) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 776 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all X all Y (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) -> s(A,Y) = s(A,X))))) # label(aWOSETu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 777 (all U_0 ((all N0 all GENR_PVARR_137 ((exists X p(s(bool,i(s(fun(num,bool),i(s(fun(bool,fun(num,bool)),i(s(fun(num,fun(bool,fun(num,bool))),setspec),s(num,GENR_PVARR_137))),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,X))),s(num,N0))))),s(num,X))))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))),s(num,GENR_PVARR_137)))))) -> (all N0 exists V (s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),gspec),s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))))) = s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(fun(num,bool),fun(fun(num,bool),fun(num,bool))),i(s(fun(bool,fun(fun(num,bool),fun(fun(num,bool),fun(num,bool)))),cond),s(bool,V))),s(fun(num,bool),empty))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) & (p(s(bool,V)) <-> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,N0)))))) # label(aNUMSEGu_LT) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 778 (all X1 all X2 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),X2)))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),trealu_neg),s(prod(hreal,hreal),X1))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),trealu_neg),s(prod(hreal,hreal),X2)))))))) # label(aTREALu_NEGu_WELLDEF) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 779 (all P0 ((exists X p(s(bool,i(s(fun(int,bool),P0),s(int,i(s(fun(int,int),intu_abs),s(int,X))))))) <-> (exists N0 p(s(bool,i(s(fun(int,bool),P0),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))))))) # label(aINTu_EXISTSu_ABS) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 780 (all W all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,W))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,W))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0)))))))) # label(aREALu_LETu_ADD2) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 781 (all M0 all N0 all P0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,N0))),s(num,P0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))))) # label(aMODu_MULT2) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 782 (all Q18794 all Q18797 all Q18804 s(list(Q18794),i(s(fun(list(Q18804),list(Q18794)),i(s(fun(list(Q18797),fun(list(Q18804),list(Q18794))),i(s(fun(fun(Q18797,fun(Q18804,Q18794)),fun(list(Q18797),fun(list(Q18804),list(Q18794)))),map2),s(fun(Q18797,fun(Q18804,Q18794)),f))),s(list(Q18797),i(s(fun(list(Q18797),list(Q18797)),i(s(fun(Q18797,fun(list(Q18797),list(Q18797))),cons),s(Q18797,h1))),s(list(Q18797),t1))))),s(list(Q18804),l0))) = s(list(Q18794),i(s(fun(list(Q18794),list(Q18794)),i(s(fun(Q18794,fun(list(Q18794),list(Q18794))),cons),s(Q18794,i(s(fun(Q18804,Q18794),i(s(fun(Q18797,fun(Q18804,Q18794)),f),s(Q18797,h1))),s(Q18804,i(s(fun(list(Q18804),Q18804),hd),s(list(Q18804),l0))))))),s(list(Q18794),i(s(fun(list(Q18804),list(Q18794)),i(s(fun(list(Q18797),fun(list(Q18804),list(Q18794))),i(s(fun(fun(Q18797,fun(Q18804,Q18794)),fun(list(Q18797),fun(list(Q18804),list(Q18794)))),map2),s(fun(Q18797,fun(Q18804,Q18794)),f))),s(list(Q18797),t1))),s(list(Q18804),i(s(fun(list(Q18804),list(Q18804)),tl),s(list(Q18804),l0)))))))) # label(aMAP2u_DEFu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 783 (all A all X all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0)))))))) # label(aFINITEu_RULESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 784 (all N0 s(bool,t) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,u_0))),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_LEu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 785 (all A all B ((exists X exists C0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),s0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(B,fun(num,bool)),i(s(fun(fun(A,bool),fun(B,fun(num,bool))),i(s(fun(B,fun(fun(A,bool),fun(B,fun(num,bool)))),i(s(fun(fun(A,fun(B,B)),fun(B,fun(fun(A,bool),fun(B,fun(num,bool))))),finrec),s(fun(A,fun(B,B)),f))),s(B,b0))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),s0))),s(A,X))))),s(B,C0))),s(num,n)))) & s(B,a0) = s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),f),s(A,X))),s(B,C0))))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(B,fun(num,bool)),i(s(fun(fun(A,bool),fun(B,fun(num,bool))),i(s(fun(B,fun(fun(A,bool),fun(B,fun(num,bool)))),i(s(fun(fun(A,fun(B,B)),fun(B,fun(fun(A,bool),fun(B,fun(num,bool))))),finrec),s(fun(A,fun(B,B)),f))),s(B,b0))),s(fun(A,bool),s0))),s(B,a0))),s(num,i(s(fun(num,num),suc),s(num,n)))))))) # label(aFINRECu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 786 (all X all Y all H0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_abs),s(int,H0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(int,int),intu_abs),s(int,Y))))),s(int,i(s(fun(int,int),intu_abs),s(int,X)))))))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,H0))))))),s(int,i(s(fun(int,int),intu_abs),s(int,Y)))))))) # label(aINTu_ABSu_CIRCLE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 787 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y))))) = s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y)))))) # label(aintu_maxu_th) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 788 (all Q66575 all OP (p(s(bool,i(s(fun(fun(Q66575,fun(Q66575,Q66575)),bool),monoidal),s(fun(Q66575,fun(Q66575,Q66575)),OP)))) -> (all M0 all N0 s(Q66575,i(s(fun(fun(num,Q66575),Q66575),i(s(fun(fun(num,bool),fun(fun(num,Q66575),Q66575)),i(s(fun(fun(Q66575,fun(Q66575,Q66575)),fun(fun(num,bool),fun(fun(num,Q66575),Q66575))),iterate),s(fun(Q66575,fun(Q66575,Q66575)),OP))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(fun(num,Q66575),f))) = s(Q66575,i(s(fun(Q66575,Q66575),i(s(fun(Q66575,fun(Q66575,Q66575)),i(s(fun(bool,fun(Q66575,fun(Q66575,Q66575))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(Q66575,i(s(fun(Q66575,Q66575),i(s(fun(Q66575,fun(Q66575,Q66575)),OP),s(Q66575,i(s(fun(fun(num,Q66575),Q66575),i(s(fun(fun(num,bool),fun(fun(num,Q66575),Q66575)),i(s(fun(fun(Q66575,fun(Q66575,Q66575)),fun(fun(num,bool),fun(fun(num,Q66575),Q66575))),iterate),s(fun(Q66575,fun(Q66575,Q66575)),OP))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,Q66575),f))))),s(Q66575,i(s(fun(num,Q66575),f),s(num,i(s(fun(num,num),suc),s(num,N0))))))))),s(Q66575,i(s(fun(fun(num,Q66575),Q66575),i(s(fun(fun(num,bool),fun(fun(num,Q66575),Q66575)),i(s(fun(fun(Q66575,fun(Q66575,Q66575)),fun(fun(num,bool),fun(fun(num,Q66575),Q66575))),iterate),s(fun(Q66575,fun(Q66575,Q66575)),OP))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,Q66575),f)))))) & (all M0 exists V ((s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> p(s(bool,V))) & s(Q66575,i(s(fun(fun(num,Q66575),Q66575),i(s(fun(fun(num,bool),fun(fun(num,Q66575),Q66575)),i(s(fun(fun(Q66575,fun(Q66575,Q66575)),fun(fun(num,bool),fun(fun(num,Q66575),Q66575))),iterate),s(fun(Q66575,fun(Q66575,Q66575)),OP))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(num,Q66575),f))) = s(Q66575,i(s(fun(Q66575,Q66575),i(s(fun(Q66575,fun(Q66575,Q66575)),i(s(fun(bool,fun(Q66575,fun(Q66575,Q66575))),cond),s(bool,V))),s(Q66575,i(s(fun(num,Q66575),f),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(Q66575,i(s(fun(fun(Q66575,fun(Q66575,Q66575)),Q66575),neutral),s(fun(Q66575,fun(Q66575,Q66575)),OP))))))))) # label(aITERATEu_CLAUSESu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 789 (all Q20493 all U_0 ((all P0 all X s(bool,i(s(fun(Q20493,bool),i(s(fun(Q20493,fun(Q20493,bool)),P0),s(Q20493,X))),s(Q20493,X))) = s(bool,i(s(fun(Q20493,bool),i(s(fun(fun(Q20493,fun(Q20493,bool)),fun(Q20493,bool)),U_0),s(fun(Q20493,fun(Q20493,bool)),P0))),s(Q20493,X)))) -> (all P0 all L s(bool,i(s(fun(list(Q20493),bool),i(s(fun(list(Q20493),fun(list(Q20493),bool)),i(s(fun(fun(Q20493,fun(Q20493,bool)),fun(list(Q20493),fun(list(Q20493),bool))),all2),s(fun(Q20493,fun(Q20493,bool)),P0))),s(list(Q20493),L))),s(list(Q20493),L))) = s(bool,i(s(fun(list(Q20493),bool),i(s(fun(fun(Q20493,bool),fun(list(Q20493),bool)),all0),s(fun(Q20493,bool),i(s(fun(fun(Q20493,fun(Q20493,bool)),fun(Q20493,bool)),U_0),s(fun(Q20493,fun(Q20493,bool)),P0))))),s(list(Q20493),L)))))) # label(aALL2u_ALL) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 790 (all B all A all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) | p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(B,bool),fun(fun(A,bool),bool)),l_u_c),s(fun(B,bool),T0))),s(fun(A,bool),S0)))) | p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))))) # label(aCARDu_LTu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 791 (all M0 all N0 all P0 s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,N0))),s(hreal,P0))) = s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,M0))),s(hreal,N0))))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,M0))),s(hreal,P0)))))) # label(aHREALu_LEu_ADDu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 792 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,M0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))))) # label(aLTu_MULT) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 793 (all A all P0 all Q0 ((p(s(bool,P0)) -> (all X p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))) <-> (all X (p(s(bool,P0)) -> p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))))) # label(aRIGHTu_FORALLu_IMPu_THM) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 794 (all A all P0 all Q0 ((exists X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> p(s(bool,Q0)))) <-> ((all X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) -> p(s(bool,Q0))))) # label(aLEFTu_EXISTSu_IMPu_THM) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 795 (all A all P0 all M0 ((all X ((all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(A,int),M0),s(A,Y))))),s(int,i(s(fun(A,int),M0),s(A,X)))))) -> p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))))) -> p(s(bool,i(s(fun(A,bool),P0),s(A,X)))))) & (all X p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(A,int),M0),s(A,X))))))) -> (all X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) # label(aWFu_INTu_MEASURE) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 796 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_neg),s(real,X)))))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))))) # label(aREALu_LEu_NEGTOTAL) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 797 (all T0 ((p(s(bool,f0)) <-> p(s(bool,T0)) & p(s(bool,f0))) & (p(s(bool,T0)) & p(s(bool,T0)) <-> p(s(bool,T0))) & (p(s(bool,f0)) <-> p(s(bool,T0)) & p(s(bool,f0))) & (p(s(bool,T0)) & p(s(bool,t)) <-> p(s(bool,T0))) & (p(s(bool,T0)) <-> p(s(bool,T0)) & p(s(bool,t))))) # label(aANDu_CLAUSES) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 798 (all M0 all N0 all P0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,P0))),s(num,N0))))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))),s(num,N0))))) # label(aMODu_MULTu_RMOD) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 799 (all X s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,i(s(fun(int,int),intu_neg),s(int,X)))))) # label(aINTu_LEu_NEGR) # label(axiom) # label(non_clause). [assumption]. 13.98/13.99 800 (all E0 s(real,E0) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,E0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,E0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) # label(aREALu_HALFu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 801 (all A all L all A5 all X (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),i(s(fun(A,fun(prod(A,A),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(prod(A,A),bool))),linseg),s(fun(prod(A,A),bool),L))),s(A,A5))))),s(A,X))) = s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,A5))))))) # label(aLINSEGu_FL) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 802 (all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))) # label(aLEu_ADDR) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 803 (all X all Y all Z0 p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),Z0))))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y))))),s(prod(hreal,hreal),Z0))))))) # label(aTREALu_MULu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 804 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Z0))),s(real,X)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0)))))) # label(aREALu_ABSu_BETWEEN1) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 805 (all D all A all B all P all C all U_1 ((all G0 all Y all F0 all X s(D,i(s(fun(P,D),i(s(fun(fun(A,B),fun(P,D)),i(s(fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D))),i(s(fun(fun(fun(A,B),fun(P,fun(C,D))),fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D)))),U_1),s(fun(fun(A,B),fun(P,fun(C,D))),G0))),s(fun(fun(A,B),fun(P,C)),Y))),s(fun(A,B),F0))),s(P,X))) = s(D,i(s(fun(C,D),i(s(fun(P,fun(C,D)),i(s(fun(fun(A,B),fun(P,fun(C,D))),G0),s(fun(A,B),F0))),s(P,X))),s(C,i(s(fun(P,C),i(s(fun(fun(A,B),fun(P,C)),Y),s(fun(A,B),F0))),s(P,X)))))) -> (all U_0 ((all G0 all Y all F0 s(fun(P,D),i(s(fun(fun(A,B),fun(P,D)),i(s(fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D))),i(s(fun(fun(fun(A,B),fun(P,fun(C,D))),fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D)))),U_1),s(fun(fun(A,B),fun(P,fun(C,D))),G0))),s(fun(fun(A,B),fun(P,C)),Y))),s(fun(A,B),F0))) = s(fun(P,D),i(s(fun(fun(A,B),fun(P,D)),i(s(fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D))),i(s(fun(fun(fun(A,B),fun(P,fun(C,D))),fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D)))),U_0),s(fun(fun(A,B),fun(P,fun(C,D))),G0))),s(fun(fun(A,B),fun(P,C)),Y))),s(fun(A,B),F0)))) -> (all L_L_ all P0 all S0 all G0 all Y (p(s(bool,i(s(fun(fun(fun(A,B),fun(P,fun(C,D))),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,fun(C,D))),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,fun(C,D))),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,fun(C,D))),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,fun(C,D))),G0)))) & p(s(bool,i(s(fun(fun(fun(A,B),fun(P,C)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,C)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,C)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,C)),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,C)),Y)))) -> p(s(bool,i(s(fun(fun(fun(A,B),fun(P,D)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,D)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,D)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,D)),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,D)),i(s(fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D))),i(s(fun(fun(fun(A,B),fun(P,fun(C,D))),fun(fun(fun(A,B),fun(P,C)),fun(fun(A,B),fun(P,D)))),U_0),s(fun(fun(A,B),fun(P,fun(C,D))),G0))),s(fun(fun(A,B),fun(P,C)),Y)))))))))))) # label(aADMISSIBLEu_COMB) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 806 (all Q89780 all Q89779 all F0 all S0 p(s(bool,i(s(fun(fun(Q89779,bool),bool),i(s(fun(fun(Q89780,bool),fun(fun(Q89779,bool),bool)),l_a_u_c),s(fun(Q89780,bool),i(s(fun(fun(Q89779,bool),fun(Q89780,bool)),i(s(fun(fun(Q89779,Q89780),fun(fun(Q89779,bool),fun(Q89780,bool))),image),s(fun(Q89779,Q89780),F0))),s(fun(Q89779,bool),S0))))),s(fun(Q89779,bool),S0))))) # label(aCARDu_LEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 807 (all A ((all H0 ((all F0 all G0 all X ((all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Z0))),s(A,X)))) -> s(num,i(s(fun(A,num),F0),s(A,Z0))) = s(num,i(s(fun(A,num),G0),s(A,Z0))))) -> s(num,i(s(fun(A,num),i(s(fun(fun(A,num),fun(A,num)),H0),s(fun(A,num),G0))),s(A,X))) = s(num,i(s(fun(A,num),i(s(fun(fun(A,num),fun(A,num)),H0),s(fun(A,num),F0))),s(A,X))))) -> (exists F0 all X s(num,i(s(fun(A,num),i(s(fun(fun(A,num),fun(A,num)),H0),s(fun(A,num),F0))),s(A,X))) = s(num,i(s(fun(A,num),F0),s(A,X)))))) -> p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))))) # label(aWFu_RECu_WF) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 808 (all A all P0 all S0 all T0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),fun(A,bool))),hull),s(fun(fun(A,bool),bool),P0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),fun(A,bool))),hull),s(fun(fun(A,bool),bool),P0))),s(fun(A,bool),T0))))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),fun(A,bool))),hull),s(fun(fun(A,bool),bool),P0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aHULLu_UNIONu_RIGHT) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 809 (all A all L all X all Y (s(A,X) != s(A,Y) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) <-> p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))))) # label(aless) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 810 (all A all S0 -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),empty))))) # label(aNOTu_PSUBSETu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 811 (all X (s(int,X) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(int,i(s(fun(int,int),intu_sgn),s(int,X))) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aINTu_SGNu_EQu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 812 (all A all U_0 ((all S0 all GENR_PVARR_3 ((exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_3))),s(bool,V))),s(A,X)))) & (p(s(bool,V)) <-> (all U (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),U))),s(fun(fun(A,bool),bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U))))))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),U_0),s(fun(fun(A,bool),bool),S0))),s(A,GENR_PVARR_3)))))) -> (all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),U_0),s(fun(fun(A,bool),bool),S0))))) = s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),inters),s(fun(fun(A,bool),bool),S0)))))) # label(aINTERS) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 813 (all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,M0))))))) # label(aSsrnato_lequ_addr) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 814 (all A s(fun(A,bool),univ) != s(fun(A,bool),empty)) # label(aEMPTYu_NOTu_UNIV) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 815 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aDIVu_LT) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 816 (all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))))) # label(aSUMu_TRIVu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 817 (all X all Y (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(prod(hreal,hreal),X)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(prod(hreal,hreal),Y)))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))))))) # label(aTREALu_LEu_MUL) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 818 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),infinite),s(fun(B,bool),T0)))))) # label(aCARDu_LEu_INFINITE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 819 (all X all N0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) & s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(real,real),realu_abs),s(real,X))))) # label(aREALu_POWu_EQu_1u_IMP) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 820 (all Q20216 all Q20218 all L1 all L2 (s(num,i(s(fun(list(Q20218),num),length),s(list(Q20218),L2))) = s(num,i(s(fun(list(Q20216),num),length),s(list(Q20216),L1))) -> s(list(Q20218),L2) = s(list(Q20218),i(s(fun(list(prod(Q20216,Q20218)),list(Q20218)),i(s(fun(fun(prod(Q20216,Q20218),Q20218),fun(list(prod(Q20216,Q20218)),list(Q20218))),map0),s(fun(prod(Q20216,Q20218),Q20218),snd))),s(list(prod(Q20216,Q20218)),i(s(fun(list(Q20218),list(prod(Q20216,Q20218))),i(s(fun(list(Q20216),fun(list(Q20218),list(prod(Q20216,Q20218)))),zip0),s(list(Q20216),L1))),s(list(Q20218),L2))))))) # label(aMAPu_SNDu_ZIP) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 821 (all A all P0 all Q0 (((exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) -> p(s(bool,Q0))) <-> (all X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> p(s(bool,Q0)))))) # label(aLEFTu_FORALLu_IMPu_THM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 822 (all U_0 ((all X all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(int,fun(num,bool)),U_0),s(int,X))),s(num,N0)))) <-> s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))) = s(int,X))) -> (all X s(num,i(s(fun(int,num),numu_ofu_int),s(int,X))) = s(num,i(s(fun(fun(num,bool),num),h_),s(fun(num,bool),i(s(fun(int,fun(num,bool)),U_0),s(int,X)))))))) # label(anumu_ofu_int) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 823 (all N0 all X (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0)))))))) # label(aINTu_POWu_LEu_1) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 824 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) <-> -p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))))) # label(aNOTu_LT) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 825 (all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aDIVu_0) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 826 (all A all B all U_0 ((all S0 all T0 all GENR_PVARR_79 ((exists X exists Y exists V ((p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(bool,fun(prod(A,B),bool)),i(s(fun(prod(A,B),fun(bool,fun(prod(A,B),bool))),setspec),s(prod(A,B),GENR_PVARR_79))),s(bool,V))),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))))) <-> p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(prod(A,B),GENR_PVARR_79)))))) -> (all S0 all M0 all T0 all N0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(B,bool),fun(num,bool)),hasu_size),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X))))),s(num,N0)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,M0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(prod(A,B),bool),fun(num,bool)),hasu_size),s(fun(prod(A,B),bool),i(s(fun(fun(prod(A,B),bool),fun(prod(A,B),bool)),gspec),s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))))))) # label(aHASu_SIZEu_PRODUCTu_DEPENDENT) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 827 (all Q64627 all Q64645 all OP (p(s(bool,i(s(fun(fun(Q64645,fun(Q64645,Q64645)),bool),monoidal),s(fun(Q64645,fun(Q64645,Q64645)),OP)))) -> (all S0 all T0 all F0 (p(s(bool,i(s(fun(fun(Q64627,bool),bool),finite),s(fun(Q64627,bool),S0)))) & p(s(bool,i(s(fun(fun(Q64627,bool),bool),finite),s(fun(Q64627,bool),T0)))) -> s(Q64645,i(s(fun(Q64645,Q64645),i(s(fun(Q64645,fun(Q64645,Q64645)),OP),s(Q64645,i(s(fun(fun(Q64627,Q64645),Q64645),i(s(fun(fun(Q64627,bool),fun(fun(Q64627,Q64645),Q64645)),i(s(fun(fun(Q64645,fun(Q64645,Q64645)),fun(fun(Q64627,bool),fun(fun(Q64627,Q64645),Q64645))),iterate),s(fun(Q64645,fun(Q64645,Q64645)),OP))),s(fun(Q64627,bool),S0))),s(fun(Q64627,Q64645),F0))))),s(Q64645,i(s(fun(fun(Q64627,Q64645),Q64645),i(s(fun(fun(Q64627,bool),fun(fun(Q64627,Q64645),Q64645)),i(s(fun(fun(Q64645,fun(Q64645,Q64645)),fun(fun(Q64627,bool),fun(fun(Q64627,Q64645),Q64645))),iterate),s(fun(Q64645,fun(Q64645,Q64645)),OP))),s(fun(Q64627,bool),T0))),s(fun(Q64627,Q64645),F0))))) = s(Q64645,i(s(fun(Q64645,Q64645),i(s(fun(Q64645,fun(Q64645,Q64645)),OP),s(Q64645,i(s(fun(fun(Q64627,Q64645),Q64645),i(s(fun(fun(Q64627,bool),fun(fun(Q64627,Q64645),Q64645)),i(s(fun(fun(Q64645,fun(Q64645,Q64645)),fun(fun(Q64627,bool),fun(fun(Q64627,Q64645),Q64645))),iterate),s(fun(Q64645,fun(Q64645,Q64645)),OP))),s(fun(Q64627,bool),i(s(fun(fun(Q64627,bool),fun(Q64627,bool)),i(s(fun(fun(Q64627,bool),fun(fun(Q64627,bool),fun(Q64627,bool))),union),s(fun(Q64627,bool),S0))),s(fun(Q64627,bool),T0))))),s(fun(Q64627,Q64645),F0))))),s(Q64645,i(s(fun(fun(Q64627,Q64645),Q64645),i(s(fun(fun(Q64627,bool),fun(fun(Q64627,Q64645),Q64645)),i(s(fun(fun(Q64645,fun(Q64645,Q64645)),fun(fun(Q64627,bool),fun(fun(Q64627,Q64645),Q64645))),iterate),s(fun(Q64645,fun(Q64645,Q64645)),OP))),s(fun(Q64627,bool),i(s(fun(fun(Q64627,bool),fun(Q64627,bool)),i(s(fun(fun(Q64627,bool),fun(fun(Q64627,bool),fun(Q64627,bool))),inter),s(fun(Q64627,bool),S0))),s(fun(Q64627,bool),T0))))),s(fun(Q64627,Q64645),F0))))))))) # label(aITERATEu_INCLu_EXCL) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 828 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,i(s(fun(int,int),intu_neg),s(int,Y))))) = s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y)))))) # label(aINTu_MULu_RNEG) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 829 (all Q69133 all U all V all F0 (p(s(bool,i(s(fun(fun(Q69133,bool),bool),i(s(fun(fun(Q69133,bool),fun(fun(Q69133,bool),bool)),subset),s(fun(Q69133,bool),U))),s(fun(Q69133,bool),V)))) & p(s(bool,i(s(fun(fun(Q69133,bool),bool),finite),s(fun(Q69133,bool),V)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(Q69133,num),num),i(s(fun(fun(Q69133,bool),fun(fun(Q69133,num),num)),nsum),s(fun(Q69133,bool),U))),s(fun(Q69133,num),F0))))),s(num,i(s(fun(fun(Q69133,num),num),i(s(fun(fun(Q69133,bool),fun(fun(Q69133,num),num)),nsum),s(fun(Q69133,bool),V))),s(fun(Q69133,num),F0)))))))) # label(aNSUMu_SUBSETu_SIMPLE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 830 (all Q97725 all U_0 ((all P0 all Q0 all X (p(s(bool,i(s(fun(fun(Q97725,bool),bool),i(s(fun(fun(fun(Q97725,bool),bool),fun(fun(Q97725,bool),bool)),i(s(fun(fun(fun(Q97725,bool),bool),fun(fun(fun(Q97725,bool),bool),fun(fun(Q97725,bool),bool))),U_0),s(fun(fun(Q97725,bool),bool),P0))),s(fun(fun(Q97725,bool),bool),Q0))),s(fun(Q97725,bool),X)))) <-> p(s(bool,i(s(fun(fun(Q97725,bool),bool),Q0),s(fun(Q97725,bool),X)))) & p(s(bool,i(s(fun(fun(Q97725,bool),bool),P0),s(fun(Q97725,bool),X)))))) -> (all P0 all Q0 ((all F0 ((all S0 (p(s(bool,i(s(fun(fun(fun(Q97725,bool),bool),bool),i(s(fun(fun(Q97725,bool),fun(fun(fun(Q97725,bool),bool),bool)),in),s(fun(Q97725,bool),S0))),s(fun(fun(Q97725,bool),bool),F0)))) -> p(s(bool,i(s(fun(fun(Q97725,bool),bool),Q0),s(fun(Q97725,bool),S0)))))) -> p(s(bool,i(s(fun(fun(Q97725,bool),bool),Q0),s(fun(Q97725,bool),i(s(fun(fun(fun(Q97725,bool),bool),fun(Q97725,bool)),inters),s(fun(fun(Q97725,bool),bool),F0)))))))) & (all S0 (p(s(bool,i(s(fun(fun(Q97725,bool),bool),Q0),s(fun(Q97725,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q97725,bool),bool),Q0),s(fun(Q97725,bool),i(s(fun(fun(Q97725,bool),fun(Q97725,bool)),i(s(fun(fun(fun(Q97725,bool),bool),fun(fun(Q97725,bool),fun(Q97725,bool))),hull),s(fun(fun(Q97725,bool),bool),P0))),s(fun(Q97725,bool),S0)))))))) & (all F0 ((all S0 (p(s(bool,i(s(fun(fun(fun(Q97725,bool),bool),bool),i(s(fun(fun(Q97725,bool),fun(fun(fun(Q97725,bool),bool),bool)),in),s(fun(Q97725,bool),S0))),s(fun(fun(Q97725,bool),bool),F0)))) -> p(s(bool,i(s(fun(fun(Q97725,bool),bool),P0),s(fun(Q97725,bool),S0)))))) -> p(s(bool,i(s(fun(fun(Q97725,bool),bool),P0),s(fun(Q97725,bool),i(s(fun(fun(fun(Q97725,bool),bool),fun(Q97725,bool)),inters),s(fun(fun(Q97725,bool),bool),F0)))))))) -> s(fun(Q97725,bool),i(s(fun(fun(Q97725,bool),fun(Q97725,bool)),i(s(fun(fun(fun(Q97725,bool),bool),fun(fun(Q97725,bool),fun(Q97725,bool))),hull),s(fun(fun(Q97725,bool),bool),i(s(fun(fun(fun(Q97725,bool),bool),fun(fun(Q97725,bool),bool)),i(s(fun(fun(fun(Q97725,bool),bool),fun(fun(fun(Q97725,bool),bool),fun(fun(Q97725,bool),bool))),U_0),s(fun(fun(Q97725,bool),bool),P0))),s(fun(fun(Q97725,bool),bool),Q0))))),s(fun(Q97725,bool),s0))) = s(fun(Q97725,bool),i(s(fun(fun(Q97725,bool),fun(Q97725,bool)),i(s(fun(fun(fun(Q97725,bool),bool),fun(fun(Q97725,bool),fun(Q97725,bool))),hull),s(fun(fun(Q97725,bool),bool),P0))),s(fun(Q97725,bool),i(s(fun(fun(Q97725,bool),fun(Q97725,bool)),i(s(fun(fun(fun(Q97725,bool),bool),fun(fun(Q97725,bool),fun(Q97725,bool))),hull),s(fun(fun(Q97725,bool),bool),Q0))),s(fun(Q97725,bool),s0))))))))) # label(aHULLu_Pu_ANDu_Q) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 831 (all M0 all N0 all P0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,P0) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,N0))),s(num,P0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,P0)))))))) # label(aMULTu_DIVu_LE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 832 (all Q48280 all Q48276 all F0 all S0 all X (p(s(bool,i(s(fun(fun(Q48276,bool),bool),i(s(fun(Q48276,fun(fun(Q48276,bool),bool)),in),s(Q48276,X))),s(fun(Q48276,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q48280,bool),bool),i(s(fun(Q48280,fun(fun(Q48280,bool),bool)),in),s(Q48280,i(s(fun(Q48276,Q48280),F0),s(Q48276,X))))),s(fun(Q48280,bool),i(s(fun(fun(Q48276,bool),fun(Q48280,bool)),i(s(fun(fun(Q48276,Q48280),fun(fun(Q48276,bool),fun(Q48280,bool))),image),s(fun(Q48276,Q48280),F0))),s(fun(Q48276,bool),S0)))))))) # label(aFUNu_INu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 833 (all X all N0 (s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,X) & s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aINTu_POWu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 834 (all Q92699 all U_0 ((all S0 all P0 all GENR_PVARR_226 (p(s(bool,i(s(fun(Q92699,bool),i(s(fun(fun(Q92699,bool),fun(Q92699,bool)),i(s(fun(fun(Q92699,bool),fun(fun(Q92699,bool),fun(Q92699,bool))),U_0),s(fun(Q92699,bool),S0))),s(fun(Q92699,bool),P0))),s(Q92699,GENR_PVARR_226)))) <-> (exists X exists V (p(s(bool,i(s(fun(Q92699,bool),i(s(fun(bool,fun(Q92699,bool)),i(s(fun(Q92699,fun(bool,fun(Q92699,bool))),setspec),s(Q92699,GENR_PVARR_226))),s(bool,V))),s(Q92699,X)))) & (p(s(bool,i(s(fun(fun(Q92699,bool),bool),i(s(fun(Q92699,fun(fun(Q92699,bool),bool)),in),s(Q92699,X))),s(fun(Q92699,bool),S0)))) & p(s(bool,i(s(fun(Q92699,bool),P0),s(Q92699,X)))) <-> p(s(bool,V))))))) -> (all S0 all P0 (p(s(bool,i(s(fun(fun(Q92699,bool),bool),countable),s(fun(Q92699,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q92699,bool),bool),countable),s(fun(Q92699,bool),i(s(fun(fun(Q92699,bool),fun(Q92699,bool)),gspec),s(fun(Q92699,bool),i(s(fun(fun(Q92699,bool),fun(Q92699,bool)),i(s(fun(fun(Q92699,bool),fun(fun(Q92699,bool),fun(Q92699,bool))),U_0),s(fun(Q92699,bool),S0))),s(fun(Q92699,bool),P0)))))))))))) # label(aCOUNTABLEu_RESTRICT) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 835 (all M0 all N0 all P0 all Q0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,Q0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,P0))),s(num,M0)))) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))) <-> p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(fun(num,bool),fun(fun(num,bool),bool)),subset),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,P0))),s(num,Q0)))))))) # label(aSUBSETu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 836 (all A ((p(s(bool,c)) -> p(s(bool,i(s(fun(A,bool),p0),s(A,x))))) & (-p(s(bool,c)) -> p(s(bool,i(s(fun(A,bool),p0),s(A,y))))) <-> p(s(bool,i(s(fun(A,bool),p0),s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),i(s(fun(bool,fun(A,fun(A,A))),cond),s(bool,c))),s(A,x))),s(A,y)))))))) # label(aCONDu_ELIMu_THM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 837 (all D0 (s(num,a0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,b0))),s(num,D0))) | s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,D0) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,a0))),s(num,b0)))) -> p(s(bool,i(s(fun(num,bool),p0),s(num,D0)))))) <-> p(s(bool,i(s(fun(num,bool),p0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,a0))),s(num,b0)))))) # label(aSUBu_ELIMu_THM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 838 (all A all B all U_2 ((all F0 all J0 all I0 s(num,i(s(fun(B,num),i(s(fun(A,fun(B,num)),F0),s(A,I0))),s(B,J0))) = s(num,i(s(fun(A,num),i(s(fun(B,fun(A,num)),i(s(fun(fun(A,fun(B,num)),fun(B,fun(A,num))),U_2),s(fun(A,fun(B,num)),F0))),s(B,J0))),s(A,I0)))) -> (all U_1 ((all S0 all F0 all J0 s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(B,fun(A,num)),i(s(fun(fun(A,fun(B,num)),fun(B,fun(A,num))),U_2),s(fun(A,fun(B,num)),F0))),s(B,J0))))) = s(num,i(s(fun(B,num),i(s(fun(fun(A,fun(B,num)),fun(B,num)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,num)),fun(B,num))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,num)),F0))),s(B,J0)))) -> (all U_0 ((all T0 all F0 all I0 s(num,i(s(fun(A,num),i(s(fun(fun(A,fun(B,num)),fun(A,num)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,num)),fun(A,num))),U_0),s(fun(B,bool),T0))),s(fun(A,fun(B,num)),F0))),s(A,I0))) = s(num,i(s(fun(fun(B,num),num),i(s(fun(fun(B,bool),fun(fun(B,num),num)),nsum),s(fun(B,bool),T0))),s(fun(B,num),i(s(fun(A,fun(B,num)),F0),s(A,I0)))))) -> (all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) -> s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(fun(A,fun(B,num)),fun(A,num)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,num)),fun(A,num))),U_0),s(fun(B,bool),T0))),s(fun(A,fun(B,num)),F0))))) = s(num,i(s(fun(fun(B,num),num),i(s(fun(fun(B,bool),fun(fun(B,num),num)),nsum),s(fun(B,bool),T0))),s(fun(B,num),i(s(fun(fun(A,fun(B,num)),fun(B,num)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,num)),fun(B,num))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,num)),F0))))))))))))) # label(aNSUMu_SWAP) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 839 (all A all A5 all B0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),B0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),B0))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),A5)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),A5))),s(fun(A,bool),B0)))) -> s(fun(A,bool),B0) = s(fun(A,bool),A5))) # label(aCARDu_SUBSETu_LE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 840 (all A all S0 all T0 all U s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),T0))),s(fun(A,bool),U))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,bool),U)))) # label(aUNIONu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 841 (all A all B all P0 ((all X all Y p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y))))) <-> (all Y all X p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y))))))) # label(aSWAPu_FORALLu_THM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 842 (all A all S0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),univ))))) # label(aSUBSETu_UNIV) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 843 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,M0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))) # label(aADDu_SYM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 844 (all B all A all F0 ((exists G0 ((all X s(A,X) = s(A,i(s(fun(B,A),G0),s(B,i(s(fun(A,B),F0),s(A,X)))))) & (all Y s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,i(s(fun(B,A),G0),s(B,Y)))))))) <-> (all X all Y (s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) -> s(A,Y) = s(A,X))) & (all Y exists X s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y)))) # label(aBIJECTIVEu_LEFTu_RIGHTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 845 (all A all P0 (-(all X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) <-> (exists X -p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) # label(aNOTu_FORALLu_THM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 846 (all S0 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) & s(fun(real,bool),S0) != s(fun(real,bool),empty) -> (exists B0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,X)))))) & p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,B0))),s(fun(real,bool),S0)))))))) # label(aINFu_FINITEu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 847 (all A all L all M0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),M0))),s(fun(prod(A,A),bool),L)))) & s(fun(prod(A,A),bool),M0) != s(fun(prod(A,A),bool),L) -> (exists A5 (-p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),M0))),s(A,A5)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,A5)))))))) # label(aINSEGu_PROPERu_SUBSETu_FL) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 848 (all X all Y -(p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,X)))))) # label(aINTu_LETu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 849 (all N0 s(num,u_0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,u_0)))) # label(aARITHu_MULTu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 850 (all F0 all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) -> s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))),s(fun(num,real),F0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))),s(fun(num,real),F0))))))) # label(aSUMu_ADDu_SPLIT) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 851 (all Q46638 s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),q))),s(fun(Q46638,bool),p1))) = s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),p1))),s(fun(Q46638,bool),q)))) # label(aINTERu_ACIu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 852 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) | p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))))) # label(aFINITEu_INTER) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 853 (all Q92567 all S0 s(bool,i(s(fun(fun(Q92567,bool),bool),countable),s(fun(Q92567,bool),S0))) = s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(fun(Q92567,bool),fun(fun(num,bool),bool)),l_a_u_c),s(fun(Q92567,bool),S0))),s(fun(num,bool),univ)))) # label(aCOUNTABLEu_ALT) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 854 (all B all A all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) | p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(B,bool),fun(fun(A,bool),bool)),l_u_c),s(fun(B,bool),T0))),s(fun(A,bool),S0)))))) # label(aCARDu_LETu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 855 (all X all Y all N0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,N0))))) = s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))))),s(num,N0)))) # label(aINTu_POWu_MUL) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 856 (all A5 all B0 all C0 all D0 (p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,A5))),s(hreal,B0)))) & p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,C0))),s(hreal,D0)))) -> p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,A5))),s(hreal,C0))))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,B0))),s(hreal,D0)))))))) # label(aHREALu_LEu_ADD2) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 857 (all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,u_0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,u_0))),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_LTu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 858 (all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))))) # label(aLEu_1u_conjunct4) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 859 (all A all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (exists A5 all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,A5)))))))) # label(aUPPERu_BOUNDu_FINITEu_SET) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 860 (all X s(int,i(s(fun(int,int),intu_abs),s(int,X))) = s(int,i(s(fun(real,int),intu_ofu_real),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X)))))))) # label(aintu_abs) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 861 (all A all T1 all T2 (s(A,T2) = s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),i(s(fun(bool,fun(A,fun(A,A))),cond),s(bool,f0))),s(A,T1))),s(A,T2))) & s(A,T1) = s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),i(s(fun(bool,fun(A,fun(A,A))),cond),s(bool,t))),s(A,T1))),s(A,T2))))) # label(aCONDu_CLAUSES) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 862 (all Q4537 all Q4545 all Q4544 all U_0 ((all T0 all F0 (p(s(bool,i(s(fun(fun(prod(Q4545,Q4544),Q4537),bool),i(s(fun(fun(prod(Q4545,Q4544),Q4537),fun(fun(prod(Q4545,Q4544),Q4537),bool)),U_0),s(fun(prod(Q4545,Q4544),Q4537),T0))),s(fun(prod(Q4545,Q4544),Q4537),F0)))) <-> (all X all Y p(s(bool,i(s(fun(Q4537,bool),i(s(fun(Q4537,fun(Q4537,bool)),geq),s(Q4537,i(s(fun(prod(Q4545,Q4544),Q4537),F0),s(prod(Q4545,Q4544),i(s(fun(Q4544,prod(Q4545,Q4544)),i(s(fun(Q4545,fun(Q4544,prod(Q4545,Q4544))),c_),s(Q4545,X))),s(Q4544,Y))))))),s(Q4537,i(s(fun(prod(Q4545,Q4544),Q4537),T0),s(prod(Q4545,Q4544),i(s(fun(Q4544,prod(Q4545,Q4544)),i(s(fun(Q4545,fun(Q4544,prod(Q4545,Q4544))),c_),s(Q4545,X))),s(Q4544,Y))))))))))) -> (all T0 all X s(Q4537,i(s(fun(prod(Q4545,Q4544),Q4537),i(s(fun(fun(fun(prod(Q4545,Q4544),Q4537),bool),fun(prod(Q4545,Q4544),Q4537)),gabs),s(fun(fun(prod(Q4545,Q4544),Q4537),bool),i(s(fun(fun(prod(Q4545,Q4544),Q4537),fun(fun(prod(Q4545,Q4544),Q4537),bool)),U_0),s(fun(prod(Q4545,Q4544),Q4537),T0))))),s(prod(Q4545,Q4544),X))) = s(Q4537,i(s(fun(prod(Q4545,Q4544),Q4537),T0),s(prod(Q4545,Q4544),X)))))) # label(aLAMBDAu_PAIRu_THM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 863 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))) = s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0))))) # label(aCARDu_FINITEu_CONG) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 864 (all Q67819 all Q67795 all F0 all G0 all S0 ((all X all Y (p(s(bool,i(s(fun(fun(Q67819,bool),bool),i(s(fun(Q67819,fun(fun(Q67819,bool),bool)),in),s(Q67819,X))),s(fun(Q67819,bool),S0)))) & s(Q67795,i(s(fun(Q67819,Q67795),F0),s(Q67819,X))) = s(Q67795,i(s(fun(Q67819,Q67795),F0),s(Q67819,Y))) & p(s(bool,i(s(fun(fun(Q67819,bool),bool),i(s(fun(Q67819,fun(fun(Q67819,bool),bool)),in),s(Q67819,Y))),s(fun(Q67819,bool),S0)))) -> s(Q67819,X) = s(Q67819,Y))) -> s(num,i(s(fun(fun(Q67795,num),num),i(s(fun(fun(Q67795,bool),fun(fun(Q67795,num),num)),nsum),s(fun(Q67795,bool),i(s(fun(fun(Q67819,bool),fun(Q67795,bool)),i(s(fun(fun(Q67819,Q67795),fun(fun(Q67819,bool),fun(Q67795,bool))),image),s(fun(Q67819,Q67795),F0))),s(fun(Q67819,bool),S0))))),s(fun(Q67795,num),G0))) = s(num,i(s(fun(fun(Q67819,num),num),i(s(fun(fun(Q67819,bool),fun(fun(Q67819,num),num)),nsum),s(fun(Q67819,bool),S0))),s(fun(Q67819,num),i(s(fun(fun(Q67819,Q67795),fun(Q67819,num)),i(s(fun(fun(Q67795,num),fun(fun(Q67819,Q67795),fun(Q67819,num))),o),s(fun(Q67795,num),G0))),s(fun(Q67819,Q67795),F0))))))) # label(aNSUMu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 865 (all A all X all Y all S0 (s(A,X) = s(A,Y) | p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,Y))),s(fun(A,bool),S0)))))))) # label(aINu_INSERT) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 866 (all A all B all P0 exists X exists Y s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y))) = s(prod(A,B),P0)) # label(aPAIRu_SURJECTIVE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 867 (all X all Y s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,Y))),s(hreal,X))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,X))),s(hreal,Y)))) # label(aHREALu_MULu_SYM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 868 (all M0 all N0 (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,M0))))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,N0)))))) <-> s(num,M0) = s(num,N0))) # label(aNADDu_OFu_NUMu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 869 (all M0 all N0 all P0 all Q0 (s(num,M0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,Q0))),s(num,P0))))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,P0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,N0))),s(num,P0))))) # label(aMODu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 870 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,M0))))),s(num,i(s(fun(num,num),numeral),s(num,N0)))))) # label(aARITHu_LTu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 871 (all X all Y all N0 (s(num,X) = s(num,Y) | s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,N0) <-> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,Y))),s(num,N0))))) # label(aEXPu_MONOu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 872 (all Q54808 all S0 all T0 (p(s(bool,i(s(fun(fun(Q54808,bool),bool),finite),s(fun(Q54808,bool),T0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(Q54808,bool),num),card),s(fun(Q54808,bool),i(s(fun(fun(Q54808,bool),fun(Q54808,bool)),i(s(fun(fun(Q54808,bool),fun(fun(Q54808,bool),fun(Q54808,bool))),union),s(fun(Q54808,bool),S0))),s(fun(Q54808,bool),T0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(Q54808,bool),num),card),s(fun(Q54808,bool),S0))))),s(num,i(s(fun(fun(Q54808,bool),num),card),s(fun(Q54808,bool),T0)))))))) & p(s(bool,i(s(fun(fun(Q54808,bool),bool),finite),s(fun(Q54808,bool),S0)))) -> s(fun(Q54808,bool),i(s(fun(fun(Q54808,bool),fun(Q54808,bool)),i(s(fun(fun(Q54808,bool),fun(fun(Q54808,bool),fun(Q54808,bool))),inter),s(fun(Q54808,bool),S0))),s(fun(Q54808,bool),T0))) != s(fun(Q54808,bool),empty))) # label(aCARDu_UNIONu_OVERLAP) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 873 (all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X))) = s(real,X)) # label(aREALu_MULu_LID) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 874 (all M0 all N0 all P0 (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,N0))),s(num,P0))))) # label(aDIVu_MULT2) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 875 (all T1 all T2 (p(s(bool,T1)) & p(s(bool,T2)) <-> p(s(bool,T2)) & p(s(bool,T1)))) # label(aCONJu_SYM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.00 876 (all A all S0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,N0)))) -> (exists F0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> (all M0 all XI_ (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,XI_))),s(num,N0)))) & s(A,i(s(fun(num,A),F0),s(num,XI_))) = s(A,X) & s(A,X) = s(A,i(s(fun(num,A),F0),s(num,M0))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> s(num,M0) = s(num,XI_))) & (exists M0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) & s(A,i(s(fun(num,A),F0),s(num,M0))) = s(A,X))))) & (all M0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(num,A),F0),s(num,M0))))),s(fun(A,bool),S0)))))))))) # label(aHASu_SIZEu_INDEX) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 877 (all X all XI_ ((all R0 ((p(s(bool,X)) -> p(s(bool,R0))) -> ((p(s(bool,XI_)) -> p(s(bool,R0))) -> p(s(bool,R0))))) <-> p(s(bool,X)) | p(s(bool,XI_)))) # label(aORu_DEF) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 878 (all X all Y all Z0 s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,X))),s(hreal,Y))))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,X))),s(hreal,Z0))))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,X))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,Y))),s(hreal,Z0)))))) # label(aHREALu_ADDu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 879 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,Y))))),s(real,Z0)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0)))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Z0)))))) # label(aREALu_MINu_LT) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 880 (all Q48322 all Q48318 all S0 all T0 ((all X s(bool,i(s(fun(fun(Q48318,bool),bool),i(s(fun(Q48318,fun(fun(Q48318,bool),bool)),in),s(Q48318,i(s(fun(Q48322,Q48318),f),s(Q48322,X))))),s(fun(Q48318,bool),T0))) = s(bool,i(s(fun(fun(Q48322,bool),bool),i(s(fun(Q48322,fun(fun(Q48322,bool),bool)),in),s(Q48322,X))),s(fun(Q48322,bool),S0)))) & (all Y (p(s(bool,i(s(fun(fun(Q48318,bool),bool),i(s(fun(Q48318,fun(fun(Q48318,bool),bool)),in),s(Q48318,Y))),s(fun(Q48318,bool),T0)))) -> (exists X s(Q48318,Y) = s(Q48318,i(s(fun(Q48322,Q48318),f),s(Q48322,X)))))) -> s(fun(Q48318,bool),T0) = s(fun(Q48318,bool),i(s(fun(fun(Q48322,bool),fun(Q48318,bool)),i(s(fun(fun(Q48322,Q48318),fun(fun(Q48322,bool),fun(Q48318,bool))),image),s(fun(Q48322,Q48318),f))),s(fun(Q48322,bool),S0))))) # label(aSURJECTIVEu_IMAGEu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 881 (all A all B all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all S0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(B,i(s(fun(fun(B,fun(B,B)),B),neutral),s(fun(B,fun(B,B)),OP))) = s(B,i(s(fun(A,B),F0),s(A,X))))) -> s(B,i(s(fun(fun(B,fun(B,B)),B),neutral),s(fun(B,fun(B,B)),OP))) = s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))))))) # label(aITERATEu_EQu_NEUTRAL) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 882 (all A all U_0 ((all F0 all T0 s(num,i(s(fun(fun(A,bool),num),i(s(fun(fun(A,num),fun(fun(A,bool),num)),U_0),s(fun(A,num),F0))),s(fun(A,bool),T0))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),T0))),s(fun(A,num),F0)))) -> (all F0 all S0 (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),finite),s(fun(fun(A,bool),bool),S0)))) & (all T0 (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T0))),s(fun(fun(A,bool),bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))))) & (all T1 all T2 all X (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T2))),s(fun(fun(A,bool),bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T2)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T1)))) & s(fun(A,bool),T1) != s(fun(A,bool),T2) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T1))),s(fun(fun(A,bool),bool),S0)))) -> s(num,i(s(fun(A,num),F0),s(A,X))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(num,i(s(fun(fun(fun(A,bool),num),num),i(s(fun(fun(fun(A,bool),bool),fun(fun(fun(A,bool),num),num)),nsum),s(fun(fun(A,bool),bool),S0))),s(fun(fun(A,bool),num),i(s(fun(fun(A,num),fun(fun(A,bool),num)),U_0),s(fun(A,num),F0))))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),unions),s(fun(fun(A,bool),bool),S0))))),s(fun(A,num),F0))))))) # label(aNSUMu_UNIONSu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 883 (all Q56227 all Q56231 all S0 all T0 (s(fun(prod(Q56227,Q56231),bool),i(s(fun(fun(Q56231,bool),fun(prod(Q56227,Q56231),bool)),i(s(fun(fun(Q56227,bool),fun(fun(Q56231,bool),fun(prod(Q56227,Q56231),bool))),cross0),s(fun(Q56227,bool),S0))),s(fun(Q56231,bool),T0))) = s(fun(prod(Q56227,Q56231),bool),empty) <-> s(fun(Q56231,bool),empty) = s(fun(Q56231,bool),T0) | s(fun(Q56227,bool),empty) = s(fun(Q56227,bool),S0))) # label(aCROSSu_EQu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 884 (all Q48393 all U_0 ((all A5 all GENR_PVARR_16 (p(s(bool,i(s(fun(Q48393,bool),i(s(fun(Q48393,fun(Q48393,bool)),U_0),s(Q48393,A5))),s(Q48393,GENR_PVARR_16)))) <-> (exists X exists V (p(s(bool,i(s(fun(Q48393,bool),i(s(fun(bool,fun(Q48393,bool)),i(s(fun(Q48393,fun(bool,fun(Q48393,bool))),setspec),s(Q48393,GENR_PVARR_16))),s(bool,V))),s(Q48393,X)))) & (s(Q48393,X) = s(Q48393,A5) <-> p(s(bool,V))))))) -> (all A5 s(fun(Q48393,bool),i(s(fun(fun(Q48393,bool),fun(Q48393,bool)),gspec),s(fun(Q48393,bool),i(s(fun(Q48393,fun(Q48393,bool)),U_0),s(Q48393,A5))))) = s(fun(Q48393,bool),i(s(fun(fun(Q48393,bool),fun(Q48393,bool)),i(s(fun(Q48393,fun(fun(Q48393,bool),fun(Q48393,bool))),insert),s(Q48393,A5))),s(fun(Q48393,bool),empty)))))) # label(aSINGu_GSPECu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 885 (all X all Y all Z0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0))))),s(int,Y))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y))),s(int,Z0)))))) # label(aINTu_LEu_SUBu_LADD) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 886 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,i(s(fun(int,int),intu_neg),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,X)))) # label(aINTu_LTu_NEG) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 887 (all N0 s(num,u_0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,u_0))),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_MULTu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 888 (all X all N0 (s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(int,X) -> s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))) != s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aINTu_POWu_NZ) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 889 (all N0 all X all Y (p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))) -> (s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))) <-> s(real,X) = s(real,Y)))) # label(aREALu_POWu_EQu_ODDu_EQ) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 890 (all A all S0 all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),inters),s(fun(fun(A,bool),bool),S0)))))) <-> (all T0 (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T0))),s(fun(fun(A,bool),bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))))))) # label(aINu_INTERS) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 891 (all N0 (-p(s(bool,i(s(fun(num,bool),even),s(num,N0)))) <-> p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))))) # label(aNOTu_EVEN) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 892 (all X s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aREALu_POW2u_ABS) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 893 (all N0 ((exists M0 s(num,N0) = s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0)))))) <-> p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))))) # label(aODDu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 894 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Z0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Z0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Y))),s(int,Z0)))))))) # label(aINTu_LEu_RMUL) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 895 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Y))),s(real,X))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))) # label(aREALu_ADDu_SYM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 896 (all X all Y all Z0 (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Z0))),s(real,Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Z0))),s(real,X))) & s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(real,Z0) -> s(real,X) = s(real,Y))) # label(aREALu_EQu_LCANCELu_IMP) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 897 (all A all U_0 ((all L all X all Y (-p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(A,bool))),U_0),s(fun(prod(A,A),bool),L))),s(A,X))),s(A,Y)))))) -> (all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),L)))) <-> (all X (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) -> s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(A,bool))),U_0),s(fun(prod(A,A),bool),L))),s(A,X))))) = s(A,X))) & p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))))))) # label(aordinal) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 898 (all M0 all N0 s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_ADDu_conjunct8) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 899 (all A all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),univ))),s(fun(A,bool),S0))) = s(fun(A,bool),univ)) # label(aUNIONu_UNIVu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 900 (all A all M0 p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),i(s(fun(fun(A,num),fun(A,fun(A,bool))),measure0),s(fun(A,num),M0))))))) # label(aWFu_MEASURE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 901 (all X s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,X)))))) # label(aREALu_LEu_DOUBLE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 902 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,N0)))))) # label(aARITHu_EXPu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 903 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) -> s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))) = s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(fun(num,bool),fun(fun(num,bool),fun(num,bool))),union),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))))) # label(aNUMSEGu_ADDu_SPLIT) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 904 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,P0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0)))))) # label(aSUBu_ADDu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 905 (all A all P0 all L ((all M0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),P0),s(fun(prod(A,A),bool),M0)))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),M0))),s(fun(prod(A,A),bool),L)))))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),i(s(fun(fun(fun(prod(A,A),bool),bool),fun(prod(A,A),bool)),unions),s(fun(fun(prod(A,A),bool),bool),P0))))),s(fun(prod(A,A),bool),L)))))) # label(aUNIONu_INSEG) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 906 (all A all B all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all S0 all A5 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,A5))),s(fun(A,bool),S0)))) -> s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))) = s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),OP),s(B,i(s(fun(A,B),F0),s(A,A5))))),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,A5))))),s(fun(A,B),F0))))))))) # label(aITERATEu_DELETE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 907 (all X all Y -(p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,X)))))) # label(aREALu_LETu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 908 p(s(bool,r0)) | p(s(bool,p1)) | p(s(bool,q)) <-> p(s(bool,q)) | p(s(bool,r0)) | p(s(bool,p1)) # label(aDISJu_ACIu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 909 (all Q90309 all Q90290 all X s(bool,i(s(fun(fun(Q90290,bool),bool),i(s(fun(Q90290,fun(fun(Q90290,bool),bool)),in),s(Q90290,X))),s(fun(Q90290,bool),s0))) = s(bool,i(s(fun(fun(sum0(Q90290,Q90309),bool),bool),i(s(fun(sum0(Q90290,Q90309),fun(fun(sum0(Q90290,Q90309),bool),bool)),in),s(sum0(Q90290,Q90309),i(s(fun(Q90290,sum0(Q90290,Q90309)),inl),s(Q90290,X))))),s(fun(sum0(Q90290,Q90309),bool),i(s(fun(fun(Q90309,bool),fun(sum0(Q90290,Q90309),bool)),i(s(fun(fun(Q90290,bool),fun(fun(Q90309,bool),fun(sum0(Q90290,Q90309),bool))),p_u_c),s(fun(Q90290,bool),s0))),s(fun(Q90309,bool),t0)))))) # label(aINu_CARDu_ADDu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 910 (all X all Y (s(int,X) = s(int,Y) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))))) # label(aINTu_EQu_IMPu_LE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 911 (all X s(real,i(s(fun(real,real),realu_sgn),s(real,X))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))),s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) # label(arealu_sgn) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 912 (all A all X all Y all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,Y))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,Y))),s(fun(A,bool),S0)))))) # label(aINSERTu_COMM) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 913 (all A all B s(B,i(s(fun(sum0(A,B),B),outr),s(sum0(A,B),i(s(fun(B,sum0(A,B)),inr),s(B,y))))) = s(B,y)) # label(aOUTR) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 914 (all Q50997 all S0 (p(s(bool,i(s(fun(fun(fun(Q50997,bool),bool),bool),finite),s(fun(fun(Q50997,bool),bool),S0)))) -> (p(s(bool,i(s(fun(fun(Q50997,bool),bool),finite),s(fun(Q50997,bool),i(s(fun(fun(fun(Q50997,bool),bool),fun(Q50997,bool)),unions),s(fun(fun(Q50997,bool),bool),S0)))))) <-> (all T0 (p(s(bool,i(s(fun(fun(fun(Q50997,bool),bool),bool),i(s(fun(fun(Q50997,bool),fun(fun(fun(Q50997,bool),bool),bool)),in),s(fun(Q50997,bool),T0))),s(fun(fun(Q50997,bool),bool),S0)))) -> p(s(bool,i(s(fun(fun(Q50997,bool),bool),finite),s(fun(Q50997,bool),T0))))))))) # label(aFINITEu_FINITEu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 915 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),even),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))) <-> p(s(bool,i(s(fun(num,bool),even),s(num,M0)))) | p(s(bool,i(s(fun(num,bool),even),s(num,N0)))))) # label(aEVENu_MULT) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 916 (all X all N0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(num,N0))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0)))))) # label(aREALu_ABSu_POW) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 917 (all X all Y s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,i(s(fun(real,real),realu_neg),s(real,Y))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,Y)))) # label(aREALu_MINu_MAX) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 918 (all M0 all N0 s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))) = s(num,N0)) # label(aDISTu_RADDu_0) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 919 (all A all B all C all U_1 ((all F0 all A5 all B0 s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),i(s(fun(fun(prod(A,B),C),fun(A,fun(B,C))),U_1),s(fun(prod(A,B),C),F0))),s(A,A5))),s(B,B0))) = s(C,i(s(fun(prod(A,B),C),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,A5))),s(B,B0)))))) -> (all U_0 ((all F0 all A5 s(fun(B,C),i(s(fun(A,fun(B,C)),i(s(fun(fun(prod(A,B),C),fun(A,fun(B,C))),U_1),s(fun(prod(A,B),C),F0))),s(A,A5))) = s(fun(B,C),i(s(fun(A,fun(B,C)),i(s(fun(fun(prod(A,B),C),fun(A,fun(B,C))),U_0),s(fun(prod(A,B),C),F0))),s(A,A5)))) -> (all P0 ((all F0 p(s(bool,i(s(fun(fun(A,fun(B,C)),bool),P0),s(fun(A,fun(B,C)),F0))))) <-> (all F0 p(s(bool,i(s(fun(fun(A,fun(B,C)),bool),P0),s(fun(A,fun(B,C)),i(s(fun(fun(prod(A,B),C),fun(A,fun(B,C))),U_0),s(fun(prod(A,B),C),F0))))))))))))) # label(aFORALLu_UNCURRY) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 920 (all Q12545 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(Q12545,num),m),s(Q12545,a0))))),s(num,i(s(fun(Q12545,num),m),s(Q12545,b0)))))) <-> (all Y (p(s(bool,i(s(fun(Q12545,bool),i(s(fun(Q12545,fun(Q12545,bool)),i(s(fun(fun(Q12545,num),fun(Q12545,fun(Q12545,bool))),measure0),s(fun(Q12545,num),m))),s(Q12545,Y))),s(Q12545,a0)))) -> p(s(bool,i(s(fun(Q12545,bool),i(s(fun(Q12545,fun(Q12545,bool)),i(s(fun(fun(Q12545,num),fun(Q12545,fun(Q12545,bool))),measure0),s(fun(Q12545,num),m))),s(Q12545,Y))),s(Q12545,b0)))))))) # label(aMEASUREu_LE) # label(axiom) # label(non_clause). [assumption]. 13.98/14.01 921 (all U_0 ((all P0 all I0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,I0))),s(num,P0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),U_0),s(num,P0))),s(num,I0)))) -> (all M0 all N0 all P0 s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(fun(num,num),fun(fun(num,bool),fun(num,bool))),image),s(fun(num,num),i(s(fun(num,fun(num,num)),U_0),s(num,P0))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))) = s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0)))))))) # label(aNUMSEGu_OFFSETu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 922 (all U_0 ((all U ((exists X exists Y (p(s(bool,i(s(fun(nadd,bool),i(s(fun(hreal,fun(nadd,bool)),destu_hreal),s(hreal,x))),s(nadd,X)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(hreal,fun(nadd,bool)),destu_hreal),s(hreal,y))),s(nadd,Y)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Y))))),s(nadd,U)))))) <-> p(s(bool,i(s(fun(nadd,bool),U_0),s(nadd,U)))))) -> s(hreal,i(s(fun(fun(nadd,bool),hreal),mku_hreal),s(fun(nadd,bool),U_0))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,x))),s(hreal,y))))) # label(ahrealu_add) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 923 (all C all A all B all P0 all R0 ((all S0 (p(s(bool,i(s(fun(A,bool),P0),s(A,S0)))) -> (exists A5 exists N0 p(s(bool,i(s(fun(C,bool),i(s(fun(B,fun(C,bool)),i(s(fun(A,fun(B,fun(C,bool))),R0),s(A,S0))),s(B,A5))),s(C,N0))))))) & (all N1 all N2 all S0 all A10 all A20 (p(s(bool,i(s(fun(C,bool),i(s(fun(B,fun(C,bool)),i(s(fun(A,fun(B,fun(C,bool))),R0),s(A,S0))),s(B,A10))),s(C,N1)))) & p(s(bool,i(s(fun(C,bool),i(s(fun(B,fun(C,bool)),i(s(fun(A,fun(B,fun(C,bool))),R0),s(A,S0))),s(B,A20))),s(C,N2)))) -> s(C,N2) = s(C,N1) & s(B,A10) = s(B,A20))) -> (exists F0 all S0 all A5 (p(s(bool,i(s(fun(A,bool),P0),s(A,S0)))) -> (s(B,i(s(fun(A,B),F0),s(A,S0))) = s(B,A5) <-> (exists N0 p(s(bool,i(s(fun(C,bool),i(s(fun(B,fun(C,bool)),i(s(fun(A,fun(B,fun(C,bool))),R0),s(A,S0))),s(B,A5))),s(C,N0)))))))))) # label(aFINRECu_FUNu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 924 (all A all X all S0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(fun(A,bool),S0))))) # label(aDELETEu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 925 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),suc),s(num,N0))))))) # label(aLTu_0) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 926 (all X (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,X) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),realu_abs),s(real,X))))) # label(aREALu_ABSu_ZERO) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 927 (all A all B all X all Y s(prod(A,B),i(s(fun(fun(A,fun(B,bool)),prod(A,B)),absu_prod),s(fun(A,fun(B,bool)),i(s(fun(B,fun(A,fun(B,bool))),i(s(fun(A,fun(B,fun(A,fun(B,bool)))),mku_pair),s(A,X))),s(B,Y))))) = s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))) # label(aCOMMAu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 928 (all X (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),realu_sgn),s(real,X))) <-> s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aREALu_SGNu_EQu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 929 (all X all N0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0)))))))) # label(aREALu_POWu_LT) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 930 (all B all A all F0 all H0 all T0 s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,H0))),s(list(A),T0))))) = s(list(B),i(s(fun(list(B),list(B)),i(s(fun(B,fun(list(B),list(B))),cons),s(B,i(s(fun(A,B),F0),s(A,H0))))),s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),T0)))))) # label(aMAPu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 931 (all X all Y s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),decimal),s(num,X))),s(num,Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(num,real),realu_ofu_num),s(num,X))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,Y)))))) # label(aDECIMAL) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 932 (all A all Q92630 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(Q92630,bool),fun(fun(A,bool),bool)),a_u_c),s(fun(Q92630,bool),S0))),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q92630,bool),bool),countable),s(fun(Q92630,bool),S0)))))) # label(aCARDu_EQu_COUNTABLE) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 933 (all Q49215 all Q49201 all U_1 ((all P0 all F0 all GENR_PVARR_36 ((exists A5 exists V (p(s(bool,i(s(fun(Q49201,bool),i(s(fun(bool,fun(Q49201,bool)),i(s(fun(Q49201,fun(bool,fun(Q49201,bool))),setspec),s(Q49201,GENR_PVARR_36))),s(bool,V))),s(Q49201,A5)))) & ((all X (p(s(bool,i(s(fun(Q49215,bool),P0),s(Q49215,X)))) -> p(s(bool,i(s(fun(fun(Q49201,bool),bool),i(s(fun(Q49201,fun(fun(Q49201,bool),bool)),in),s(Q49201,A5))),s(fun(Q49201,bool),i(s(fun(Q49215,fun(Q49201,bool)),F0),s(Q49215,X)))))))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(Q49201,bool),i(s(fun(fun(Q49215,fun(Q49201,bool)),fun(Q49201,bool)),i(s(fun(fun(Q49215,bool),fun(fun(Q49215,fun(Q49201,bool)),fun(Q49201,bool))),U_1),s(fun(Q49215,bool),P0))),s(fun(Q49215,fun(Q49201,bool)),F0))),s(Q49201,GENR_PVARR_36)))))) -> (all U_0 ((all P0 all F0 all GENR_PVARR_35 (p(s(bool,i(s(fun(fun(Q49201,bool),bool),i(s(fun(fun(Q49215,fun(Q49201,bool)),fun(fun(Q49201,bool),bool)),i(s(fun(fun(Q49215,bool),fun(fun(Q49215,fun(Q49201,bool)),fun(fun(Q49201,bool),bool))),U_0),s(fun(Q49215,bool),P0))),s(fun(Q49215,fun(Q49201,bool)),F0))),s(fun(Q49201,bool),GENR_PVARR_35)))) <-> (exists X p(s(bool,i(s(fun(fun(Q49201,bool),bool),i(s(fun(bool,fun(fun(Q49201,bool),bool)),i(s(fun(fun(Q49201,bool),fun(bool,fun(fun(Q49201,bool),bool))),setspec),s(fun(Q49201,bool),GENR_PVARR_35))),s(bool,i(s(fun(Q49215,bool),P0),s(Q49215,X))))),s(fun(Q49201,bool),i(s(fun(Q49215,fun(Q49201,bool)),F0),s(Q49215,X))))))))) -> (all P0 all F0 s(fun(Q49201,bool),i(s(fun(fun(fun(Q49201,bool),bool),fun(Q49201,bool)),inters),s(fun(fun(Q49201,bool),bool),i(s(fun(fun(fun(Q49201,bool),bool),fun(fun(Q49201,bool),bool)),gspec),s(fun(fun(Q49201,bool),bool),i(s(fun(fun(Q49215,fun(Q49201,bool)),fun(fun(Q49201,bool),bool)),i(s(fun(fun(Q49215,bool),fun(fun(Q49215,fun(Q49201,bool)),fun(fun(Q49201,bool),bool))),U_0),s(fun(Q49215,bool),P0))),s(fun(Q49215,fun(Q49201,bool)),F0))))))) = s(fun(Q49201,bool),i(s(fun(fun(Q49201,bool),fun(Q49201,bool)),gspec),s(fun(Q49201,bool),i(s(fun(fun(Q49215,fun(Q49201,bool)),fun(Q49201,bool)),i(s(fun(fun(Q49215,bool),fun(fun(Q49215,fun(Q49201,bool)),fun(Q49201,bool))),U_1),s(fun(Q49215,bool),P0))),s(fun(Q49215,fun(Q49201,bool)),F0)))))))))) # label(aINTERSu_GSPECu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 934 (all E0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,E0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) # label(aREALu_HALFu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 935 (all X all N0 (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(real,X) -> s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aREALu_POWu_NZ) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 936 (all A all P0 all Q0 (((all X p(s(bool,P0))) -> (exists X p(s(bool,Q0)))) <-> (exists X (p(s(bool,P0)) -> p(s(bool,Q0)))))) # label(aTRIVu_EXISTSu_IMPu_THM) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 937 (all Q60043 all Q60040 all S0 all T0 (p(s(bool,i(s(fun(fun(Q60043,bool),bool),i(s(fun(fun(Q60040,bool),fun(fun(Q60043,bool),bool)),l_a_u_c),s(fun(Q60040,bool),S0))),s(fun(Q60043,bool),T0)))) <-> (exists G0 all X (p(s(bool,i(s(fun(fun(Q60040,bool),bool),i(s(fun(Q60040,fun(fun(Q60040,bool),bool)),in),s(Q60040,X))),s(fun(Q60040,bool),S0)))) -> (exists Y (s(Q60040,X) = s(Q60040,i(s(fun(Q60043,Q60040),G0),s(Q60043,Y))) & p(s(bool,i(s(fun(fun(Q60043,bool),bool),i(s(fun(Q60043,fun(fun(Q60043,bool),bool)),in),s(Q60043,Y))),s(fun(Q60043,bool),T0)))))))))) # label(aLEu_C) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 938 (all Q48848 all Q48784 all Q48783 all U_0 ((all P0 all F0 all GENR_PVARR_25 (p(s(bool,i(s(fun(Q48848,bool),i(s(fun(fun(Q48784,fun(Q48783,Q48848)),fun(Q48848,bool)),i(s(fun(fun(Q48784,fun(Q48783,bool)),fun(fun(Q48784,fun(Q48783,Q48848)),fun(Q48848,bool))),U_0),s(fun(Q48784,fun(Q48783,bool)),P0))),s(fun(Q48784,fun(Q48783,Q48848)),F0))),s(Q48848,GENR_PVARR_25)))) <-> (exists X exists Y p(s(bool,i(s(fun(Q48848,bool),i(s(fun(bool,fun(Q48848,bool)),i(s(fun(Q48848,fun(bool,fun(Q48848,bool))),setspec),s(Q48848,GENR_PVARR_25))),s(bool,i(s(fun(Q48783,bool),i(s(fun(Q48784,fun(Q48783,bool)),P0),s(Q48784,X))),s(Q48783,Y))))),s(Q48848,i(s(fun(Q48783,Q48848),i(s(fun(Q48784,fun(Q48783,Q48848)),F0),s(Q48784,X))),s(Q48783,Y))))))))) -> (all P0 all F0 ((exists Z0 (p(s(bool,i(s(fun(fun(Q48848,bool),bool),i(s(fun(Q48848,fun(fun(Q48848,bool),bool)),in),s(Q48848,Z0))),s(fun(Q48848,bool),i(s(fun(fun(Q48848,bool),fun(Q48848,bool)),gspec),s(fun(Q48848,bool),i(s(fun(fun(Q48784,fun(Q48783,Q48848)),fun(Q48848,bool)),i(s(fun(fun(Q48784,fun(Q48783,bool)),fun(fun(Q48784,fun(Q48783,Q48848)),fun(Q48848,bool))),U_0),s(fun(Q48784,fun(Q48783,bool)),P0))),s(fun(Q48784,fun(Q48783,Q48848)),F0)))))))) & p(s(bool,i(s(fun(Q48848,bool),q0),s(Q48848,Z0)))))) <-> (exists X exists Y (p(s(bool,i(s(fun(Q48783,bool),i(s(fun(Q48784,fun(Q48783,bool)),P0),s(Q48784,X))),s(Q48783,Y)))) & p(s(bool,i(s(fun(Q48848,bool),q0),s(Q48848,i(s(fun(Q48783,Q48848),i(s(fun(Q48784,fun(Q48783,Q48848)),F0),s(Q48784,X))),s(Q48783,Y)))))))))))) # label(aEXISTSu_INu_GSPECu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 939 (all Q77782 all Q77792 all X all I0 s(Q77782,i(s(fun(num,Q77782),i(s(fun(cart(Q77782,Q77792),fun(num,Q77782)),d_),s(cart(Q77782,Q77792),X))),s(num,I0))) = s(Q77782,i(s(fun(finite_image(Q77792),Q77782),i(s(fun(cart(Q77782,Q77792),fun(finite_image(Q77792),Q77782)),destu_cart),s(cart(Q77782,Q77792),X))),s(finite_image(Q77792),i(s(fun(num,finite_image(Q77792)),finiteu_index),s(num,I0)))))) # label(afiniteu_index) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 940 (all A all X all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),rest),s(fun(A,bool),S0)))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(A,X) != s(A,i(s(fun(fun(A,bool),A),choice0),s(fun(A,bool),S0))))) # label(aINu_REST) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 941 (all A all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),S0))) = s(fun(A,bool),empty)) # label(aDIFFu_EQu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 942 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_gt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,M0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0)))))) # label(aINTu_OFu_NUMu_GT) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 943 (all Q97015 all P0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q97015,bool),bool),i(s(fun(fun(Q97015,bool),fun(fun(Q97015,bool),bool)),subset),s(fun(Q97015,bool),S0))),s(fun(Q97015,bool),T0)))) & p(s(bool,i(s(fun(fun(Q97015,bool),bool),P0),s(fun(Q97015,bool),T0)))) & (all TI_ (p(s(bool,i(s(fun(fun(Q97015,bool),bool),i(s(fun(fun(Q97015,bool),fun(fun(Q97015,bool),bool)),subset),s(fun(Q97015,bool),S0))),s(fun(Q97015,bool),TI_)))) & p(s(bool,i(s(fun(fun(Q97015,bool),bool),P0),s(fun(Q97015,bool),TI_)))) -> p(s(bool,i(s(fun(fun(Q97015,bool),bool),i(s(fun(fun(Q97015,bool),fun(fun(Q97015,bool),bool)),subset),s(fun(Q97015,bool),T0))),s(fun(Q97015,bool),TI_)))))) -> s(fun(Q97015,bool),i(s(fun(fun(Q97015,bool),fun(Q97015,bool)),i(s(fun(fun(fun(Q97015,bool),bool),fun(fun(Q97015,bool),fun(Q97015,bool))),hull),s(fun(fun(Q97015,bool),bool),P0))),s(fun(Q97015,bool),S0))) = s(fun(Q97015,bool),T0))) # label(aHULLu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 944 (all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,u_0))),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(bool,t)) # label(aARITHu_LTu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 945 (all B all A all F0 all B0 ((all X all Y all S0 (s(A,X) != s(A,Y) -> s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,S0))))) = s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,S0))))))) -> (exists G0 (s(B,B0) = s(B,i(s(fun(fun(A,bool),B),G0),s(fun(A,bool),empty))) & (all S0 all X (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,i(s(fun(fun(A,bool),B),G0),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))))) = s(B,i(s(fun(fun(A,bool),B),G0),s(fun(A,bool),S0))))))))) # label(aFINRECu_FUN) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 946 (all N0 s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))) # label(aREALu_ABSu_NUM) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 947 (all Q20730 all L (s(list(Q20730),L) != s(list(Q20730),nil) -> s(list(Q20730),i(s(fun(list(Q20730),list(Q20730)),i(s(fun(list(Q20730),fun(list(Q20730),list(Q20730))),append),s(list(Q20730),i(s(fun(list(Q20730),list(Q20730)),butlast),s(list(Q20730),L))))),s(list(Q20730),i(s(fun(list(Q20730),list(Q20730)),i(s(fun(Q20730,fun(list(Q20730),list(Q20730))),cons),s(Q20730,i(s(fun(list(Q20730),Q20730),last0),s(list(Q20730),L))))),s(list(Q20730),nil))))) = s(list(Q20730),L))) # label(aAPPENDu_BUTLASTu_LAST) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 948 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Z0)))))) # label(aREALu_LEu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 949 (all S0 all A5 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) & s(fun(real,bool),S0) != s(fun(real,bool),empty) -> (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))))),s(real,A5)))) <-> (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,A5))))))))) # label(aREALu_SUPu_LTu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.01/14.01 950 (all M0 all P0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,P0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,P0))),s(num,N0)))) -> s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))) = s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(fun(num,bool),fun(fun(num,bool),fun(num,bool))),union),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,P0))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,P0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))))) # label(aNUMSEGu_COMBINEu_R) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 951 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0))))))) # label(aREALu_LTu_RMULu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 952 (all Q18797 all Q18804 all Q18794 s(list(Q18794),i(s(fun(list(Q18804),list(Q18794)),i(s(fun(list(Q18797),fun(list(Q18804),list(Q18794))),i(s(fun(fun(Q18797,fun(Q18804,Q18794)),fun(list(Q18797),fun(list(Q18804),list(Q18794)))),map2),s(fun(Q18797,fun(Q18804,Q18794)),f))),s(list(Q18797),nil))),s(list(Q18804),l0))) = s(list(Q18794),nil)) # label(aMAP2u_DEFu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 953 (all P0 ((exists M0 all X (p(s(bool,i(s(fun(num,bool),P0),s(num,X)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,X))),s(num,M0)))))) & (exists X p(s(bool,i(s(fun(num,bool),P0),s(num,X))))) <-> (exists M0 ((all X (p(s(bool,i(s(fun(num,bool),P0),s(num,X)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,X))),s(num,M0)))))) & p(s(bool,i(s(fun(num,bool),P0),s(num,M0)))))))) # label(anumu_MAX) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 954 (all Q47560 all S0 all F0 (p(s(bool,i(s(fun(fun(Q47560,bool),bool),i(s(fun(fun(Q47560,bool),fun(fun(Q47560,bool),bool)),subset),s(fun(Q47560,bool),S0))),s(fun(Q47560,bool),i(s(fun(fun(fun(Q47560,bool),bool),fun(Q47560,bool)),inters),s(fun(fun(Q47560,bool),bool),F0)))))) <-> (all T0 (p(s(bool,i(s(fun(fun(fun(Q47560,bool),bool),bool),i(s(fun(fun(Q47560,bool),fun(fun(fun(Q47560,bool),bool),bool)),in),s(fun(Q47560,bool),T0))),s(fun(fun(Q47560,bool),bool),F0)))) -> p(s(bool,i(s(fun(fun(Q47560,bool),bool),i(s(fun(fun(Q47560,bool),fun(fun(Q47560,bool),bool)),subset),s(fun(Q47560,bool),S0))),s(fun(Q47560,bool),T0)))))))) # label(aSUBSETu_INTERS) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 955 (all Q48214 all Q48227 all U_1 ((all P0 all GENR_PVARR_13 ((exists X p(s(bool,i(s(fun(Q48227,bool),i(s(fun(bool,fun(Q48227,bool)),i(s(fun(Q48227,fun(bool,fun(Q48227,bool))),setspec),s(Q48227,GENR_PVARR_13))),s(bool,i(s(fun(Q48227,bool),P0),s(Q48227,X))))),s(Q48227,X))))) <-> p(s(bool,i(s(fun(Q48227,bool),i(s(fun(fun(Q48227,bool),fun(Q48227,bool)),U_1),s(fun(Q48227,bool),P0))),s(Q48227,GENR_PVARR_13)))))) -> (all U_0 ((all P0 all F0 all GENR_PVARR_12 ((exists X p(s(bool,i(s(fun(Q48214,bool),i(s(fun(bool,fun(Q48214,bool)),i(s(fun(Q48214,fun(bool,fun(Q48214,bool))),setspec),s(Q48214,GENR_PVARR_12))),s(bool,i(s(fun(Q48227,bool),P0),s(Q48227,X))))),s(Q48214,i(s(fun(Q48227,Q48214),F0),s(Q48227,X))))))) <-> p(s(bool,i(s(fun(Q48214,bool),i(s(fun(fun(Q48227,Q48214),fun(Q48214,bool)),i(s(fun(fun(Q48227,bool),fun(fun(Q48227,Q48214),fun(Q48214,bool))),U_0),s(fun(Q48227,bool),P0))),s(fun(Q48227,Q48214),F0))),s(Q48214,GENR_PVARR_12)))))) -> (all F0 all P0 s(fun(Q48214,bool),i(s(fun(fun(Q48214,bool),fun(Q48214,bool)),gspec),s(fun(Q48214,bool),i(s(fun(fun(Q48227,Q48214),fun(Q48214,bool)),i(s(fun(fun(Q48227,bool),fun(fun(Q48227,Q48214),fun(Q48214,bool))),U_0),s(fun(Q48227,bool),P0))),s(fun(Q48227,Q48214),F0))))) = s(fun(Q48214,bool),i(s(fun(fun(Q48227,bool),fun(Q48214,bool)),i(s(fun(fun(Q48227,Q48214),fun(fun(Q48227,bool),fun(Q48214,bool))),image),s(fun(Q48227,Q48214),F0))),s(fun(Q48227,bool),i(s(fun(fun(Q48227,bool),fun(Q48227,bool)),gspec),s(fun(Q48227,bool),i(s(fun(fun(Q48227,bool),fun(Q48227,bool)),U_1),s(fun(Q48227,bool),P0)))))))))))) # label(aSIMPLEu_IMAGEu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 956 (all A s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(list(A),num),length),s(list(A),nil)))) # label(aLENGTHu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 957 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,Y))),s(int,X))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y)))) # label(aINTu_MAXu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 958 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) -> s(fun(A,bool),T0) = s(fun(A,bool),S0))) # label(aSUBSETu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 959 (all Q19522 all U_0 ((all P0 all X (p(s(bool,i(s(fun(Q19522,bool),i(s(fun(fun(Q19522,bool),fun(Q19522,bool)),U_0),s(fun(Q19522,bool),P0))),s(Q19522,X)))) <-> -p(s(bool,i(s(fun(Q19522,bool),P0),s(Q19522,X)))))) -> (all P0 all L (p(s(bool,i(s(fun(list(Q19522),bool),i(s(fun(fun(Q19522,bool),fun(list(Q19522),bool)),ex0),s(fun(Q19522,bool),i(s(fun(fun(Q19522,bool),fun(Q19522,bool)),U_0),s(fun(Q19522,bool),P0))))),s(list(Q19522),L)))) <-> -p(s(bool,i(s(fun(list(Q19522),bool),i(s(fun(fun(Q19522,bool),fun(list(Q19522),bool)),all0),s(fun(Q19522,bool),P0))),s(list(Q19522),L)))))))) # label(aNOTu_ALL) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 960 (all B all A all U_0 ((all G0 all F0 ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(B,bool),num),dimindex),s(fun(B,bool),univ)))))) -> s(A,i(s(fun(num,A),i(s(fun(cart(A,B),fun(num,A)),d_),s(cart(A,B),F0))),s(num,I0))) = s(A,i(s(fun(num,A),G0),s(num,I0))))) <-> p(s(bool,i(s(fun(cart(A,B),bool),i(s(fun(fun(num,A),fun(cart(A,B),bool)),U_0),s(fun(num,A),G0))),s(cart(A,B),F0)))))) -> (all G0 s(cart(A,B),i(s(fun(fun(cart(A,B),bool),cart(A,B)),h_),s(fun(cart(A,B),bool),i(s(fun(fun(num,A),fun(cart(A,B),bool)),U_0),s(fun(num,A),G0))))) = s(cart(A,B),i(s(fun(fun(num,A),cart(A,B)),lambda),s(fun(num,A),G0)))))) # label(alambda) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 961 (all Q18865 s(Q18865,i(s(fun(list(Q18865),Q18865),i(s(fun(num,fun(list(Q18865),Q18865)),el),s(num,i(s(fun(num,num),suc),s(num,n))))),s(list(Q18865),l0))) = s(Q18865,i(s(fun(list(Q18865),Q18865),i(s(fun(num,fun(list(Q18865),Q18865)),el),s(num,n))),s(list(Q18865),i(s(fun(list(Q18865),list(Q18865)),tl),s(list(Q18865),l0)))))) # label(aELu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 962 (all A all C all B all D all S0 all SI_ all T0 all TI_ (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),SI_)))) & p(s(bool,i(s(fun(fun(D,bool),bool),i(s(fun(fun(C,bool),fun(fun(D,bool),bool)),l_a_u_c),s(fun(C,bool),T0))),s(fun(D,bool),TI_)))) -> p(s(bool,i(s(fun(fun(prod(B,D),bool),bool),i(s(fun(fun(prod(A,C),bool),fun(fun(prod(B,D),bool),bool)),l_a_u_c),s(fun(prod(A,C),bool),i(s(fun(fun(C,bool),fun(prod(A,C),bool)),i(s(fun(fun(A,bool),fun(fun(C,bool),fun(prod(A,C),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(C,bool),T0))))),s(fun(prod(B,D),bool),i(s(fun(fun(D,bool),fun(prod(B,D),bool)),i(s(fun(fun(B,bool),fun(fun(D,bool),fun(prod(B,D),bool))),t_u_c),s(fun(B,bool),SI_))),s(fun(D,bool),TI_)))))))) # label(aCARDu_LEu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 963 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),poset),s(fun(prod(A,A),bool),L)))) -> (all X all Y all Z0 (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,Z0)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Z0)))))))))) # label(aPOSETu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 964 (all Q19034 all Q19035 s(list(prod(Q19034,Q19035)),nil) = s(list(prod(Q19034,Q19035)),i(s(fun(list(Q19035),list(prod(Q19034,Q19035))),i(s(fun(list(Q19034),fun(list(Q19035),list(prod(Q19034,Q19035)))),zip0),s(list(Q19034),nil))),s(list(Q19035),nil)))) # label(aZIPu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 965 (all B all A all F0 ((all S0 all T0 (s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))) = s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),T0))) -> s(fun(A,bool),T0) = s(fun(A,bool),S0))) <-> (all X all Y (s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,i(s(fun(A,B),F0),s(A,X))) -> s(A,Y) = s(A,X))))) # label(aINJECTIVEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 966 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),min),s(num,M0))),s(num,N0)))) # label(aMIN) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 967 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),L)))) -> (all X p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X))))) | (exists M0 exists X (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),M0)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),M0))),s(A,X)))) & -p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))))))) # label(aORDINALu_UP) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 968 (all A all S0 all T0 s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),T0))) = s(num,i(s(fun(fun(finite_image(A),bool),num),dimindex),s(fun(finite_image(A),bool),S0)))) # label(aDIMINDEXu_FINITEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 969 (all M0 all N0 (s(num,N0) = s(num,M0) <-> s(num,i(s(fun(num,num),numeral),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,M0))))) # label(aARITHu_EQu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 970 (all A all S0 all T0 all U (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),T0))),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),U)))))) # label(aPSUBSETu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 971 (all U_0 ((all F0 all P0 all I0 s(num,i(s(fun(num,num),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,I0))),s(num,P0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(fun(num,num),fun(num,fun(num,num))),U_0),s(fun(num,num),F0))),s(num,P0))),s(num,I0)))) -> (all P0 all F0 all M0 all N0 s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(fun(num,num),fun(num,fun(num,num))),U_0),s(fun(num,num),F0))),s(num,P0))))) = s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))),s(fun(num,num),F0)))))) # label(aNSUMu_OFFSET) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 972 (all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,u_0))),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(bool,t)) # label(aARITHu_LEu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 973 (all A all S0 all T0 all X (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))))) # label(aINu_DIFF) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 974 (all A all F0 all G0 s(fun(A,n10),F0) = s(fun(A,n10),G0)) # label(aoneu_axiom) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 975 (all X all N0 s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),realu_inv),s(real,X))))),s(num,N0)))) # label(aREALu_POWu_INV) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 976 (all M0 all N0 all P0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,P0)))) # label(aLTu_ADDu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 977 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,N0))),s(num,M0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,i(s(fun(num,num),bit0),s(num,M0)))))) # label(aARITHu_GEu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 978 (all Q87739 all Q87740 ((exists X p(s(bool,i(s(fun(fun(Q87740,bool),bool),i(s(fun(Q87740,fun(fun(Q87740,bool),bool)),in),s(Q87740,X))),s(fun(Q87740,bool),s0))))) -> ((all X all Y (s(Q87739,i(s(fun(Q87740,Q87739),f),s(Q87740,Y))) = s(Q87739,i(s(fun(Q87740,Q87739),f),s(Q87740,X))) & p(s(bool,i(s(fun(fun(Q87740,bool),bool),i(s(fun(Q87740,fun(fun(Q87740,bool),bool)),in),s(Q87740,Y))),s(fun(Q87740,bool),s0)))) & p(s(bool,i(s(fun(fun(Q87740,bool),bool),i(s(fun(Q87740,fun(fun(Q87740,bool),bool)),in),s(Q87740,X))),s(fun(Q87740,bool),s0)))) -> s(Q87740,X) = s(Q87740,Y))) <-> (exists G0 ((all X (p(s(bool,i(s(fun(fun(Q87740,bool),bool),i(s(fun(Q87740,fun(fun(Q87740,bool),bool)),in),s(Q87740,X))),s(fun(Q87740,bool),s0)))) -> s(Q87740,X) = s(Q87740,i(s(fun(Q87739,Q87740),G0),s(Q87739,i(s(fun(Q87740,Q87739),f),s(Q87740,X))))))) & (all Y (p(s(bool,i(s(fun(fun(Q87739,bool),bool),i(s(fun(Q87739,fun(fun(Q87739,bool),bool)),in),s(Q87739,Y))),s(fun(Q87739,bool),t0)))) -> p(s(bool,i(s(fun(fun(Q87740,bool),bool),i(s(fun(Q87740,fun(fun(Q87740,bool),bool)),in),s(Q87740,i(s(fun(Q87739,Q87740),G0),s(Q87739,Y))))),s(fun(Q87740,bool),s0))))))))))) # label(aINJECTIVEu_LEFTu_INVERSEu_NONEMPTY) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 979 (all B all A all U_1 ((all S0 all F0 all Y all GENR_PVARR_186 (p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))),s(A,GENR_PVARR_186)))) <-> (exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_186))),s(bool,V))),s(A,X)))) & (s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> p(s(bool,V))))))) -> (all U_0 ((all S0 all F0 all G0 all Y s(real,i(s(fun(B,real),i(s(fun(fun(A,real),fun(B,real)),i(s(fun(fun(A,B),fun(fun(A,real),fun(B,real))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,real),fun(B,real)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,real),G0))),s(B,Y))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))))))),s(fun(A,real),G0)))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),G0))) = s(real,i(s(fun(fun(B,real),real),i(s(fun(fun(B,bool),fun(fun(B,real),real)),sum),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,real),i(s(fun(fun(A,real),fun(B,real)),i(s(fun(fun(A,B),fun(fun(A,real),fun(B,real))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,real),fun(B,real)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,real),G0))))))))))) # label(aSUMu_IMAGEu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 980 (all X all Y (s(real,X) = s(real,Y) <-> s(real,i(s(fun(real,real),realu_neg),s(real,X))) = s(real,i(s(fun(real,real),realu_neg),s(real,Y))))) # label(aREALu_EQu_NEG2) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 981 (all A all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),empty))),s(fun(A,bool),S0))) = s(fun(A,bool),S0)) # label(aUNIONu_EMPTYu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 982 (all M0 all N0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,M0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) # label(aINTu_OFu_NUMu_LE) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 983 (all B all P all A all U_1 ((all F0 all T0 all X s(B,i(s(fun(P,B),i(s(fun(fun(P,A),fun(P,B)),i(s(fun(fun(A,B),fun(fun(P,A),fun(P,B))),U_1),s(fun(A,B),F0))),s(fun(P,A),T0))),s(P,X))) = s(B,i(s(fun(A,B),F0),s(A,i(s(fun(P,A),T0),s(P,X)))))) -> (all U_0 ((all T0 all F0 s(fun(P,B),i(s(fun(fun(P,A),fun(P,B)),i(s(fun(fun(A,B),fun(fun(P,A),fun(P,B))),U_1),s(fun(A,B),F0))),s(fun(P,A),T0))) = s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(P,A),fun(fun(A,B),fun(P,B))),U_0),s(fun(P,A),T0))),s(fun(A,B),F0)))) -> (all L_L_ all P0 all S0 all T0 ((all F0 all A5 (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,A5)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,i(s(fun(P,A),T0),s(P,A5))))),s(A,i(s(fun(P,A),S0),s(P,A5)))))))) -> p(s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(P,A),fun(fun(A,B),fun(P,B))),U_0),s(fun(P,A),T0)))))))))))) # label(aADMISSIBLEu_BASE) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 984 (all A all U_0 ((all L all A5 all F0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(A,fun(fun(prod(A,A),bool),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(fun(prod(A,A),bool),bool))),U_0),s(fun(prod(A,A),bool),L))),s(A,A5))),s(fun(prod(A,A),bool),F0)))) <-> (all X all Y exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(A,A),bool),F0),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y))))))),s(bool,V)))) & ((p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) | s(A,X) = s(A,A5)) & s(A,Y) = s(A,A5) | p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) <-> p(s(bool,V))))))) -> (all L all A5 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),i(s(fun(fun(fun(prod(A,A),bool),bool),fun(prod(A,A),bool)),gabs),s(fun(fun(prod(A,A),bool),bool),i(s(fun(A,fun(fun(prod(A,A),bool),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(fun(prod(A,A),bool),bool))),U_0),s(fun(prod(A,A),bool),L))),s(A,A5))))))),s(A,x)))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,x)))) | s(A,x) = s(A,A5))))) # label(aFLu_SUC) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 985 (all A all U_0 ((all A5 all X exists V ((s(A,A5) = s(A,X) <-> p(s(bool,V))) & s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,V))),s(num,b0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(num,i(s(fun(A,num),i(s(fun(A,fun(A,num)),U_0),s(A,A5))),s(A,X))))) -> (all S0 all A5 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,A5))),s(fun(A,bool),S0))))),s(num,b0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(A,fun(A,num)),U_0),s(A,A5)))))))) # label(aNSUMu_DELTA) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 986 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,P0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,P0)))))) # label(aLEu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 987 (all B all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(B,bool),fun(fun(A,bool),bool)),l_a_u_c),s(fun(B,bool),T0))),s(fun(A,bool),S0)))) | p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))))) # label(aCARDu_LEu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 988 (all A all S0 all T0 all X s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(fun(A,bool),T0))) = s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(A,X)))) # label(aDELETEu_INTER) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 989 (all A all L_L_ (p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),L_L_)))) <-> (all P0 ((exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) -> (exists X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) & (all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,X)))) -> -p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))))))))))) # label(aWF) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 990 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) # label(aintu_le) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 991 (all Q56133 all Q56136 all S0 all T0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q56136,bool),fun(num,bool)),hasu_size),s(fun(Q56136,bool),T0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q56133,bool),fun(num,bool)),hasu_size),s(fun(Q56133,bool),S0))),s(num,M0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(prod(Q56133,Q56136),bool),fun(num,bool)),hasu_size),s(fun(prod(Q56133,Q56136),bool),i(s(fun(fun(Q56136,bool),fun(prod(Q56133,Q56136),bool)),i(s(fun(fun(Q56133,bool),fun(fun(Q56136,bool),fun(prod(Q56133,Q56136),bool))),cross0),s(fun(Q56133,bool),S0))),s(fun(Q56136,bool),T0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))))) # label(aHASu_SIZEu_CROSS) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 992 (all A s(A,i(s(fun(list(A),A),last0),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,k))),s(list(A),t0))))) = s(A,i(s(fun(list(A),A),last0),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,h0))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,k))),s(list(A),t0)))))))) # label(aLASTu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 993 (all X s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),intu_neg),s(int,X))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aINTu_NEGu_GT0) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 994 (all Q20555 all Q20542 all Q20544 all F0 all L all M0 (s(num,i(s(fun(list(Q20544),num),length),s(list(Q20544),M0))) = s(num,i(s(fun(list(Q20542),num),length),s(list(Q20542),L))) -> s(num,i(s(fun(list(Q20544),num),length),s(list(Q20544),M0))) = s(num,i(s(fun(list(Q20555),num),length),s(list(Q20555),i(s(fun(list(Q20544),list(Q20555)),i(s(fun(list(Q20542),fun(list(Q20544),list(Q20555))),i(s(fun(fun(Q20542,fun(Q20544,Q20555)),fun(list(Q20542),fun(list(Q20544),list(Q20555)))),map2),s(fun(Q20542,fun(Q20544,Q20555)),F0))),s(list(Q20542),L))),s(list(Q20544),M0))))))) # label(aLENGTHu_MAP2) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 995 (all Q47879 all Q47880 all F0 all S0 all A5 ((all X (s(Q47879,i(s(fun(Q47880,Q47879),F0),s(Q47880,X))) = s(Q47879,i(s(fun(Q47880,Q47879),F0),s(Q47880,A5))) -> s(Q47880,X) = s(Q47880,A5))) -> s(fun(Q47879,bool),i(s(fun(fun(Q47880,bool),fun(Q47879,bool)),i(s(fun(fun(Q47880,Q47879),fun(fun(Q47880,bool),fun(Q47879,bool))),image),s(fun(Q47880,Q47879),F0))),s(fun(Q47880,bool),i(s(fun(Q47880,fun(Q47880,bool)),i(s(fun(fun(Q47880,bool),fun(Q47880,fun(Q47880,bool))),delete),s(fun(Q47880,bool),S0))),s(Q47880,A5))))) = s(fun(Q47879,bool),i(s(fun(Q47879,fun(Q47879,bool)),i(s(fun(fun(Q47879,bool),fun(Q47879,fun(Q47879,bool))),delete),s(fun(Q47879,bool),i(s(fun(fun(Q47880,bool),fun(Q47879,bool)),i(s(fun(fun(Q47880,Q47879),fun(fun(Q47880,bool),fun(Q47879,bool))),image),s(fun(Q47880,Q47879),F0))),s(fun(Q47880,bool),S0))))),s(Q47879,i(s(fun(Q47880,Q47879),F0),s(Q47880,A5))))))) # label(aIMAGEu_DELETEu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 996 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,X)))))) # label(aREALu_LTEu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 997 (all X all M0 all N0 (s(real,X) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))))))),s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,M0))))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,M0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))))) # label(aREALu_DIVu_POW2u_ALT) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 998 (all X all Y s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X)))))) # label(aREALu_ABSu_SUB) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 999 (all A all U_0 ((all F0 ((all C1 all C2 exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(A,bool),fun(A,bool)),bool),F0),s(prod(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),prod(fun(A,bool),fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,bool),prod(fun(A,bool),fun(A,bool)))),c_),s(fun(A,bool),C1))),s(fun(A,bool),C2))))))),s(bool,V)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),c0))),s(fun(A,bool),C1)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),C1))),s(fun(A,bool),C2)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(A,bool),bool)),chain),s(fun(prod(A,A),bool),l0))),s(fun(A,bool),C2))))))) <-> p(s(bool,i(s(fun(fun(prod(fun(A,bool),fun(A,bool)),bool),bool),U_0),s(fun(prod(fun(A,bool),fun(A,bool)),bool),F0)))))) -> p(s(bool,i(s(fun(fun(prod(fun(A,bool),fun(A,bool)),bool),bool),poset),s(fun(prod(fun(A,bool),fun(A,bool)),bool),i(s(fun(fun(fun(prod(fun(A,bool),fun(A,bool)),bool),bool),fun(prod(fun(A,bool),fun(A,bool)),bool)),gabs),s(fun(fun(prod(fun(A,bool),fun(A,bool)),bool),bool),U_0)))))))) # label(aKLu_POSETu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1000 (all A all X all Y (s(A,Y) = s(A,X) -> s(A,X) = s(A,Y))) # label(aEQu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1001 (all N0 all M0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,M0))),s(num,N0)))) # label(aGE) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1002 (all M0 all N0 all P0 (s(num,N0) = s(num,M0) <-> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))) # label(aEQu_ADDu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1003 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,M0)))) # label(aMULTu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1004 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),intu_abs),s(int,X))))),s(int,i(s(fun(int,int),intu_abs),s(int,Y))))) = s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y)))))) # label(aINTu_ABSu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1005 (all X all Y (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y)))) <-> (exists B0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,Y))),s(num,N0))))),s(num,B0))))))))) # label(anaddu_le) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1006 (all A all X s(fun(A,bool),univ) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),univ)))) # label(aINSERTu_UNIV) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1007 (all Q53037 all U_1 ((all N0 s(num,i(s(fun(num,num),suc),s(num,N0))) = s(num,i(s(fun(num,num),U_1),s(num,N0)))) -> (all U_0 ((all X s(fun(num,num),U_1) = s(fun(num,num),i(s(fun(Q53037,fun(num,num)),U_0),s(Q53037,X)))) -> (all S0 s(num,i(s(fun(num,num),i(s(fun(fun(Q53037,bool),fun(num,num)),i(s(fun(fun(Q53037,fun(num,num)),fun(fun(Q53037,bool),fun(num,num))),itset),s(fun(Q53037,fun(num,num)),U_0))),s(fun(Q53037,bool),S0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(num,i(s(fun(fun(Q53037,bool),num),card),s(fun(Q53037,bool),S0)))))))) # label(aCARD) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1008 (all Q96506 all Q96509 all Q96508 all U_0 ((all F0 ((all X all Y p(s(bool,i(s(fun(Q96506,bool),i(s(fun(Q96506,fun(Q96506,bool)),geq),s(Q96506,i(s(fun(prod(Q96509,Q96508),Q96506),F0),s(prod(Q96509,Q96508),i(s(fun(Q96508,prod(Q96509,Q96508)),i(s(fun(Q96509,fun(Q96508,prod(Q96509,Q96508))),c_),s(Q96509,X))),s(Q96508,Y))))))),s(Q96506,i(s(fun(Q96508,Q96506),i(s(fun(Q96509,fun(Q96508,Q96506)),p0),s(Q96509,X))),s(Q96508,Y))))))) <-> p(s(bool,i(s(fun(fun(prod(Q96509,Q96508),Q96506),bool),U_0),s(fun(prod(Q96509,Q96508),Q96506),F0)))))) -> (all X s(Q96506,i(s(fun(Q96508,Q96506),i(s(fun(Q96509,fun(Q96508,Q96506)),p0),s(Q96509,i(s(fun(prod(Q96509,Q96508),Q96509),fst),s(prod(Q96509,Q96508),X))))),s(Q96508,i(s(fun(prod(Q96509,Q96508),Q96508),snd),s(prod(Q96509,Q96508),X))))) = s(Q96506,i(s(fun(prod(Q96509,Q96508),Q96506),i(s(fun(fun(fun(prod(Q96509,Q96508),Q96506),bool),fun(prod(Q96509,Q96508),Q96506)),gabs),s(fun(fun(prod(Q96509,Q96508),Q96506),bool),U_0))),s(prod(Q96509,Q96508),X)))))) # label(aLAMBDAu_PAIR) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1009 (all A all P0 all Q0 ((exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) | (exists X p(s(bool,i(s(fun(A,bool),Q0),s(A,X))))) <-> (exists X (p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))) | p(s(bool,i(s(fun(A,bool),P0),s(A,X)))))))) # label(aORu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1010 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) -> s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X))))) # label(aINTu_LEu_MULu_EQu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1011 (all X s(int,X) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),intu_sgn),s(int,X))))),s(int,i(s(fun(int,int),intu_abs),s(int,X)))))) # label(aINTu_SGNu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1012 (all A all X all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))) != s(fun(A,bool),empty)) # label(aNOTu_EMPTYu_INSERT) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1013 (all A all B all D0 all I0 all S0 ((all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(A,X) != s(A,Y) & s(B,i(s(fun(A,B),I0),s(A,Y))) = s(B,i(s(fun(A,B),I0),s(A,X))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(B,real),D0),s(B,i(s(fun(A,B),I0),s(A,X))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(real,i(s(fun(fun(B,real),real),i(s(fun(fun(B,bool),fun(fun(B,real),real)),sum),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),I0))),s(fun(A,bool),S0))))),s(fun(B,real),D0))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(fun(A,B),fun(A,real)),i(s(fun(fun(B,real),fun(fun(A,B),fun(A,real))),o),s(fun(B,real),D0))),s(fun(A,B),I0))))))) # label(aSUMu_IMAGEu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1014 (all P0 ((exists N0 p(s(bool,i(s(fun(int,bool),P0),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))))) <-> (exists I0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,I0)))) & p(s(bool,i(s(fun(int,bool),P0),s(int,I0)))))))) # label(aINTu_EXISTSu_POS) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1015 (all Q56161 all Q56163 all S0 all T0 (p(s(bool,i(s(fun(fun(Q56161,bool),bool),finite),s(fun(Q56161,bool),S0)))) & p(s(bool,i(s(fun(fun(Q56163,bool),bool),finite),s(fun(Q56163,bool),T0)))) -> p(s(bool,i(s(fun(fun(prod(Q56161,Q56163),bool),bool),finite),s(fun(prod(Q56161,Q56163),bool),i(s(fun(fun(Q56163,bool),fun(prod(Q56161,Q56163),bool)),i(s(fun(fun(Q56161,bool),fun(fun(Q56163,bool),fun(prod(Q56161,Q56163),bool))),cross0),s(fun(Q56161,bool),S0))),s(fun(Q56163,bool),T0)))))))) # label(aFINITEu_CROSS) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1016 (all X all Y all N0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,X))),s(num,Y)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,Y))),s(num,N0)))))))) # label(aEXPu_MONOu_LTu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1017 (all A all U_0 ((all X all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),U_0),s(A,X))),s(A,Y)))) <-> s(A,X) = s(A,Y))) -> (all X s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),i(s(fun(A,fun(A,bool)),U_0),s(A,X))))) = s(A,X)))) # label(aSELECTu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1018 (all X all Y all Z0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Y))),s(real,Z0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0)))))) # label(aREALu_ADDu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1019 (all A all S0 all T0 (s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))) = s(fun(A,bool),empty) -> p(s(bool,i(s(fun(fun(sum0(A,A),bool),bool),i(s(fun(fun(A,bool),fun(fun(sum0(A,A),bool),bool)),a_u_c),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(sum0(A,A),bool),i(s(fun(fun(A,bool),fun(sum0(A,A),bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(sum0(A,A),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))))) # label(aCARDu_DISJOINTu_UNION) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1020 (all M0 all N0 s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_SUBu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 14.01/14.02 1021 (all P0 ((exists X p(s(bool,i(s(fun(real,bool),P0),s(real,X))))) & (exists M0 all X (p(s(bool,i(s(fun(real,bool),P0),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,M0)))))) -> (exists M0 ((all MI_ ((all X (p(s(bool,i(s(fun(real,bool),P0),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,MI_)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,M0))),s(real,MI_)))))) & (all X (p(s(bool,i(s(fun(real,bool),P0),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,M0)))))))))) # label(aREALu_COMPLETE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1022 (all Q58517 all L p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(Q58517,bool),num),card),s(fun(Q58517,bool),i(s(fun(list(Q58517),fun(Q58517,bool)),setu_ofu_list),s(list(Q58517),L))))))),s(num,i(s(fun(list(Q58517),num),length),s(list(Q58517),L))))))) # label(aCARDu_SETu_OFu_LISTu_LE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1023 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0)))))))) # label(aCARDu_LEu_CARDu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1024 (all Q67625 all S0 (p(s(bool,i(s(fun(fun(Q67625,bool),bool),finite),s(fun(Q67625,bool),S0)))) -> ((all X (p(s(bool,i(s(fun(fun(Q67625,bool),bool),i(s(fun(Q67625,fun(fun(Q67625,bool),bool)),in),s(Q67625,X))),s(fun(Q67625,bool),S0)))) -> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(Q67625,num),f),s(Q67625,X))))) <-> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(fun(Q67625,num),num),i(s(fun(fun(Q67625,bool),fun(fun(Q67625,num),num)),nsum),s(fun(Q67625,bool),S0))),s(fun(Q67625,num),f)))))) # label(aNSUMu_EQu_0u_IFF) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1025 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))) <-> -p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,X)))))) # label(aINTu_LT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1026 (all Q49581 all U_0 ((all S0 all U all GENR_PVARR_46 ((exists T0 p(s(bool,i(s(fun(fun(Q49581,bool),bool),i(s(fun(bool,fun(fun(Q49581,bool),bool)),i(s(fun(fun(Q49581,bool),fun(bool,fun(fun(Q49581,bool),bool))),setspec),s(fun(Q49581,bool),GENR_PVARR_46))),s(bool,i(s(fun(fun(fun(Q49581,bool),bool),bool),i(s(fun(fun(Q49581,bool),fun(fun(fun(Q49581,bool),bool),bool)),in),s(fun(Q49581,bool),T0))),s(fun(fun(Q49581,bool),bool),S0))))),s(fun(Q49581,bool),i(s(fun(fun(Q49581,bool),fun(Q49581,bool)),i(s(fun(fun(Q49581,bool),fun(fun(Q49581,bool),fun(Q49581,bool))),diff),s(fun(Q49581,bool),U))),s(fun(Q49581,bool),T0))))))) <-> p(s(bool,i(s(fun(fun(Q49581,bool),bool),i(s(fun(fun(Q49581,bool),fun(fun(Q49581,bool),bool)),i(s(fun(fun(fun(Q49581,bool),bool),fun(fun(Q49581,bool),fun(fun(Q49581,bool),bool))),U_0),s(fun(fun(Q49581,bool),bool),S0))),s(fun(Q49581,bool),U))),s(fun(Q49581,bool),GENR_PVARR_46)))))) -> (all U all S0 (s(fun(fun(Q49581,bool),bool),S0) != s(fun(fun(Q49581,bool),bool),empty) -> s(fun(Q49581,bool),i(s(fun(fun(Q49581,bool),fun(Q49581,bool)),i(s(fun(fun(Q49581,bool),fun(fun(Q49581,bool),fun(Q49581,bool))),diff),s(fun(Q49581,bool),U))),s(fun(Q49581,bool),i(s(fun(fun(fun(Q49581,bool),bool),fun(Q49581,bool)),unions),s(fun(fun(Q49581,bool),bool),S0))))) = s(fun(Q49581,bool),i(s(fun(fun(fun(Q49581,bool),bool),fun(Q49581,bool)),inters),s(fun(fun(Q49581,bool),bool),i(s(fun(fun(fun(Q49581,bool),bool),fun(fun(Q49581,bool),bool)),gspec),s(fun(fun(Q49581,bool),bool),i(s(fun(fun(Q49581,bool),fun(fun(Q49581,bool),bool)),i(s(fun(fun(fun(Q49581,bool),bool),fun(fun(Q49581,bool),fun(fun(Q49581,bool),bool))),U_0),s(fun(fun(Q49581,bool),bool),S0))),s(fun(Q49581,bool),U))))))))))) # label(aDIFFu_UNIONSu_NONEMPTY) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1027 (all A all S0 ((exists X exists T0 (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) & s(fun(A,bool),S0) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),T0))))) | s(fun(A,bool),empty) = s(fun(A,bool),S0))) # label(aSETu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1028 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))))),s(int,Y)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))))) # label(aINTu_ABSu_SIGN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1029 (all A all B all U_0 ((all S0 all F0 all A5 all GENR_PVARR_57 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(B,bool),fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(B,bool),A5))),s(A,GENR_PVARR_57)))) <-> (exists X exists V ((p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),A5)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_57))),s(bool,V))),s(A,X)))))))) -> (all F0 all A5 all S0 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),A5)))) & (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,i(s(fun(A,B),F0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,Y) = s(A,X))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(B,bool),fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(B,bool),A5)))))))))))) # label(aFINITEu_IMAGEu_INJu_GENERAL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1030 (all X all Y s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X)))) # label(aREALu_NEGu_SUB) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1031 (all A5 all B0 all C0 all D0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,B0) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,C0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,A5))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,D0)))))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,C0))),s(num,D0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,A5))),s(num,B0)))))))) # label(aDIVu_LEu_EXCLUSION) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1032 (all Q19821 all U_0 ((all X (p(s(bool,i(s(fun(Q19821,bool),p0),s(Q19821,X)))) & p(s(bool,i(s(fun(Q19821,bool),q0),s(Q19821,X)))) <-> p(s(bool,i(s(fun(Q19821,bool),U_0),s(Q19821,X)))))) -> (all L (p(s(bool,i(s(fun(list(Q19821),bool),i(s(fun(fun(Q19821,bool),fun(list(Q19821),bool)),all0),s(fun(Q19821,bool),p0))),s(list(Q19821),L)))) & p(s(bool,i(s(fun(list(Q19821),bool),i(s(fun(fun(Q19821,bool),fun(list(Q19821),bool)),all0),s(fun(Q19821,bool),q0))),s(list(Q19821),L)))) <-> p(s(bool,i(s(fun(list(Q19821),bool),i(s(fun(fun(Q19821,bool),fun(list(Q19821),bool)),all0),s(fun(Q19821,bool),U_0))),s(list(Q19821),L)))))))) # label(aANDu_ALL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1033 (all Q72353 all F0 all X s(real,i(s(fun(fun(Q72353,real),real),i(s(fun(fun(Q72353,bool),fun(fun(Q72353,real),real)),sum),s(fun(Q72353,bool),i(s(fun(fun(Q72353,bool),fun(Q72353,bool)),i(s(fun(Q72353,fun(fun(Q72353,bool),fun(Q72353,bool))),insert),s(Q72353,X))),s(fun(Q72353,bool),empty))))),s(fun(Q72353,real),F0))) = s(real,i(s(fun(Q72353,real),F0),s(Q72353,X)))) # label(aSUMu_SING) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1034 (all X all XI_ all XI_I_ (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),u_guardedu_pattern),s(bool,X))),s(bool,XI_))),s(bool,XI_I_)))) <-> p(s(bool,XI_)) & p(s(bool,XI_I_)) & p(s(bool,X)))) # label(au_GUARDEDu_PATTERN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1035 (all A all P0 ((all X all XI_ (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,XI_)))) -> s(A,X) = s(A,XI_))) & (exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) <-> (exists X all Y (p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))) <-> s(A,X) = s(A,Y))))) # label(aEXISTSu_UNIQUEu_ALT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1036 (all A all B all Q92493 all S0 all T0 all U (p(s(bool,i(s(fun(fun(Q92493,bool),bool),i(s(fun(fun(A,bool),fun(fun(Q92493,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(Q92493,bool),U)))) & p(s(bool,i(s(fun(fun(Q92493,bool),bool),infinite),s(fun(Q92493,bool),U)))) & p(s(bool,i(s(fun(fun(Q92493,bool),bool),i(s(fun(fun(B,bool),fun(fun(Q92493,bool),bool)),l_u_c),s(fun(B,bool),T0))),s(fun(Q92493,bool),U)))) -> p(s(bool,i(s(fun(fun(Q92493,bool),bool),i(s(fun(fun(prod(A,B),bool),fun(fun(Q92493,bool),bool)),l_u_c),s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(Q92493,bool),U)))))) # label(aCARDu_MULu_LTu_INFINITE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1037 (all N0 all M0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,M0))),s(real,N0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,M0))),s(real,N0))))),s(real,N0))),s(real,M0)))) # label(arealu_max) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1038 (all Q89936 all Q89935 all U_0 ((all S0 all T0 all GENR_PVARR_218 (p(s(bool,i(s(fun(prod(Q89936,Q89935),bool),i(s(fun(fun(Q89935,bool),fun(prod(Q89936,Q89935),bool)),i(s(fun(fun(Q89936,bool),fun(fun(Q89935,bool),fun(prod(Q89936,Q89935),bool))),U_0),s(fun(Q89936,bool),S0))),s(fun(Q89935,bool),T0))),s(prod(Q89936,Q89935),GENR_PVARR_218)))) <-> (exists X exists Y exists V (p(s(bool,i(s(fun(prod(Q89936,Q89935),bool),i(s(fun(bool,fun(prod(Q89936,Q89935),bool)),i(s(fun(prod(Q89936,Q89935),fun(bool,fun(prod(Q89936,Q89935),bool))),setspec),s(prod(Q89936,Q89935),GENR_PVARR_218))),s(bool,V))),s(prod(Q89936,Q89935),i(s(fun(Q89935,prod(Q89936,Q89935)),i(s(fun(Q89936,fun(Q89935,prod(Q89936,Q89935))),c_),s(Q89936,X))),s(Q89935,Y)))))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(Q89936,bool),bool),i(s(fun(Q89936,fun(fun(Q89936,bool),bool)),in),s(Q89936,X))),s(fun(Q89936,bool),S0)))) & p(s(bool,i(s(fun(fun(Q89935,bool),bool),i(s(fun(Q89935,fun(fun(Q89935,bool),bool)),in),s(Q89935,Y))),s(fun(Q89935,bool),T0))))))))) -> (all S0 all T0 s(fun(prod(Q89936,Q89935),bool),i(s(fun(fun(prod(Q89936,Q89935),bool),fun(prod(Q89936,Q89935),bool)),gspec),s(fun(prod(Q89936,Q89935),bool),i(s(fun(fun(Q89935,bool),fun(prod(Q89936,Q89935),bool)),i(s(fun(fun(Q89936,bool),fun(fun(Q89935,bool),fun(prod(Q89936,Q89935),bool))),U_0),s(fun(Q89936,bool),S0))),s(fun(Q89935,bool),T0))))) = s(fun(prod(Q89936,Q89935),bool),i(s(fun(fun(Q89935,bool),fun(prod(Q89936,Q89935),bool)),i(s(fun(fun(Q89936,bool),fun(fun(Q89935,bool),fun(prod(Q89936,Q89935),bool))),t_u_c),s(fun(Q89936,bool),S0))),s(fun(Q89935,bool),T0)))))) # label(amulu_c) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1039 (all S0 all T0 ((exists B0 all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),T0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))) & p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(fun(real,bool),fun(fun(real,bool),bool)),subset),s(fun(real,bool),S0))),s(fun(real,bool),T0)))) & s(fun(real,bool),empty) != s(fun(real,bool),S0) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))))),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),T0)))))))) # label(aREALu_SUPu_LEu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1040 (all M0 all N0 -(p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))))) # label(aLTu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1041 (all M0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))),s(num,M0)))))) # label(aMODu_LE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1042 (all X all Y (s(int,Y) = s(int,i(s(fun(int,int),intu_neg),s(int,X))) <-> s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))) # label(aINTu_RNEGu_UNIQ) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1043 (all A all B all U_2 ((all T0 all R0 all I0 all GENR_PVARR_183 ((exists J0 exists V (p(s(bool,i(s(fun(B,bool),i(s(fun(bool,fun(B,bool)),i(s(fun(B,fun(bool,fun(B,bool))),setspec),s(B,GENR_PVARR_183))),s(bool,V))),s(B,J0)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),R0),s(A,I0))),s(B,J0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),T0))))))) <-> p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),i(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,fun(B,bool)))),U_2),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0))),s(B,GENR_PVARR_183)))))) -> (all U_1 ((all T0 all R0 all I0 s(real,i(s(fun(A,real),i(s(fun(fun(A,fun(B,bool)),fun(A,real)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,real))),U_1),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),gspec),s(fun(B,bool),i(s(fun(A,fun(B,bool)),i(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,fun(B,bool)))),U_2),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0)))))))))) -> (all U_0 ((all S0 all R0 all J0 all GENR_PVARR_182 ((exists I0 exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),R0),s(A,I0))),s(B,J0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_182))),s(bool,V))),s(A,I0)))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,fun(B,bool)),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(B,fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),R0))),s(B,J0))),s(A,GENR_PVARR_182)))))) -> (all R0 all S0 all T0 all K0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all J0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),T0)))) -> s(num,K0) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,fun(B,bool)),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(B,fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),R0))),s(B,J0))))))))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) -> s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(fun(A,fun(B,bool)),fun(A,real)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,real))),U_1),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,K0))),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))))))))))))))) # label(aSUMu_MULTICOUNT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.03 1044 (all A all M0 all X all X0 (s(num,M0) = s(num,X) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),i(s(fun(num,fun(num,fun(A,bool))),injn),s(num,M0))),s(num,X))),s(A,X0)))))) # label(aINJN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1045 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))),s(real,X))) = s(real,Y)) # label(aREALu_ADDu_SUB) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1046 (all A all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0)))))) -> (exists T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),T0))),s(num,N0)))))))))) # label(aCHOOSEu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1047 (all X (s(int,X) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),intu_abs),s(int,X)))))))) # label(aINTu_ABSu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1048 (all X all Y all A5 all U all V (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,A5)))) & s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,U))),s(real,V))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,V)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,U)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,b0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,U))),s(real,X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,V))),s(real,Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,U))),s(real,A5))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,V))),s(real,b0)))))))))) # label(aREALu_CONVEXu_BOUND2u_LT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1049 (all A all S0 all F0 all B0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & s(fun(A,bool),empty) != s(fun(A,bool),S0) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,B0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0)))))))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))),s(real,B0)))))) # label(aSUMu_BOUNDu_LTu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1050 (all A all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,i(s(fun(A,real),G0),s(A,X)))))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,i(s(fun(A,real),G0),s(A,X)))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),G0)))))))) # label(aSUMu_LT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1051 (all A all C all B all D all S0 all SI_ all T0 all TI_ (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(B,bool),SI_)))) & p(s(bool,i(s(fun(fun(D,bool),bool),i(s(fun(fun(C,bool),fun(fun(D,bool),bool)),l_u_c),s(fun(C,bool),T0))),s(fun(D,bool),TI_)))) -> p(s(bool,i(s(fun(fun(sum0(B,D),bool),bool),i(s(fun(fun(sum0(A,C),bool),fun(fun(sum0(B,D),bool),bool)),l_u_c),s(fun(sum0(A,C),bool),i(s(fun(fun(C,bool),fun(sum0(A,C),bool)),i(s(fun(fun(A,bool),fun(fun(C,bool),fun(sum0(A,C),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(C,bool),T0))))),s(fun(sum0(B,D),bool),i(s(fun(fun(D,bool),fun(sum0(B,D),bool)),i(s(fun(fun(B,bool),fun(fun(D,bool),fun(sum0(B,D),bool))),p_u_c),s(fun(B,bool),SI_))),s(fun(D,bool),TI_)))))))) # label(aCARDu_LTu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1052 (all X all K0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,K0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_neg),s(real,K0))))),s(real,X)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,K0)))))) # label(aREALu_BOUNDSu_LE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1053 (all Q56184 all Q56186 all S0 all T0 (p(s(bool,i(s(fun(fun(Q56184,bool),bool),finite),s(fun(Q56184,bool),S0)))) & p(s(bool,i(s(fun(fun(Q56186,bool),bool),finite),s(fun(Q56186,bool),T0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(fun(Q56184,bool),num),card),s(fun(Q56184,bool),S0))))),s(num,i(s(fun(fun(Q56186,bool),num),card),s(fun(Q56186,bool),T0))))) = s(num,i(s(fun(fun(prod(Q56184,Q56186),bool),num),card),s(fun(prod(Q56184,Q56186),bool),i(s(fun(fun(Q56186,bool),fun(prod(Q56184,Q56186),bool)),i(s(fun(fun(Q56184,bool),fun(fun(Q56186,bool),fun(prod(Q56184,Q56186),bool))),cross0),s(fun(Q56184,bool),S0))),s(fun(Q56186,bool),T0))))))) # label(aCARDu_CROSS) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1054 (all Q63859 all Q63626 all F0 s(fun(Q63626,bool),i(s(fun(fun(Q63626,bool),fun(Q63626,bool)),i(s(fun(fun(Q63626,Q63859),fun(fun(Q63626,bool),fun(Q63626,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63626,Q63859),fun(fun(Q63626,bool),fun(Q63626,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63626,Q63859),F0))),s(fun(Q63626,bool),empty))) = s(fun(Q63626,bool),empty)) # label(aSUPPORTu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1055 (all AP all BP all A all B all U_3 ((all H0 all A5 s(B,i(s(fun(A,B),i(s(fun(fun(AP,BP),fun(A,B)),U_3),s(fun(AP,BP),H0))),s(A,A5))) = s(B,i(s(fun(BP,B),gi_),s(BP,i(s(fun(AP,BP),H0),s(AP,i(s(fun(A,AP),f),s(A,A5)))))))) -> (all U_2 ((all H0 s(fun(A,B),i(s(fun(fun(AP,BP),fun(A,B)),U_3),s(fun(AP,BP),H0))) = s(fun(A,B),i(s(fun(fun(AP,BP),fun(A,B)),U_2),s(fun(AP,BP),H0)))) -> (all U_1 ((all H0 all AI_ s(BP,i(s(fun(B,BP),g),s(B,i(s(fun(A,B),H0),s(A,i(s(fun(AP,A),fi_),s(AP,AI_))))))) = s(BP,i(s(fun(AP,BP),i(s(fun(fun(A,B),fun(AP,BP)),U_1),s(fun(A,B),H0))),s(AP,AI_)))) -> (all U_0 ((all H0 s(fun(AP,BP),i(s(fun(fun(A,B),fun(AP,BP)),U_0),s(fun(A,B),H0))) = s(fun(AP,BP),i(s(fun(fun(A,B),fun(AP,BP)),U_1),s(fun(A,B),H0)))) -> (p(s(bool,i(s(fun(fun(BP,B),bool),i(s(fun(fun(B,BP),fun(fun(BP,B),bool)),iso0),s(fun(B,BP),g))),s(fun(BP,B),gi_)))) & p(s(bool,i(s(fun(fun(AP,A),bool),i(s(fun(fun(A,AP),fun(fun(AP,A),bool)),iso0),s(fun(A,AP),f))),s(fun(AP,A),fi_)))) -> p(s(bool,i(s(fun(fun(fun(AP,BP),fun(A,B)),bool),i(s(fun(fun(fun(A,B),fun(AP,BP)),fun(fun(fun(AP,BP),fun(A,B)),bool)),iso0),s(fun(fun(A,B),fun(AP,BP)),U_0))),s(fun(fun(AP,BP),fun(A,B)),U_2))))))))))))) # label(aISOu_FUN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1056 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) <-> s(fun(A,bool),T0) != s(fun(A,bool),S0) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aPSUBSET) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1057 (all Q18845 all Q18839 all Q18838 s(list(Q18845),i(s(fun(list(Q18838),list(Q18845)),i(s(fun(list(Q18839),fun(list(Q18838),list(Q18845))),i(s(fun(fun(Q18839,fun(Q18838,Q18845)),fun(list(Q18839),fun(list(Q18838),list(Q18845)))),map2),s(fun(Q18839,fun(Q18838,Q18845)),f))),s(list(Q18839),i(s(fun(list(Q18839),list(Q18839)),i(s(fun(Q18839,fun(list(Q18839),list(Q18839))),cons),s(Q18839,h1))),s(list(Q18839),t1))))),s(list(Q18838),i(s(fun(list(Q18838),list(Q18838)),i(s(fun(Q18838,fun(list(Q18838),list(Q18838))),cons),s(Q18838,h2))),s(list(Q18838),t2))))) = s(list(Q18845),i(s(fun(list(Q18845),list(Q18845)),i(s(fun(Q18845,fun(list(Q18845),list(Q18845))),cons),s(Q18845,i(s(fun(Q18838,Q18845),i(s(fun(Q18839,fun(Q18838,Q18845)),f),s(Q18839,h1))),s(Q18838,h2))))),s(list(Q18845),i(s(fun(list(Q18838),list(Q18845)),i(s(fun(list(Q18839),fun(list(Q18838),list(Q18845))),i(s(fun(fun(Q18839,fun(Q18838,Q18845)),fun(list(Q18839),fun(list(Q18838),list(Q18845)))),map2),s(fun(Q18839,fun(Q18838,Q18845)),f))),s(list(Q18839),t1))),s(list(Q18838),t2)))))) # label(aMAP2u_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1058 (all A all C1 all I1 all R1 all C2 all I2 all R2 (s(fun(num,recspace(A)),R1) = s(fun(num,recspace(A)),R2) & s(A,I2) = s(A,I1) & s(num,C2) = s(num,C1) <-> s(recspace(A),i(s(fun(fun(num,recspace(A)),recspace(A)),i(s(fun(A,fun(fun(num,recspace(A)),recspace(A))),i(s(fun(num,fun(A,fun(fun(num,recspace(A)),recspace(A)))),constr),s(num,C1))),s(A,I1))),s(fun(num,recspace(A)),R1))) = s(recspace(A),i(s(fun(fun(num,recspace(A)),recspace(A)),i(s(fun(A,fun(fun(num,recspace(A)),recspace(A))),i(s(fun(num,fun(A,fun(fun(num,recspace(A)),recspace(A)))),constr),s(num,C2))),s(A,I2))),s(fun(num,recspace(A)),R2))))) # label(aCONSTRu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1059 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_gt),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_gt),s(int,X))),s(int,Y)))) # label(aintu_gt) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1060 (all X1 all X2 (s(ind0,X1) = s(ind0,X2) <-> s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,X2))) = s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,X1))))) # label(aINDu_SUCu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1061 (all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) <-> p(s(bool,i(s(fun(num,bool),even),s(num,N0)))))) # label(aEVENu_MOD) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1062 (all N0 exists V (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(num,N0))) & (p(s(bool,V)) <-> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,N0)))) # label(aREALu_POWu_ZERO) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1063 (all X all Y s(int,i(s(fun(int,int),intu_neg),s(int,Y))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y)))))) # label(aINTu_ADDu_SUB2) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1064 (all Q53889 all S0 s(bool,i(s(fun(fun(Q53889,bool),bool),finite),s(fun(Q53889,bool),S0))) = s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53889,bool),fun(num,bool)),hasu_size),s(fun(Q53889,bool),S0))),s(num,i(s(fun(fun(Q53889,bool),num),card),s(fun(Q53889,bool),S0)))))) # label(aFINITEu_HASu_SIZE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1065 (all A all S0 all F0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,A),fun(fun(A,bool),fun(A,bool))),image),s(fun(A,A),F0))),s(fun(A,bool),S0))))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> ((all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) -> (exists X (s(A,i(s(fun(A,A),F0),s(A,X))) = s(A,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))))) <-> (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(A,i(s(fun(A,A),F0),s(A,Y))) = s(A,i(s(fun(A,A),F0),s(A,X))) -> s(A,Y) = s(A,X)))))) # label(aSURJECTIVEu_IFFu_INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1066 (all N0 s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),suc),s(num,N0))))) = s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),numeral),s(num,N0)))))) # label(aARITHu_SUCu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1067 (all A all L all M0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),M0))),s(fun(prod(A,A),bool),L)))) -> (all X (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),M0))),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))))))) # label(aINSEGu_SUBSETu_FL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1068 (all A all B all F0 ((all T0 exists S0 s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))) = s(fun(B,bool),T0)) <-> (all Y exists X s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X)))))) # label(aSURJECTIVEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1069 (all X all Y (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))) <-> s(real,Y) = s(real,i(s(fun(real,real),realu_neg),s(real,X))))) # label(aREALu_RNEGu_UNIQ) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1070 (all A all X all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))) = s(fun(A,bool),S0))) # label(aINSERTu_DELETE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1071 (all Q58163 all S0 (p(s(bool,i(s(fun(fun(Q58163,bool),bool),finite),s(fun(Q58163,bool),S0)))) -> s(fun(Q58163,bool),S0) = s(fun(Q58163,bool),i(s(fun(list(Q58163),fun(Q58163,bool)),setu_ofu_list),s(list(Q58163),i(s(fun(fun(Q58163,bool),list(Q58163)),listu_ofu_set),s(fun(Q58163,bool),S0))))))) # label(aSETu_OFu_LISTu_OFu_SET) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1072 (all N0 s(num,i(s(fun(num,num),bit0),s(num,N0))) = s(num,i(s(fun(num,num),pre),s(num,i(s(fun(num,num),bit1),s(num,N0)))))) # label(aARITHu_PREu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1073 (all S0 all L all E0 (s(fun(real,bool),S0) != s(fun(real,bool),empty) & (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,L))))))),s(real,E0)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))))),s(real,L))))))),s(real,E0)))))) # label(aREALu_SUPu_ASCLOSE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1074 (all A all N0 all S0 all U (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),U)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),U))))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,N0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),U)))) -> (exists T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),T0))),s(num,N0)))))))) # label(aCHOOSEu_SUBSETu_BETWEEN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1075 (all A all B all P0 all M0 ((all X all Y ((all XI_ all YI_ (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(B,int),i(s(fun(A,fun(B,int)),M0),s(A,XI_))),s(B,YI_))))),s(int,i(s(fun(B,int),i(s(fun(A,fun(B,int)),M0),s(A,X))),s(B,Y)))))) -> p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,XI_))),s(B,YI_)))))) -> p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y)))))) & (all X all Y p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(B,int),i(s(fun(A,fun(B,int)),M0),s(A,X))),s(B,Y))))))) -> (all X all Y p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y))))))) # label(aWFu_INTu_MEASUREu_2) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1076 (all A all L s(list(A),L) = s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),L))),s(list(A),nil)))) # label(aAPPENDu_NIL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1077 (all A all P0 all F0 all S0 ((all Y exists X s(A,i(s(fun(A,A),F0),s(A,X))) = s(A,Y)) & (all X all Y (s(A,i(s(fun(A,A),F0),s(A,Y))) = s(A,i(s(fun(A,A),F0),s(A,X))) -> s(A,X) = s(A,Y))) & (all S0 s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),S0))) = s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,A),fun(fun(A,bool),fun(A,bool))),image),s(fun(A,A),F0))),s(fun(A,bool),S0)))))) & (all S0 p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),fun(A,bool))),hull),s(fun(fun(A,bool),bool),P0))),s(fun(A,bool),S0))))))) -> s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,A),fun(fun(A,bool),fun(A,bool))),image),s(fun(A,A),F0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),fun(A,bool))),hull),s(fun(fun(A,bool),bool),P0))),s(fun(A,bool),S0))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),fun(A,bool))),hull),s(fun(fun(A,bool),bool),P0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,A),fun(fun(A,bool),fun(A,bool))),image),s(fun(A,A),F0))),s(fun(A,bool),S0))))))) # label(aHULLu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1078 (all Q4002 all Q4005 all X all XI_ all X0 exists V (s(fun(Q4002,bool),i(s(fun(fun(Q4002,bool),fun(Q4002,bool)),i(s(fun(fun(Q4002,bool),fun(fun(Q4002,bool),fun(Q4002,bool))),i(s(fun(bool,fun(fun(Q4002,bool),fun(fun(Q4002,bool),fun(Q4002,bool)))),cond),s(bool,V))),s(fun(Q4002,bool),i(s(fun(Q4005,fun(Q4002,bool)),X),s(Q4005,X0))))),s(fun(Q4002,bool),i(s(fun(Q4005,fun(Q4002,bool)),XI_),s(Q4005,X0))))) = s(fun(Q4002,bool),i(s(fun(Q4005,fun(Q4002,bool)),i(s(fun(fun(Q4005,fun(Q4002,bool)),fun(Q4005,fun(Q4002,bool))),i(s(fun(fun(Q4005,fun(Q4002,bool)),fun(fun(Q4005,fun(Q4002,bool)),fun(Q4005,fun(Q4002,bool)))),u_seqpattern),s(fun(Q4005,fun(Q4002,bool)),X))),s(fun(Q4005,fun(Q4002,bool)),XI_))),s(Q4005,X0))) & (p(s(bool,V)) <-> (exists Y p(s(bool,i(s(fun(Q4002,bool),i(s(fun(Q4005,fun(Q4002,bool)),X),s(Q4005,X0))),s(Q4002,Y)))))))) # label(au_SEQPATTERN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1079 (all Q73206 all U_1 ((all P0 all F0 all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(Q73206,bool),P0),s(Q73206,X))))),s(real,i(s(fun(Q73206,real),F0),s(Q73206,X))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(Q73206,real),i(s(fun(fun(Q73206,real),fun(Q73206,real)),i(s(fun(fun(Q73206,bool),fun(fun(Q73206,real),fun(Q73206,real))),U_1),s(fun(Q73206,bool),P0))),s(fun(Q73206,real),F0))),s(Q73206,X)))) -> (all U_0 ((all S0 all P0 all GENR_PVARR_176 (p(s(bool,i(s(fun(Q73206,bool),i(s(fun(fun(Q73206,bool),fun(Q73206,bool)),i(s(fun(fun(Q73206,bool),fun(fun(Q73206,bool),fun(Q73206,bool))),U_0),s(fun(Q73206,bool),S0))),s(fun(Q73206,bool),P0))),s(Q73206,GENR_PVARR_176)))) <-> (exists X exists V (p(s(bool,i(s(fun(Q73206,bool),i(s(fun(bool,fun(Q73206,bool)),i(s(fun(Q73206,fun(bool,fun(Q73206,bool))),setspec),s(Q73206,GENR_PVARR_176))),s(bool,V))),s(Q73206,X)))) & (p(s(bool,i(s(fun(fun(Q73206,bool),bool),i(s(fun(Q73206,fun(fun(Q73206,bool),bool)),in),s(Q73206,X))),s(fun(Q73206,bool),S0)))) & p(s(bool,i(s(fun(Q73206,bool),P0),s(Q73206,X)))) <-> p(s(bool,V))))))) -> (all P0 all S0 all F0 s(real,i(s(fun(fun(Q73206,real),real),i(s(fun(fun(Q73206,bool),fun(fun(Q73206,real),real)),sum),s(fun(Q73206,bool),S0))),s(fun(Q73206,real),i(s(fun(fun(Q73206,real),fun(Q73206,real)),i(s(fun(fun(Q73206,bool),fun(fun(Q73206,real),fun(Q73206,real))),U_1),s(fun(Q73206,bool),P0))),s(fun(Q73206,real),F0))))) = s(real,i(s(fun(fun(Q73206,real),real),i(s(fun(fun(Q73206,bool),fun(fun(Q73206,real),real)),sum),s(fun(Q73206,bool),i(s(fun(fun(Q73206,bool),fun(Q73206,bool)),gspec),s(fun(Q73206,bool),i(s(fun(fun(Q73206,bool),fun(Q73206,bool)),i(s(fun(fun(Q73206,bool),fun(fun(Q73206,bool),fun(Q73206,bool))),U_0),s(fun(Q73206,bool),S0))),s(fun(Q73206,bool),P0))))))),s(fun(Q73206,real),F0)))))))) # label(aSUMu_RESTRICTu_SET) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1080 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) -> s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(num,fun(fun(num,bool),fun(num,bool))),insert),s(num,i(s(fun(num,num),suc),s(num,N0))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))) = s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))) # label(aNUMSEGu_REC) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1081 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),poset),s(fun(prod(A,A),bool),L)))) & (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L)))))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) | p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))))) <-> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),toset),s(fun(prod(A,A),bool),L)))))) # label(atoset) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1082 (all Q88501 all Q88505 all S0 (p(s(bool,i(s(fun(fun(Q88501,bool),bool),i(s(fun(fun(Q88505,bool),fun(fun(Q88501,bool),bool)),l_a_u_c),s(fun(Q88505,bool),S0))),s(fun(Q88501,bool),empty)))) <-> s(fun(Q88505,bool),S0) = s(fun(Q88505,bool),empty))) # label(aCARDu_LEu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1083 (all A all S0 all T0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),T0))),s(fun(A,bool),S0))))))) # label(aSUBSETu_UNIONu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1084 (all M0 all N0 all P0 (s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,M0))),s(hreal,P0))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,N0))),s(hreal,P0))) <-> s(hreal,M0) = s(hreal,N0))) # label(aHREALu_EQu_ADDu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1085 (all B all A all F0 ((all X1 all X2 (s(B,i(s(fun(A,B),F0),s(A,X1))) = s(B,i(s(fun(A,B),F0),s(A,X2))) -> s(A,X2) = s(A,X1))) <-> p(s(bool,i(s(fun(fun(A,B),bool),oneu_one),s(fun(A,B),F0)))))) # label(aONEu_ONE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1086 (all U_0 ((all F0 all M0 all I0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(fun(num,num),fun(num,fun(num,num))),U_0),s(fun(num,num),F0))),s(num,M0))),s(num,I0))) = s(num,i(s(fun(num,num),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,I0))),s(num,M0)))))) -> (all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,M0))))))),s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(fun(num,num),fun(num,fun(num,num))),U_0),s(fun(num,num),F0))),s(num,M0))))) = s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),F0))))))) # label(aNSUMu_OFFSETu_0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1087 (all X all Y all Z0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Z0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Y))),s(int,Z0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))),s(int,Z0)))) # label(aINTu_SUBu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1088 (all B all A all P0 all G0 all H0 exists F0 all X s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,i(s(fun(A,bool),P0),s(A,X))))),s(B,i(s(fun(A,B),F0),s(A,i(s(fun(A,A),G0),s(A,X))))))),s(B,i(s(fun(A,B),H0),s(A,X))))) = s(B,i(s(fun(A,B),F0),s(A,X)))) # label(aWFu_RECu_TAIL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1089 (all X all XI_ all Y all YI_ (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,Y))),s(nadd,YI_)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,XI_)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,XI_))),s(nadd,YI_)))))) # label(aNADDu_LEu_WELLDEFu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1090 (all S0 ((exists B0 all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))) & s(fun(real,bool),S0) != s(fun(real,bool),empty) -> (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0)))))))) & (all B0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))))),s(real,B0)))))))) # label(aSUP) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1091 (all B all A all C all S0 all T0 all U (p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(B,bool),fun(fun(C,bool),bool)),l_a_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(A,bool),fun(fun(C,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(C,bool),U)))))) # label(aCARDu_LEu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1092 (all X all Y (s(int,Y) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))) = s(int,X))) # label(aINTu_EQu_ADDu_LCANCELu_0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1093 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),suc),s(num,N0))))))) # label(aHypermapo_GEu_1) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1094 (all Q71509 all U_0 ((all F0 all G0 all X s(real,i(s(fun(Q71509,real),i(s(fun(fun(Q71509,real),fun(Q71509,real)),i(s(fun(fun(Q71509,real),fun(fun(Q71509,real),fun(Q71509,real))),U_0),s(fun(Q71509,real),F0))),s(fun(Q71509,real),G0))),s(Q71509,X))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(Q71509,real),F0),s(Q71509,X))))),s(real,i(s(fun(Q71509,real),G0),s(Q71509,X)))))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q71509,bool),bool),finite),s(fun(Q71509,bool),S0)))) -> s(real,i(s(fun(fun(Q71509,real),real),i(s(fun(fun(Q71509,bool),fun(fun(Q71509,real),real)),sum),s(fun(Q71509,bool),S0))),s(fun(Q71509,real),i(s(fun(fun(Q71509,real),fun(Q71509,real)),i(s(fun(fun(Q71509,real),fun(fun(Q71509,real),fun(Q71509,real))),U_0),s(fun(Q71509,real),F0))),s(fun(Q71509,real),G0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(fun(Q71509,real),real),i(s(fun(fun(Q71509,bool),fun(fun(Q71509,real),real)),sum),s(fun(Q71509,bool),S0))),s(fun(Q71509,real),F0))))),s(real,i(s(fun(fun(Q71509,real),real),i(s(fun(fun(Q71509,bool),fun(fun(Q71509,real),real)),sum),s(fun(Q71509,bool),S0))),s(fun(Q71509,real),G0))))))))) # label(aSUMu_SUB) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1095 (all A all P0 ((all X all XI_ (p(s(bool,i(s(fun(A,bool),P0),s(A,XI_)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> s(A,X) = s(A,XI_))) & (exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) <-> (exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) & (all X all XI_ (p(s(bool,i(s(fun(A,bool),P0),s(A,XI_)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> s(A,X) = s(A,XI_))))) # label(aEXISTSu_UNIQUEu_THM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1096 (all F0 all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) -> s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))),s(fun(num,num),F0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),F0))))),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))),s(fun(num,num),F0))))))) # label(aNSUMu_ADDu_SPLIT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1097 (all U_0 ((all S0 all A5 (p(s(bool,i(s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),U_0),s(fun(real,bool),S0))),s(real,A5)))) <-> (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X)))))) & (all B0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,X)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,A5)))))))) -> (all S0 s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))) = s(real,i(s(fun(fun(real,bool),real),h_),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),U_0),s(fun(real,bool),S0)))))))) # label(ainf) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1098 (all N0 ((-p(s(bool,i(s(fun(num,bool),even),s(num,N0)))) -> (exists M0 s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))) = s(num,N0))) & (p(s(bool,i(s(fun(num,bool),even),s(num,N0)))) -> (exists M0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))) = s(num,N0))))) # label(aEVENu_EXISTSu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.03/14.04 1099 (all N all A all U_1 ((all P0 all GENR_PVARR_238 (p(s(bool,i(s(fun(cart(A,N),bool),i(s(fun(fun(num,fun(A,bool)),fun(cart(A,N),bool)),U_1),s(fun(num,fun(A,bool)),P0))),s(cart(A,N),GENR_PVARR_238)))) <-> (exists V exists V0 (((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),P0),s(num,I0))),s(A,i(s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),d_),s(cart(A,N),V))),s(num,I0)))))))) <-> p(s(bool,V0))) & p(s(bool,i(s(fun(cart(A,N),bool),i(s(fun(bool,fun(cart(A,N),bool)),i(s(fun(cart(A,N),fun(bool,fun(cart(A,N),bool))),setspec),s(cart(A,N),GENR_PVARR_238))),s(bool,V0))),s(cart(A,N),V)))))))) -> (all U_0 ((all P0 all I0 all GENR_PVARR_237 (p(s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(A,bool)),fun(num,fun(A,bool))),U_0),s(fun(num,fun(A,bool)),P0))),s(num,I0))),s(A,GENR_PVARR_237)))) <-> (exists X p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_237))),s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),P0),s(num,I0))),s(A,X))))),s(A,X))))))) -> (all P0 ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(A,bool)),fun(num,fun(A,bool))),U_0),s(fun(num,fun(A,bool)),P0))),s(num,I0)))))))))) -> p(s(bool,i(s(fun(fun(cart(A,N),bool),bool),countable),s(fun(cart(A,N),bool),i(s(fun(fun(cart(A,N),bool),fun(cart(A,N),bool)),gspec),s(fun(cart(A,N),bool),i(s(fun(fun(num,fun(A,bool)),fun(cart(A,N),bool)),U_1),s(fun(num,fun(A,bool)),P0)))))))))))))) # label(aCOUNTABLEu_CART) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1100 (all Q63885 all Q63913 all U_0 ((all A5 all F0 all OP all X exists V ((s(Q63913,X) = s(Q63913,A5) <-> p(s(bool,V))) & s(Q63885,i(s(fun(Q63913,Q63885),i(s(fun(fun(Q63885,fun(Q63885,Q63885)),fun(Q63913,Q63885)),i(s(fun(fun(Q63913,Q63885),fun(fun(Q63885,fun(Q63885,Q63885)),fun(Q63913,Q63885))),i(s(fun(Q63913,fun(fun(Q63913,Q63885),fun(fun(Q63885,fun(Q63885,Q63885)),fun(Q63913,Q63885)))),U_0),s(Q63913,A5))),s(fun(Q63913,Q63885),F0))),s(fun(Q63885,fun(Q63885,Q63885)),OP))),s(Q63913,X))) = s(Q63885,i(s(fun(Q63885,Q63885),i(s(fun(Q63885,fun(Q63885,Q63885)),i(s(fun(bool,fun(Q63885,fun(Q63885,Q63885))),cond),s(bool,V))),s(Q63885,i(s(fun(Q63913,Q63885),F0),s(Q63913,X))))),s(Q63885,i(s(fun(fun(Q63885,fun(Q63885,Q63885)),Q63885),neutral),s(fun(Q63885,fun(Q63885,Q63885)),OP))))))) -> (all OP all S0 all F0 all A5 s(fun(Q63913,bool),i(s(fun(fun(Q63913,bool),fun(Q63913,bool)),i(s(fun(fun(Q63913,bool),fun(fun(Q63913,bool),fun(Q63913,bool))),i(s(fun(bool,fun(fun(Q63913,bool),fun(fun(Q63913,bool),fun(Q63913,bool)))),cond),s(bool,i(s(fun(fun(Q63913,bool),bool),i(s(fun(Q63913,fun(fun(Q63913,bool),bool)),in),s(Q63913,A5))),s(fun(Q63913,bool),S0))))),s(fun(Q63913,bool),i(s(fun(fun(Q63913,bool),fun(Q63913,bool)),i(s(fun(fun(Q63913,Q63885),fun(fun(Q63913,bool),fun(Q63913,bool))),i(s(fun(fun(Q63885,fun(Q63885,Q63885)),fun(fun(Q63913,Q63885),fun(fun(Q63913,bool),fun(Q63913,bool)))),support),s(fun(Q63885,fun(Q63885,Q63885)),OP))),s(fun(Q63913,Q63885),F0))),s(fun(Q63913,bool),i(s(fun(fun(Q63913,bool),fun(Q63913,bool)),i(s(fun(Q63913,fun(fun(Q63913,bool),fun(Q63913,bool))),insert),s(Q63913,A5))),s(fun(Q63913,bool),empty))))))),s(fun(Q63913,bool),empty))) = s(fun(Q63913,bool),i(s(fun(fun(Q63913,bool),fun(Q63913,bool)),i(s(fun(fun(Q63913,Q63885),fun(fun(Q63913,bool),fun(Q63913,bool))),i(s(fun(fun(Q63885,fun(Q63885,Q63885)),fun(fun(Q63913,Q63885),fun(fun(Q63913,bool),fun(Q63913,bool)))),support),s(fun(Q63885,fun(Q63885,Q63885)),OP))),s(fun(Q63913,Q63885),i(s(fun(fun(Q63885,fun(Q63885,Q63885)),fun(Q63913,Q63885)),i(s(fun(fun(Q63913,Q63885),fun(fun(Q63885,fun(Q63885,Q63885)),fun(Q63913,Q63885))),i(s(fun(Q63913,fun(fun(Q63913,Q63885),fun(fun(Q63885,fun(Q63885,Q63885)),fun(Q63913,Q63885)))),U_0),s(Q63913,A5))),s(fun(Q63913,Q63885),F0))),s(fun(Q63885,fun(Q63885,Q63885)),OP))))),s(fun(Q63913,bool),S0)))))) # label(aSUPPORTu_DELTA) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1101 (all Q20165 all P0 all L (p(s(bool,i(s(fun(list(Q20165),bool),i(s(fun(fun(Q20165,bool),fun(list(Q20165),bool)),ex0),s(fun(Q20165,bool),P0))),s(list(Q20165),L)))) <-> (exists X (p(s(bool,i(s(fun(Q20165,bool),P0),s(Q20165,X)))) & p(s(bool,i(s(fun(list(Q20165),bool),i(s(fun(Q20165,fun(list(Q20165),bool)),mem),s(Q20165,X))),s(list(Q20165),L)))))))) # label(aEXu_MEM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1102 (all Q63514 all Q63525 all OP all F0 all S0 s(fun(Q63525,bool),i(s(fun(fun(Q63525,bool),fun(Q63525,bool)),i(s(fun(fun(Q63525,Q63514),fun(fun(Q63525,bool),fun(Q63525,bool))),i(s(fun(fun(Q63514,fun(Q63514,Q63514)),fun(fun(Q63525,Q63514),fun(fun(Q63525,bool),fun(Q63525,bool)))),support),s(fun(Q63514,fun(Q63514,Q63514)),OP))),s(fun(Q63525,Q63514),F0))),s(fun(Q63525,bool),S0))) = s(fun(Q63525,bool),i(s(fun(fun(Q63525,bool),fun(Q63525,bool)),i(s(fun(fun(Q63525,Q63514),fun(fun(Q63525,bool),fun(Q63525,bool))),i(s(fun(fun(Q63514,fun(Q63514,Q63514)),fun(fun(Q63525,Q63514),fun(fun(Q63525,bool),fun(Q63525,bool)))),support),s(fun(Q63514,fun(Q63514,Q63514)),OP))),s(fun(Q63525,Q63514),F0))),s(fun(Q63525,bool),i(s(fun(fun(Q63525,bool),fun(Q63525,bool)),i(s(fun(fun(Q63525,Q63514),fun(fun(Q63525,bool),fun(Q63525,bool))),i(s(fun(fun(Q63514,fun(Q63514,Q63514)),fun(fun(Q63525,Q63514),fun(fun(Q63525,bool),fun(Q63525,bool)))),support),s(fun(Q63514,fun(Q63514,Q63514)),OP))),s(fun(Q63525,Q63514),F0))),s(fun(Q63525,bool),S0)))))) # label(aSUPPORTu_SUPPORT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1103 (all X s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))) = s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(int,int),intu_neg),s(int,X)))))) # label(aintu_negu_th) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1104 (all A all S0 all T0 all U (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),U)))))) # label(aPSUBSETu_SUBSETu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1105 (all A all S0 all F0 all B0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,B0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))))),s(real,B0)))))))) # label(aSUMu_BOUND) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1106 (all M0 all N0 (s(num,N0) = s(num,M0) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))))) # label(aEQu_IMPu_LE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1107 p(s(bool,f0)) <-> (all P0 p(s(bool,P0))) # label(aFu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1108 (all Q92647 all Q92648 all S0 all T0 (p(s(bool,i(s(fun(fun(Q92648,bool),bool),i(s(fun(fun(Q92647,bool),fun(fun(Q92648,bool),bool)),a_u_c),s(fun(Q92647,bool),S0))),s(fun(Q92648,bool),T0)))) -> s(bool,i(s(fun(fun(Q92647,bool),bool),countable),s(fun(Q92647,bool),S0))) = s(bool,i(s(fun(fun(Q92648,bool),bool),countable),s(fun(Q92648,bool),T0))))) # label(aCARDu_COUNTABLEu_CONG) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1109 (all U_1 ((all G0 all F0 all K0 s(real,i(s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),i(s(fun(fun(num,real),fun(fun(num,real),fun(num,real))),U_1),s(fun(num,real),G0))),s(fun(num,real),F0))),s(num,K0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),G0),s(num,K0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),F0),s(num,K0)))))))) -> (all U_0 ((all F0 all G0 all K0 s(real,i(s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),i(s(fun(fun(num,real),fun(fun(num,real),fun(num,real))),U_0),s(fun(num,real),F0))),s(fun(num,real),G0))),s(num,K0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),F0),s(num,K0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),G0),s(num,K0))))),s(real,i(s(fun(num,real),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) -> (all F0 all G0 all M0 all N0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),i(s(fun(fun(num,real),fun(fun(num,real),fun(num,real))),U_0),s(fun(num,real),F0))),s(fun(num,real),G0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),G0),s(num,N0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),F0),s(num,M0))))),s(real,i(s(fun(num,real),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),i(s(fun(fun(num,real),fun(fun(num,real),fun(num,real))),U_1),s(fun(num,real),G0))),s(fun(num,real),F0))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))))) # label(aSUMu_PARTIALu_PRE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1110 (all A all T0 ((exists X p(s(bool,T0))) <-> p(s(bool,T0)))) # label(aEXISTSu_SIMP) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1111 (all X all Y all Z0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Y))),s(int,Z0))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) # label(aINTu_LEu_RADD) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1112 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(B,bool),fun(fun(A,bool),bool)),l_a_u_c),s(fun(B,bool),T0))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))))) # label(aCARDu_LEu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1113 (all A all REL all X all Y s(bool,i(s(fun(fun(A,fun(A,bool)),bool),i(s(fun(A,fun(fun(A,fun(A,bool)),bool)),i(s(fun(A,fun(A,fun(fun(A,fun(A,bool)),bool))),a_a_),s(A,X))),s(A,Y))),s(fun(A,fun(A,bool)),REL))) = s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),REL),s(A,X))),s(A,Y)))) # label(acong) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1114 (all A all F0 all U all V ((all X (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V)))) -> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(A,num),F0),s(A,X))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),U)))) -> s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),U))),s(fun(A,bool),V))))),s(fun(A,num),F0))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),U))),s(fun(A,num),F0))))) # label(aNSUMu_UNIONu_RZERO) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1115 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0)))))))) # label(aREALu_LEu_LMUL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1116 (all B all A ((exists R0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),s0)))) -> (exists Y (p(s(bool,i(s(fun(prod(A,B),bool),R0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),t0)))))) & (all Y all XI_ (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),t0)))) & p(s(bool,i(s(fun(prod(A,B),bool),R0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))) & p(s(bool,i(s(fun(prod(A,B),bool),R0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,XI_)))))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,XI_))),s(fun(B,bool),t0)))) -> s(B,XI_) = s(B,Y))))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),t0)))) -> (exists X (p(s(bool,i(s(fun(prod(A,B),bool),R0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),s0)))))) & (all X all XI_ (p(s(bool,i(s(fun(prod(A,B),bool),R0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,XI_))),s(B,Y)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),s0)))) & p(s(bool,i(s(fun(prod(A,B),bool),R0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),s0)))) -> s(A,X) = s(A,XI_))))) & (all X all Y (p(s(bool,i(s(fun(prod(A,B),bool),R0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),s0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),t0)))))))) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),s0))),s(fun(B,bool),t0)))))) # label(aEQu_C) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1117 (all X all N0 s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(num,N0)))) # label(aintu_powu_th) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1118 (all U_0 ((all U (p(s(bool,i(s(fun(bool,bool),U_0),s(bool,U)))) <-> (exists X1 exists Y1 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(real,fun(prod(hreal,hreal),bool)),destu_real),s(real,y1))),s(prod(hreal,hreal),Y1)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(real,fun(prod(hreal,hreal),bool)),destu_real),s(real,x1))),s(prod(hreal,hreal),X1)))) & s(bool,U) = s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),Y1))))))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,x1))),s(real,y1))) = s(bool,i(s(fun(fun(bool,bool),bool),h_),s(fun(bool,bool),U_0))))) # label(arealu_le) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1119 (all Q20886 all L (s(list(Q20886),L) != s(list(Q20886),nil) -> s(Q20886,i(s(fun(list(Q20886),Q20886),last0),s(list(Q20886),L))) = s(Q20886,i(s(fun(list(Q20886),Q20886),i(s(fun(num,fun(list(Q20886),Q20886)),el),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(list(Q20886),num),length),s(list(Q20886),L))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(list(Q20886),L))))) # label(aLASTu_EL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1120 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,X)))) # label(aINTu_SUBu_LT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1121 (all W all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,Z0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,W))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,W))),s(int,Y))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0)))))))) # label(aINTu_LTu_ADD2) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1122 (all B all A all C all S0 all T0 all U (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(B,bool),fun(fun(C,bool),bool)),l_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U)))) -> p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(A,bool),fun(fun(C,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(C,bool),U)))))) # label(aCARDu_LTu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1123 (all A all B all F0 all G0 all S0 all T0 all I0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> (exists Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) & s(A,X) = s(A,i(s(fun(B,A),I0),s(B,Y))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,i(s(fun(B,real),G0),s(B,Y)))))))))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(B,real),G0),s(B,Y)))))))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))),s(real,i(s(fun(fun(B,real),real),i(s(fun(fun(B,bool),fun(fun(B,real),real)),sum),s(fun(B,bool),T0))),s(fun(B,real),G0)))))))) # label(aSUMu_LEu_INCLUDED) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1124 (all Q78417 all Q78414 all Q78412 all Z0 s(cart(Q78417,finite_sum(Q78414,Q78412)),Z0) = s(cart(Q78417,finite_sum(Q78414,Q78412)),i(s(fun(cart(Q78417,Q78412),cart(Q78417,finite_sum(Q78414,Q78412))),i(s(fun(cart(Q78417,Q78414),fun(cart(Q78417,Q78412),cart(Q78417,finite_sum(Q78414,Q78412)))),pastecart),s(cart(Q78417,Q78414),i(s(fun(cart(Q78417,finite_sum(Q78414,Q78412)),cart(Q78417,Q78414)),fstcart),s(cart(Q78417,finite_sum(Q78414,Q78412)),Z0))))),s(cart(Q78417,Q78412),i(s(fun(cart(Q78417,finite_sum(Q78414,Q78412)),cart(Q78417,Q78412)),sndcart),s(cart(Q78417,finite_sum(Q78414,Q78412)),Z0)))))) # label(aPASTECARTu_FSTu_SND) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1125 (all X all Y s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X))),s(hreal,Y))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,Y))),s(hreal,X)))) # label(aHREALu_ADDu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1126 (all A all B (p(s(bool,i(s(fun(num,bool),i(s(fun(B,fun(num,bool)),i(s(fun(fun(A,bool),fun(B,fun(num,bool))),i(s(fun(B,fun(fun(A,bool),fun(B,fun(num,bool)))),i(s(fun(fun(A,fun(B,B)),fun(B,fun(fun(A,bool),fun(B,fun(num,bool))))),finrec),s(fun(A,fun(B,B)),f))),s(B,b0))),s(fun(A,bool),s0))),s(B,a0))),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) <-> s(fun(A,bool),empty) = s(fun(A,bool),s0) & s(B,a0) = s(B,b0))) # label(aFINRECu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1127 (all A all P0 (p(s(bool,i(s(fun(list(A),bool),P0),s(list(A),nil)))) & (all A01 all A10 (p(s(bool,i(s(fun(list(A),bool),P0),s(list(A),A10)))) -> p(s(bool,i(s(fun(list(A),bool),P0),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,A01))),s(list(A),A10)))))))) -> (all X p(s(bool,i(s(fun(list(A),bool),P0),s(list(A),X))))))) # label(alistu_INDUCT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1128 (all A5 s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),i(s(fun(real,fun(fun(real,bool),fun(real,bool))),insert),s(real,A5))),s(fun(real,bool),empty))))) = s(real,A5)) # label(aINFu_SING) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1129 (all Q50480 all Q50479 all Q50467 all F0 all G0 ((exists H0 s(fun(Q50479,Q50480),F0) = s(fun(Q50479,Q50480),i(s(fun(fun(Q50479,Q50467),fun(Q50479,Q50480)),i(s(fun(fun(Q50467,Q50480),fun(fun(Q50479,Q50467),fun(Q50479,Q50480))),o),s(fun(Q50467,Q50480),G0))),s(fun(Q50479,Q50467),H0)))) <-> (all X exists Y s(Q50480,i(s(fun(Q50479,Q50480),F0),s(Q50479,X))) = s(Q50480,i(s(fun(Q50467,Q50480),G0),s(Q50467,Y)))))) # label(aFUNCTIONu_FACTORSu_RIGHT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1130 (all A5 all B0 s(num,i(s(fun(int,num),numu_ofu_int),s(int,i(s(fun(prod(int,int),int),intu_gcd),s(prod(int,int),i(s(fun(int,prod(int,int)),i(s(fun(int,fun(int,prod(int,int))),c_),s(int,i(s(fun(num,int),intu_ofu_num),s(num,A5))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,B0))))))))) = s(num,i(s(fun(prod(num,num),num),numu_gcd),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,A5))),s(num,B0)))))) # label(anumu_gcd) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1131 (all NUMU_REPI_ ((all I0 (p(s(bool,i(s(fun(ind0,bool),NUMU_REPI_),s(ind0,I0)))) -> p(s(bool,i(s(fun(ind0,bool),NUMU_REPI_),s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,I0)))))))) & p(s(bool,i(s(fun(ind0,bool),NUMU_REPI_),s(ind0,indu_0)))) -> (all A5 (p(s(bool,i(s(fun(ind0,bool),numu_rep),s(ind0,A5)))) -> p(s(bool,i(s(fun(ind0,bool),NUMU_REPI_),s(ind0,A5)))))))) # label(aNUMu_REPu_INDUCT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1132 (all U_0 ((all F0 all G0 all I0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),F0),s(num,I0))))),s(num,i(s(fun(num,num),G0),s(num,I0))))) = s(num,i(s(fun(num,num),i(s(fun(fun(num,num),fun(num,num)),i(s(fun(fun(num,num),fun(fun(num,num),fun(num,num))),U_0),s(fun(num,num),F0))),s(fun(num,num),G0))),s(num,I0)))) -> (all F0 all G0 all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),F0))))),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),G0))))) = s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),i(s(fun(fun(num,num),fun(num,num)),i(s(fun(fun(num,num),fun(fun(num,num),fun(num,num))),U_0),s(fun(num,num),F0))),s(fun(num,num),G0)))))))) # label(aNSUMu_ADDu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1133 (all X0 all X all Y0 all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,X0))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y0))),s(real,X0)))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,Y0))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y0))),s(real,X0)))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X0))),s(real,Y0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))))) # label(aREALu_ABSu_BETWEEN2) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1134 (all A all P0 all Q0 ((all X (p(s(bool,Q0)) | p(s(bool,i(s(fun(A,bool),P0),s(A,X)))))) <-> p(s(bool,Q0)) | (all X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) # label(aLEFTu_ORu_FORALLu_THM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1135 (all X (s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(real,i(s(fun(real,real),realu_inv),s(real,X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aREALu_INVu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1136 (all A all A5 (p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),zrecspace),s(fun(num,fun(A,bool)),A5)))) <-> s(fun(num,fun(A,bool)),A5) = s(fun(num,fun(A,bool)),zbot) | (exists C0 exists I0 exists R0 (s(fun(num,fun(A,bool)),A5) = s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))),i(s(fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool)))),i(s(fun(num,fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))))),zconstr),s(num,C0))),s(A,I0))),s(fun(num,fun(num,fun(A,bool))),R0))) & (all N0 p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),zrecspace),s(fun(num,fun(A,bool)),i(s(fun(num,fun(num,fun(A,bool))),R0),s(num,N0))))))))))) # label(aZRECSPACEu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1137 (all N0 s(num,i(s(fun(num,num),bit0),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,N0)))) # label(aBIT0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1138 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,X))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Y))),s(int,Y))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y)))))) # label(aINTu_DIFFSQ) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1139 (all M0 all N0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,M0))),s(real,N0))))),s(real,M0))),s(real,N0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,M0))),s(real,N0)))) # label(arealu_min) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1140 (all Q18865 s(Q18865,i(s(fun(list(Q18865),Q18865),i(s(fun(num,fun(list(Q18865),Q18865)),el),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(list(Q18865),l0))) = s(Q18865,i(s(fun(list(Q18865),Q18865),hd),s(list(Q18865),l0)))) # label(aELu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1141 (all M0 all N0 s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,M0))))) = s(num,N0)) # label(aDISTu_LADDu_0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1142 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,Y))),s(int,X)))) # label(aINTu_MINu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1143 (all A all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),unions),s(fun(fun(A,bool),bool),S0)))))) <-> (all T0 (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T0))),s(fun(fun(A,bool),bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))))) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),finite),s(fun(fun(A,bool),bool),S0)))))) # label(aFINITEu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1144 (all Q48147 all Q48152 all U_0 ((all C0 all X s(Q48152,i(s(fun(Q48147,Q48152),i(s(fun(Q48152,fun(Q48147,Q48152)),U_0),s(Q48152,C0))),s(Q48147,X))) = s(Q48152,C0)) -> (all S0 all C0 exists V (s(fun(Q48152,bool),i(s(fun(fun(Q48152,bool),fun(Q48152,bool)),i(s(fun(fun(Q48152,bool),fun(fun(Q48152,bool),fun(Q48152,bool))),i(s(fun(bool,fun(fun(Q48152,bool),fun(fun(Q48152,bool),fun(Q48152,bool)))),cond),s(bool,V))),s(fun(Q48152,bool),empty))),s(fun(Q48152,bool),i(s(fun(fun(Q48152,bool),fun(Q48152,bool)),i(s(fun(Q48152,fun(fun(Q48152,bool),fun(Q48152,bool))),insert),s(Q48152,C0))),s(fun(Q48152,bool),empty))))) = s(fun(Q48152,bool),i(s(fun(fun(Q48147,bool),fun(Q48152,bool)),i(s(fun(fun(Q48147,Q48152),fun(fun(Q48147,bool),fun(Q48152,bool))),image),s(fun(Q48147,Q48152),i(s(fun(Q48152,fun(Q48147,Q48152)),U_0),s(Q48152,C0))))),s(fun(Q48147,bool),S0))) & (p(s(bool,V)) <-> s(fun(Q48147,bool),S0) = s(fun(Q48147,bool),empty)))))) # label(aIMAGEu_CONST) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1145 (all X all Y all Z0 (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Y))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Z0)))))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,Y))),s(nadd,Z0)))))) # label(aNADDu_ADDu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1146 (all M0 all N0 all P0 all Q0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,Q0))),s(num,P0)))) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,Q0))),s(num,M0)))) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,P0)))) <-> p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(fun(num,bool),fun(fun(num,bool),bool)),disjoint),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,P0))),s(num,Q0)))))))) # label(aDISJOINTu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1147 (all A all B all C all OP (p(s(bool,i(s(fun(fun(C,fun(C,C)),bool),monoidal),s(fun(C,fun(C,C)),OP)))) -> (all S0 all T0 all F0 all G0 all H0 all K0 ((all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> s(B,i(s(fun(A,B),H0),s(A,i(s(fun(B,A),K0),s(B,Y))))) = s(B,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(B,A),K0),s(B,Y))))),s(fun(A,bool),S0)))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,X) = s(A,i(s(fun(B,A),K0),s(B,i(s(fun(A,B),H0),s(A,X))))) & s(C,i(s(fun(A,C),F0),s(A,X))) = s(C,i(s(fun(B,C),G0),s(B,i(s(fun(A,B),H0),s(A,X))))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),H0),s(A,X))))),s(fun(B,bool),T0)))))) -> s(C,i(s(fun(fun(A,C),C),i(s(fun(fun(A,bool),fun(fun(A,C),C)),i(s(fun(fun(C,fun(C,C)),fun(fun(A,bool),fun(fun(A,C),C))),iterate),s(fun(C,fun(C,C)),OP))),s(fun(A,bool),S0))),s(fun(A,C),F0))) = s(C,i(s(fun(fun(B,C),C),i(s(fun(fun(B,bool),fun(fun(B,C),C)),i(s(fun(fun(C,fun(C,C)),fun(fun(B,bool),fun(fun(B,C),C))),iterate),s(fun(C,fun(C,C)),OP))),s(fun(B,bool),T0))),s(fun(B,C),G0))))))) # label(aITERATEu_EQu_GENERALu_INVERSES) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1148 (all M0 all N0 all P0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))))),s(num,P0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0))))))) # label(aDIVu_DIV) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1149 (all A all X s(bool,i(s(fun(fun(A,bool),bool),q_),s(fun(A,bool),X))) = s(bool,i(s(fun(A,bool),X),s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),X)))))) # label(aEXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1150 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,N0)))))))) # label(aARITHu_EXPu_conjunct8) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1151 (all X all Y all N0 s(bool,i(s(fun(fun(int,fun(int,bool)),bool),i(s(fun(int,fun(fun(int,fun(int,bool)),bool)),i(s(fun(int,fun(int,fun(fun(int,fun(int,bool)),bool))),a_a_),s(int,i(s(fun(num,int),intu_ofu_num),s(num,X))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,Y))))),s(fun(int,fun(int,bool)),i(s(fun(int,fun(int,fun(int,bool))),intu_mod),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))))) = s(bool,i(s(fun(fun(num,fun(num,bool)),bool),i(s(fun(num,fun(fun(num,fun(num,bool)),bool)),i(s(fun(num,fun(num,fun(fun(num,fun(num,bool)),bool))),a_a_),s(num,X))),s(num,Y))),s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),numu_mod),s(num,N0)))))) # label(anumu_congruent) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1152 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,u_0))),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(num,u_0)) # label(aARITHu_SUBu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1153 (all A all B all R0 (s(num,R0) = s(num,i(s(fun(finite_sum(A,B),num),destu_finiteu_sum),s(finite_sum(A,B),i(s(fun(num,finite_sum(A,B)),mku_finiteu_sum),s(num,R0))))) <-> p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,R0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),univ))))),s(num,i(s(fun(fun(B,bool),num),dimindex),s(fun(B,bool),univ)))))))))))) # label(afiniteu_sumu_tybiju_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1154 (all A all X s(A,X) = s(A,X)) # label(aEQu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1155 (all B all A all A5 all AI_ (s(A,A5) = s(A,AI_) <-> s(sum0(A,B),i(s(fun(A,sum0(A,B)),inl),s(A,A5))) = s(sum0(A,B),i(s(fun(A,sum0(A,B)),inl),s(A,AI_))))) # label(asumu_INJECTIVEu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.05 1156 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,M0))) = s(num,N0)) # label(aADDu_SUB2) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1157 (all Q52983 all U_0 ((all S0 all P0 all GENR_PVARR_66 (p(s(bool,i(s(fun(Q52983,bool),i(s(fun(fun(Q52983,bool),fun(Q52983,bool)),i(s(fun(fun(Q52983,bool),fun(fun(Q52983,bool),fun(Q52983,bool))),U_0),s(fun(Q52983,bool),S0))),s(fun(Q52983,bool),P0))),s(Q52983,GENR_PVARR_66)))) <-> (exists X exists V (p(s(bool,i(s(fun(Q52983,bool),i(s(fun(bool,fun(Q52983,bool)),i(s(fun(Q52983,fun(bool,fun(Q52983,bool))),setspec),s(Q52983,GENR_PVARR_66))),s(bool,V))),s(Q52983,X)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(Q52983,bool),P0),s(Q52983,X)))) & p(s(bool,i(s(fun(fun(Q52983,bool),bool),i(s(fun(Q52983,fun(fun(Q52983,bool),bool)),in),s(Q52983,X))),s(fun(Q52983,bool),S0))))))))) -> (all S0 all P0 p(s(bool,i(s(fun(fun(Q52983,bool),bool),i(s(fun(fun(Q52983,bool),fun(fun(Q52983,bool),bool)),subset),s(fun(Q52983,bool),i(s(fun(fun(Q52983,bool),fun(Q52983,bool)),gspec),s(fun(Q52983,bool),i(s(fun(fun(Q52983,bool),fun(Q52983,bool)),i(s(fun(fun(Q52983,bool),fun(fun(Q52983,bool),fun(Q52983,bool))),U_0),s(fun(Q52983,bool),S0))),s(fun(Q52983,bool),P0))))))),s(fun(Q52983,bool),S0))))))) # label(aSUBSETu_RESTRICT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1158 (all A all U_0 ((all S0 all T0 all GENR_PVARR_2 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,bool),T0))),s(A,GENR_PVARR_2)))) <-> (exists X exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_2))),s(bool,V))),s(A,X)))))))) -> (all S0 all T0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))))) # label(aINTER) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1159 (all X all Y all Z0 (p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,Y))),s(hreal,Z0)))) & p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,Y)))) -> p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,Z0)))))) # label(aHREALu_LEu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1160 (all M0 s(num,i(s(fun(num,num),bit1),s(num,u_0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,u_0)))) # label(aARITHu_EXPu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1161 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) <-> (exists U (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),U)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),U))),s(fun(B,bool),T0)))))))) # label(aCARDu_LEu_EQu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1162 (all M0 all N0 (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))))) # label(aSsrnato_leqE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1163 (all A all U_0 ((all A5 all X exists V ((p(s(bool,V)) <-> s(A,A5) = s(A,X)) & s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,b0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(A,real),i(s(fun(A,fun(A,real)),U_0),s(A,A5))),s(A,X))))) -> (all S0 all A5 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,A5))),s(fun(A,bool),S0))))),s(real,b0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(A,fun(A,real)),U_0),s(A,A5)))))))) # label(aSUMu_DELTA) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1164 (all A all E0 all F0 exists FN (s(A,E0) = s(A,i(s(fun(num,A),FN),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & (all N0 s(A,i(s(fun(num,A),FN),s(num,i(s(fun(num,num),suc),s(num,N0))))) = s(A,i(s(fun(num,A),i(s(fun(A,fun(num,A)),F0),s(A,i(s(fun(num,A),FN),s(num,N0))))),s(num,N0)))))) # label(anumu_RECURSION) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1165 (all X s(nadd,i(s(fun(nadd,nadd),naddu_inv),s(nadd,X))) = s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),i(s(fun(bool,fun(nadd,fun(nadd,nadd))),cond),s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(nadd,i(s(fun(fun(num,num),nadd),mku_nadd),s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X)))))))) # label(anaddu_inv) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1166 (all X all Y all Z0 (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Z0))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,Y))),s(nadd,Z0)))))))) # label(aNADDu_LEu_RMUL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1167 (all Q88389 all Q88390 all S0 all T0 (p(s(bool,i(s(fun(fun(Q88390,bool),bool),i(s(fun(fun(Q88389,bool),fun(fun(Q88390,bool),bool)),a_u_c),s(fun(Q88389,bool),S0))),s(fun(Q88390,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q88390,bool),bool),i(s(fun(fun(Q88389,bool),fun(fun(Q88390,bool),bool)),l_a_u_c),s(fun(Q88389,bool),S0))),s(fun(Q88390,bool),T0)))))) # label(aCARDu_EQu_IMPu_LE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1168 (all P0 all A5 all B0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),P0),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & (all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),P0),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))),s(num,B0))))))) -> (exists B0 all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),P0),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))))))) # label(aBOUNDSu_NOTZERO) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1169 (all M0 all N0 (s(real,i(s(fun(num,real),realu_ofu_num),s(num,M0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))) <-> s(num,M0) = s(num,N0))) # label(aREALu_OFu_NUMu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1170 (all A all F0 all U all V ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V)))) & -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) -> s(real,i(s(fun(A,real),F0),s(A,X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),U)))) -> s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),U))),s(fun(A,bool),V))))),s(fun(A,real),F0))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),U))),s(fun(A,real),F0))))) # label(aSUMu_UNIONu_RZERO) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1171 (all A all S0 all T0 all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) | p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))))) # label(aINu_UNION) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1172 (all U_0 ((all A5 all B0 all GENR_PVARR_129 ((exists X exists V ((p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_129))),s(bool,V))),s(real,X)))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),i(s(fun(real,fun(real,fun(real,bool))),U_0),s(real,A5))),s(real,B0))),s(real,GENR_PVARR_129)))))) -> (all A5 all B0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,A5))) = s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(real,fun(real,bool)),i(s(fun(real,fun(real,fun(real,bool))),U_0),s(real,A5))),s(real,B0)))))))))) # label(aFINITEu_REALu_INTERVALu_conjunct7) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1173 (all A all P0 exists L (s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))) = s(fun(A,bool),P0) & p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))))) # label(aWO) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1174 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,N0))),s(num,M0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,i(s(fun(num,num),numeral),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,M0)))))) # label(aARITHu_GEu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1175 (all X exists N0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(num,N0))))))) # label(aREALu_ARCHu_POW2) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1176 (all A all B all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all X all S0 (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,bool),fun(A,bool)))),support),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,bool),S0)))))) -> s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))))),s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),OP),s(B,i(s(fun(A,B),F0),s(A,X))))),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))))))) = s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))),s(fun(A,B),F0))))) & (all F0 s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),empty))),s(fun(A,B),F0))) = s(B,i(s(fun(fun(B,fun(B,B)),B),neutral),s(fun(B,fun(B,B)),OP)))))) # label(aITERATEu_CLAUSESu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1177 (all A all L all M0 (s(fun(prod(A,A),bool),M0) != s(fun(prod(A,A),bool),L) & p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),M0))),s(fun(prod(A,A),bool),L)))) -> (exists X exists Y (-p(s(bool,i(s(fun(prod(A,A),bool),M0),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))))))) # label(aINSEGu_PROPERu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1178 (all X all Y all Z0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Y))),s(int,Z0))))),s(int,X))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,i(s(fun(int,int),intu_neg),s(int,Z0)))))))) # label(aINTu_LTu_ADDNEG) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1179 (all A all S0 all T0 all U s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),T0))),s(fun(A,bool),U))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,bool),U)))) # label(aINTERu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1180 (all Q19544 all Q19543 all P0 all F0 all L s(bool,i(s(fun(list(Q19544),bool),i(s(fun(fun(Q19544,bool),fun(list(Q19544),bool)),all0),s(fun(Q19544,bool),P0))),s(list(Q19544),i(s(fun(list(Q19543),list(Q19544)),i(s(fun(fun(Q19543,Q19544),fun(list(Q19543),list(Q19544))),map0),s(fun(Q19543,Q19544),F0))),s(list(Q19543),L))))) = s(bool,i(s(fun(list(Q19543),bool),i(s(fun(fun(Q19543,bool),fun(list(Q19543),bool)),all0),s(fun(Q19543,bool),i(s(fun(fun(Q19543,Q19544),fun(Q19543,bool)),i(s(fun(fun(Q19544,bool),fun(fun(Q19543,Q19544),fun(Q19543,bool))),o),s(fun(Q19544,bool),P0))),s(fun(Q19543,Q19544),F0))))),s(list(Q19543),L)))) # label(aALLu_MAP) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1181 (all Q79737 all Q79745 all Q79739 all U_1 ((all A5 s(bool,t) = s(bool,i(s(fun(Q79745,bool),U_1),s(Q79745,A5)))) -> (all U_0 ((all F0 s(fun(Q79745,bool),U_1) = s(fun(Q79745,bool),i(s(fun(fun(Q79737,Q79739),fun(Q79745,bool)),U_0),s(fun(Q79737,Q79739),F0)))) -> (all L_L_ all P0 all S0 all T0 (p(s(bool,i(s(fun(fun(fun(Q79737,Q79739),fun(Q79745,Q79739)),bool),i(s(fun(fun(Q79745,Q79737),fun(fun(fun(Q79737,Q79739),fun(Q79745,Q79739)),bool)),i(s(fun(fun(fun(Q79737,Q79739),fun(Q79745,bool)),fun(fun(Q79745,Q79737),fun(fun(fun(Q79737,Q79739),fun(Q79745,Q79739)),bool))),i(s(fun(fun(Q79737,fun(Q79737,bool)),fun(fun(fun(Q79737,Q79739),fun(Q79745,bool)),fun(fun(Q79745,Q79737),fun(fun(fun(Q79737,Q79739),fun(Q79745,Q79739)),bool)))),superadmissible),s(fun(Q79737,fun(Q79737,bool)),L_L_))),s(fun(fun(Q79737,Q79739),fun(Q79745,bool)),P0))),s(fun(Q79745,Q79737),S0))),s(fun(fun(Q79737,Q79739),fun(Q79745,Q79739)),T0)))) <-> (p(s(bool,i(s(fun(fun(fun(Q79737,Q79739),fun(Q79745,bool)),bool),i(s(fun(fun(Q79745,Q79737),fun(fun(fun(Q79737,Q79739),fun(Q79745,bool)),bool)),i(s(fun(fun(fun(Q79737,Q79739),fun(Q79745,bool)),fun(fun(Q79745,Q79737),fun(fun(fun(Q79737,Q79739),fun(Q79745,bool)),bool))),i(s(fun(fun(Q79737,fun(Q79737,bool)),fun(fun(fun(Q79737,Q79739),fun(Q79745,bool)),fun(fun(Q79745,Q79737),fun(fun(fun(Q79737,Q79739),fun(Q79745,bool)),bool)))),admissible),s(fun(Q79737,fun(Q79737,bool)),L_L_))),s(fun(fun(Q79737,Q79739),fun(Q79745,bool)),U_0))),s(fun(Q79745,Q79737),S0))),s(fun(fun(Q79737,Q79739),fun(Q79745,bool)),P0)))) -> p(s(bool,i(s(fun(fun(fun(Q79737,Q79739),fun(Q79745,Q79739)),bool),i(s(fun(fun(Q79745,Q79737),fun(fun(fun(Q79737,Q79739),fun(Q79745,Q79739)),bool)),i(s(fun(fun(fun(Q79737,Q79739),fun(Q79745,bool)),fun(fun(Q79745,Q79737),fun(fun(fun(Q79737,Q79739),fun(Q79745,Q79739)),bool))),i(s(fun(fun(Q79737,fun(Q79737,bool)),fun(fun(fun(Q79737,Q79739),fun(Q79745,bool)),fun(fun(Q79745,Q79737),fun(fun(fun(Q79737,Q79739),fun(Q79745,Q79739)),bool)))),tailadmissible),s(fun(Q79737,fun(Q79737,bool)),L_L_))),s(fun(fun(Q79737,Q79739),fun(Q79745,bool)),P0))),s(fun(Q79745,Q79737),S0))),s(fun(fun(Q79737,Q79739),fun(Q79745,Q79739)),T0))))))))))) # label(asuperadmissible) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1182 (all A5 all B0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,B0)))) <-> (exists X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))))) # label(aREALu_LEu_BETWEEN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1183 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,Z0)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Z0)))))) # label(aINTu_LETu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1184 (all A all F0 all B0 all S0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))))),s(num,B0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,B0)))))))) # label(aNSUMu_POSu_BOUND) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1185 (all Q58308 all L (s(list(Q58308),L) = s(list(Q58308),nil) <-> s(fun(Q58308,bool),i(s(fun(list(Q58308),fun(Q58308,bool)),setu_ofu_list),s(list(Q58308),L))) = s(fun(Q58308,bool),empty))) # label(aSETu_OFu_LISTu_EQu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1186 (all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),F0),s(num,M0))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(fun(num,real),F0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))))) # label(aSUMu_CLAUSESu_LEFT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1187 (all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) # label(aREALu_MULu_LZERO) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1188 (all A all S0 all X all XI_ (s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,XI_))))) = s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))) <-> s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0))) = s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))) # label(aINu_DELETEu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1189 (all X all Y (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))) <-> s(real,Y) = s(real,X))) # label(aREALu_SUBu_0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1190 (all A all B all U_1 ((all R0 all S0 all R1 all S1 all F0 (p(s(bool,i(s(fun(fun(prod(A,B),bool),bool),i(s(fun(B,fun(fun(prod(A,B),bool),bool)),i(s(fun(A,fun(B,fun(fun(prod(A,B),bool),bool))),i(s(fun(fun(A,fun(B,fun(B,bool))),fun(A,fun(B,fun(fun(prod(A,B),bool),bool)))),i(s(fun(fun(A,fun(A,bool)),fun(fun(A,fun(B,fun(B,bool))),fun(A,fun(B,fun(fun(prod(A,B),bool),bool))))),U_1),s(fun(A,fun(A,bool)),R0))),s(fun(A,fun(B,fun(B,bool))),S0))),s(A,R1))),s(B,S1))),s(fun(prod(A,B),bool),F0)))) <-> (all R2 all S2 exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(A,B),bool),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,R2))),s(B,S2))))))),s(bool,V)))) & (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),R0),s(A,R1))),s(A,R2)))) | s(A,R1) = s(A,R2) & p(s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),i(s(fun(A,fun(B,fun(B,bool))),S0),s(A,R1))),s(B,S1))),s(B,S2)))) <-> p(s(bool,V))))))) -> (all U_0 ((all R0 all S0 all F0 ((all R1 all S1 p(s(bool,i(s(fun(fun(prod(A,B),bool),bool),i(s(fun(fun(prod(A,B),bool),fun(fun(prod(A,B),bool),bool)),geq),s(fun(prod(A,B),bool),i(s(fun(prod(A,B),fun(prod(A,B),bool)),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,R1))),s(B,S1))))))),s(fun(prod(A,B),bool),i(s(fun(fun(fun(prod(A,B),bool),bool),fun(prod(A,B),bool)),gabs),s(fun(fun(prod(A,B),bool),bool),i(s(fun(B,fun(fun(prod(A,B),bool),bool)),i(s(fun(A,fun(B,fun(fun(prod(A,B),bool),bool))),i(s(fun(fun(A,fun(B,fun(B,bool))),fun(A,fun(B,fun(fun(prod(A,B),bool),bool)))),i(s(fun(fun(A,fun(A,bool)),fun(fun(A,fun(B,fun(B,bool))),fun(A,fun(B,fun(fun(prod(A,B),bool),bool))))),U_1),s(fun(A,fun(A,bool)),R0))),s(fun(A,fun(B,fun(B,bool))),S0))),s(A,R1))),s(B,S1))))))))) <-> p(s(bool,i(s(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),i(s(fun(fun(A,fun(B,fun(B,bool))),fun(fun(prod(A,B),fun(prod(A,B),bool)),bool)),i(s(fun(fun(A,fun(A,bool)),fun(fun(A,fun(B,fun(B,bool))),fun(fun(prod(A,B),fun(prod(A,B),bool)),bool))),U_0),s(fun(A,fun(A,bool)),R0))),s(fun(A,fun(B,fun(B,bool))),S0))),s(fun(prod(A,B),fun(prod(A,B),bool)),F0)))))) -> (all R0 all S0 ((all A5 p(s(bool,i(s(fun(fun(B,fun(B,bool)),bool),wf),s(fun(B,fun(B,bool)),i(s(fun(A,fun(B,fun(B,bool))),S0),s(A,A5))))))) & p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),R0)))) -> p(s(bool,i(s(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),wf),s(fun(prod(A,B),fun(prod(A,B),bool)),i(s(fun(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),fun(prod(A,B),fun(prod(A,B),bool))),gabs),s(fun(fun(prod(A,B),fun(prod(A,B),bool)),bool),i(s(fun(fun(A,fun(B,fun(B,bool))),fun(fun(prod(A,B),fun(prod(A,B),bool)),bool)),i(s(fun(fun(A,fun(A,bool)),fun(fun(A,fun(B,fun(B,bool))),fun(fun(prod(A,B),fun(prod(A,B),bool)),bool))),U_0),s(fun(A,fun(A,bool)),R0))),s(fun(A,fun(B,fun(B,bool))),S0)))))))))))))) # label(aWFu_LEXu_DEPENDENT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1191 (all Q93147 all Q93149 all S0 all T0 (p(s(bool,i(s(fun(fun(Q93149,bool),bool),countable),s(fun(Q93149,bool),T0)))) & p(s(bool,i(s(fun(fun(Q93147,bool),bool),countable),s(fun(Q93147,bool),S0)))) -> p(s(bool,i(s(fun(fun(prod(Q93147,Q93149),bool),bool),countable),s(fun(prod(Q93147,Q93149),bool),i(s(fun(fun(Q93149,bool),fun(prod(Q93147,Q93149),bool)),i(s(fun(fun(Q93147,bool),fun(fun(Q93149,bool),fun(prod(Q93147,Q93149),bool))),cross0),s(fun(Q93147,bool),S0))),s(fun(Q93149,bool),T0)))))))) # label(aCOUNTABLEu_CROSS) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1192 (all X (s(int,i(s(fun(int,int),intu_sgn),s(int,X))) = s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) | s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(int,i(s(fun(int,int),intu_sgn),s(int,X))) | s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,i(s(fun(int,int),intu_sgn),s(int,X))))) # label(aINTu_SGNu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1193 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> (all Y exists N0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))),s(real,X))))))))) # label(aREALu_ARCH) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1194 (all M0 all N0 -(p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))))) # label(aLETu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1195 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_inv),s(real,Y))))),s(real,i(s(fun(real,real),realu_inv),s(real,X)))))))) # label(aREALu_LEu_INV2) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1196 (all Q18767 all Q18766 s(bool,t) = s(bool,i(s(fun(list(Q18766),bool),i(s(fun(list(Q18767),fun(list(Q18766),bool)),i(s(fun(fun(Q18767,fun(Q18766,bool)),fun(list(Q18767),fun(list(Q18766),bool))),all2),s(fun(Q18767,fun(Q18766,bool)),p0))),s(list(Q18767),nil))),s(list(Q18766),nil)))) # label(aALL2u_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1197 (all B0 all T1 all T2 (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,B0))),s(bool,T1))),s(bool,T2)))) <-> (-p(s(bool,B0)) | p(s(bool,T1))) & (p(s(bool,T2)) | p(s(bool,B0))))) # label(aCONDu_EXPAND) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1198 (all A all B all C all S0 all T0 all U p(s(bool,i(s(fun(fun(prod(prod(A,B),C),bool),bool),i(s(fun(fun(prod(A,prod(B,C)),bool),fun(fun(prod(prod(A,B),C),bool),bool)),a_u_c),s(fun(prod(A,prod(B,C)),bool),i(s(fun(fun(prod(B,C),bool),fun(prod(A,prod(B,C)),bool)),i(s(fun(fun(A,bool),fun(fun(prod(B,C),bool),fun(prod(A,prod(B,C)),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(prod(B,C),bool),i(s(fun(fun(C,bool),fun(prod(B,C),bool)),i(s(fun(fun(B,bool),fun(fun(C,bool),fun(prod(B,C),bool))),t_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U))))))),s(fun(prod(prod(A,B),C),bool),i(s(fun(fun(C,bool),fun(prod(prod(A,B),C),bool)),i(s(fun(fun(prod(A,B),bool),fun(fun(C,bool),fun(prod(prod(A,B),C),bool))),t_u_c),s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(C,bool),U))))))) # label(aCARDu_MULu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1199 (all A all B all F0 (s(fun(A,B),F0) = s(fun(A,B),i(s(fun(fun(A,A),fun(A,B)),i(s(fun(fun(A,B),fun(fun(A,A),fun(A,B))),o),s(fun(A,B),F0))),s(fun(A,A),i1))) & s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),i(s(fun(fun(B,B),fun(fun(A,B),fun(A,B))),o),s(fun(B,B),i1))),s(fun(A,B),F0))) = s(fun(A,B),F0))) # label(aIu_Ou_ID) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1200 (all Q71770 all U_0 ((all F0 all X s(real,i(s(fun(Q71770,real),i(s(fun(fun(Q71770,real),fun(Q71770,real)),U_0),s(fun(Q71770,real),F0))),s(Q71770,X))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(Q71770,real),F0),s(Q71770,X)))))) -> (all F0 all S0 (p(s(bool,i(s(fun(fun(Q71770,bool),bool),finite),s(fun(Q71770,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(fun(Q71770,real),real),i(s(fun(fun(Q71770,bool),fun(fun(Q71770,real),real)),sum),s(fun(Q71770,bool),S0))),s(fun(Q71770,real),F0))))))),s(real,i(s(fun(fun(Q71770,real),real),i(s(fun(fun(Q71770,bool),fun(fun(Q71770,real),real)),sum),s(fun(Q71770,bool),S0))),s(fun(Q71770,real),i(s(fun(fun(Q71770,real),fun(Q71770,real)),U_0),s(fun(Q71770,real),F0)))))))))))) # label(aSUMu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1201 (all A all L all M0 exists V ((s(list(A),L) = s(list(A),nil) <-> p(s(bool,V))) & s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),i(s(fun(bool,fun(A,fun(A,A))),cond),s(bool,V))),s(A,i(s(fun(list(A),A),hd),s(list(A),M0))))),s(A,i(s(fun(list(A),A),hd),s(list(A),L))))) = s(A,i(s(fun(list(A),A),hd),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),L))),s(list(A),M0))))))) # label(aHDu_APPEND) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1202 (all Q20110 all Q20117 all P0 all F0 all L s(list(Q20110),i(s(fun(list(Q20117),list(Q20110)),i(s(fun(fun(Q20117,Q20110),fun(list(Q20117),list(Q20110))),map0),s(fun(Q20117,Q20110),F0))),s(list(Q20117),i(s(fun(list(Q20117),list(Q20117)),i(s(fun(fun(Q20117,bool),fun(list(Q20117),list(Q20117))),filter0),s(fun(Q20117,bool),i(s(fun(fun(Q20117,Q20110),fun(Q20117,bool)),i(s(fun(fun(Q20110,bool),fun(fun(Q20117,Q20110),fun(Q20117,bool))),o),s(fun(Q20110,bool),P0))),s(fun(Q20117,Q20110),F0))))),s(list(Q20117),L))))) = s(list(Q20110),i(s(fun(list(Q20110),list(Q20110)),i(s(fun(fun(Q20110,bool),fun(list(Q20110),list(Q20110))),filter0),s(fun(Q20110,bool),P0))),s(list(Q20110),i(s(fun(list(Q20117),list(Q20110)),i(s(fun(fun(Q20117,Q20110),fun(list(Q20117),list(Q20110))),map0),s(fun(Q20117,Q20110),F0))),s(list(Q20117),L)))))) # label(aFILTERu_MAP) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1203 (all X all Y (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))) <-> s(real,X) = s(real,i(s(fun(real,real),realu_neg),s(real,Y))))) # label(aREALu_LNEGu_UNIQ) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1204 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_gt),s(real,X))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) <-> s(real,i(s(fun(real,real),realu_sgn),s(real,X))) = s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) # label(aINTu_SGNu_EQu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1205 (all A all L (s(list(A),nil) = s(list(A),L) | (exists H0 exists T0 s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,H0))),s(list(A),T0))) = s(list(A),L)))) # label(alistu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1206 (all A all X all Y (s(A,X) = s(A,Y) <-> s(A,Y) = s(A,X))) # label(aEQu_SYMu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1207 (all A all L all M0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(list(A),num),length),s(list(A),L))))),s(num,i(s(fun(list(A),num),length),s(list(A),M0))))) = s(num,i(s(fun(list(A),num),length),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),L))),s(list(A),M0)))))) # label(aLENGTHu_APPEND) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1208 (all Q96944 all P0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q96944,bool),bool),i(s(fun(fun(Q96944,bool),fun(fun(Q96944,bool),bool)),subset),s(fun(Q96944,bool),S0))),s(fun(Q96944,bool),T0)))) & p(s(bool,i(s(fun(fun(Q96944,bool),bool),P0),s(fun(Q96944,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q96944,bool),bool),i(s(fun(fun(Q96944,bool),fun(fun(Q96944,bool),bool)),subset),s(fun(Q96944,bool),i(s(fun(fun(Q96944,bool),fun(Q96944,bool)),i(s(fun(fun(fun(Q96944,bool),bool),fun(fun(Q96944,bool),fun(Q96944,bool))),hull),s(fun(fun(Q96944,bool),bool),P0))),s(fun(Q96944,bool),S0))))),s(fun(Q96944,bool),T0)))))) # label(aHULLu_MINIMAL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1209 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y)))))) # label(aINTu_LEu_ADDL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1210 (all Q88371 all Q88370 all S0 all T0 s(bool,i(s(fun(fun(Q88370,bool),bool),i(s(fun(fun(Q88371,bool),fun(fun(Q88370,bool),bool)),a_u_c),s(fun(Q88371,bool),T0))),s(fun(Q88370,bool),S0))) = s(bool,i(s(fun(fun(Q88371,bool),bool),i(s(fun(fun(Q88370,bool),fun(fun(Q88371,bool),bool)),a_u_c),s(fun(Q88370,bool),S0))),s(fun(Q88371,bool),T0)))) # label(aCARDu_EQu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1211 (all Q92581 all S0 (p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(fun(Q92581,bool),fun(fun(num,bool),bool)),a_u_c),s(fun(Q92581,bool),S0))),s(fun(num,bool),univ)))) | p(s(bool,i(s(fun(fun(Q92581,bool),bool),finite),s(fun(Q92581,bool),S0)))) <-> p(s(bool,i(s(fun(fun(Q92581,bool),bool),countable),s(fun(Q92581,bool),S0)))))) # label(aCOUNTABLEu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1212 (all X all Y all Z0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))),s(real,Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0)))))) # label(aREALu_MULu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1213 (all U_0 ((all X all I0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))),s(num,I0)))) -> (all X all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,M0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),suc),s(num,N0))))))))))) # label(aSUMu_GPu_MULTIPLIED) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1214 (all A ((exists S0 p(s(bool,i(s(fun(fun(A,bool),bool),p0),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),univ))),s(fun(A,bool),S0))))))) <-> (exists S0 p(s(bool,i(s(fun(fun(A,bool),bool),p0),s(fun(A,bool),S0))))))) # label(aEXISTSu_DIFF) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1215 (all X s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,X)) # label(aREALu_POWu_1) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1216 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,X)))))) # label(aREALu_LEu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1217 (all N0 all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0)))))))) # label(aREALu_POWu_LE2) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1218 (all Q52643 all Q52644 all U_0 ((all B0 all F0 all G0 (p(s(bool,i(s(fun(fun(fun(Q52644,bool),Q52643),bool),i(s(fun(fun(Q52644,fun(Q52643,Q52643)),fun(fun(fun(Q52644,bool),Q52643),bool)),i(s(fun(Q52643,fun(fun(Q52644,fun(Q52643,Q52643)),fun(fun(fun(Q52644,bool),Q52643),bool))),U_0),s(Q52643,B0))),s(fun(Q52644,fun(Q52643,Q52643)),F0))),s(fun(fun(Q52644,bool),Q52643),G0)))) <-> s(Q52643,B0) = s(Q52643,i(s(fun(fun(Q52644,bool),Q52643),G0),s(fun(Q52644,bool),empty))) & (all X all S0 (p(s(bool,i(s(fun(fun(Q52644,bool),bool),finite),s(fun(Q52644,bool),S0)))) -> s(Q52643,i(s(fun(fun(Q52644,bool),Q52643),G0),s(fun(Q52644,bool),i(s(fun(fun(Q52644,bool),fun(Q52644,bool)),i(s(fun(Q52644,fun(fun(Q52644,bool),fun(Q52644,bool))),insert),s(Q52644,X))),s(fun(Q52644,bool),S0))))) = s(Q52643,i(s(fun(Q52643,Q52643),i(s(fun(Q52643,fun(Q52643,Q52643)),i(s(fun(bool,fun(Q52643,fun(Q52643,Q52643))),cond),s(bool,i(s(fun(fun(Q52644,bool),bool),i(s(fun(Q52644,fun(fun(Q52644,bool),bool)),in),s(Q52644,X))),s(fun(Q52644,bool),S0))))),s(Q52643,i(s(fun(fun(Q52644,bool),Q52643),G0),s(fun(Q52644,bool),S0))))),s(Q52643,i(s(fun(Q52643,Q52643),i(s(fun(Q52644,fun(Q52643,Q52643)),F0),s(Q52644,X))),s(Q52643,i(s(fun(fun(Q52644,bool),Q52643),G0),s(fun(Q52644,bool),S0))))))))))) -> (all B0 all F0 all S0 s(Q52643,i(s(fun(fun(Q52644,bool),Q52643),i(s(fun(fun(fun(fun(Q52644,bool),Q52643),bool),fun(fun(Q52644,bool),Q52643)),h_),s(fun(fun(fun(Q52644,bool),Q52643),bool),i(s(fun(fun(Q52644,fun(Q52643,Q52643)),fun(fun(fun(Q52644,bool),Q52643),bool)),i(s(fun(Q52643,fun(fun(Q52644,fun(Q52643,Q52643)),fun(fun(fun(Q52644,bool),Q52643),bool))),U_0),s(Q52643,B0))),s(fun(Q52644,fun(Q52643,Q52643)),F0))))),s(fun(Q52644,bool),S0))) = s(Q52643,i(s(fun(Q52643,Q52643),i(s(fun(fun(Q52644,bool),fun(Q52643,Q52643)),i(s(fun(fun(Q52644,fun(Q52643,Q52643)),fun(fun(Q52644,bool),fun(Q52643,Q52643))),itset),s(fun(Q52644,fun(Q52643,Q52643)),F0))),s(fun(Q52644,bool),S0))),s(Q52643,B0)))))) # label(aITSET) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1219 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),poset),s(fun(prod(A,A),bool),L)))))) # label(aWOSETu_POSET) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1220 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,i(s(fun(int,int),intu_neg),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,X)))) # label(aINTu_LEu_NEG) # label(axiom) # label(non_clause). [assumption]. 14.03/14.06 1221 (all A all X all Y (s(fun(num,fun(A,bool)),i(s(fun(recspace(A),fun(num,fun(A,bool))),u_destu_rec),s(recspace(A),X))) = s(fun(num,fun(A,bool)),i(s(fun(recspace(A),fun(num,fun(A,bool))),u_destu_rec),s(recspace(A),Y))) <-> s(recspace(A),X) = s(recspace(A),Y))) # label(aDESTu_RECu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1222 (all X ((exists N0 s(int,X) = s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0)))))) | (exists N0 s(int,X) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0)))))) # label(aINTu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1223 (all X all Y (s(int,Y) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) | s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,X) <-> s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aINTu_ENTIRE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1224 (all A all B all A5 s(cart(A,B),A5) = s(cart(A,B),i(s(fun(fun(finite_image(B),A),cart(A,B)),mku_cart),s(fun(finite_image(B),A),i(s(fun(cart(A,B),fun(finite_image(B),A)),destu_cart),s(cart(A,B),A5)))))) # label(acartu_tybiju_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1225 (all M0 all N0 (s(num,i(s(fun(num,num),bit0),s(num,M0))) = s(num,i(s(fun(num,num),bit0),s(num,N0))) <-> s(num,M0) = s(num,N0))) # label(aARITHu_EQu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1226 (all A all U_2 ((all P0 all X (-p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_2),s(fun(A,bool),P0))),s(A,X)))))) -> (all U_1 ((all S0 all P0 all GENR_PVARR_170 ((exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_170))),s(bool,V))),s(A,X)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),P0))),s(A,GENR_PVARR_170)))))) -> (all U_0 ((all P0 all F0 all G0 all X s(num,i(s(fun(A,num),i(s(fun(fun(A,num),fun(A,num)),i(s(fun(fun(A,num),fun(fun(A,num),fun(A,num))),i(s(fun(fun(A,bool),fun(fun(A,num),fun(fun(A,num),fun(A,num)))),U_0),s(fun(A,bool),P0))),s(fun(A,num),F0))),s(fun(A,num),G0))),s(A,X))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(A,bool),P0),s(A,X))))),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,i(s(fun(A,num),G0),s(A,X)))))) -> (all S0 all P0 all F0 all G0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(fun(A,num),fun(A,num)),i(s(fun(fun(A,num),fun(fun(A,num),fun(A,num))),i(s(fun(fun(A,bool),fun(fun(A,num),fun(fun(A,num),fun(A,num)))),U_0),s(fun(A,bool),P0))),s(fun(A,num),F0))),s(fun(A,num),G0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),P0))))))),s(fun(A,num),F0))))),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_2),s(fun(A,bool),P0))))))))),s(fun(A,num),G0))))))))))))) # label(aNSUMu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1227 (all X p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,X))))) # label(aINTu_LEu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1228 (all U_2 ((all A5 all Y all J0 all I0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),A5),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,I0))),s(num,J0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(real,fun(num,fun(num,real))),i(s(fun(fun(num,real),fun(real,fun(num,fun(num,real)))),U_2),s(fun(num,real),A5))),s(real,Y))),s(num,J0))),s(num,I0)))) -> (all U_1 ((all N0 all A5 all Y all J0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,J0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(real,fun(num,fun(num,real))),i(s(fun(fun(num,real),fun(real,fun(num,fun(num,real)))),U_2),s(fun(num,real),A5))),s(real,Y))),s(num,J0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),i(s(fun(num,fun(fun(num,real),fun(real,fun(num,real)))),U_1),s(num,N0))),s(fun(num,real),A5))),s(real,Y))),s(num,J0)))) -> (all U_0 ((all A5 all X all I0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),A5))),s(real,X))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),A5),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0)))))) -> (all A5 all X all Y all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),i(s(fun(num,fun(fun(num,real),fun(real,fun(num,real)))),U_1),s(num,N0))),s(fun(num,real),A5))),s(real,Y))))),s(real,X))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),A5))),s(real,X))))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),A5))),s(real,Y))))))))))))))) # label(aREALu_SUBu_POLYFUN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1229 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,i(s(fun(int,int),intu_neg),s(int,Y)))))) # label(aINTu_SUB) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1230 (all X exists A5 exists B0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,N0))))),s(num,B0))))))) # label(aNADDu_BOUND) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1231 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Y))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))) = s(int,X)) # label(aINTu_SUBu_ADD2) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1232 (all A all S0 s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,i(s(fun(fun(A,bool),A),choice0),s(fun(A,bool),S0))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),rest),s(fun(A,bool),S0)))) # label(aREST) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1233 (all S0 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) & s(fun(real,bool),S0) != s(fun(real,bool),empty) -> ((all Y (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,Y))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,a0))),s(real,Y)))))) & p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,a0))),s(fun(real,bool),S0)))) <-> s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))) = s(real,a0)))) # label(aINFu_UNIQUEu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1234 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,a0))),s(num,d))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,c))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,b0)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,b0))),s(num,c))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,d)))))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,c))),s(num,d))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,a0))),s(num,b0))) # label(aDIVu_EQu_EXCLUSION) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1235 (all Q49279 all Q49278 all Q49259 all U_1 ((all P0 all F0 all GENR_PVARR_38 ((exists A5 exists V ((p(s(bool,V)) <-> (all X all Y (p(s(bool,i(s(fun(Q49278,bool),i(s(fun(Q49279,fun(Q49278,bool)),P0),s(Q49279,X))),s(Q49278,Y)))) -> p(s(bool,i(s(fun(fun(Q49259,bool),bool),i(s(fun(Q49259,fun(fun(Q49259,bool),bool)),in),s(Q49259,A5))),s(fun(Q49259,bool),i(s(fun(Q49278,fun(Q49259,bool)),i(s(fun(Q49279,fun(Q49278,fun(Q49259,bool))),F0),s(Q49279,X))),s(Q49278,Y))))))))) & p(s(bool,i(s(fun(Q49259,bool),i(s(fun(bool,fun(Q49259,bool)),i(s(fun(Q49259,fun(bool,fun(Q49259,bool))),setspec),s(Q49259,GENR_PVARR_38))),s(bool,V))),s(Q49259,A5)))))) <-> p(s(bool,i(s(fun(Q49259,bool),i(s(fun(fun(Q49279,fun(Q49278,fun(Q49259,bool))),fun(Q49259,bool)),i(s(fun(fun(Q49279,fun(Q49278,bool)),fun(fun(Q49279,fun(Q49278,fun(Q49259,bool))),fun(Q49259,bool))),U_1),s(fun(Q49279,fun(Q49278,bool)),P0))),s(fun(Q49279,fun(Q49278,fun(Q49259,bool))),F0))),s(Q49259,GENR_PVARR_38)))))) -> (all U_0 ((all P0 all F0 all GENR_PVARR_37 (p(s(bool,i(s(fun(fun(Q49259,bool),bool),i(s(fun(fun(Q49279,fun(Q49278,fun(Q49259,bool))),fun(fun(Q49259,bool),bool)),i(s(fun(fun(Q49279,fun(Q49278,bool)),fun(fun(Q49279,fun(Q49278,fun(Q49259,bool))),fun(fun(Q49259,bool),bool))),U_0),s(fun(Q49279,fun(Q49278,bool)),P0))),s(fun(Q49279,fun(Q49278,fun(Q49259,bool))),F0))),s(fun(Q49259,bool),GENR_PVARR_37)))) <-> (exists X exists Y p(s(bool,i(s(fun(fun(Q49259,bool),bool),i(s(fun(bool,fun(fun(Q49259,bool),bool)),i(s(fun(fun(Q49259,bool),fun(bool,fun(fun(Q49259,bool),bool))),setspec),s(fun(Q49259,bool),GENR_PVARR_37))),s(bool,i(s(fun(Q49278,bool),i(s(fun(Q49279,fun(Q49278,bool)),P0),s(Q49279,X))),s(Q49278,Y))))),s(fun(Q49259,bool),i(s(fun(Q49278,fun(Q49259,bool)),i(s(fun(Q49279,fun(Q49278,fun(Q49259,bool))),F0),s(Q49279,X))),s(Q49278,Y))))))))) -> (all P0 all F0 s(fun(Q49259,bool),i(s(fun(fun(fun(Q49259,bool),bool),fun(Q49259,bool)),inters),s(fun(fun(Q49259,bool),bool),i(s(fun(fun(fun(Q49259,bool),bool),fun(fun(Q49259,bool),bool)),gspec),s(fun(fun(Q49259,bool),bool),i(s(fun(fun(Q49279,fun(Q49278,fun(Q49259,bool))),fun(fun(Q49259,bool),bool)),i(s(fun(fun(Q49279,fun(Q49278,bool)),fun(fun(Q49279,fun(Q49278,fun(Q49259,bool))),fun(fun(Q49259,bool),bool))),U_0),s(fun(Q49279,fun(Q49278,bool)),P0))),s(fun(Q49279,fun(Q49278,fun(Q49259,bool))),F0))))))) = s(fun(Q49259,bool),i(s(fun(fun(Q49259,bool),fun(Q49259,bool)),gspec),s(fun(Q49259,bool),i(s(fun(fun(Q49279,fun(Q49278,fun(Q49259,bool))),fun(Q49259,bool)),i(s(fun(fun(Q49279,fun(Q49278,bool)),fun(fun(Q49279,fun(Q49278,fun(Q49259,bool))),fun(Q49259,bool))),U_1),s(fun(Q49279,fun(Q49278,bool)),P0))),s(fun(Q49279,fun(Q49278,fun(Q49259,bool))),F0)))))))))) # label(aINTERSu_GSPECu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1236 (all A all U_0 ((all S0 all GENR_PVARR_225 ((exists T0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_225))),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0))))),s(fun(A,bool),T0))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))),s(fun(A,bool),GENR_PVARR_225)))))) -> (all S0 p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))))))))))) # label(aCANTORu_THM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1237 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),intu_abs),s(int,X))))),s(int,i(s(fun(int,int),intu_abs),s(int,Y)))))) # label(aINTu_LEu_SQUAREu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1238 (all P0 ((all N0 p(s(bool,i(s(fun(int,bool),P0),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))))) <-> (all X p(s(bool,i(s(fun(int,bool),P0),s(int,i(s(fun(int,int),intu_abs),s(int,X))))))))) # label(aINTu_FORALLu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1239 (all Q63550 all Q63564 all OP all F0 all S0 (s(fun(Q63564,bool),i(s(fun(fun(Q63564,bool),fun(Q63564,bool)),i(s(fun(fun(Q63564,Q63550),fun(fun(Q63564,bool),fun(Q63564,bool))),i(s(fun(fun(Q63550,fun(Q63550,Q63550)),fun(fun(Q63564,Q63550),fun(fun(Q63564,bool),fun(Q63564,bool)))),support),s(fun(Q63550,fun(Q63550,Q63550)),OP))),s(fun(Q63564,Q63550),F0))),s(fun(Q63564,bool),S0))) = s(fun(Q63564,bool),empty) <-> (all X (p(s(bool,i(s(fun(fun(Q63564,bool),bool),i(s(fun(Q63564,fun(fun(Q63564,bool),bool)),in),s(Q63564,X))),s(fun(Q63564,bool),S0)))) -> s(Q63550,i(s(fun(fun(Q63550,fun(Q63550,Q63550)),Q63550),neutral),s(fun(Q63550,fun(Q63550,Q63550)),OP))) = s(Q63550,i(s(fun(Q63564,Q63550),F0),s(Q63564,X))))))) # label(aSUPPORTu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1240 (all N0 s(num,i(s(fun(num,num),pre),s(num,i(s(fun(num,num),numeral),s(num,N0))))) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),pre),s(num,N0)))))) # label(aARITHu_PREu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1241 (all A all U_0 ((all F0 all C0 all X s(num,i(s(fun(A,num),i(s(fun(num,fun(A,num)),i(s(fun(fun(A,num),fun(num,fun(A,num))),U_0),s(fun(A,num),F0))),s(num,C0))),s(A,X))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,C0)))) -> (all F0 all C0 all S0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))))),s(num,C0))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(num,fun(A,num)),i(s(fun(fun(A,num),fun(num,fun(A,num))),U_0),s(fun(A,num),F0))),s(num,C0)))))))) # label(aNSUMu_RMUL) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1242 (all N0 s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))) = s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0)))))) # label(aINTu_ABSu_NUM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1243 (all M0 all N0 exists Q0 exists R0 exists V ((exists VI_ ((s(int,N0) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> p(s(bool,VI_))) & (exists VI_I_ (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,VI_))),s(bool,V))),s(bool,VI_I_)))) & (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,R0)))) & s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Q0))),s(int,N0))))),s(int,R0))) = s(int,M0) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,R0))),s(int,i(s(fun(int,int),intu_abs),s(int,N0)))))) <-> p(s(bool,VI_I_))))))) & (p(s(bool,V)) <-> s(int,M0) = s(int,R0) & s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,Q0)))) # label(aINTu_DIVMODu_EXISTu_0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1244 (all X all Y (s(int,Y) = s(int,X) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,X)))))) # label(aINTu_LEu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1245 (all Q4820 all Q4819 all U_0 ((all P0 all F0 (p(s(bool,i(s(fun(fun(prod(Q4820,Q4819),bool),bool),i(s(fun(fun(Q4820,fun(Q4819,bool)),fun(fun(prod(Q4820,Q4819),bool),bool)),U_0),s(fun(Q4820,fun(Q4819,bool)),P0))),s(fun(prod(Q4820,Q4819),bool),F0)))) <-> (all X all Y p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(Q4820,Q4819),bool),F0),s(prod(Q4820,Q4819),i(s(fun(Q4819,prod(Q4820,Q4819)),i(s(fun(Q4820,fun(Q4819,prod(Q4820,Q4819))),c_),s(Q4820,X))),s(Q4819,Y))))))),s(bool,i(s(fun(Q4819,bool),i(s(fun(Q4820,fun(Q4819,bool)),P0),s(Q4820,X))),s(Q4819,Y))))))))) -> (all P0 (p(s(bool,i(s(fun(fun(prod(Q4820,Q4819),bool),bool),q_),s(fun(prod(Q4820,Q4819),bool),i(s(fun(fun(fun(prod(Q4820,Q4819),bool),bool),fun(prod(Q4820,Q4819),bool)),gabs),s(fun(fun(prod(Q4820,Q4819),bool),bool),i(s(fun(fun(Q4820,fun(Q4819,bool)),fun(fun(prod(Q4820,Q4819),bool),bool)),U_0),s(fun(Q4820,fun(Q4819,bool)),P0)))))))) <-> (exists X exists Y p(s(bool,i(s(fun(Q4819,bool),i(s(fun(Q4820,fun(Q4819,bool)),P0),s(Q4820,X))),s(Q4819,Y))))))))) # label(aEXISTSu_PAIREDu_THM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1246 (all M0 all N0 (s(bool,i(s(fun(num,bool),odd),s(num,N0))) != s(bool,i(s(fun(num,bool),odd),s(num,M0))) <-> p(s(bool,i(s(fun(num,bool),odd),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))))) # label(aODDu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1247 (all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),hasu_size),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))))) # label(aHASu_SIZEu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1248 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,Y))))),s(real,Z0)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Z0)))))) # label(aREALu_MAXu_LT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1249 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))) <-> s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))) = s(fun(num,bool),empty))) # label(aNUMSEGu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1250 (all Q97080 all P0 all S0 all T0 s(fun(Q97080,bool),i(s(fun(fun(Q97080,bool),fun(Q97080,bool)),i(s(fun(fun(fun(Q97080,bool),bool),fun(fun(Q97080,bool),fun(Q97080,bool))),hull),s(fun(fun(Q97080,bool),bool),P0))),s(fun(Q97080,bool),i(s(fun(fun(Q97080,bool),fun(Q97080,bool)),i(s(fun(fun(Q97080,bool),fun(fun(Q97080,bool),fun(Q97080,bool))),union),s(fun(Q97080,bool),i(s(fun(fun(Q97080,bool),fun(Q97080,bool)),i(s(fun(fun(fun(Q97080,bool),bool),fun(fun(Q97080,bool),fun(Q97080,bool))),hull),s(fun(fun(Q97080,bool),bool),P0))),s(fun(Q97080,bool),S0))))),s(fun(Q97080,bool),i(s(fun(fun(Q97080,bool),fun(Q97080,bool)),i(s(fun(fun(fun(Q97080,bool),bool),fun(fun(Q97080,bool),fun(Q97080,bool))),hull),s(fun(fun(Q97080,bool),bool),P0))),s(fun(Q97080,bool),T0))))))) = s(fun(Q97080,bool),i(s(fun(fun(Q97080,bool),fun(Q97080,bool)),i(s(fun(fun(fun(Q97080,bool),bool),fun(fun(Q97080,bool),fun(Q97080,bool))),hull),s(fun(fun(Q97080,bool),bool),P0))),s(fun(Q97080,bool),i(s(fun(fun(Q97080,bool),fun(Q97080,bool)),i(s(fun(fun(Q97080,bool),fun(fun(Q97080,bool),fun(Q97080,bool))),union),s(fun(Q97080,bool),S0))),s(fun(Q97080,bool),T0)))))) # label(aHULLu_UNION) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1251 (all B all A all S0 all T0 all F0 (s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))) = s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))) & s(fun(B,bool),T0) = s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,i(s(fun(A,B),F0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) -> s(A,X) = s(A,Y))))) # label(aIMAGEu_IMPu_INJECTIVEu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1252 (all Q58395 all R0 all X s(bool,t) = s(bool,i(s(fun(fun(Q58395,bool),bool),i(s(fun(fun(Q58395,fun(Q58395,bool)),fun(fun(Q58395,bool),bool)),pairwise),s(fun(Q58395,fun(Q58395,bool)),R0))),s(fun(Q58395,bool),i(s(fun(fun(Q58395,bool),fun(Q58395,bool)),i(s(fun(Q58395,fun(fun(Q58395,bool),fun(Q58395,bool))),insert),s(Q58395,X))),s(fun(Q58395,bool),empty)))))) # label(aPAIRWISEu_SING) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1253 (all N0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> p(s(bool,i(s(fun(num,bool),p0),s(num,N0)))))) <-> (all N0 p(s(bool,i(s(fun(num,bool),p0),s(num,i(s(fun(num,num),suc),s(num,N0))))))) # label(aFORALLu_SUC) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1254 (all U_1 ((all G0 all K0 s(real,i(s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),U_1),s(fun(num,real),G0))),s(num,K0))) = s(real,i(s(fun(num,real),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) -> (all U_0 ((all F0 all G0 all K0 s(real,i(s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),i(s(fun(fun(num,real),fun(fun(num,real),fun(num,real))),U_0),s(fun(num,real),F0))),s(fun(num,real),G0))),s(num,K0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),F0),s(num,K0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),G0),s(num,K0)))))))) -> (all F0 all G0 all M0 all N0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),i(s(fun(fun(num,real),fun(fun(num,real),fun(num,real))),U_0),s(fun(num,real),F0))),s(fun(num,real),G0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),F0),s(num,M0))))),s(real,i(s(fun(num,real),G0),s(num,M0))))))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),i(s(fun(fun(num,real),fun(fun(num,real),fun(num,real))),U_0),s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),U_1),s(fun(num,real),G0))))),s(fun(num,real),F0))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))))) # label(aSUMu_PARTIALu_SUC) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1255 (all A all B all C all U_0 ((all S0 all T0 all F0 all GENR_PVARR_84 (p(s(bool,i(s(fun(C,bool),i(s(fun(fun(A,fun(B,C)),fun(C,bool)),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(C,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(C,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,C)),F0))),s(C,GENR_PVARR_84)))) <-> (exists X exists Y exists V (p(s(bool,i(s(fun(C,bool),i(s(fun(bool,fun(C,bool)),i(s(fun(C,fun(bool,fun(C,bool))),setspec),s(C,GENR_PVARR_84))),s(bool,V))),s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),F0),s(A,X))),s(B,Y)))))) & (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> p(s(bool,V))))))) -> (all F0 all S0 all T0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,X)))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(C,bool),bool),finite),s(fun(C,bool),i(s(fun(fun(C,bool),fun(C,bool)),gspec),s(fun(C,bool),i(s(fun(fun(A,fun(B,C)),fun(C,bool)),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(C,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(C,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,C)),F0)))))))))))) # label(aFINITEu_PRODUCTu_DEPENDENT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.07 1256 (all A all FINITEI_ ((all X all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),FINITEI_),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),FINITEI_),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0)))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),FINITEI_),s(fun(A,bool),empty)))) -> (all A5 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),A5)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),FINITEI_),s(fun(A,bool),A5)))))))) # label(aFINITEu_INDUCT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.08 1257 (all X all Y (s(int,X) = s(int,i(s(fun(int,int),intu_neg),s(int,Y))) <-> s(int,i(s(fun(int,int),intu_neg),s(int,X))) = s(int,Y))) # label(aINTu_NEGu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.03/14.08 1258 (all U_2 ((all F0 all J0 all I0 s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),F0),s(num,I0))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(num,fun(num,real)),fun(num,fun(num,real))),U_2),s(fun(num,fun(num,real)),F0))),s(num,J0))),s(num,I0)))) -> (all U_1 ((all F0 all J0 s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(num,fun(num,real)),fun(num,fun(num,real))),U_2),s(fun(num,fun(num,real)),F0))),s(num,J0))) = s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(num,fun(num,real)),fun(num,fun(num,real))),U_1),s(fun(num,fun(num,real)),F0))),s(num,J0)))) -> (all U_0 ((all C0 all D0 all F0 all I0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,C0))),s(num,D0))))),s(fun(num,real),i(s(fun(num,fun(num,real)),F0),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(fun(num,fun(num,real)),fun(num,real)),i(s(fun(num,fun(fun(num,fun(num,real)),fun(num,real))),i(s(fun(num,fun(num,fun(fun(num,fun(num,real)),fun(num,real)))),U_0),s(num,C0))),s(num,D0))),s(fun(num,fun(num,real)),F0))),s(num,I0)))) -> (all A5 all B0 all C0 all D0 all F0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,A5))),s(num,B0))))),s(fun(num,real),i(s(fun(fun(num,fun(num,real)),fun(num,real)),i(s(fun(num,fun(fun(num,fun(num,real)),fun(num,real))),i(s(fun(num,fun(num,fun(fun(num,fun(num,real)),fun(num,real)))),U_0),s(num,C0))),s(num,D0))),s(fun(num,fun(num,real)),F0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,C0))),s(num,D0))))),s(fun(num,real),i(s(fun(fun(num,fun(num,real)),fun(num,real)),i(s(fun(num,fun(fun(num,fun(num,real)),fun(num,real))),i(s(fun(num,fun(num,fun(fun(num,fun(num,real)),fun(num,real)))),U_0),s(num,A5))),s(num,B0))),s(fun(num,fun(num,real)),i(s(fun(fun(num,fun(num,real)),fun(num,fun(num,real))),U_1),s(fun(num,fun(num,real)),F0)))))))))))))) # label(aSUMu_SWAPu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.03/14.08 1259 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_LEu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 14.03/14.08 1260 (all A all B all U_3 ((all K0 all I0 s(num,i(s(fun(B,num),K0),s(B,I0))) = s(num,i(s(fun(B,num),i(s(fun(fun(B,num),fun(B,num)),U_3),s(fun(B,num),K0))),s(B,I0)))) -> (all U_2 ((all T0 all R0 all I0 all GENR_PVARR_162 (p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),i(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,fun(B,bool)))),U_2),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0))),s(B,GENR_PVARR_162)))) <-> (exists J0 exists V (p(s(bool,i(s(fun(B,bool),i(s(fun(bool,fun(B,bool)),i(s(fun(B,fun(bool,fun(B,bool))),setspec),s(B,GENR_PVARR_162))),s(bool,V))),s(B,J0)))) & (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),R0),s(A,I0))),s(B,J0)))) <-> p(s(bool,V))))))) -> (all U_1 ((all T0 all R0 all I0 s(num,i(s(fun(A,num),i(s(fun(fun(A,fun(B,bool)),fun(A,num)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,num))),U_1),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0))) = s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),gspec),s(fun(B,bool),i(s(fun(A,fun(B,bool)),i(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,fun(B,bool)))),U_2),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0)))))))) -> (all U_0 ((all S0 all R0 all J0 all GENR_PVARR_161 ((exists I0 exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_161))),s(bool,V))),s(A,I0)))) & (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),R0),s(A,I0))),s(B,J0)))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,fun(B,bool)),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(B,fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),R0))),s(B,J0))),s(A,GENR_PVARR_161)))))) -> (all R0 all S0 all T0 all K0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all J0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),T0)))) -> s(num,i(s(fun(B,num),K0),s(B,J0))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,fun(B,bool)),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(B,fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),R0))),s(B,J0))))))))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) -> s(num,i(s(fun(fun(B,num),num),i(s(fun(fun(B,bool),fun(fun(B,num),num)),nsum),s(fun(B,bool),T0))),s(fun(B,num),i(s(fun(fun(B,num),fun(B,num)),U_3),s(fun(B,num),K0))))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(fun(A,fun(B,bool)),fun(A,num)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,num))),U_1),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))))))))))))))) # label(aNSUMu_MULTICOUNTu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.03/14.08 1261 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y))))) # label(aINTu_LTu_MULu_EQu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.08 1262 (all A all B all F0 s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),nil))) = s(list(B),nil)) # label(aMAPu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.03/14.08 1263 (all Q79231 all Q79230 all Q79232 all U_0 ((all P0 all GENR_PVARR_211 (p(s(bool,i(s(fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool),i(s(fun(fun(cart(Q79230,Q79231),fun(cart(Q79230,Q79232),bool)),fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool)),U_0),s(fun(cart(Q79230,Q79231),fun(cart(Q79230,Q79232),bool)),P0))),s(cart(Q79230,finite_sum(Q79231,Q79232)),GENR_PVARR_211)))) <-> (exists X exists Y p(s(bool,i(s(fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool),i(s(fun(bool,fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool)),i(s(fun(cart(Q79230,finite_sum(Q79231,Q79232)),fun(bool,fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool))),setspec),s(cart(Q79230,finite_sum(Q79231,Q79232)),GENR_PVARR_211))),s(bool,i(s(fun(cart(Q79230,Q79232),bool),i(s(fun(cart(Q79230,Q79231),fun(cart(Q79230,Q79232),bool)),P0),s(cart(Q79230,Q79231),X))),s(cart(Q79230,Q79232),Y))))),s(cart(Q79230,finite_sum(Q79231,Q79232)),i(s(fun(cart(Q79230,Q79232),cart(Q79230,finite_sum(Q79231,Q79232))),i(s(fun(cart(Q79230,Q79231),fun(cart(Q79230,Q79232),cart(Q79230,finite_sum(Q79231,Q79232)))),pastecart),s(cart(Q79230,Q79231),X))),s(cart(Q79230,Q79232),Y))))))))) -> (all P0 all A5 all B0 s(bool,i(s(fun(fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool),bool),i(s(fun(cart(Q79230,finite_sum(Q79231,Q79232)),fun(fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool),bool)),in),s(cart(Q79230,finite_sum(Q79231,Q79232)),i(s(fun(cart(Q79230,Q79232),cart(Q79230,finite_sum(Q79231,Q79232))),i(s(fun(cart(Q79230,Q79231),fun(cart(Q79230,Q79232),cart(Q79230,finite_sum(Q79231,Q79232)))),pastecart),s(cart(Q79230,Q79231),A5))),s(cart(Q79230,Q79232),B0))))),s(fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool),i(s(fun(fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool),fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool)),gspec),s(fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool),i(s(fun(fun(cart(Q79230,Q79231),fun(cart(Q79230,Q79232),bool)),fun(cart(Q79230,finite_sum(Q79231,Q79232)),bool)),U_0),s(fun(cart(Q79230,Q79231),fun(cart(Q79230,Q79232),bool)),P0))))))) = s(bool,i(s(fun(cart(Q79230,Q79232),bool),i(s(fun(cart(Q79230,Q79231),fun(cart(Q79230,Q79232),bool)),P0),s(cart(Q79230,Q79231),A5))),s(cart(Q79230,Q79232),B0)))))) # label(aINu_ELIMu_PASTECARTu_THM) # label(axiom) # label(non_clause). [assumption]. 14.03/14.08 1264 (all Q48078 all Q48062 all P0 all F0 all S0 ((all T0 (p(s(bool,i(s(fun(fun(Q48062,bool),bool),i(s(fun(fun(Q48062,bool),fun(fun(Q48062,bool),bool)),subset),s(fun(Q48062,bool),T0))),s(fun(Q48062,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q48078,bool),bool),P0),s(fun(Q48078,bool),i(s(fun(fun(Q48062,bool),fun(Q48078,bool)),i(s(fun(fun(Q48062,Q48078),fun(fun(Q48062,bool),fun(Q48078,bool))),image),s(fun(Q48062,Q48078),F0))),s(fun(Q48062,bool),T0)))))))) <-> (all T0 (p(s(bool,i(s(fun(fun(Q48078,bool),bool),i(s(fun(fun(Q48078,bool),fun(fun(Q48078,bool),bool)),subset),s(fun(Q48078,bool),T0))),s(fun(Q48078,bool),i(s(fun(fun(Q48062,bool),fun(Q48078,bool)),i(s(fun(fun(Q48062,Q48078),fun(fun(Q48062,bool),fun(Q48078,bool))),image),s(fun(Q48062,Q48078),F0))),s(fun(Q48062,bool),S0)))))) -> p(s(bool,i(s(fun(fun(Q48078,bool),bool),P0),s(fun(Q48078,bool),T0)))))))) # label(aFORALLu_SUBSETu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.03/14.08 1265 (all A all ZRECSPACEI_ ((all C0 all I0 all R0 ((all N0 p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),ZRECSPACEI_),s(fun(num,fun(A,bool)),i(s(fun(num,fun(num,fun(A,bool))),R0),s(num,N0))))))) -> p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),ZRECSPACEI_),s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))),i(s(fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool)))),i(s(fun(num,fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))))),zconstr),s(num,C0))),s(A,I0))),s(fun(num,fun(num,fun(A,bool))),R0)))))))) & p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),ZRECSPACEI_),s(fun(num,fun(A,bool)),zbot)))) -> (all A5 (p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),zrecspace),s(fun(num,fun(A,bool)),A5)))) -> p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),ZRECSPACEI_),s(fun(num,fun(A,bool)),A5)))))))) # label(aZRECSPACEu_INDUCT) # label(axiom) # label(non_clause). [assumption]. 14.03/14.08 1266 (all A all B all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all S0 all T0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) -> s(B,i(s(fun(fun(B,fun(B,B)),B),neutral),s(fun(B,fun(B,B)),OP))) = s(B,i(s(fun(A,B),F0),s(A,X))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,B),F0))) = s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),OP),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))))),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),T0))),s(fun(A,B),F0))))))))) # label(aITERATEu_UNIONu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 14.41/14.45 1267 (all A all P0 all A5 ((exists X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) & s(A,A5) = s(A,X))) <-> p(s(bool,i(s(fun(A,bool),P0),s(A,A5)))))) # label(aUNWINDu_THM2) # label(axiom) # label(non_clause). [assumption]. 14.41/14.45 1268 (all Q83010 all Q83030 all Q83026 all U_6 ((all F0 all F1 (p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(Q83010,Q83026),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),U_6),s(fun(Q83010,Q83026),F0))),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F1)))) <-> (all S0 all T0 exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F1),s(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))))),c_),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))),s(bool,V)))) & ((all X s(Q83026,i(s(fun(Q83030,Q83026),i(s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0),s(fun(Q83010,Q83026),F0))),s(Q83030,X))) = s(Q83026,i(s(fun(Q83010,Q83026),F0),s(Q83010,i(s(fun(Q83030,Q83010),S0),s(Q83030,X)))))) <-> p(s(bool,V))))))) -> (all U_5 ((all S0 all T0 all F0 (p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool))),U_5),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0)))) <-> (all SI_ all TI_ exists V (((all F1 all X all Y (s(Q83010,i(s(fun(Q83030,Q83010),SI_),s(Q83030,Y))) = s(Q83010,i(s(fun(Q83030,Q83010),S0),s(Q83030,X))) -> s(Q83026,i(s(fun(Q83030,Q83026),i(s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),TI_),s(fun(Q83010,Q83026),F1))),s(Q83030,Y))) = s(Q83026,i(s(fun(Q83030,Q83026),i(s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0),s(fun(Q83010,Q83026),F1))),s(Q83030,X))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0),s(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))))),c_),s(fun(Q83030,Q83010),SI_))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),TI_))))))),s(bool,V)))))))) -> (all U_4 ((all F0 ((all S0 all T0 p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),geq),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),i(s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),F0),s(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))))),c_),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),i(s(fun(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),gabs),s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool))),U_5),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))))) <-> p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),bool),U_4),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),F0)))))) -> (all U_3 ((all F0 (p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),U_3),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0)))) <-> (all S0 all T0 exists V ((p(s(bool,V)) <-> (all F1 all X all Y (s(Q83010,i(s(fun(Q83030,Q83010),S0),s(Q83030,X))) = s(Q83010,i(s(fun(Q83030,Q83010),S0),s(Q83030,Y))) -> s(Q83026,i(s(fun(Q83030,Q83026),i(s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0),s(fun(Q83010,Q83026),F1))),s(Q83030,X))) = s(Q83026,i(s(fun(Q83030,Q83026),i(s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0),s(fun(Q83010,Q83026),F1))),s(Q83030,Y)))))) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0),s(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))))),c_),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))),s(bool,V)))))))) -> (all U_2 ((all A5 s(bool,i(s(fun(Q83030,bool),U_2),s(Q83030,A5))) = s(bool,t)) -> (all U_1 ((all F0 s(fun(Q83030,bool),i(s(fun(fun(Q83010,Q83026),fun(Q83030,bool)),U_1),s(fun(Q83010,Q83026),F0))) = s(fun(Q83030,bool),U_2)) -> (all U_0 ((all L_L_ all F0 (p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(Q83010,fun(Q83010,bool)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),U_0),s(fun(Q83010,fun(Q83010,bool)),L_L_))),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0)))) <-> (all S0 all T0 p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0),s(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))))),c_),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))),s(bool,i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),bool),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),bool)),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,bool)),fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),bool))),i(s(fun(fun(Q83010,fun(Q83010,bool)),fun(fun(fun(Q83010,Q83026),fun(Q83030,bool)),fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),bool)))),tailadmissible),s(fun(Q83010,fun(Q83010,bool)),L_L_))),s(fun(fun(Q83010,Q83026),fun(Q83030,bool)),U_1))),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))))) -> (all CLAUSES ((exists L_L_ (p(s(bool,i(s(fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool),i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool)),all0),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),i(s(fun(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),gabs),s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(Q83010,fun(Q83010,bool)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),U_0),s(fun(Q83010,fun(Q83010,bool)),L_L_))))))),s(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),CLAUSES)))) & p(s(bool,i(s(fun(fun(Q83010,fun(Q83010,bool)),bool),wf),s(fun(Q83010,fun(Q83010,bool)),L_L_)))))) & p(s(bool,i(s(fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool),i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool)),pairwise0),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),i(s(fun(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),bool),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool))),gabs),s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),bool),U_4))))),s(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),CLAUSES)))) & p(s(bool,i(s(fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool),i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool)),all0),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),i(s(fun(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),gabs),s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),U_3))))),s(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),CLAUSES)))) -> (exists F0 p(s(bool,i(s(fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool),i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool)),all0),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),i(s(fun(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),gabs),s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(Q83010,Q83026),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),U_6),s(fun(Q83010,Q83026),F0))))))),s(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),CLAUSES))))))))))))))))))))) # label(aRECURSIONu_CASEWISEu_PAIRWISE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.45 1269 (all Q20283 all P0 all L1 all L2 (p(s(bool,i(s(fun(list(Q20283),bool),i(s(fun(fun(Q20283,bool),fun(list(Q20283),bool)),all0),s(fun(Q20283,bool),P0))),s(list(Q20283),L1)))) & p(s(bool,i(s(fun(list(Q20283),bool),i(s(fun(fun(Q20283,bool),fun(list(Q20283),bool)),all0),s(fun(Q20283,bool),P0))),s(list(Q20283),L2)))) <-> p(s(bool,i(s(fun(list(Q20283),bool),i(s(fun(fun(Q20283,bool),fun(list(Q20283),bool)),all0),s(fun(Q20283,bool),P0))),s(list(Q20283),i(s(fun(list(Q20283),list(Q20283)),i(s(fun(list(Q20283),fun(list(Q20283),list(Q20283))),append),s(list(Q20283),L1))),s(list(Q20283),L2)))))))) # label(aALLu_APPEND) # label(axiom) # label(non_clause). [assumption]. 14.41/14.45 1270 (all U_0 ((all X all Y all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,Y))),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),i(s(fun(nadd,fun(nadd,fun(num,num))),U_0),s(nadd,X))),s(nadd,Y))),s(num,N0)))) -> (all X all Y s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Y))) = s(nadd,i(s(fun(fun(num,num),nadd),mku_nadd),s(fun(num,num),i(s(fun(nadd,fun(num,num)),i(s(fun(nadd,fun(nadd,fun(num,num))),U_0),s(nadd,X))),s(nadd,Y)))))))) # label(anaddu_add) # label(axiom) # label(non_clause). [assumption]. 14.41/14.45 1271 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,M0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0)))))) # label(aINTu_OFu_NUMu_LT) # label(axiom) # label(non_clause). [assumption]. 14.41/14.45 1272 (all X1 all X2 all Y (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),X2)))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),Y))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X2))),s(prod(hreal,hreal),Y)))))))) # label(aTREALu_MULu_WELLDEFR) # label(axiom) # label(non_clause). [assumption]. 14.41/14.45 1273 (all A all S0 all F0 all B0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,B0))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0)))))))))) & s(fun(A,bool),S0) != s(fun(A,bool),empty) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))))),s(num,B0)))))) # label(aNSUMu_BOUNDu_LTu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.41/14.45 1274 (all M0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) <-> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aDIVu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 14.41/14.45 1275 (all Q49162 all Q49161 all Q49160 all Q49136 all U_1 ((all P0 all F0 all GENR_PVARR_34 (p(s(bool,i(s(fun(Q49136,bool),i(s(fun(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),fun(Q49136,bool)),i(s(fun(fun(Q49162,fun(Q49161,fun(Q49160,bool))),fun(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),fun(Q49136,bool))),U_1),s(fun(Q49162,fun(Q49161,fun(Q49160,bool))),P0))),s(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),F0))),s(Q49136,GENR_PVARR_34)))) <-> (exists A5 exists V (((exists X exists Y exists Z0 (p(s(bool,i(s(fun(Q49160,bool),i(s(fun(Q49161,fun(Q49160,bool)),i(s(fun(Q49162,fun(Q49161,fun(Q49160,bool))),P0),s(Q49162,X))),s(Q49161,Y))),s(Q49160,Z0)))) & p(s(bool,i(s(fun(fun(Q49136,bool),bool),i(s(fun(Q49136,fun(fun(Q49136,bool),bool)),in),s(Q49136,A5))),s(fun(Q49136,bool),i(s(fun(Q49160,fun(Q49136,bool)),i(s(fun(Q49161,fun(Q49160,fun(Q49136,bool))),i(s(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),F0),s(Q49162,X))),s(Q49161,Y))),s(Q49160,Z0)))))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(Q49136,bool),i(s(fun(bool,fun(Q49136,bool)),i(s(fun(Q49136,fun(bool,fun(Q49136,bool))),setspec),s(Q49136,GENR_PVARR_34))),s(bool,V))),s(Q49136,A5)))))))) -> (all U_0 ((all P0 all F0 all GENR_PVARR_33 (p(s(bool,i(s(fun(fun(Q49136,bool),bool),i(s(fun(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),fun(fun(Q49136,bool),bool)),i(s(fun(fun(Q49162,fun(Q49161,fun(Q49160,bool))),fun(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),fun(fun(Q49136,bool),bool))),U_0),s(fun(Q49162,fun(Q49161,fun(Q49160,bool))),P0))),s(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),F0))),s(fun(Q49136,bool),GENR_PVARR_33)))) <-> (exists X exists Y exists Z0 p(s(bool,i(s(fun(fun(Q49136,bool),bool),i(s(fun(bool,fun(fun(Q49136,bool),bool)),i(s(fun(fun(Q49136,bool),fun(bool,fun(fun(Q49136,bool),bool))),setspec),s(fun(Q49136,bool),GENR_PVARR_33))),s(bool,i(s(fun(Q49160,bool),i(s(fun(Q49161,fun(Q49160,bool)),i(s(fun(Q49162,fun(Q49161,fun(Q49160,bool))),P0),s(Q49162,X))),s(Q49161,Y))),s(Q49160,Z0))))),s(fun(Q49136,bool),i(s(fun(Q49160,fun(Q49136,bool)),i(s(fun(Q49161,fun(Q49160,fun(Q49136,bool))),i(s(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),F0),s(Q49162,X))),s(Q49161,Y))),s(Q49160,Z0))))))))) -> (all P0 all F0 s(fun(Q49136,bool),i(s(fun(fun(Q49136,bool),fun(Q49136,bool)),gspec),s(fun(Q49136,bool),i(s(fun(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),fun(Q49136,bool)),i(s(fun(fun(Q49162,fun(Q49161,fun(Q49160,bool))),fun(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),fun(Q49136,bool))),U_1),s(fun(Q49162,fun(Q49161,fun(Q49160,bool))),P0))),s(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),F0))))) = s(fun(Q49136,bool),i(s(fun(fun(fun(Q49136,bool),bool),fun(Q49136,bool)),unions),s(fun(fun(Q49136,bool),bool),i(s(fun(fun(fun(Q49136,bool),bool),fun(fun(Q49136,bool),bool)),gspec),s(fun(fun(Q49136,bool),bool),i(s(fun(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),fun(fun(Q49136,bool),bool)),i(s(fun(fun(Q49162,fun(Q49161,fun(Q49160,bool))),fun(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),fun(fun(Q49136,bool),bool))),U_0),s(fun(Q49162,fun(Q49161,fun(Q49160,bool))),P0))),s(fun(Q49162,fun(Q49161,fun(Q49160,fun(Q49136,bool)))),F0)))))))))))) # label(aUNIONSu_GSPECu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1276 (all Q19472 all P0 all Q0 all L (p(s(bool,i(s(fun(list(Q19472),bool),i(s(fun(fun(Q19472,bool),fun(list(Q19472),bool)),all0),s(fun(Q19472,bool),P0))),s(list(Q19472),L)))) & (all X (p(s(bool,i(s(fun(Q19472,bool),P0),s(Q19472,X)))) & p(s(bool,i(s(fun(list(Q19472),bool),i(s(fun(Q19472,fun(list(Q19472),bool)),mem),s(Q19472,X))),s(list(Q19472),L)))) -> p(s(bool,i(s(fun(Q19472,bool),Q0),s(Q19472,X)))))) -> p(s(bool,i(s(fun(list(Q19472),bool),i(s(fun(fun(Q19472,bool),fun(list(Q19472),bool)),all0),s(fun(Q19472,bool),Q0))),s(list(Q19472),L)))))) # label(aALLu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1277 (all Q68586 all Q68585 all U_5 ((all F0 all Y all X s(num,i(s(fun(Q68586,num),i(s(fun(Q68585,fun(Q68586,num)),i(s(fun(fun(Q68586,fun(Q68585,num)),fun(Q68585,fun(Q68586,num))),U_5),s(fun(Q68586,fun(Q68585,num)),F0))),s(Q68585,Y))),s(Q68586,X))) = s(num,i(s(fun(Q68585,num),i(s(fun(Q68586,fun(Q68585,num)),F0),s(Q68586,X))),s(Q68585,Y)))) -> (all U_4 ((all S0 all R0 all Y all GENR_PVARR_159 (p(s(bool,i(s(fun(Q68586,bool),i(s(fun(Q68585,fun(Q68586,bool)),i(s(fun(fun(Q68586,fun(Q68585,bool)),fun(Q68585,fun(Q68586,bool))),i(s(fun(fun(Q68586,bool),fun(fun(Q68586,fun(Q68585,bool)),fun(Q68585,fun(Q68586,bool)))),U_4),s(fun(Q68586,bool),S0))),s(fun(Q68586,fun(Q68585,bool)),R0))),s(Q68585,Y))),s(Q68586,GENR_PVARR_159)))) <-> (exists X exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(Q68585,bool),i(s(fun(Q68586,fun(Q68585,bool)),R0),s(Q68586,X))),s(Q68585,Y)))) & p(s(bool,i(s(fun(fun(Q68586,bool),bool),i(s(fun(Q68586,fun(fun(Q68586,bool),bool)),in),s(Q68586,X))),s(fun(Q68586,bool),S0))))) & p(s(bool,i(s(fun(Q68586,bool),i(s(fun(bool,fun(Q68586,bool)),i(s(fun(Q68586,fun(bool,fun(Q68586,bool))),setspec),s(Q68586,GENR_PVARR_159))),s(bool,V))),s(Q68586,X)))))))) -> (all U_3 ((all S0 all R0 all F0 all Y s(num,i(s(fun(fun(Q68586,num),num),i(s(fun(fun(Q68586,bool),fun(fun(Q68586,num),num)),nsum),s(fun(Q68586,bool),i(s(fun(fun(Q68586,bool),fun(Q68586,bool)),gspec),s(fun(Q68586,bool),i(s(fun(Q68585,fun(Q68586,bool)),i(s(fun(fun(Q68586,fun(Q68585,bool)),fun(Q68585,fun(Q68586,bool))),i(s(fun(fun(Q68586,bool),fun(fun(Q68586,fun(Q68585,bool)),fun(Q68585,fun(Q68586,bool)))),U_4),s(fun(Q68586,bool),S0))),s(fun(Q68586,fun(Q68585,bool)),R0))),s(Q68585,Y))))))),s(fun(Q68586,num),i(s(fun(Q68585,fun(Q68586,num)),i(s(fun(fun(Q68586,fun(Q68585,num)),fun(Q68585,fun(Q68586,num))),U_5),s(fun(Q68586,fun(Q68585,num)),F0))),s(Q68585,Y))))) = s(num,i(s(fun(Q68585,num),i(s(fun(fun(Q68586,fun(Q68585,num)),fun(Q68585,num)),i(s(fun(fun(Q68586,fun(Q68585,bool)),fun(fun(Q68586,fun(Q68585,num)),fun(Q68585,num))),i(s(fun(fun(Q68586,bool),fun(fun(Q68586,fun(Q68585,bool)),fun(fun(Q68586,fun(Q68585,num)),fun(Q68585,num)))),U_3),s(fun(Q68586,bool),S0))),s(fun(Q68586,fun(Q68585,bool)),R0))),s(fun(Q68586,fun(Q68585,num)),F0))),s(Q68585,Y)))) -> (all U_2 ((all F0 all X all Y s(num,i(s(fun(Q68585,num),i(s(fun(Q68586,fun(Q68585,num)),F0),s(Q68586,X))),s(Q68585,Y))) = s(num,i(s(fun(Q68585,num),i(s(fun(Q68586,fun(Q68585,num)),i(s(fun(fun(Q68586,fun(Q68585,num)),fun(Q68586,fun(Q68585,num))),U_2),s(fun(Q68586,fun(Q68585,num)),F0))),s(Q68586,X))),s(Q68585,Y)))) -> (all U_1 ((all T0 all R0 all X all GENR_PVARR_158 ((exists Y exists V (p(s(bool,i(s(fun(Q68585,bool),i(s(fun(bool,fun(Q68585,bool)),i(s(fun(Q68585,fun(bool,fun(Q68585,bool))),setspec),s(Q68585,GENR_PVARR_158))),s(bool,V))),s(Q68585,Y)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(Q68585,bool),i(s(fun(Q68586,fun(Q68585,bool)),R0),s(Q68586,X))),s(Q68585,Y)))) & p(s(bool,i(s(fun(fun(Q68585,bool),bool),i(s(fun(Q68585,fun(fun(Q68585,bool),bool)),in),s(Q68585,Y))),s(fun(Q68585,bool),T0))))))) <-> p(s(bool,i(s(fun(Q68585,bool),i(s(fun(Q68586,fun(Q68585,bool)),i(s(fun(fun(Q68586,fun(Q68585,bool)),fun(Q68586,fun(Q68585,bool))),i(s(fun(fun(Q68585,bool),fun(fun(Q68586,fun(Q68585,bool)),fun(Q68586,fun(Q68585,bool)))),U_1),s(fun(Q68585,bool),T0))),s(fun(Q68586,fun(Q68585,bool)),R0))),s(Q68586,X))),s(Q68585,GENR_PVARR_158)))))) -> (all U_0 ((all T0 all R0 all F0 all X s(num,i(s(fun(fun(Q68585,num),num),i(s(fun(fun(Q68585,bool),fun(fun(Q68585,num),num)),nsum),s(fun(Q68585,bool),i(s(fun(fun(Q68585,bool),fun(Q68585,bool)),gspec),s(fun(Q68585,bool),i(s(fun(Q68586,fun(Q68585,bool)),i(s(fun(fun(Q68586,fun(Q68585,bool)),fun(Q68586,fun(Q68585,bool))),i(s(fun(fun(Q68585,bool),fun(fun(Q68586,fun(Q68585,bool)),fun(Q68586,fun(Q68585,bool)))),U_1),s(fun(Q68585,bool),T0))),s(fun(Q68586,fun(Q68585,bool)),R0))),s(Q68586,X))))))),s(fun(Q68585,num),i(s(fun(Q68586,fun(Q68585,num)),i(s(fun(fun(Q68586,fun(Q68585,num)),fun(Q68586,fun(Q68585,num))),U_2),s(fun(Q68586,fun(Q68585,num)),F0))),s(Q68586,X))))) = s(num,i(s(fun(Q68586,num),i(s(fun(fun(Q68586,fun(Q68585,num)),fun(Q68586,num)),i(s(fun(fun(Q68586,fun(Q68585,bool)),fun(fun(Q68586,fun(Q68585,num)),fun(Q68586,num))),i(s(fun(fun(Q68585,bool),fun(fun(Q68586,fun(Q68585,bool)),fun(fun(Q68586,fun(Q68585,num)),fun(Q68586,num)))),U_0),s(fun(Q68585,bool),T0))),s(fun(Q68586,fun(Q68585,bool)),R0))),s(fun(Q68586,fun(Q68585,num)),F0))),s(Q68586,X)))) -> (all R0 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q68586,bool),bool),finite),s(fun(Q68586,bool),S0)))) & p(s(bool,i(s(fun(fun(Q68585,bool),bool),finite),s(fun(Q68585,bool),T0)))) -> s(num,i(s(fun(fun(Q68586,num),num),i(s(fun(fun(Q68586,bool),fun(fun(Q68586,num),num)),nsum),s(fun(Q68586,bool),S0))),s(fun(Q68586,num),i(s(fun(fun(Q68586,fun(Q68585,num)),fun(Q68586,num)),i(s(fun(fun(Q68586,fun(Q68585,bool)),fun(fun(Q68586,fun(Q68585,num)),fun(Q68586,num))),i(s(fun(fun(Q68585,bool),fun(fun(Q68586,fun(Q68585,bool)),fun(fun(Q68586,fun(Q68585,num)),fun(Q68586,num)))),U_0),s(fun(Q68585,bool),T0))),s(fun(Q68586,fun(Q68585,bool)),R0))),s(fun(Q68586,fun(Q68585,num)),F0))))) = s(num,i(s(fun(fun(Q68585,num),num),i(s(fun(fun(Q68585,bool),fun(fun(Q68585,num),num)),nsum),s(fun(Q68585,bool),T0))),s(fun(Q68585,num),i(s(fun(fun(Q68586,fun(Q68585,num)),fun(Q68585,num)),i(s(fun(fun(Q68586,fun(Q68585,bool)),fun(fun(Q68586,fun(Q68585,num)),fun(Q68585,num))),i(s(fun(fun(Q68586,bool),fun(fun(Q68586,fun(Q68585,bool)),fun(fun(Q68586,fun(Q68585,num)),fun(Q68585,num)))),U_3),s(fun(Q68586,bool),S0))),s(fun(Q68586,fun(Q68585,bool)),R0))),s(fun(Q68586,fun(Q68585,num)),F0))))))))))))))))))) # label(aNSUMu_NSUMu_RESTRICT) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1278 (all Q4732 all Q4731 all Q4725 all U_0 ((all F0 all F1 (p(s(bool,i(s(fun(fun(prod(Q4732,Q4731),Q4725),bool),i(s(fun(fun(Q4732,fun(Q4731,Q4725)),fun(fun(prod(Q4732,Q4731),Q4725),bool)),U_0),s(fun(Q4732,fun(Q4731,Q4725)),F0))),s(fun(prod(Q4732,Q4731),Q4725),F1)))) <-> (all A5 all B0 p(s(bool,i(s(fun(Q4725,bool),i(s(fun(Q4725,fun(Q4725,bool)),geq),s(Q4725,i(s(fun(prod(Q4732,Q4731),Q4725),F1),s(prod(Q4732,Q4731),i(s(fun(Q4731,prod(Q4732,Q4731)),i(s(fun(Q4732,fun(Q4731,prod(Q4732,Q4731))),c_),s(Q4732,A5))),s(Q4731,B0))))))),s(Q4725,i(s(fun(Q4731,Q4725),i(s(fun(Q4732,fun(Q4731,Q4725)),F0),s(Q4732,A5))),s(Q4731,B0))))))))) -> (all P0 ((exists F0 p(s(bool,i(s(fun(fun(prod(Q4732,Q4731),Q4725),bool),P0),s(fun(prod(Q4732,Q4731),Q4725),i(s(fun(fun(fun(prod(Q4732,Q4731),Q4725),bool),fun(prod(Q4732,Q4731),Q4725)),gabs),s(fun(fun(prod(Q4732,Q4731),Q4725),bool),i(s(fun(fun(Q4732,fun(Q4731,Q4725)),fun(fun(prod(Q4732,Q4731),Q4725),bool)),U_0),s(fun(Q4732,fun(Q4731,Q4725)),F0))))))))) <-> (exists F0 p(s(bool,i(s(fun(fun(prod(Q4732,Q4731),Q4725),bool),P0),s(fun(prod(Q4732,Q4731),Q4725),F0))))))))) # label(aEXISTSu_CURRY) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1279 (all X all Y (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y)))) -> (all B0 exists N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,Y))),s(num,N0))))),s(num,B0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0)))))) & s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0))))) # label(aNADDu_LEu_TOTALu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1280 (all M0 all N0 (s(num,i(s(fun(num,num),bit1),s(num,M0))) = s(num,i(s(fun(num,num),bit0),s(num,N0))) <-> p(s(bool,f0)))) # label(aARITHu_EQu_conjunct8) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1281 (all S0 all B0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))) & (all BI_ (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,BI_))),s(real,B0)))) -> (exists X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,BI_))),s(real,X)))) & p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))))))) -> s(real,B0) = s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))))) # label(aREALu_SUPu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1282 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,P0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0)))))) # label(aRIGHTu_ADDu_DISTRIB) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1283 (all X all Y all Z0 (s(int,Z0) = s(int,Y) <-> s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))) # label(aINTu_EQu_ADDu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1284 (all M0 all N0 (s(num,N0) = s(num,M0) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,M0))))),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,N0)))))))) # label(aTREALu_OFu_NUMu_WELLDEF) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1285 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),numeral),s(num,M0))))),s(num,i(s(fun(num,num),numeral),s(num,N0))))) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))) # label(aARITHu_ADDu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1286 (all M0 all N0 s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(num,int),intu_ofu_num),s(num,M0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0)))))) # label(aINTu_OFu_NUMu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1287 (all A all B all P0 ((exists Y exists X p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y))))) <-> (exists X exists Y p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y))))))) # label(aSWAPu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1288 (all A5 all B0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,A5))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,B0))),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,N0))))),s(num,B0))))),s(num,N0))))) # label(aDIVu_MULTu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1289 (all X all Y all Z0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))),s(real,Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Y))),s(real,Z0)))))) # label(aREALu_ADDu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1290 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))) # label(aREALu_LEu_ADDL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1291 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))))) # label(aREALu_LEu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1292 (all X all Y all Z0 ((all N0 p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,N0))))),s(nadd,X))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,N0))))),s(nadd,Y))))),s(nadd,Z0))))))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y)))))) # label(aNADDu_ARCHu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1293 (all P0 ((exists M0 all X (p(s(bool,i(s(fun(hreal,bool),P0),s(hreal,X)))) -> p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,M0)))))) & (exists X p(s(bool,i(s(fun(hreal,bool),P0),s(hreal,X))))) -> (exists M0 ((all MI_ ((all X (p(s(bool,i(s(fun(hreal,bool),P0),s(hreal,X)))) -> p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,MI_)))))) -> p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,M0))),s(hreal,MI_)))))) & (all X (p(s(bool,i(s(fun(hreal,bool),P0),s(hreal,X)))) -> p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,M0)))))))))) # label(aHREALu_COMPLETE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1294 (all X s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) # label(aREALu_LEu_NEGL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1295 (all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),F0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),F0),s(num,M0))))),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(fun(num,num),F0))))))) # label(aNSUMu_CLAUSESu_LEFT) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1296 (all M0 all N0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_gt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,M0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,M0))),s(num,N0)))) # label(aREALu_OFu_NUMu_GT) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1297 (all A all S0 all T0 ((exists Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),T0)))) & -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aPSUBSETu_MEMBER) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1298 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (exists B0 exists N0 all M0 all N1 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,N1)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,N1))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N1))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,M0))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N1)))))))))))) # label(aNADDu_MULu_LINVu_LEMMA7) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1299 (all Q64412 all Q64416 all OP (p(s(bool,i(s(fun(fun(Q64416,fun(Q64416,Q64416)),bool),monoidal),s(fun(Q64416,fun(Q64416,Q64416)),OP)))) -> (all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q64412,bool),bool),finite),s(fun(Q64412,bool),S0)))) & p(s(bool,i(s(fun(fun(Q64412,bool),bool),i(s(fun(fun(Q64412,bool),fun(fun(Q64412,bool),bool)),subset),s(fun(Q64412,bool),T0))),s(fun(Q64412,bool),S0)))) -> s(Q64416,i(s(fun(Q64416,Q64416),i(s(fun(Q64416,fun(Q64416,Q64416)),OP),s(Q64416,i(s(fun(fun(Q64412,Q64416),Q64416),i(s(fun(fun(Q64412,bool),fun(fun(Q64412,Q64416),Q64416)),i(s(fun(fun(Q64416,fun(Q64416,Q64416)),fun(fun(Q64412,bool),fun(fun(Q64412,Q64416),Q64416))),iterate),s(fun(Q64416,fun(Q64416,Q64416)),OP))),s(fun(Q64412,bool),i(s(fun(fun(Q64412,bool),fun(Q64412,bool)),i(s(fun(fun(Q64412,bool),fun(fun(Q64412,bool),fun(Q64412,bool))),diff),s(fun(Q64412,bool),S0))),s(fun(Q64412,bool),T0))))),s(fun(Q64412,Q64416),F0))))),s(Q64416,i(s(fun(fun(Q64412,Q64416),Q64416),i(s(fun(fun(Q64412,bool),fun(fun(Q64412,Q64416),Q64416)),i(s(fun(fun(Q64416,fun(Q64416,Q64416)),fun(fun(Q64412,bool),fun(fun(Q64412,Q64416),Q64416))),iterate),s(fun(Q64416,fun(Q64416,Q64416)),OP))),s(fun(Q64412,bool),T0))),s(fun(Q64412,Q64416),F0))))) = s(Q64416,i(s(fun(fun(Q64412,Q64416),Q64416),i(s(fun(fun(Q64412,bool),fun(fun(Q64412,Q64416),Q64416)),i(s(fun(fun(Q64416,fun(Q64416,Q64416)),fun(fun(Q64412,bool),fun(fun(Q64412,Q64416),Q64416))),iterate),s(fun(Q64416,fun(Q64416,Q64416)),OP))),s(fun(Q64412,bool),S0))),s(fun(Q64412,Q64416),F0))))))) # label(aITERATEu_DIFF) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1300 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))))) # label(aREALu_LTu_IMPu_LE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1301 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,i(s(fun(real,real),realu_abs),s(real,Y))))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y)))))) # label(aREALu_ABSu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1302 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))) | s(num,M0) = s(num,N0))) # label(aLTu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1303 (all X all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Y))),s(real,Z0)))))) # label(aREALu_LEu_RADD) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1304 (all Q48347 all U_0 ((all GENR_PVARR_14 ((exists X p(s(bool,i(s(fun(Q48347,bool),i(s(fun(bool,fun(Q48347,bool)),i(s(fun(Q48347,fun(bool,fun(Q48347,bool))),setspec),s(Q48347,GENR_PVARR_14))),s(bool,f0))),s(Q48347,X))))) <-> p(s(bool,i(s(fun(Q48347,bool),U_0),s(Q48347,GENR_PVARR_14)))))) -> s(fun(Q48347,bool),i(s(fun(fun(Q48347,bool),fun(Q48347,bool)),gspec),s(fun(Q48347,bool),U_0))) = s(fun(Q48347,bool),empty))) # label(aEMPTYu_GSPEC) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1305 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (exists B0 exists N0 all M0 all N1 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,N1)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N1))))),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,N1))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N1))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,M0))))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N1))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N1)))))))))))))) # label(aNADDu_MULu_LINVu_LEMMA6) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1306 (all A all B all D0 all I0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),I0),s(A,X))) = s(B,i(s(fun(A,B),I0),s(A,Y))) & s(A,Y) != s(A,X) -> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(B,num),D0),s(B,i(s(fun(A,B),I0),s(A,X))))))) -> s(num,i(s(fun(fun(B,num),num),i(s(fun(fun(B,bool),fun(fun(B,num),num)),nsum),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),I0))),s(fun(A,bool),S0))))),s(fun(B,num),D0))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(fun(A,B),fun(A,num)),i(s(fun(fun(B,num),fun(fun(A,B),fun(A,num))),o),s(fun(B,num),D0))),s(fun(A,B),I0))))))) # label(aNSUMu_IMAGEu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1307 (all Q19059 all Q19060 s(list(prod(Q19059,Q19060)),i(s(fun(list(Q19060),list(prod(Q19059,Q19060))),i(s(fun(list(Q19059),fun(list(Q19060),list(prod(Q19059,Q19060)))),zip0),s(list(Q19059),i(s(fun(list(Q19059),list(Q19059)),i(s(fun(Q19059,fun(list(Q19059),list(Q19059))),cons),s(Q19059,h1))),s(list(Q19059),t1))))),s(list(Q19060),i(s(fun(list(Q19060),list(Q19060)),i(s(fun(Q19060,fun(list(Q19060),list(Q19060))),cons),s(Q19060,h2))),s(list(Q19060),t2))))) = s(list(prod(Q19059,Q19060)),i(s(fun(list(prod(Q19059,Q19060)),list(prod(Q19059,Q19060))),i(s(fun(prod(Q19059,Q19060),fun(list(prod(Q19059,Q19060)),list(prod(Q19059,Q19060)))),cons),s(prod(Q19059,Q19060),i(s(fun(Q19060,prod(Q19059,Q19060)),i(s(fun(Q19059,fun(Q19060,prod(Q19059,Q19060))),c_),s(Q19059,h1))),s(Q19060,h2))))),s(list(prod(Q19059,Q19060)),i(s(fun(list(Q19060),list(prod(Q19059,Q19060))),i(s(fun(list(Q19059),fun(list(Q19060),list(prod(Q19059,Q19060)))),zip0),s(list(Q19059),t1))),s(list(Q19060),t2)))))) # label(aZIPu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1308 (all A all S0 s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(num,bool),fun(fun(A,bool),bool)),l_a_u_c),s(fun(num,bool),univ))),s(fun(A,bool),S0))) = s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),S0)))) # label(aINFINITEu_CARDu_LE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1309 (all Q45021 all P0 all A5 all S0 ((all X (p(s(bool,i(s(fun(fun(Q45021,bool),bool),i(s(fun(Q45021,fun(fun(Q45021,bool),bool)),in),s(Q45021,X))),s(fun(Q45021,bool),S0)))) -> p(s(bool,i(s(fun(Q45021,bool),P0),s(Q45021,X)))))) & p(s(bool,i(s(fun(Q45021,bool),P0),s(Q45021,A5)))) <-> (all X (p(s(bool,i(s(fun(fun(Q45021,bool),bool),i(s(fun(Q45021,fun(fun(Q45021,bool),bool)),in),s(Q45021,X))),s(fun(Q45021,bool),i(s(fun(fun(Q45021,bool),fun(Q45021,bool)),i(s(fun(Q45021,fun(fun(Q45021,bool),fun(Q45021,bool))),insert),s(Q45021,A5))),s(fun(Q45021,bool),S0)))))) -> p(s(bool,i(s(fun(Q45021,bool),P0),s(Q45021,X)))))))) # label(aFORALLu_INu_INSERT) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1310 (all A all S0 all T0 all X s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))),s(fun(A,bool),T0))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),i(s(fun(bool,fun(fun(A,bool),fun(fun(A,bool),fun(A,bool)))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))))) # label(aINSERTu_DIFF) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1311 (all B all A all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all X s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),empty))))),s(fun(A,B),F0)))))) # label(aITERATEu_SING) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1312 (all N0 all X all Y ((exists V ((exists VI_ ((s(real,Y) = s(real,X) <-> p(s(bool,VI_))) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,i(s(fun(num,bool),even),s(num,N0))))),s(bool,V))),s(bool,VI_)))))) & (p(s(bool,V)) <-> s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) | s(real,i(s(fun(real,real),realu_abs),s(real,X))) = s(real,i(s(fun(real,real),realu_abs),s(real,Y)))))) <-> s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))) # label(aREALu_POWu_EQu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1313 (all A5 all B0 all C0 all D0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,A5))),s(real,B0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,C0))),s(real,D0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,A5))),s(real,C0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,B0))),s(real,D0)))))) # label(aREALu_ADD2u_SUB2) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1314 (all X all Y p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Y))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,Y))),s(nadd,X))))))) # label(aNADDu_MULu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1315 (all X all Y exists A5 exists B0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,Y))),s(num,N0))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,Y))),s(num,N0))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,N0))))),s(num,B0))))))) # label(aNADDu_ALTMUL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1316 (all U_0 ((all F0 all I0 s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),F0),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(fun(num,num),fun(num,real)),U_0),s(fun(num,num),F0))),s(num,I0)))) -> (all F0 all M0 all N0 s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),F0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(fun(num,num),fun(num,real)),U_0),s(fun(num,num),F0)))))))) # label(aREALu_OFu_NUMu_SUMu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1317 (all F0 all M0 all N0 ((all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,P0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,P0))),s(num,N0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(num,real),F0),s(num,P0)))))))) & s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> (all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,P0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,P0)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(num,real),F0),s(num,P0))))))) # label(aSUMu_POSu_EQu_0u_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1318 (all A all F0 all B0 all S0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))),s(real,B0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(A,real),F0),s(A,X)))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,B0)))))))) # label(aSUMu_POSu_BOUND) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1319 (all Q46571 s(fun(Q46571,bool),i(s(fun(fun(Q46571,bool),fun(Q46571,bool)),i(s(fun(Q46571,fun(fun(Q46571,bool),fun(Q46571,bool))),insert),s(Q46571,x))),s(fun(Q46571,bool),i(s(fun(fun(Q46571,bool),fun(Q46571,bool)),i(s(fun(Q46571,fun(fun(Q46571,bool),fun(Q46571,bool))),insert),s(Q46571,y))),s(fun(Q46571,bool),s0))))) = s(fun(Q46571,bool),i(s(fun(fun(Q46571,bool),fun(Q46571,bool)),i(s(fun(Q46571,fun(fun(Q46571,bool),fun(Q46571,bool))),insert),s(Q46571,y))),s(fun(Q46571,bool),i(s(fun(fun(Q46571,bool),fun(Q46571,bool)),i(s(fun(Q46571,fun(fun(Q46571,bool),fun(Q46571,bool))),insert),s(Q46571,x))),s(fun(Q46571,bool),s0)))))) # label(aINSERTu_ACu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.41/14.46 1320 s(bool,b0) = s(bool,a0) <-> (p(s(bool,b0)) -> p(s(bool,a0))) & (p(s(bool,a0)) -> p(s(bool,b0))) # label(aGeomdetailo_EQu_EXPAND) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1321 (all Q19500 all U_0 ((all P0 all X (-p(s(bool,i(s(fun(Q19500,bool),P0),s(Q19500,X)))) <-> p(s(bool,i(s(fun(Q19500,bool),i(s(fun(fun(Q19500,bool),fun(Q19500,bool)),U_0),s(fun(Q19500,bool),P0))),s(Q19500,X)))))) -> (all P0 all L (-p(s(bool,i(s(fun(list(Q19500),bool),i(s(fun(fun(Q19500,bool),fun(list(Q19500),bool)),ex0),s(fun(Q19500,bool),P0))),s(list(Q19500),L)))) <-> p(s(bool,i(s(fun(list(Q19500),bool),i(s(fun(fun(Q19500,bool),fun(list(Q19500),bool)),all0),s(fun(Q19500,bool),i(s(fun(fun(Q19500,bool),fun(Q19500,bool)),U_0),s(fun(Q19500,bool),P0))))),s(list(Q19500),L)))))))) # label(aNOTu_EX) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1322 (all Q58981 all P0 ((all X (p(s(bool,i(s(fun(fun(Q58981,bool),bool),i(s(fun(Q58981,fun(fun(Q58981,bool),bool)),in),s(Q58981,X))),s(fun(Q58981,bool),empty)))) -> p(s(bool,i(s(fun(Q58981,bool),P0),s(Q58981,X)))))) <-> p(s(bool,t)))) # label(aFORALLu_INu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1323 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,i(s(fun(int,int),intu_neg),s(int,Y))))) = s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y)))))) # label(aINTu_NEGu_RMUL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1324 (all Q87847 all Q87844 ((all Y (p(s(bool,i(s(fun(fun(Q87844,bool),bool),i(s(fun(Q87844,fun(fun(Q87844,bool),bool)),in),s(Q87844,Y))),s(fun(Q87844,bool),t0)))) -> (exists X (p(s(bool,i(s(fun(fun(Q87847,bool),bool),i(s(fun(Q87847,fun(fun(Q87847,bool),bool)),in),s(Q87847,X))),s(fun(Q87847,bool),s0)))) & s(Q87844,i(s(fun(Q87847,Q87844),f),s(Q87847,X))) = s(Q87844,Y))) & (all X all XI_ (s(Q87844,i(s(fun(Q87847,Q87844),f),s(Q87847,X))) = s(Q87844,Y) & s(Q87844,i(s(fun(Q87847,Q87844),f),s(Q87847,XI_))) = s(Q87844,Y) & p(s(bool,i(s(fun(fun(Q87847,bool),bool),i(s(fun(Q87847,fun(fun(Q87847,bool),bool)),in),s(Q87847,XI_))),s(fun(Q87847,bool),s0)))) & p(s(bool,i(s(fun(fun(Q87847,bool),bool),i(s(fun(Q87847,fun(fun(Q87847,bool),bool)),in),s(Q87847,X))),s(fun(Q87847,bool),s0)))) -> s(Q87847,XI_) = s(Q87847,X))))) & (all X (p(s(bool,i(s(fun(fun(Q87847,bool),bool),i(s(fun(Q87847,fun(fun(Q87847,bool),bool)),in),s(Q87847,X))),s(fun(Q87847,bool),s0)))) -> p(s(bool,i(s(fun(fun(Q87844,bool),bool),i(s(fun(Q87844,fun(fun(Q87844,bool),bool)),in),s(Q87844,i(s(fun(Q87847,Q87844),f),s(Q87847,X))))),s(fun(Q87844,bool),t0)))))) <-> (all X all Y (p(s(bool,i(s(fun(fun(Q87847,bool),bool),i(s(fun(Q87847,fun(fun(Q87847,bool),bool)),in),s(Q87847,X))),s(fun(Q87847,bool),s0)))) & p(s(bool,i(s(fun(fun(Q87847,bool),bool),i(s(fun(Q87847,fun(fun(Q87847,bool),bool)),in),s(Q87847,Y))),s(fun(Q87847,bool),s0)))) & s(Q87844,i(s(fun(Q87847,Q87844),f),s(Q87847,X))) = s(Q87844,i(s(fun(Q87847,Q87844),f),s(Q87847,Y))) -> s(Q87847,X) = s(Q87847,Y))) & (all Y (p(s(bool,i(s(fun(fun(Q87844,bool),bool),i(s(fun(Q87844,fun(fun(Q87844,bool),bool)),in),s(Q87844,Y))),s(fun(Q87844,bool),t0)))) -> (exists X (p(s(bool,i(s(fun(fun(Q87847,bool),bool),i(s(fun(Q87847,fun(fun(Q87847,bool),bool)),in),s(Q87847,X))),s(fun(Q87847,bool),s0)))) & s(Q87844,i(s(fun(Q87847,Q87844),f),s(Q87847,X))) = s(Q87844,Y))))) & (all X (p(s(bool,i(s(fun(fun(Q87847,bool),bool),i(s(fun(Q87847,fun(fun(Q87847,bool),bool)),in),s(Q87847,X))),s(fun(Q87847,bool),s0)))) -> p(s(bool,i(s(fun(fun(Q87844,bool),bool),i(s(fun(Q87844,fun(fun(Q87844,bool),bool)),in),s(Q87844,i(s(fun(Q87847,Q87844),f),s(Q87847,X))))),s(fun(Q87844,bool),t0)))))))) # label(aBIJECTIVEu_INJECTIVEu_SURJECTIVE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1325 (all A all P0 all A5 ((exists X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) & s(A,X) = s(A,A5))) <-> p(s(bool,i(s(fun(A,bool),P0),s(A,A5)))))) # label(aUNWINDu_THM1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1326 (all X all S0 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) -> (exists V ((p(s(bool,V)) <-> s(fun(real,bool),S0) = s(fun(real,bool),empty)) & s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))))) = s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),i(s(fun(real,fun(fun(real,bool),fun(real,bool))),insert),s(real,X))),s(fun(real,bool),S0))))))))) # label(aINFu_INSERTu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1327 (all X s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(int,int),intu_sgn),s(int,X))))) = s(int,i(s(fun(int,int),intu_sgn),s(int,i(s(fun(int,int),intu_neg),s(int,X)))))) # label(aINTu_SGNu_NEG) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1328 (all X s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_inv),s(real,X))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) # label(aREALu_LEu_INVu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1329 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) | s(num,N0) = s(num,M0) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))))) # label(aLEu_LT) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1330 (all Q63228 all U_0 ((all OP all X (p(s(bool,i(s(fun(Q63228,bool),i(s(fun(fun(Q63228,fun(Q63228,Q63228)),fun(Q63228,bool)),U_0),s(fun(Q63228,fun(Q63228,Q63228)),OP))),s(Q63228,X)))) <-> (all Y (s(Q63228,Y) = s(Q63228,i(s(fun(Q63228,Q63228),i(s(fun(Q63228,fun(Q63228,Q63228)),OP),s(Q63228,Y))),s(Q63228,X))) & s(Q63228,i(s(fun(Q63228,Q63228),i(s(fun(Q63228,fun(Q63228,Q63228)),OP),s(Q63228,X))),s(Q63228,Y))) = s(Q63228,Y))))) -> (all OP s(Q63228,i(s(fun(fun(Q63228,fun(Q63228,Q63228)),Q63228),neutral),s(fun(Q63228,fun(Q63228,Q63228)),OP))) = s(Q63228,i(s(fun(fun(Q63228,bool),Q63228),h_),s(fun(Q63228,bool),i(s(fun(fun(Q63228,fun(Q63228,Q63228)),fun(Q63228,bool)),U_0),s(fun(Q63228,fun(Q63228,Q63228)),OP)))))))) # label(aneutral) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1331 (all X all Y (p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,Y))),s(hreal,X)))) | p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,Y)))))) # label(aHREALu_LEu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1332 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),suc),s(num,M0))))),s(num,i(s(fun(num,num),suc),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0)))) # label(aSUBu_SUC) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1333 (all A all U_0 ((all N0 s(num,i(s(fun(A,num),U_0),s(A,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))) -> (all S0 s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),U_0)))))) # label(aNSUMu_0) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1334 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),poset),s(fun(prod(A,A),bool),L)))) <-> (all X all Y (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) -> s(A,X) = s(A,Y))) & (all X all Y all Z0 (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,Z0)))))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Z0)))))))) & (all X (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,X)))))))))) # label(aposet) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1335 (all A all S0 all T0 all F0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),T0))),s(fun(A,real),F0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,real),F0))))),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,real),F0))))))) # label(aSUMu_INCLu_EXCL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1336 (all X all Y all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,X))),s(num,Y)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,Y))),s(num,N0)))))))) # label(aEXPu_MONOu_LEu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1337 (all M0 all N0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_ge),s(int,i(s(fun(num,int),intu_ofu_num),s(num,M0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,M0))),s(num,N0)))) # label(aINTu_OFu_NUMu_GE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1338 (all X (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,X) <-> s(real,i(s(fun(real,real),realu_inv),s(real,X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) # label(aREALu_INVu_EQu_1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1339 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,N0))),s(num,N0))))) # label(aGEu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1340 (all X all Y all Z0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y))))),s(int,Z0))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,Y))),s(int,Z0)))))) # label(aINTu_MAXu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1341 (all N0 all X all Y (s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0))) & s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(real,i(s(fun(real,real),realu_abs),s(real,Y))) = s(real,i(s(fun(real,real),realu_abs),s(real,X))))) # label(aREALu_POWu_EQu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1342 (all Q74430 all F0 all P0 all S0 ((all X (p(s(bool,i(s(fun(fun(Q74430,bool),bool),i(s(fun(Q74430,fun(fun(Q74430,bool),bool)),in),s(Q74430,X))),s(fun(Q74430,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q74430,bool),bool),i(s(fun(Q74430,fun(fun(Q74430,bool),bool)),in),s(Q74430,i(s(fun(Q74430,Q74430),P0),s(Q74430,X))))),s(fun(Q74430,bool),S0)))))) & (all X all Y (p(s(bool,i(s(fun(fun(Q74430,bool),bool),i(s(fun(Q74430,fun(fun(Q74430,bool),bool)),in),s(Q74430,X))),s(fun(Q74430,bool),S0)))) & s(Q74430,i(s(fun(Q74430,Q74430),P0),s(Q74430,X))) = s(Q74430,i(s(fun(Q74430,Q74430),P0),s(Q74430,Y))) & p(s(bool,i(s(fun(fun(Q74430,bool),bool),i(s(fun(Q74430,fun(fun(Q74430,bool),bool)),in),s(Q74430,Y))),s(fun(Q74430,bool),S0)))) -> s(Q74430,X) = s(Q74430,Y))) & p(s(bool,i(s(fun(fun(Q74430,bool),bool),finite),s(fun(Q74430,bool),S0)))) -> s(real,i(s(fun(fun(Q74430,real),real),i(s(fun(fun(Q74430,bool),fun(fun(Q74430,real),real)),sum),s(fun(Q74430,bool),S0))),s(fun(Q74430,real),F0))) = s(real,i(s(fun(fun(Q74430,real),real),i(s(fun(fun(Q74430,bool),fun(fun(Q74430,real),real)),sum),s(fun(Q74430,bool),S0))),s(fun(Q74430,real),i(s(fun(fun(Q74430,Q74430),fun(Q74430,real)),i(s(fun(fun(Q74430,real),fun(fun(Q74430,Q74430),fun(Q74430,real))),o),s(fun(Q74430,real),F0))),s(fun(Q74430,Q74430),P0))))))) # label(aSUMu_INJECTION) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1343 (all Q59992 all Q59993 all T0 all S0 s(bool,i(s(fun(fun(Q59992,bool),bool),i(s(fun(fun(Q59993,bool),fun(fun(Q59992,bool),bool)),g_a_u_c),s(fun(Q59993,bool),S0))),s(fun(Q59992,bool),T0))) = s(bool,i(s(fun(fun(Q59993,bool),bool),i(s(fun(fun(Q59992,bool),fun(fun(Q59993,bool),bool)),l_a_u_c),s(fun(Q59992,bool),T0))),s(fun(Q59993,bool),S0)))) # label(ageu_c) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1344 (all N0 s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) # label(aINTu_POWu_ONE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1345 (all P0 ((exists M0 all X (p(s(bool,i(s(fun(real,bool),P0),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,M0)))))) & (exists X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),P0),s(real,X)))))) -> (exists M0 ((all X (p(s(bool,i(s(fun(real,bool),P0),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,M0)))))) & (all MI_ ((all X (p(s(bool,i(s(fun(real,bool),P0),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,MI_)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,M0))),s(real,MI_)))))))))) # label(aREALu_COMPLETEu_SOMEPOS) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1346 (all A all X all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) & -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),T0))),s(A,X)))))))) # label(aSUBSETu_DELETE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1347 (all Q71711 all F0 all G0 all S0 ((all X (p(s(bool,i(s(fun(fun(Q71711,bool),bool),i(s(fun(Q71711,fun(fun(Q71711,bool),bool)),in),s(Q71711,X))),s(fun(Q71711,bool),S0)))) -> s(real,i(s(fun(Q71711,real),G0),s(Q71711,X))) = s(real,i(s(fun(Q71711,real),F0),s(Q71711,X))))) -> s(real,i(s(fun(fun(Q71711,real),real),i(s(fun(fun(Q71711,bool),fun(fun(Q71711,real),real)),sum),s(fun(Q71711,bool),S0))),s(fun(Q71711,real),G0))) = s(real,i(s(fun(fun(Q71711,real),real),i(s(fun(fun(Q71711,bool),fun(fun(Q71711,real),real)),sum),s(fun(Q71711,bool),S0))),s(fun(Q71711,real),F0))))) # label(aSUMu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1348 (all X all Y all Z0 p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,Y))),s(nadd,Z0))))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Y))))),s(nadd,Z0))))))) # label(aNADDu_ADDu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1349 (all Q68010 all U_0 ((all S0 all F0 all X s(num,i(s(fun(Q68010,num),i(s(fun(fun(Q68010,num),fun(Q68010,num)),i(s(fun(fun(Q68010,bool),fun(fun(Q68010,num),fun(Q68010,num))),U_0),s(fun(Q68010,bool),S0))),s(fun(Q68010,num),F0))),s(Q68010,X))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(fun(Q68010,bool),bool),i(s(fun(Q68010,fun(fun(Q68010,bool),bool)),in),s(Q68010,X))),s(fun(Q68010,bool),S0))))),s(num,i(s(fun(Q68010,num),F0),s(Q68010,X))))),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) -> (all F0 all S0 (p(s(bool,i(s(fun(fun(Q68010,bool),bool),finite),s(fun(Q68010,bool),S0)))) -> s(num,i(s(fun(fun(Q68010,num),num),i(s(fun(fun(Q68010,bool),fun(fun(Q68010,num),num)),nsum),s(fun(Q68010,bool),S0))),s(fun(Q68010,num),F0))) = s(num,i(s(fun(fun(Q68010,num),num),i(s(fun(fun(Q68010,bool),fun(fun(Q68010,num),num)),nsum),s(fun(Q68010,bool),S0))),s(fun(Q68010,num),i(s(fun(fun(Q68010,num),fun(Q68010,num)),i(s(fun(fun(Q68010,bool),fun(fun(Q68010,num),fun(Q68010,num))),U_0),s(fun(Q68010,bool),S0))),s(fun(Q68010,num),F0))))))))) # label(aNSUMu_RESTRICT) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1350 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(real,X))) # label(aREALu_POSu_NZ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1351 (all Q48678 all Q48681 all Q48680 all Q48679 all U_0 ((all P0 all F0 all GENR_PVARR_23 (p(s(bool,i(s(fun(Q48678,bool),i(s(fun(fun(Q48681,fun(Q48680,fun(Q48679,Q48678))),fun(Q48678,bool)),i(s(fun(fun(Q48681,fun(Q48680,fun(Q48679,bool))),fun(fun(Q48681,fun(Q48680,fun(Q48679,Q48678))),fun(Q48678,bool))),U_0),s(fun(Q48681,fun(Q48680,fun(Q48679,bool))),P0))),s(fun(Q48681,fun(Q48680,fun(Q48679,Q48678))),F0))),s(Q48678,GENR_PVARR_23)))) <-> (exists W exists X exists Y p(s(bool,i(s(fun(Q48678,bool),i(s(fun(bool,fun(Q48678,bool)),i(s(fun(Q48678,fun(bool,fun(Q48678,bool))),setspec),s(Q48678,GENR_PVARR_23))),s(bool,i(s(fun(Q48679,bool),i(s(fun(Q48680,fun(Q48679,bool)),i(s(fun(Q48681,fun(Q48680,fun(Q48679,bool))),P0),s(Q48681,W))),s(Q48680,X))),s(Q48679,Y))))),s(Q48678,i(s(fun(Q48679,Q48678),i(s(fun(Q48680,fun(Q48679,Q48678)),i(s(fun(Q48681,fun(Q48680,fun(Q48679,Q48678))),F0),s(Q48681,W))),s(Q48680,X))),s(Q48679,Y))))))))) -> (all P0 all F0 ((all Z0 (p(s(bool,i(s(fun(fun(Q48678,bool),bool),i(s(fun(Q48678,fun(fun(Q48678,bool),bool)),in),s(Q48678,Z0))),s(fun(Q48678,bool),i(s(fun(fun(Q48678,bool),fun(Q48678,bool)),gspec),s(fun(Q48678,bool),i(s(fun(fun(Q48681,fun(Q48680,fun(Q48679,Q48678))),fun(Q48678,bool)),i(s(fun(fun(Q48681,fun(Q48680,fun(Q48679,bool))),fun(fun(Q48681,fun(Q48680,fun(Q48679,Q48678))),fun(Q48678,bool))),U_0),s(fun(Q48681,fun(Q48680,fun(Q48679,bool))),P0))),s(fun(Q48681,fun(Q48680,fun(Q48679,Q48678))),F0)))))))) -> p(s(bool,i(s(fun(Q48678,bool),q0),s(Q48678,Z0)))))) <-> (all W all X all Y (p(s(bool,i(s(fun(Q48679,bool),i(s(fun(Q48680,fun(Q48679,bool)),i(s(fun(Q48681,fun(Q48680,fun(Q48679,bool))),P0),s(Q48681,W))),s(Q48680,X))),s(Q48679,Y)))) -> p(s(bool,i(s(fun(Q48678,bool),q0),s(Q48678,i(s(fun(Q48679,Q48678),i(s(fun(Q48680,fun(Q48679,Q48678)),i(s(fun(Q48681,fun(Q48680,fun(Q48679,Q48678))),F0),s(Q48681,W))),s(Q48680,X))),s(Q48679,Y)))))))))))) # label(aFORALLu_INu_GSPECu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1352 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,M0))))),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,N0)))))) # label(aHREALu_OFu_NUMu_LE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1353 (all A all C all B all D all S0 all SI_ all T0 all TI_ (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),SI_)))) & p(s(bool,i(s(fun(fun(D,bool),bool),i(s(fun(fun(C,bool),fun(fun(D,bool),bool)),a_u_c),s(fun(C,bool),T0))),s(fun(D,bool),TI_)))) -> s(bool,i(s(fun(fun(D,bool),bool),i(s(fun(fun(B,bool),fun(fun(D,bool),bool)),l_a_u_c),s(fun(B,bool),SI_))),s(fun(D,bool),TI_))) = s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(A,bool),fun(fun(C,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(C,bool),T0))))) # label(aCARDu_LEu_CONG) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1354 (all A all T0 all H0 s(A,i(s(fun(list(A),A),hd),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,H0))),s(list(A),T0))))) = s(A,H0)) # label(aSeq2o_HD) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1355 (all N all A all U_1 ((all P0 all GENR_PVARR_210 (p(s(bool,i(s(fun(cart(A,N),bool),i(s(fun(fun(num,fun(A,bool)),fun(cart(A,N),bool)),U_1),s(fun(num,fun(A,bool)),P0))),s(cart(A,N),GENR_PVARR_210)))) <-> (exists V exists V0 (p(s(bool,i(s(fun(cart(A,N),bool),i(s(fun(bool,fun(cart(A,N),bool)),i(s(fun(cart(A,N),fun(bool,fun(cart(A,N),bool))),setspec),s(cart(A,N),GENR_PVARR_210))),s(bool,V0))),s(cart(A,N),V)))) & (p(s(bool,V0)) <-> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),P0),s(num,I0))),s(A,i(s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),d_),s(cart(A,N),V))),s(num,I0))))))))))))) -> (all U_0 ((all P0 all I0 all GENR_PVARR_209 ((exists X p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_209))),s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),P0),s(num,I0))),s(A,X))))),s(A,X))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(A,bool)),fun(num,fun(A,bool))),U_0),s(fun(num,fun(A,bool)),P0))),s(num,I0))),s(A,GENR_PVARR_209)))))) -> (all P0 ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(A,bool)),fun(num,fun(A,bool))),U_0),s(fun(num,fun(A,bool)),P0))),s(num,I0)))))))))) -> p(s(bool,i(s(fun(fun(cart(A,N),bool),bool),finite),s(fun(cart(A,N),bool),i(s(fun(fun(cart(A,N),bool),fun(cart(A,N),bool)),gspec),s(fun(cart(A,N),bool),i(s(fun(fun(num,fun(A,bool)),fun(cart(A,N),bool)),U_1),s(fun(num,fun(A,bool)),P0)))))))))))))) # label(aFINITEu_CART) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1356 (all A all U_0 ((all L_L_ all X all GENR_PVARR_133 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))),U_0),s(fun(A,fun(A,bool)),L_L_))),s(A,X))),s(A,GENR_PVARR_133)))) <-> (exists Y p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_133))),s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,X))))),s(A,Y))))))) -> (all L_L_ ((all X p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,fun(A,bool)),fun(A,fun(A,bool))),U_0),s(fun(A,fun(A,bool)),L_L_))),s(A,X))))))))) & (all X all Y all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,Z0)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,X))),s(A,Y)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,X))),s(A,Z0)))))) & (all X -p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,X))),s(A,X))))) -> p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),L_L_)))))))) # label(aWFu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1357 (all N0 s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))) # label(aEXPu_ONE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1358 (all X all Y -(p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,X)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))))) # label(aINTu_LTu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1359 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))) # label(aREALu_LEu_LNEG) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1360 (all X all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) & s(real,X) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,M0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,M0))))))) # label(aREALu_POWu_SUB) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1361 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Z0))),s(real,X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Z0))),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))))) # label(aREALu_LEu_LMULu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1362 (all X all N0 s(int,i(s(fun(real,int),intu_ofu_real),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(num,N0))))) = s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0)))) # label(aintu_pow) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1363 (all S0 all T0 ((all B0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),T0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))) <-> (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))))) -> s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))) = s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),T0))))) # label(aSUPu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1364 (all A all H0 all T0 s(list(A),nil) != s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,H0))),s(list(A),T0)))) # label(aNOTu_CONSu_NIL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1365 (all Q47464 ((all X (p(s(bool,i(s(fun(fun(fun(Q47464,bool),bool),bool),i(s(fun(fun(Q47464,bool),fun(fun(fun(Q47464,bool),bool),bool)),in),s(fun(Q47464,bool),X))),s(fun(fun(Q47464,bool),bool),s0)))) -> (exists Y (p(s(bool,i(s(fun(fun(Q47464,bool),bool),i(s(fun(fun(Q47464,bool),fun(fun(Q47464,bool),bool)),subset),s(fun(Q47464,bool),X))),s(fun(Q47464,bool),Y)))) & p(s(bool,i(s(fun(fun(fun(Q47464,bool),bool),bool),i(s(fun(fun(Q47464,bool),fun(fun(fun(Q47464,bool),bool),bool)),in),s(fun(Q47464,bool),Y))),s(fun(fun(Q47464,bool),bool),t0)))))))) -> p(s(bool,i(s(fun(fun(Q47464,bool),bool),i(s(fun(fun(Q47464,bool),fun(fun(Q47464,bool),bool)),subset),s(fun(Q47464,bool),i(s(fun(fun(fun(Q47464,bool),bool),fun(Q47464,bool)),unions),s(fun(fun(Q47464,bool),bool),s0))))),s(fun(Q47464,bool),i(s(fun(fun(fun(Q47464,bool),bool),fun(Q47464,bool)),unions),s(fun(fun(Q47464,bool),bool),t0)))))))) # label(aUNIONSu_MONO) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1366 (all Q45062 all P0 all A5 all S0 ((exists X (p(s(bool,i(s(fun(fun(Q45062,bool),bool),i(s(fun(Q45062,fun(fun(Q45062,bool),bool)),in),s(Q45062,X))),s(fun(Q45062,bool),i(s(fun(fun(Q45062,bool),fun(Q45062,bool)),i(s(fun(Q45062,fun(fun(Q45062,bool),fun(Q45062,bool))),insert),s(Q45062,A5))),s(fun(Q45062,bool),S0)))))) & p(s(bool,i(s(fun(Q45062,bool),P0),s(Q45062,X)))))) <-> p(s(bool,i(s(fun(Q45062,bool),P0),s(Q45062,A5)))) | (exists X (p(s(bool,i(s(fun(Q45062,bool),P0),s(Q45062,X)))) & p(s(bool,i(s(fun(fun(Q45062,bool),bool),i(s(fun(Q45062,fun(fun(Q45062,bool),bool)),in),s(Q45062,X))),s(fun(Q45062,bool),S0)))))))) # label(aEXISTSu_INu_INSERT) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1367 (all A all B all S0 all T0 all F0 all G0 ((all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(B,A),G0),s(B,Y))))),s(fun(A,bool),S0)))) & s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,i(s(fun(B,A),G0),s(B,Y))))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,X) = s(A,i(s(fun(B,A),G0),s(B,i(s(fun(A,B),F0),s(A,X))))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0)))))) -> (all N0 s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(fun(B,bool),fun(num,bool)),hasu_size),s(fun(B,bool),T0))),s(num,N0)))))) # label(aBIJECTIONSu_HASu_SIZEu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1368 (all A all U all V all F0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),V)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),U))),s(fun(A,bool),V)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),V))),s(fun(A,bool),U)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(A,real),F0),s(A,X)))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),U))),s(fun(A,real),F0))))),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),V))),s(fun(A,real),F0)))))))) # label(aSUMu_SUBSETu_SIMPLE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1369 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y)))))) # label(aREALu_SUBu_LE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.47 1370 (all A all U_2 ((all A5 all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),U_2),s(A,A5))),s(fun(A,bool),S0))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,A5))),s(fun(A,bool),S0)))) -> (all U_1 ((all T0 all GENR_PVARR_102 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_1),s(fun(A,bool),T0))),s(fun(A,bool),GENR_PVARR_102)))) <-> (exists S0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_102))),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,bool),S0))))))) -> (all U_0 ((all A5 all T0 all GENR_PVARR_101 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),i(s(fun(A,fun(fun(A,bool),fun(fun(A,bool),bool))),U_0),s(A,A5))),s(fun(A,bool),T0))),s(fun(A,bool),GENR_PVARR_101)))) <-> (exists S0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_101))),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,A5))),s(fun(A,bool),T0))))))),s(fun(A,bool),S0))))))) -> (all A5 all T0 s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),i(s(fun(fun(fun(A,bool),bool),fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool))),union),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_1),s(fun(A,bool),T0))))))),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),i(s(fun(fun(fun(A,bool),fun(A,bool)),fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool))),image),s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),U_2),s(A,A5))))),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_1),s(fun(A,bool),T0))))))))) = s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),i(s(fun(A,fun(fun(A,bool),fun(fun(A,bool),bool))),U_0),s(A,A5))),s(fun(A,bool),T0)))))))))))) # label(aPOWERSETu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1371 (all X all Y s(real,X) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Y))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y)))))) # label(aREALu_SUBu_ADD2) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1372 (all A all P0 all Q0 ((all X (p(s(bool,P0)) | p(s(bool,Q0)))) <-> (all X p(s(bool,P0))) | (all X p(s(bool,Q0))))) # label(aTRIVu_ORu_FORALLu_THM) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1373 (all M0 all N0 all Q0 all R0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,R0))),s(num,N0)))) & s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,Q0))),s(num,N0))))),s(num,R0))) = s(num,M0) -> s(num,R0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))) # label(aMODu_UNIQ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1374 (all M0 all N0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))))),s(num,M0)))))) # label(aDIVu_LE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1375 (all A all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),empty))),s(fun(A,bool),S0))) = s(fun(A,bool),empty)) # label(aEMPTYu_DIFF) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1376 (all Q46704 s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),q))),s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),p1))),s(fun(Q46704,bool),r0))))) = s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),p1))),s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),q))),s(fun(Q46704,bool),r0)))))) # label(aUNIONu_ACIu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1377 (all D all A all B all C all F0 all X all Y all Z0 s(D,i(s(fun(prod(A,prod(B,C)),D),i(s(fun(fun(prod(prod(A,B),C),D),fun(prod(A,prod(B,C)),D)),passoc),s(fun(prod(prod(A,B),C),D),F0))),s(prod(A,prod(B,C)),i(s(fun(prod(B,C),prod(A,prod(B,C))),i(s(fun(A,fun(prod(B,C),prod(A,prod(B,C)))),c_),s(A,X))),s(prod(B,C),i(s(fun(C,prod(B,C)),i(s(fun(B,fun(C,prod(B,C))),c_),s(B,Y))),s(C,Z0))))))) = s(D,i(s(fun(prod(prod(A,B),C),D),F0),s(prod(prod(A,B),C),i(s(fun(C,prod(prod(A,B),C)),i(s(fun(prod(A,B),fun(C,prod(prod(A,B),C))),c_),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y))))),s(C,Z0)))))) # label(aPASSOCu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1378 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,i(s(fun(real,real),realu_neg),s(real,Y))))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))) # label(aREALu_NEGu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1379 (all N0 s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,i(s(fun(num,num),fact),s(num,N0)))) # label(aFACTu_NZ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1380 (all A all B s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),t_u_c),s(fun(A,bool),univ))),s(fun(B,bool),univ))) = s(fun(prod(A,B),bool),univ)) # label(aMULu_Cu_UNIV) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1381 (all M0 all N0 s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0)))))) # label(aARITHu_ADDu_conjunct9) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1382 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_inv),s(real,X))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aREALu_INVu_LEu_1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1383 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y)))))))) # label(aINTu_LEu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1384 (all A all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),S0)))) <-> -p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))))) # label(aINFINITE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1385 (all Q48419 all U_0 ((all A5 all GENR_PVARR_17 ((exists X exists V (p(s(bool,i(s(fun(Q48419,bool),i(s(fun(bool,fun(Q48419,bool)),i(s(fun(Q48419,fun(bool,fun(Q48419,bool))),setspec),s(Q48419,GENR_PVARR_17))),s(bool,V))),s(Q48419,X)))) & (p(s(bool,V)) <-> s(Q48419,A5) = s(Q48419,X)))) <-> p(s(bool,i(s(fun(Q48419,bool),i(s(fun(Q48419,fun(Q48419,bool)),U_0),s(Q48419,A5))),s(Q48419,GENR_PVARR_17)))))) -> (all A5 s(fun(Q48419,bool),i(s(fun(fun(Q48419,bool),fun(Q48419,bool)),gspec),s(fun(Q48419,bool),i(s(fun(Q48419,fun(Q48419,bool)),U_0),s(Q48419,A5))))) = s(fun(Q48419,bool),i(s(fun(fun(Q48419,bool),fun(Q48419,bool)),i(s(fun(Q48419,fun(fun(Q48419,bool),fun(Q48419,bool))),insert),s(Q48419,A5))),s(fun(Q48419,bool),empty)))))) # label(aSINGu_GSPECu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1386 (all X p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),trealu_neg),s(prod(hreal,hreal),X))))),s(prod(hreal,hreal),X))))),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) # label(aTREALu_ADDu_LINV) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1387 (all R0 ((all X all Y all Z0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,X))),s(num,Y)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,Y))),s(num,Z0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,X))),s(num,Z0)))))) & (all X p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,X))),s(num,X))))) -> ((all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,N0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))) <-> (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,M0))),s(num,N0))))))))) # label(aTRANSITIVEu_STEPWISEu_LEu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1388 (all F0 all G0 all M0 all N0 ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),F0),s(num,I0))))),s(num,i(s(fun(num,num),G0),s(num,I0)))))))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),F0))))),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),G0)))))))) # label(aNSUMu_LEu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1389 (all A all S0 all T0 all U s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),U))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),T0))),s(fun(A,bool),U)))))) # label(aINTERu_OVERu_UNION) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1390 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),pre),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),suc),s(num,M0))))),s(num,N0)))))) # label(aSUBu_PRESUC) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1391 (all Q46704 s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),p1))),s(fun(Q46704,bool),q))))),s(fun(Q46704,bool),r0))) = s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),p1))),s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),q))),s(fun(Q46704,bool),r0)))))) # label(aUNIONu_ACIu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1392 (all M0 all N0 all P0 all Q0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,Q0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,P0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,P0))),s(num,Q0)))))))) # label(aLETu_ADD2) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1393 (all A all S0 s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),univ))) = s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),S0)))) # label(aDIMINDEXu_UNIV) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1394 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X)))) -> (exists N0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))))))) # label(aREALu_ARCHu_POW) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1395 (all A all X s(A,i(s(fun(A,A),i1),s(A,X))) = s(A,X)) # label(aIu_THM) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1396 (all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,i(s(fun(real,real),realu_abs),s(real,Y))))))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))))))) # label(aREALu_SUBu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1397 p(s(bool,p1)) | p(s(bool,p1)) <-> p(s(bool,p1)) # label(aDISJu_ACIu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1398 (all Q63859 all Q63674 all F0 all X all S0 exists V (s(fun(Q63674,bool),i(s(fun(fun(Q63674,bool),fun(Q63674,bool)),i(s(fun(fun(Q63674,bool),fun(fun(Q63674,bool),fun(Q63674,bool))),i(s(fun(bool,fun(fun(Q63674,bool),fun(fun(Q63674,bool),fun(Q63674,bool)))),cond),s(bool,V))),s(fun(Q63674,bool),i(s(fun(fun(Q63674,bool),fun(Q63674,bool)),i(s(fun(fun(Q63674,Q63859),fun(fun(Q63674,bool),fun(Q63674,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63674,Q63859),fun(fun(Q63674,bool),fun(Q63674,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63674,Q63859),F0))),s(fun(Q63674,bool),S0))))),s(fun(Q63674,bool),i(s(fun(fun(Q63674,bool),fun(Q63674,bool)),i(s(fun(Q63674,fun(fun(Q63674,bool),fun(Q63674,bool))),insert),s(Q63674,X))),s(fun(Q63674,bool),i(s(fun(fun(Q63674,bool),fun(Q63674,bool)),i(s(fun(fun(Q63674,Q63859),fun(fun(Q63674,bool),fun(Q63674,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63674,Q63859),fun(fun(Q63674,bool),fun(Q63674,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63674,Q63859),F0))),s(fun(Q63674,bool),S0))))))) = s(fun(Q63674,bool),i(s(fun(fun(Q63674,bool),fun(Q63674,bool)),i(s(fun(fun(Q63674,Q63859),fun(fun(Q63674,bool),fun(Q63674,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63674,Q63859),fun(fun(Q63674,bool),fun(Q63674,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63674,Q63859),F0))),s(fun(Q63674,bool),i(s(fun(fun(Q63674,bool),fun(Q63674,bool)),i(s(fun(Q63674,fun(fun(Q63674,bool),fun(Q63674,bool))),insert),s(Q63674,X))),s(fun(Q63674,bool),S0))))) & (s(Q63859,i(s(fun(Q63674,Q63859),F0),s(Q63674,X))) = s(Q63859,i(s(fun(fun(Q63859,fun(Q63859,Q63859)),Q63859),neutral),s(fun(Q63859,fun(Q63859,Q63859)),op))) <-> p(s(bool,V))))) # label(aSUPPORTu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1399 (all A all P0 ((all C0 ((all X all Y (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),Y))),s(fun(fun(A,bool),bool),C0)))) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),X))),s(fun(fun(A,bool),bool),C0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),Y))),s(fun(A,bool),X)))) | p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),X))),s(fun(A,bool),Y)))))) & (all X (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),X))),s(fun(fun(A,bool),bool),C0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),X)))))) -> (exists Z0 ((all X (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),X))),s(fun(fun(A,bool),bool),C0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),X))),s(fun(A,bool),Z0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),Z0)))))))) -> (exists A5 (p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),A5)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),A5))),s(fun(A,bool),X)))) & p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),X)))) -> s(fun(A,bool),X) = s(fun(A,bool),A5))))))) # label(aZLu_SUBSETS) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1400 (all A all L all M0 all N0 s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),L))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),M0))),s(list(A),N0))))) = s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),L))),s(list(A),M0))))),s(list(A),N0)))) # label(aAPPENDu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1401 (all Q70994 all X all F0 all S0 (p(s(bool,i(s(fun(fun(Q70994,bool),bool),finite),s(fun(Q70994,bool),S0)))) -> s(real,i(s(fun(fun(Q70994,real),real),i(s(fun(fun(Q70994,bool),fun(fun(Q70994,real),real)),sum),s(fun(Q70994,bool),i(s(fun(fun(Q70994,bool),fun(Q70994,bool)),i(s(fun(Q70994,fun(fun(Q70994,bool),fun(Q70994,bool))),insert),s(Q70994,X))),s(fun(Q70994,bool),S0))))),s(fun(Q70994,real),F0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(fun(Q70994,bool),bool),i(s(fun(Q70994,fun(fun(Q70994,bool),bool)),in),s(Q70994,X))),s(fun(Q70994,bool),S0))))),s(real,i(s(fun(fun(Q70994,real),real),i(s(fun(fun(Q70994,bool),fun(fun(Q70994,real),real)),sum),s(fun(Q70994,bool),S0))),s(fun(Q70994,real),F0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(Q70994,real),F0),s(Q70994,X))))),s(real,i(s(fun(fun(Q70994,real),real),i(s(fun(fun(Q70994,bool),fun(fun(Q70994,real),real)),sum),s(fun(Q70994,bool),S0))),s(fun(Q70994,real),F0))))))))) # label(aSUMu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1402 (all A all U_0 ((all F0 all T0 s(real,i(s(fun(fun(A,bool),real),i(s(fun(fun(A,real),fun(fun(A,bool),real)),U_0),s(fun(A,real),F0))),s(fun(A,bool),T0))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),T0))),s(fun(A,real),F0)))) -> (all F0 all S0 ((all T0 (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T0))),s(fun(fun(A,bool),bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))))) & (all T1 all T2 all X (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T1))),s(fun(fun(A,bool),bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T2)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T1)))) & s(fun(A,bool),T1) != s(fun(A,bool),T2) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T2))),s(fun(fun(A,bool),bool),S0)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(A,real),F0),s(A,X))))) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),finite),s(fun(fun(A,bool),bool),S0)))) -> s(real,i(s(fun(fun(fun(A,bool),real),real),i(s(fun(fun(fun(A,bool),bool),fun(fun(fun(A,bool),real),real)),sum),s(fun(fun(A,bool),bool),S0))),s(fun(fun(A,bool),real),i(s(fun(fun(A,real),fun(fun(A,bool),real)),U_0),s(fun(A,real),F0))))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),unions),s(fun(fun(A,bool),bool),S0))))),s(fun(A,real),F0))))))) # label(aSUMu_UNIONSu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1403 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))) # label(aREALu_LTu_MULu_EQu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1404 (all Q94935 all S0 (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(fun(Q94935,bool),fun(fun(real,bool),bool)),a_u_c),s(fun(Q94935,bool),S0))),s(fun(real,bool),univ)))) -> -p(s(bool,i(s(fun(fun(Q94935,bool),bool),countable),s(fun(Q94935,bool),S0)))))) # label(aCARDu_EQu_REALu_IMPu_UNCOUNTABLE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1405 (all Q66806 all F0 s(num,i(s(fun(fun(Q66806,num),num),i(s(fun(fun(Q66806,bool),fun(fun(Q66806,num),num)),nsum),s(fun(Q66806,bool),empty))),s(fun(Q66806,num),F0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))) # label(aNSUMu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1406 p(s(bool,i(s(fun(num,bool),p0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,a0))),s(num,b0)))))) <-> (exists D0 (p(s(bool,i(s(fun(num,bool),p0),s(num,D0)))) & (s(num,a0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,b0))),s(num,D0))) | s(num,D0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,a0))),s(num,b0))))))) # label(aSUBu_ELIMu_THMi_) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1407 (all Q47833 all Q47822 all F0 all S0 all T0 ((all X all Y (s(Q47833,i(s(fun(Q47822,Q47833),F0),s(Q47822,X))) = s(Q47833,i(s(fun(Q47822,Q47833),F0),s(Q47822,Y))) -> s(Q47822,X) = s(Q47822,Y))) -> s(fun(Q47833,bool),i(s(fun(fun(Q47822,bool),fun(Q47833,bool)),i(s(fun(fun(Q47822,Q47833),fun(fun(Q47822,bool),fun(Q47833,bool))),image),s(fun(Q47822,Q47833),F0))),s(fun(Q47822,bool),i(s(fun(fun(Q47822,bool),fun(Q47822,bool)),i(s(fun(fun(Q47822,bool),fun(fun(Q47822,bool),fun(Q47822,bool))),diff),s(fun(Q47822,bool),S0))),s(fun(Q47822,bool),T0))))) = s(fun(Q47833,bool),i(s(fun(fun(Q47833,bool),fun(Q47833,bool)),i(s(fun(fun(Q47833,bool),fun(fun(Q47833,bool),fun(Q47833,bool))),diff),s(fun(Q47833,bool),i(s(fun(fun(Q47822,bool),fun(Q47833,bool)),i(s(fun(fun(Q47822,Q47833),fun(fun(Q47822,bool),fun(Q47833,bool))),image),s(fun(Q47822,Q47833),F0))),s(fun(Q47822,bool),S0))))),s(fun(Q47833,bool),i(s(fun(fun(Q47822,bool),fun(Q47833,bool)),i(s(fun(fun(Q47822,Q47833),fun(fun(Q47822,bool),fun(Q47833,bool))),image),s(fun(Q47822,Q47833),F0))),s(fun(Q47822,bool),T0))))))) # label(aIMAGEu_DIFFu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1408 (all X all Y (s(int,i(s(fun(int,int),intu_abs),s(int,X))) = s(int,i(s(fun(int,int),intu_abs),s(int,Y))) <-> s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) # label(aINTu_EQu_SQUAREu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1409 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,X)))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))))) # label(aREALu_LETu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1410 (all X all Y s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_inv),s(real,X))))),s(real,i(s(fun(real,real),realu_inv),s(real,Y)))))) # label(aREALu_INVu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1411 (all A all U_0 ((all S0 all GENR_PVARR_1 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),U_0),s(fun(fun(A,bool),bool),S0))),s(A,GENR_PVARR_1)))) <-> (exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_1))),s(bool,V))),s(A,X)))) & (p(s(bool,V)) <-> (exists U (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),U))),s(fun(fun(A,bool),bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U))))))))))) -> (all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),U_0),s(fun(fun(A,bool),bool),S0))))) = s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),unions),s(fun(fun(A,bool),bool),S0)))))) # label(aUNIONS) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1412 (all Q97450 all P0 all F0 all G0 all S0 ((all S0 p(s(bool,i(s(fun(fun(Q97450,bool),bool),P0),s(fun(Q97450,bool),i(s(fun(fun(Q97450,bool),fun(Q97450,bool)),i(s(fun(fun(fun(Q97450,bool),bool),fun(fun(Q97450,bool),fun(Q97450,bool))),hull),s(fun(fun(Q97450,bool),bool),P0))),s(fun(Q97450,bool),S0))))))) & (all S0 all T0 s(bool,i(s(fun(fun(Q97450,bool),bool),i(s(fun(fun(Q97450,bool),fun(fun(Q97450,bool),bool)),subset),s(fun(Q97450,bool),i(s(fun(fun(Q97450,bool),fun(Q97450,bool)),i(s(fun(fun(Q97450,Q97450),fun(fun(Q97450,bool),fun(Q97450,bool))),image),s(fun(Q97450,Q97450),F0))),s(fun(Q97450,bool),S0))))),s(fun(Q97450,bool),T0))) = s(bool,i(s(fun(fun(Q97450,bool),bool),i(s(fun(fun(Q97450,bool),fun(fun(Q97450,bool),bool)),subset),s(fun(Q97450,bool),S0))),s(fun(Q97450,bool),i(s(fun(fun(Q97450,bool),fun(Q97450,bool)),i(s(fun(fun(Q97450,Q97450),fun(fun(Q97450,bool),fun(Q97450,bool))),image),s(fun(Q97450,Q97450),G0))),s(fun(Q97450,bool),T0)))))) & (all S0 (p(s(bool,i(s(fun(fun(Q97450,bool),bool),P0),s(fun(Q97450,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q97450,bool),bool),P0),s(fun(Q97450,bool),i(s(fun(fun(Q97450,bool),fun(Q97450,bool)),i(s(fun(fun(Q97450,Q97450),fun(fun(Q97450,bool),fun(Q97450,bool))),image),s(fun(Q97450,Q97450),G0))),s(fun(Q97450,bool),S0)))))))) & (all S0 (p(s(bool,i(s(fun(fun(Q97450,bool),bool),P0),s(fun(Q97450,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q97450,bool),bool),P0),s(fun(Q97450,bool),i(s(fun(fun(Q97450,bool),fun(Q97450,bool)),i(s(fun(fun(Q97450,Q97450),fun(fun(Q97450,bool),fun(Q97450,bool))),image),s(fun(Q97450,Q97450),F0))),s(fun(Q97450,bool),S0)))))))) -> s(fun(Q97450,bool),i(s(fun(fun(Q97450,bool),fun(Q97450,bool)),i(s(fun(fun(fun(Q97450,bool),bool),fun(fun(Q97450,bool),fun(Q97450,bool))),hull),s(fun(fun(Q97450,bool),bool),P0))),s(fun(Q97450,bool),i(s(fun(fun(Q97450,bool),fun(Q97450,bool)),i(s(fun(fun(Q97450,Q97450),fun(fun(Q97450,bool),fun(Q97450,bool))),image),s(fun(Q97450,Q97450),F0))),s(fun(Q97450,bool),S0))))) = s(fun(Q97450,bool),i(s(fun(fun(Q97450,bool),fun(Q97450,bool)),i(s(fun(fun(Q97450,Q97450),fun(fun(Q97450,bool),fun(Q97450,bool))),image),s(fun(Q97450,Q97450),F0))),s(fun(Q97450,bool),i(s(fun(fun(Q97450,bool),fun(Q97450,bool)),i(s(fun(fun(fun(Q97450,bool),bool),fun(fun(Q97450,bool),fun(Q97450,bool))),hull),s(fun(fun(Q97450,bool),bool),P0))),s(fun(Q97450,bool),S0))))))) # label(aHULLu_IMAGEu_GALOIS) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1413 (all A all P0 all Q0 (p(s(bool,P0)) | (all X p(s(bool,i(s(fun(A,bool),Q0),s(A,X))))) <-> (all X (p(s(bool,P0)) | p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))))) # label(aRIGHTu_ORu_FORALLu_THM) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1414 (all A all S0 s(fun(A,bool),empty) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),empty))),s(fun(A,bool),S0)))) # label(aINTERu_EMPTYu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1415 (all A all B all U_0 ((all S0 all T0 all GENR_PVARR_85 ((exists X exists Y exists V ((p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(bool,fun(prod(A,B),bool)),i(s(fun(prod(A,B),fun(bool,fun(prod(A,B),bool))),setspec),s(prod(A,B),GENR_PVARR_85))),s(bool,V))),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))))) <-> p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),U_0),s(fun(A,bool),S0))),s(fun(B,bool),T0))),s(prod(A,B),GENR_PVARR_85)))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(prod(A,B),bool),bool),finite),s(fun(prod(A,B),bool),i(s(fun(fun(prod(A,B),bool),fun(prod(A,B),bool)),gspec),s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),U_0),s(fun(A,bool),S0))),s(fun(B,bool),T0)))))))))))) # label(aFINITEu_PRODUCT) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1416 (all Q47336 all U_0 ((all S0 all T0 all GENR_PVARR_9 (p(s(bool,i(s(fun(fun(Q47336,bool),bool),i(s(fun(fun(Q47336,bool),fun(fun(Q47336,bool),bool)),i(s(fun(fun(fun(Q47336,bool),bool),fun(fun(Q47336,bool),fun(fun(Q47336,bool),bool))),U_0),s(fun(fun(Q47336,bool),bool),S0))),s(fun(Q47336,bool),T0))),s(fun(Q47336,bool),GENR_PVARR_9)))) <-> (exists X p(s(bool,i(s(fun(fun(Q47336,bool),bool),i(s(fun(bool,fun(fun(Q47336,bool),bool)),i(s(fun(fun(Q47336,bool),fun(bool,fun(fun(Q47336,bool),bool))),setspec),s(fun(Q47336,bool),GENR_PVARR_9))),s(bool,i(s(fun(fun(fun(Q47336,bool),bool),bool),i(s(fun(fun(Q47336,bool),fun(fun(fun(Q47336,bool),bool),bool)),in),s(fun(Q47336,bool),X))),s(fun(fun(Q47336,bool),bool),S0))))),s(fun(Q47336,bool),i(s(fun(fun(Q47336,bool),fun(Q47336,bool)),i(s(fun(fun(Q47336,bool),fun(fun(Q47336,bool),fun(Q47336,bool))),inter),s(fun(Q47336,bool),T0))),s(fun(Q47336,bool),X))))))))) -> (all S0 all T0 s(fun(Q47336,bool),i(s(fun(fun(fun(Q47336,bool),bool),fun(Q47336,bool)),unions),s(fun(fun(Q47336,bool),bool),i(s(fun(fun(fun(Q47336,bool),bool),fun(fun(Q47336,bool),bool)),gspec),s(fun(fun(Q47336,bool),bool),i(s(fun(fun(Q47336,bool),fun(fun(Q47336,bool),bool)),i(s(fun(fun(fun(Q47336,bool),bool),fun(fun(Q47336,bool),fun(fun(Q47336,bool),bool))),U_0),s(fun(fun(Q47336,bool),bool),S0))),s(fun(Q47336,bool),T0))))))) = s(fun(Q47336,bool),i(s(fun(fun(Q47336,bool),fun(Q47336,bool)),i(s(fun(fun(Q47336,bool),fun(fun(Q47336,bool),fun(Q47336,bool))),inter),s(fun(Q47336,bool),T0))),s(fun(Q47336,bool),i(s(fun(fun(fun(Q47336,bool),bool),fun(Q47336,bool)),unions),s(fun(fun(Q47336,bool),bool),S0)))))))) # label(aINTERu_UNIONSu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1417 (all Q4498 all Q4497 all P0 ((all P1 p(s(bool,i(s(fun(prod(Q4498,Q4497),bool),P0),s(prod(Q4498,Q4497),P1))))) <-> (all P1 all P2 p(s(bool,i(s(fun(prod(Q4498,Q4497),bool),P0),s(prod(Q4498,Q4497),i(s(fun(Q4497,prod(Q4498,Q4497)),i(s(fun(Q4498,fun(Q4497,prod(Q4498,Q4497))),c_),s(Q4498,P1))),s(Q4497,P2))))))))) # label(aFORALLu_PAIRu_THM) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1418 (all F0 all N0 s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,N0))),s(num,N0))))),s(fun(num,num),F0))) = s(num,i(s(fun(num,num),F0),s(num,N0)))) # label(aNSUMu_SINGu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1419 (all Q46704 s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),p1))),s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),p1))),s(fun(Q46704,bool),q))))) = s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),p1))),s(fun(Q46704,bool),q)))) # label(aUNIONu_ACIu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1420 (p(s(bool,p1)) -> (p(s(bool,q)) -> p(s(bool,r0)))) <-> (p(s(bool,p1)) & p(s(bool,q)) -> p(s(bool,r0))) # label(aIMPu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1421 (all X s(real,i(s(fun(real,real),realu_abs),s(real,X))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aPOWu_2u_SQRTu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1422 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),realu_inv),s(real,Y)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,i(s(fun(real,real),realu_inv),s(real,X)))))))) # label(aREALu_LTu_RINV) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1423 (all A all F0 all P0 all S0 ((all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) -> (all X all XI_ (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(A,Y) = s(A,i(s(fun(A,A),P0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0)))) & s(A,Y) = s(A,i(s(fun(A,A),P0),s(A,XI_))) -> s(A,X) = s(A,XI_))) & (exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(A,i(s(fun(A,A),P0),s(A,X))) = s(A,Y))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(A,A),P0),s(A,X))))),s(fun(A,bool),S0)))))) -> s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(fun(A,A),fun(A,real)),i(s(fun(fun(A,real),fun(fun(A,A),fun(A,real))),o),s(fun(A,real),F0))),s(fun(A,A),P0))))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))) # label(aSUMu_BIJECTION) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1424 (all A all F1 all F2 (s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))),injf),s(fun(num,fun(num,fun(A,bool))),F1))) = s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))),injf),s(fun(num,fun(num,fun(A,bool))),F2))) <-> s(fun(num,fun(num,fun(A,bool))),F2) = s(fun(num,fun(num,fun(A,bool))),F1))) # label(aINJFu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1425 (all B all A all U_1 ((all S0 all F0 all Y all GENR_PVARR_187 ((exists X exists V ((p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_187))),s(bool,V))),s(A,X)))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))),s(A,GENR_PVARR_187)))))) -> (all U_0 ((all S0 all F0 all G0 all Y s(real,i(s(fun(B,real),i(s(fun(fun(A,real),fun(B,real)),i(s(fun(fun(A,B),fun(fun(A,real),fun(B,real))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,real),fun(B,real)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,real),G0))),s(B,Y))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))))))),s(fun(A,real),G0)))) -> (all F0 all G0 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,bool),T0)))) -> s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),G0))) = s(real,i(s(fun(fun(B,real),real),i(s(fun(fun(B,bool),fun(fun(B,real),real)),sum),s(fun(B,bool),T0))),s(fun(B,real),i(s(fun(fun(A,real),fun(B,real)),i(s(fun(fun(A,B),fun(fun(A,real),fun(B,real))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,real),fun(B,real)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,real),G0))))))))))) # label(aSUMu_GROUP) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1426 (all N0 all X all Y (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,N0)))))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))))) # label(aINTu_POWu_LE2u_REV) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1427 (all X all Y p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),X))))))) # label(aTREALu_ADDu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1428 (all X all S0 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) -> (exists V (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))))))) = s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),i(s(fun(real,fun(fun(real,bool),fun(real,bool))),insert),s(real,X))),s(fun(real,bool),S0))))) & (s(fun(real,bool),empty) = s(fun(real,bool),S0) <-> p(s(bool,V))))))) # label(aSUPu_INSERTu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1429 (all N0 -p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,N0))))) # label(aLTu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1430 (all X all Y (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),X)))) | p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))))) # label(aTREALu_LEu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1431 (all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) <-> (exists K0 exists M0 (p(s(bool,i(s(fun(num,bool),odd),s(num,M0)))) & s(num,N0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,K0))))),s(num,M0))))))) # label(aEVENu_ODDu_DECOMPOSITION) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1432 (all X s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),intu_neg),s(int,X))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aINTu_NEGu_GE0) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1433 (all X all Y (s(int,X) != s(int,Y) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))))) # label(aINTu_LTu_LE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1434 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),suc),s(num,M0))))),s(num,N0))) = s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))) # label(aADDu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1435 (all A all U_0 ((all F0 all C0 all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,C0))) = s(real,i(s(fun(A,real),i(s(fun(real,fun(A,real)),i(s(fun(fun(A,real),fun(real,fun(A,real))),U_0),s(fun(A,real),F0))),s(real,C0))),s(A,X)))) -> (all F0 all C0 all S0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))),s(real,C0))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(real,fun(A,real)),i(s(fun(fun(A,real),fun(real,fun(A,real))),U_0),s(fun(A,real),F0))),s(real,C0)))))))) # label(aSUMu_RMUL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1436 (all B all A all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),S0))),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),T0)))))) <-> (exists U (s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),U))) = s(fun(B,bool),S0) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),U))),s(fun(A,bool),T0)))))))) # label(aSUBSETu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.48 1437 (all X s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,i(s(fun(int,int),intu_neg),s(int,X)))))) # label(aINTu_ADDu_RINV) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1438 (all Q4523 all Q4522 all P0 ((exists P1 exists P2 p(s(bool,i(s(fun(prod(Q4523,Q4522),bool),P0),s(prod(Q4523,Q4522),i(s(fun(Q4522,prod(Q4523,Q4522)),i(s(fun(Q4523,fun(Q4522,prod(Q4523,Q4522))),c_),s(Q4523,P1))),s(Q4522,P2))))))) <-> (exists P1 p(s(bool,i(s(fun(prod(Q4523,Q4522),bool),P0),s(prod(Q4523,Q4522),P1))))))) # label(aEXISTSu_PAIRu_THM) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1439 (all B all A all U_1 ((all S0 all F0 all Y all GENR_PVARR_167 ((exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_167))),s(bool,V))),s(A,X)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X)))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))),s(A,GENR_PVARR_167)))))) -> (all U_0 ((all S0 all F0 all G0 all Y s(num,i(s(fun(B,num),i(s(fun(fun(A,num),fun(B,num)),i(s(fun(fun(A,B),fun(fun(A,num),fun(B,num))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,num),fun(B,num)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,num),G0))),s(B,Y))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))))))),s(fun(A,num),G0)))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(fun(B,num),num),i(s(fun(fun(B,bool),fun(fun(B,num),num)),nsum),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,num),i(s(fun(fun(A,num),fun(B,num)),i(s(fun(fun(A,B),fun(fun(A,num),fun(B,num))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,num),fun(B,num)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,num),G0))))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),G0))))))))) # label(aNSUMu_IMAGEu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1440 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,X)))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))))) # label(aINTu_LEu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1441 (all C all B all A all F0 all G0 all L s(list(C),i(s(fun(list(B),list(C)),i(s(fun(fun(B,C),fun(list(B),list(C))),map0),s(fun(B,C),G0))),s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),L))))) = s(list(C),i(s(fun(list(A),list(C)),i(s(fun(fun(A,C),fun(list(A),list(C))),map0),s(fun(A,C),i(s(fun(fun(A,B),fun(A,C)),i(s(fun(fun(B,C),fun(fun(A,B),fun(A,C))),o),s(fun(B,C),G0))),s(fun(A,B),F0))))),s(list(A),L)))) # label(aMAPu_o) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1442 (all A ((all X (p(s(bool,i(s(fun(A,bool),p0),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),q0),s(A,X)))))) -> ((exists X p(s(bool,i(s(fun(A,bool),p0),s(A,X))))) -> (exists X p(s(bool,i(s(fun(A,bool),q0),s(A,X)))))))) # label(aMONOu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1443 (all M0 all N0 exists Q0 exists R0 exists V ((exists VI_ ((s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> p(s(bool,VI_))) & (exists VI_I_ ((p(s(bool,VI_I_)) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,R0))),s(num,N0)))) & s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,Q0))),s(num,N0))))),s(num,R0))) = s(num,M0)) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,VI_))),s(bool,V))),s(bool,VI_I_)))))))) & (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,Q0) & s(num,R0) = s(num,M0) <-> p(s(bool,V))))) # label(aDIVMODu_EXISTu_0) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1444 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))) -> (exists F0 exists G0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,X) = s(A,i(s(fun(B,A),G0),s(B,i(s(fun(A,B),F0),s(A,X))))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0)))))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(B,A),G0),s(B,Y))))),s(fun(A,bool),S0)))) & s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,i(s(fun(B,A),G0),s(B,Y))))))))))) # label(aCARDu_EQu_BIJECTIONS) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1445 (all A all Q84932 all P0 all L ((exists L0 (p(s(bool,i(s(fun(fun(prod(Q84932,Q84932),bool),bool),P0),s(fun(prod(Q84932,Q84932),bool),L0)))) & p(s(bool,i(s(fun(Q84932,bool),i(s(fun(fun(prod(Q84932,Q84932),bool),fun(Q84932,bool)),fl),s(fun(prod(Q84932,Q84932),bool),L0))),s(Q84932,x)))))) <-> p(s(bool,i(s(fun(Q84932,bool),i(s(fun(fun(prod(Q84932,Q84932),bool),fun(Q84932,bool)),fl),s(fun(prod(Q84932,Q84932),bool),i(s(fun(fun(fun(prod(Q84932,Q84932),bool),bool),fun(prod(Q84932,Q84932),bool)),unions),s(fun(fun(prod(Q84932,Q84932),bool),bool),P0))))),s(Q84932,x)))))) # label(aUNIONu_FL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1446 s(bool,b0) = s(bool,a0) -> (p(s(bool,a0)) -> p(s(bool,b0))) # label(aEQu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1447 (all X all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,Z0))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0))))),s(real,Y)))) # label(aREALu_LEu_SUBu_LADD) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1448 (all M0 all N0 all P0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0)))))) # label(aLTu_ADDu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1449 (all Q18624 (p(s(bool,i(s(fun(list(Q18624),bool),i(s(fun(fun(Q18624,bool),fun(list(Q18624),bool)),ex0),s(fun(Q18624,bool),p0))),s(list(Q18624),i(s(fun(list(Q18624),list(Q18624)),i(s(fun(Q18624,fun(list(Q18624),list(Q18624))),cons),s(Q18624,h0))),s(list(Q18624),t0)))))) <-> p(s(bool,i(s(fun(Q18624,bool),p0),s(Q18624,h0)))) | p(s(bool,i(s(fun(list(Q18624),bool),i(s(fun(fun(Q18624,bool),fun(list(Q18624),bool)),ex0),s(fun(Q18624,bool),p0))),s(list(Q18624),t0)))))) # label(aEXu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1450 (all Q74473 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q74473,bool),bool),finite),s(fun(Q74473,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(Q74473,bool),bool),i(s(fun(Q74473,fun(fun(Q74473,bool),bool)),in),s(Q74473,X))),s(fun(Q74473,bool),i(s(fun(fun(Q74473,bool),fun(Q74473,bool)),i(s(fun(fun(Q74473,bool),fun(fun(Q74473,bool),fun(Q74473,bool))),inter),s(fun(Q74473,bool),S0))),s(fun(Q74473,bool),T0)))))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(Q74473,real),F0),s(Q74473,X))))) & p(s(bool,i(s(fun(fun(Q74473,bool),bool),finite),s(fun(Q74473,bool),T0)))) -> s(real,i(s(fun(fun(Q74473,real),real),i(s(fun(fun(Q74473,bool),fun(fun(Q74473,real),real)),sum),s(fun(Q74473,bool),i(s(fun(fun(Q74473,bool),fun(Q74473,bool)),i(s(fun(fun(Q74473,bool),fun(fun(Q74473,bool),fun(Q74473,bool))),union),s(fun(Q74473,bool),S0))),s(fun(Q74473,bool),T0))))),s(fun(Q74473,real),F0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(Q74473,real),real),i(s(fun(fun(Q74473,bool),fun(fun(Q74473,real),real)),sum),s(fun(Q74473,bool),S0))),s(fun(Q74473,real),F0))))),s(real,i(s(fun(fun(Q74473,real),real),i(s(fun(fun(Q74473,bool),fun(fun(Q74473,real),real)),sum),s(fun(Q74473,bool),T0))),s(fun(Q74473,real),F0))))))) # label(aSUMu_UNIONu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1451 (all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,X)))) # label(aREALu_ADDu_LINV) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1452 (all A all U_0 ((all L all A5 all F0 ((all X all Y exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(A,A),bool),F0),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y))))))),s(bool,V)))) & (p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(A,fun(prod(A,A),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(prod(A,A),bool))),linseg),s(fun(prod(A,A),bool),L))),s(A,A5))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) | s(A,Y) = s(A,A5) & (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),i(s(fun(A,fun(prod(A,A),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(prod(A,A),bool))),linseg),s(fun(prod(A,A),bool),L))),s(A,A5))))),s(A,X)))) | s(A,X) = s(A,A5)) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(A,fun(fun(prod(A,A),bool),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(fun(prod(A,A),bool),bool))),U_0),s(fun(prod(A,A),bool),L))),s(A,A5))),s(fun(prod(A,A),bool),F0)))))) -> (all L all A5 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,A5)))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),i(s(fun(fun(fun(prod(A,A),bool),bool),fun(prod(A,A),bool)),gabs),s(fun(fun(prod(A,A),bool),bool),i(s(fun(A,fun(fun(prod(A,A),bool),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(fun(prod(A,A),bool),bool))),U_0),s(fun(prod(A,A),bool),L))),s(A,A5))))))),s(fun(prod(A,A),bool),L)))))))) # label(aEXTENDu_LINSEG) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1453 (all S0 all L all E0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,L))))))),s(real,E0)))))) & s(fun(real,bool),S0) != s(fun(real,bool),empty) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))),s(real,L))))))),s(real,E0)))))) # label(aREALu_INFu_ASCLOSE) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1454 (all T1 all T2 ((-p(s(bool,T2)) | -p(s(bool,T1)) <-> -(p(s(bool,T1)) & p(s(bool,T2)))) & (-(p(s(bool,T1)) | p(s(bool,T2))) <-> -p(s(bool,T2)) & -p(s(bool,T1))))) # label(aDEu_MORGANu_THM) # label(axiom) # label(non_clause). [assumption]. 14.41/14.49 1455 (all A all B all U_0 ((all S0 all F0 all OP all GENR_PVARR_142 ((exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_142))),s(bool,V))),s(A,X)))) & (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,i(s(fun(fun(B,fun(B,B)),B),neutral),s(fun(B,fun(B,B)),OP))) != s(B,i(s(fun(A,B),F0),s(A,X))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(B,fun(B,B)),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,fun(B,B)),fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(B,fun(B,B)),fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(B,fun(B,B)),OP))),s(A,GENR_PVARR_142)))))) -> (all S0 all F0 all OP s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,bool),fun(A,bool)))),support),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,bool),S0))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(B,fun(B,B)),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,fun(B,B)),fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(B,fun(B,B)),fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(B,fun(B,B)),OP)))))))) # label(asupport) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1456 (all A all B all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(fun(B,bool),bool))),inj),s(fun(A,B),F0))),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(fun(B,bool),bool))),surj),s(fun(A,B),F0))),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(fun(B,bool),bool))),bij),s(fun(A,B),F0))),s(fun(A,bool),S0))),s(fun(B,bool),T0)))))) # label(aBIJ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1457 (all X all XI_ all Y all YI_ (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,Y))),s(nadd,YI_)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,XI_)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Y))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,XI_))),s(nadd,YI_)))))))) # label(aNADDu_MULu_WELLDEF) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1458 (all A all B ((all X all Y (p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),p0),s(A,X))),s(B,Y)))) -> p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),q0),s(A,X))),s(B,Y)))))) -> (p(s(bool,i(s(fun(list(B),bool),i(s(fun(list(A),fun(list(B),bool)),i(s(fun(fun(A,fun(B,bool)),fun(list(A),fun(list(B),bool))),all2),s(fun(A,fun(B,bool)),p0))),s(list(A),l0))),s(list(B),li_0)))) -> p(s(bool,i(s(fun(list(B),bool),i(s(fun(list(A),fun(list(B),bool)),i(s(fun(fun(A,fun(B,bool)),fun(list(A),fun(list(B),bool))),all2),s(fun(A,fun(B,bool)),q0))),s(list(A),l0))),s(list(B),li_0))))))) # label(aMONOu_ALL2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1459 (all Q49425 all U_0 ((all S0 all GENR_PVARR_42 ((exists T0 p(s(bool,i(s(fun(fun(Q49425,bool),bool),i(s(fun(bool,fun(fun(Q49425,bool),bool)),i(s(fun(fun(Q49425,bool),fun(bool,fun(fun(Q49425,bool),bool))),setspec),s(fun(Q49425,bool),GENR_PVARR_42))),s(bool,i(s(fun(fun(fun(Q49425,bool),bool),bool),i(s(fun(fun(Q49425,bool),fun(fun(fun(Q49425,bool),bool),bool)),in),s(fun(Q49425,bool),T0))),s(fun(fun(Q49425,bool),bool),S0))))),s(fun(Q49425,bool),i(s(fun(fun(Q49425,bool),fun(Q49425,bool)),i(s(fun(fun(Q49425,bool),fun(fun(Q49425,bool),fun(Q49425,bool))),diff),s(fun(Q49425,bool),univ))),s(fun(Q49425,bool),T0))))))) <-> p(s(bool,i(s(fun(fun(Q49425,bool),bool),i(s(fun(fun(fun(Q49425,bool),bool),fun(fun(Q49425,bool),bool)),U_0),s(fun(fun(Q49425,bool),bool),S0))),s(fun(Q49425,bool),GENR_PVARR_42)))))) -> (all S0 s(fun(Q49425,bool),i(s(fun(fun(fun(Q49425,bool),bool),fun(Q49425,bool)),inters),s(fun(fun(Q49425,bool),bool),S0))) = s(fun(Q49425,bool),i(s(fun(fun(Q49425,bool),fun(Q49425,bool)),i(s(fun(fun(Q49425,bool),fun(fun(Q49425,bool),fun(Q49425,bool))),diff),s(fun(Q49425,bool),univ))),s(fun(Q49425,bool),i(s(fun(fun(fun(Q49425,bool),bool),fun(Q49425,bool)),unions),s(fun(fun(Q49425,bool),bool),i(s(fun(fun(fun(Q49425,bool),bool),fun(fun(Q49425,bool),bool)),gspec),s(fun(fun(Q49425,bool),bool),i(s(fun(fun(fun(Q49425,bool),bool),fun(fun(Q49425,bool),bool)),U_0),s(fun(fun(Q49425,bool),bool),S0)))))))))))) # label(aINTERSu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1460 (all X1 all X2 all Y (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),X2)))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),Y))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),X2))),s(prod(hreal,hreal),Y)))))))) # label(aTREALu_ADDu_WELLDEFR) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1461 (all Q71551 all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q71551,bool),bool),finite),s(fun(Q71551,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(Q71551,bool),bool),i(s(fun(Q71551,fun(fun(Q71551,bool),bool)),in),s(Q71551,X))),s(fun(Q71551,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(Q71551,real),F0),s(Q71551,X))))),s(real,i(s(fun(Q71551,real),G0),s(Q71551,X)))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(Q71551,real),real),i(s(fun(fun(Q71551,bool),fun(fun(Q71551,real),real)),sum),s(fun(Q71551,bool),S0))),s(fun(Q71551,real),F0))))),s(real,i(s(fun(fun(Q71551,real),real),i(s(fun(fun(Q71551,bool),fun(fun(Q71551,real),real)),sum),s(fun(Q71551,bool),S0))),s(fun(Q71551,real),G0)))))))) # label(aSUMu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1462 (all A all F0 all U all V (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),V)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) & -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V)))) -> s(num,i(s(fun(A,num),F0),s(A,X))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),U))),s(fun(A,bool),V))))),s(fun(A,num),F0))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),V))),s(fun(A,num),F0))))) # label(aNSUMu_UNIONu_LZERO) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1463 (all X all Y s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,Y))) = s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,Y))),s(nadd,X)))) # label(aNADDu_EQu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1464 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),even),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))) <-> s(bool,i(s(fun(num,bool),even),s(num,M0))) = s(bool,i(s(fun(num,bool),even),s(num,N0))))) # label(aEVENu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1465 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))))) # label(aLTEu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1466 (all X all Y (s(real,X) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))) <-> s(real,Y) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aREALu_EQu_ADDu_LCANCELu_0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1467 (all X s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,X)))) # label(aINTu_SUBu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1468 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,Z0)))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Z0)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y))))),s(int,Z0)))))) # label(aINTu_MINu_LT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1469 (all B all A all F0 ((all Y exists X s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y)) <-> p(s(bool,i(s(fun(fun(A,B),bool),onto),s(fun(A,B),F0)))))) # label(aONTO) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1470 (all S0 all A5 (s(fun(real,bool),S0) != s(fun(real,bool),empty) & p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) -> ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,A5))),s(real,X)))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,A5))),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))))))) # label(aREALu_LTu_INFu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1471 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y)))))))) # label(aINTu_LTu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1472 (all A all U_1 ((all Y s(bool,f0) = s(bool,i(s(fun(A,bool),U_1),s(A,Y)))) -> (all U_0 ((all X s(fun(A,bool),i(s(fun(A,fun(A,bool)),U_0),s(A,X))) = s(fun(A,bool),U_1)) -> p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),U_0)))))))) # label(aWFu_FALSE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1473 (all Q87171 all Q87170 ((all Z0 p(s(bool,i(s(fun(sum0(Q87171,Q87170),bool),p0),s(sum0(Q87171,Q87170),Z0))))) <-> (all X p(s(bool,i(s(fun(sum0(Q87171,Q87170),bool),p0),s(sum0(Q87171,Q87170),i(s(fun(Q87170,sum0(Q87171,Q87170)),inr),s(Q87170,X))))))) & (all X p(s(bool,i(s(fun(sum0(Q87171,Q87170),bool),p0),s(sum0(Q87171,Q87170),i(s(fun(Q87171,sum0(Q87171,Q87170)),inl),s(Q87171,X))))))))) # label(aFORALLu_SUMu_THM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1474 (all M0 all N0 s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),max),s(num,M0))),s(num,N0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,i(s(fun(num,int),intu_ofu_num),s(num,M0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0)))))) # label(aINTu_OFu_NUMu_MAX) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1475 (all A all Z all B all INLI_ all INRI_ exists FN ((all A5 s(Z,i(s(fun(sum0(A,B),Z),FN),s(sum0(A,B),i(s(fun(A,sum0(A,B)),inl),s(A,A5))))) = s(Z,i(s(fun(A,Z),INLI_),s(A,A5)))) & (all A5 s(Z,i(s(fun(sum0(A,B),Z),FN),s(sum0(A,B),i(s(fun(B,sum0(A,B)),inr),s(B,A5))))) = s(Z,i(s(fun(B,Z),INRI_),s(B,A5)))))) # label(asumu_RECURSION) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1476 (all A all F0 all P0 all S0 ((all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) -> (all X all XI_ (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(A,i(s(fun(A,A),P0),s(A,XI_))) = s(A,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0)))) & s(A,Y) = s(A,i(s(fun(A,A),P0),s(A,X))) -> s(A,X) = s(A,XI_))) & (exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(A,i(s(fun(A,A),P0),s(A,X))) = s(A,Y))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(A,A),P0),s(A,X))))),s(fun(A,bool),S0)))))) -> s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(fun(A,A),fun(A,num)),i(s(fun(fun(A,num),fun(fun(A,A),fun(A,num))),o),s(fun(A,num),F0))),s(fun(A,A),P0))))))) # label(aNSUMu_BIJECTION) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1477 (all M0 all N0 s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,M0))))),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,N0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) # label(aTREALu_OFu_NUMu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1478 (all A all H0 all T0 s(list(A),T0) = s(list(A),i(s(fun(list(A),list(A)),tl),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,H0))),s(list(A),T0)))))) # label(aSeq2o_TL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1479 (all X all Y all YI_ (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,Y))),s(nadd,YI_)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Y))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,YI_)))))))) # label(aNADDu_MULu_WELLDEFu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.50/14.49 1480 (all P all B all A all U_0 ((all L_L_ all F0 ((all S0 all T0 exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),F0),s(prod(fun(P,A),fun(fun(A,B),fun(P,B))),i(s(fun(fun(fun(A,B),fun(P,B)),prod(fun(P,A),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),prod(fun(P,A),fun(fun(A,B),fun(P,B))))),c_),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),T0))))))),s(bool,V)))) & (p(s(bool,V)) <-> (exists P0 exists G0 exists H0 ((all F1 all A5 s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F1))),s(P,A5))))),s(B,i(s(fun(A,B),F1),s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),G0),s(fun(A,B),F1))),s(P,A5))))))),s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),H0),s(fun(A,B),F1))),s(P,A5))))) = s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),T0),s(fun(A,B),F1))),s(P,A5)))) & (all F1 all G1 all A5 ((all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Z0))),s(A,i(s(fun(P,A),S0),s(P,A5)))))) -> s(B,i(s(fun(A,B),F1),s(A,Z0))) = s(B,i(s(fun(A,B),G1),s(A,Z0))))) -> s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),H0),s(fun(A,B),G1))),s(P,A5))) = s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),H0),s(fun(A,B),F1))),s(P,A5))) & s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),G0),s(fun(A,B),G1))),s(P,A5))) = s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),G0),s(fun(A,B),F1))),s(P,A5))) & s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F1))),s(P,A5))) = s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),G1))),s(P,A5))))) & (all F1 all A5 all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),G0),s(fun(A,B),F1))),s(P,A5)))))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F1))),s(P,A5)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,i(s(fun(P,A),S0),s(P,A5))))))))))))) <-> p(s(bool,i(s(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool),i(s(fun(fun(A,fun(A,bool)),fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool)),U_0),s(fun(A,fun(A,bool)),L_L_))),s(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),F0)))))) -> (all L_L_ all CLAUSES (p(s(bool,i(s(fun(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),bool),i(s(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),fun(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),bool)),all0),s(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),i(s(fun(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool),fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool)),gabs),s(fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool),i(s(fun(fun(A,fun(A,bool)),fun(fun(prod(fun(P,A),fun(fun(A,B),fun(P,B))),bool),bool)),U_0),s(fun(A,fun(A,bool)),L_L_))))))),s(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),CLAUSES)))) & p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),L_L_)))) -> (exists F0 all X s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),i(s(fun(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),fun(fun(A,B),fun(A,B))),casewise),s(list(prod(fun(P,A),fun(fun(A,B),fun(P,B)))),CLAUSES))),s(fun(A,B),F0))),s(A,X)))))))) # label(aWFu_RECu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.50/14.50 1481 (all M0 all N0 all P0 all Q0 all R0 all S0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,M0))),s(num,N0))))))),s(num,R0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,P0))),s(num,Q0))))))),s(num,S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,M0))),s(num,P0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,N0))),s(num,Q0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,R0))),s(num,S0)))))))))) # label(aDISTu_TRIANGLESu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.50 1482 (all X s(real,i(s(fun(real,real),realu_sgn),s(real,X))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,i(s(fun(real,real),realu_abs),s(real,X)))))) # label(aREALu_SGN) # label(axiom) # label(non_clause). [assumption]. 14.50/14.50 1483 (all Q19629 all Q19630 all U_0 ((all P0 all F0 all A5 s(bool,i(s(fun(Q19630,bool),i(s(fun(fun(Q19630,Q19629),fun(Q19630,bool)),i(s(fun(fun(Q19629,fun(Q19630,bool)),fun(fun(Q19630,Q19629),fun(Q19630,bool))),U_0),s(fun(Q19629,fun(Q19630,bool)),P0))),s(fun(Q19630,Q19629),F0))),s(Q19630,A5))) = s(bool,i(s(fun(Q19630,bool),i(s(fun(Q19629,fun(Q19630,bool)),P0),s(Q19629,i(s(fun(Q19630,Q19629),F0),s(Q19630,A5))))),s(Q19630,A5)))) -> (all P0 all F0 all L s(bool,i(s(fun(list(Q19630),bool),i(s(fun(list(Q19629),fun(list(Q19630),bool)),i(s(fun(fun(Q19629,fun(Q19630,bool)),fun(list(Q19629),fun(list(Q19630),bool))),all2),s(fun(Q19629,fun(Q19630,bool)),P0))),s(list(Q19629),i(s(fun(list(Q19630),list(Q19629)),i(s(fun(fun(Q19630,Q19629),fun(list(Q19630),list(Q19629))),map0),s(fun(Q19630,Q19629),F0))),s(list(Q19630),L))))),s(list(Q19630),L))) = s(bool,i(s(fun(list(Q19630),bool),i(s(fun(fun(Q19630,bool),fun(list(Q19630),bool)),all0),s(fun(Q19630,bool),i(s(fun(fun(Q19630,Q19629),fun(Q19630,bool)),i(s(fun(fun(Q19629,fun(Q19630,bool)),fun(fun(Q19630,Q19629),fun(Q19630,bool))),U_0),s(fun(Q19629,fun(Q19630,bool)),P0))),s(fun(Q19630,Q19629),F0))))),s(list(Q19630),L)))))) # label(aALL2u_MAP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.50 1484 (all X all XI_ ((p(s(bool,X)) <-> p(s(bool,X)) & p(s(bool,XI_))) <-> (p(s(bool,X)) -> p(s(bool,XI_))))) # label(aIMPu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.50/14.50 1485 (all Q50120 all Q50121 all F0 all S0 all T0 ((all X (p(s(bool,i(s(fun(fun(Q50121,bool),bool),i(s(fun(Q50121,fun(fun(Q50121,bool),bool)),in),s(Q50121,X))),s(fun(Q50121,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q50120,bool),bool),i(s(fun(Q50120,fun(fun(Q50120,bool),bool)),in),s(Q50120,i(s(fun(Q50121,Q50120),F0),s(Q50121,X))))),s(fun(Q50120,bool),T0)))))) -> ((all X all Y (s(Q50120,i(s(fun(Q50121,Q50120),F0),s(Q50121,Y))) = s(Q50120,i(s(fun(Q50121,Q50120),F0),s(Q50121,X))) & p(s(bool,i(s(fun(fun(Q50121,bool),bool),i(s(fun(Q50121,fun(fun(Q50121,bool),bool)),in),s(Q50121,Y))),s(fun(Q50121,bool),S0)))) & p(s(bool,i(s(fun(fun(Q50121,bool),bool),i(s(fun(Q50121,fun(fun(Q50121,bool),bool)),in),s(Q50121,X))),s(fun(Q50121,bool),S0)))) -> s(Q50121,X) = s(Q50121,Y))) & (all Y (p(s(bool,i(s(fun(fun(Q50120,bool),bool),i(s(fun(Q50120,fun(fun(Q50120,bool),bool)),in),s(Q50120,Y))),s(fun(Q50120,bool),T0)))) -> (exists X (s(Q50120,i(s(fun(Q50121,Q50120),F0),s(Q50121,X))) = s(Q50120,Y) & p(s(bool,i(s(fun(fun(Q50121,bool),bool),i(s(fun(Q50121,fun(fun(Q50121,bool),bool)),in),s(Q50121,X))),s(fun(Q50121,bool),S0)))))))) <-> (exists G0 ((all Y (p(s(bool,i(s(fun(fun(Q50120,bool),bool),i(s(fun(Q50120,fun(fun(Q50120,bool),bool)),in),s(Q50120,Y))),s(fun(Q50120,bool),T0)))) -> s(Q50120,Y) = s(Q50120,i(s(fun(Q50121,Q50120),F0),s(Q50121,i(s(fun(Q50120,Q50121),G0),s(Q50120,Y))))))) & (all X (p(s(bool,i(s(fun(fun(Q50121,bool),bool),i(s(fun(Q50121,fun(fun(Q50121,bool),bool)),in),s(Q50121,X))),s(fun(Q50121,bool),S0)))) -> s(Q50121,i(s(fun(Q50120,Q50121),G0),s(Q50120,i(s(fun(Q50121,Q50120),F0),s(Q50121,X))))) = s(Q50121,X))) & (all Y (p(s(bool,i(s(fun(fun(Q50120,bool),bool),i(s(fun(Q50120,fun(fun(Q50120,bool),bool)),in),s(Q50120,Y))),s(fun(Q50120,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q50121,bool),bool),i(s(fun(Q50121,fun(fun(Q50121,bool),bool)),in),s(Q50121,i(s(fun(Q50120,Q50121),G0),s(Q50120,Y))))),s(fun(Q50121,bool),S0))))))))))) # label(aBIJECTIVEu_ONu_LEFTu_RIGHTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1486 (all X (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> s(int,X) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(int,num),numu_ofu_int),s(int,X))))))) # label(aINTu_OFu_NUMu_OFu_INT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1487 (all X all Y all Z0 (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,Y))),s(nadd,Z0)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Y))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Z0)))))))) # label(aNADDu_LEu_LMUL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1488 (all A all L ((all X all Y all Z0 (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,Z0)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Z0)))))))) & (all P0 ((exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) & (all X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))))) -> (exists Y ((all Z0 (p(s(bool,i(s(fun(A,bool),P0),s(A,Z0)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,Z0)))))))) & p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))))))) & (all X all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,Y)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) | p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))))) & (all X all Y (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))) -> s(A,Y) = s(A,X))) & (all X (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,X)))))))) <-> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))))) # label(awoset) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1489 (all Q47938 all Q47939 all F0 all S0 ((all Y (p(s(bool,i(s(fun(fun(Q47938,bool),bool),i(s(fun(Q47938,fun(fun(Q47938,bool),bool)),in),s(Q47938,Y))),s(fun(Q47938,bool),i(s(fun(fun(Q47939,bool),fun(Q47938,bool)),i(s(fun(fun(Q47939,Q47938),fun(fun(Q47939,bool),fun(Q47938,bool))),image),s(fun(Q47939,Q47938),F0))),s(fun(Q47939,bool),S0)))))) -> p(s(bool,i(s(fun(Q47938,bool),p0),s(Q47938,Y)))))) <-> (all X (p(s(bool,i(s(fun(fun(Q47939,bool),bool),i(s(fun(Q47939,fun(fun(Q47939,bool),bool)),in),s(Q47939,X))),s(fun(Q47939,bool),S0)))) -> p(s(bool,i(s(fun(Q47938,bool),p0),s(Q47938,i(s(fun(Q47939,Q47938),F0),s(Q47939,X)))))))))) # label(aFORALLu_INu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1490 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,M0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))))) # label(aREALu_OFu_NUMu_LT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1491 (all Q44133 all U_0 ((all P0 all V (p(s(bool,i(s(fun(Q44133,bool),i(s(fun(fun(Q44133,bool),fun(Q44133,bool)),U_0),s(fun(Q44133,bool),P0))),s(Q44133,V)))) <-> (exists Y p(s(bool,i(s(fun(Q44133,bool),i(s(fun(bool,fun(Q44133,bool)),i(s(fun(Q44133,fun(bool,fun(Q44133,bool))),setspec),s(Q44133,V))),s(bool,i(s(fun(Q44133,bool),P0),s(Q44133,Y))))),s(Q44133,Y))))))) -> (all P0 all X s(bool,i(s(fun(fun(Q44133,bool),bool),i(s(fun(Q44133,fun(fun(Q44133,bool),bool)),in),s(Q44133,X))),s(fun(Q44133,bool),i(s(fun(fun(Q44133,bool),fun(Q44133,bool)),gspec),s(fun(Q44133,bool),i(s(fun(fun(Q44133,bool),fun(Q44133,bool)),U_0),s(fun(Q44133,bool),P0))))))) = s(bool,i(s(fun(Q44133,bool),P0),s(Q44133,X)))))) # label(aINu_ELIMu_THMu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1492 (all B all P all A all U_1 ((all T0 all F0 all X s(B,i(s(fun(A,B),F0),s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),T0),s(fun(A,B),F0))),s(P,X))))) = s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,A)),fun(fun(A,B),fun(P,B))),U_1),s(fun(fun(A,B),fun(P,A)),T0))),s(fun(A,B),F0))),s(P,X)))) -> (all U_0 ((all T0 all F0 s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,A)),fun(fun(A,B),fun(P,B))),U_1),s(fun(fun(A,B),fun(P,A)),T0))),s(fun(A,B),F0))) = s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,A)),fun(fun(A,B),fun(P,B))),U_0),s(fun(fun(A,B),fun(P,A)),T0))),s(fun(A,B),F0)))) -> (all L_L_ all P0 all S0 all T0 (p(s(bool,i(s(fun(fun(fun(A,B),fun(P,A)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,A)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,A)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,A)),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,A)),T0)))) & (all F0 all A5 (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,A5)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),T0),s(fun(A,B),F0))),s(P,A5))))),s(A,i(s(fun(P,A),S0),s(P,A5)))))))) -> p(s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,A)),fun(fun(A,B),fun(P,B))),U_0),s(fun(fun(A,B),fun(P,A)),T0)))))))))))) # label(aADMISSIBLEu_NEST) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1493 (all Q83945 all X (p(s(bool,i(s(fun(Q83945,bool),i(s(fun(fun(fun(Q83945,bool),bool),fun(Q83945,bool)),unions),s(fun(fun(Q83945,bool),bool),p0))),s(Q83945,X)))) <-> (exists P0 (p(s(bool,i(s(fun(fun(Q83945,bool),bool),p0),s(fun(Q83945,bool),P0)))) & p(s(bool,i(s(fun(Q83945,bool),P0),s(Q83945,X)))))))) # label(aUNIONSu_PRED) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1494 (all B all A s(A,i(s(fun(sum0(A,B),A),outl),s(sum0(A,B),i(s(fun(A,sum0(A,B)),inl),s(A,x))))) = s(A,x)) # label(aOUTL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1495 (all A all S0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),S0))))) # label(aSUBSETu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1496 (all A all L s(list(A),L) = s(list(A),i(s(fun(list(A),list(A)),reverse),s(list(A),i(s(fun(list(A),list(A)),reverse),s(list(A),L)))))) # label(aREVERSEu_REVERSE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1497 (all R0 ((all X p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,X))),s(num,X))))) & (all X all Y all Z0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,X))),s(num,Y)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,Y))),s(num,Z0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,X))),s(num,Z0)))))) & (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,N0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))) -> (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),R0),s(num,M0))),s(num,N0)))))))) # label(aTRANSITIVEu_STEPWISEu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1498 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y)))))) # label(aREALu_SUBu_LT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1499 (all N0 s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),numeral),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,N0))))))) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,N0)))))) # label(aBIT1u_THM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1500 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y)))))))) # label(aINTu_LTEu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1501 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (exists B0 all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,M0))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))))))) # label(aNADDu_MULu_LINVu_LEMMA8) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1502 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),bit1),s(num,N0))))),s(num,u_0))) = s(num,u_0)) # label(aARITHu_MULTu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1503 (all U_0 ((all X all I0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0)))) -> (all X all N0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),suc),s(num,N0)))))))))) # label(aSUMu_GPu_BASIC) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1504 (all N0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aREALu_OFu_NUMu_SUC) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1505 (all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,X)) # label(aREALu_SUBu_RZERO) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1506 (all T1 all T2 all T3 (p(s(bool,T1)) & p(s(bool,T3)) & p(s(bool,T2)) <-> p(s(bool,T3)) & p(s(bool,T2)) & p(s(bool,T1)))) # label(aCONJu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1507 (all N0 -p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,u_0))),s(num,i(s(fun(num,num),bit1),s(num,N0))))))) # label(aARITHu_GTu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1508 (all M all N s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))) = s(num,i(s(fun(fun(finite_sum(M,N),bool),num),dimindex),s(fun(finite_sum(M,N),bool),univ)))) # label(aDIMINDEXu_FINITEu_SUM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1509 (all A all B all S0 all T0 ((exists F0 exists G0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0)))) & s(A,i(s(fun(B,A),G0),s(B,i(s(fun(A,B),F0),s(A,X))))) = s(A,X))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(B,A),G0),s(B,Y))))),s(fun(A,bool),S0)))) & s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,i(s(fun(B,A),G0),s(B,Y))))))))) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))))) # label(aEQu_Cu_BIJECTIONS) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1510 (all Q72035 all F0 all S0 (p(s(bool,i(s(fun(fun(Q72035,bool),bool),finite),s(fun(Q72035,bool),S0)))) & s(real,i(s(fun(fun(Q72035,real),real),i(s(fun(fun(Q72035,bool),fun(fun(Q72035,real),real)),sum),s(fun(Q72035,bool),S0))),s(fun(Q72035,real),F0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & (all X (p(s(bool,i(s(fun(fun(Q72035,bool),bool),i(s(fun(Q72035,fun(fun(Q72035,bool),bool)),in),s(Q72035,X))),s(fun(Q72035,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(Q72035,real),F0),s(Q72035,X)))))))) -> (all X (p(s(bool,i(s(fun(fun(Q72035,bool),bool),i(s(fun(Q72035,fun(fun(Q72035,bool),bool)),in),s(Q72035,X))),s(fun(Q72035,bool),S0)))) -> s(real,i(s(fun(Q72035,real),F0),s(Q72035,X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) # label(aSUMu_POSu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1511 (all N0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(num,N0))))))) # label(aREALu_LEu_POW2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1512 (all Q49088 all Q49087 all Q49068 all U_1 ((all P0 all F0 all GENR_PVARR_32 ((exists A5 exists V ((p(s(bool,V)) <-> (exists X exists Y (p(s(bool,i(s(fun(fun(Q49068,bool),bool),i(s(fun(Q49068,fun(fun(Q49068,bool),bool)),in),s(Q49068,A5))),s(fun(Q49068,bool),i(s(fun(Q49087,fun(Q49068,bool)),i(s(fun(Q49088,fun(Q49087,fun(Q49068,bool))),F0),s(Q49088,X))),s(Q49087,Y)))))) & p(s(bool,i(s(fun(Q49087,bool),i(s(fun(Q49088,fun(Q49087,bool)),P0),s(Q49088,X))),s(Q49087,Y))))))) & p(s(bool,i(s(fun(Q49068,bool),i(s(fun(bool,fun(Q49068,bool)),i(s(fun(Q49068,fun(bool,fun(Q49068,bool))),setspec),s(Q49068,GENR_PVARR_32))),s(bool,V))),s(Q49068,A5)))))) <-> p(s(bool,i(s(fun(Q49068,bool),i(s(fun(fun(Q49088,fun(Q49087,fun(Q49068,bool))),fun(Q49068,bool)),i(s(fun(fun(Q49088,fun(Q49087,bool)),fun(fun(Q49088,fun(Q49087,fun(Q49068,bool))),fun(Q49068,bool))),U_1),s(fun(Q49088,fun(Q49087,bool)),P0))),s(fun(Q49088,fun(Q49087,fun(Q49068,bool))),F0))),s(Q49068,GENR_PVARR_32)))))) -> (all U_0 ((all P0 all F0 all GENR_PVARR_31 (p(s(bool,i(s(fun(fun(Q49068,bool),bool),i(s(fun(fun(Q49088,fun(Q49087,fun(Q49068,bool))),fun(fun(Q49068,bool),bool)),i(s(fun(fun(Q49088,fun(Q49087,bool)),fun(fun(Q49088,fun(Q49087,fun(Q49068,bool))),fun(fun(Q49068,bool),bool))),U_0),s(fun(Q49088,fun(Q49087,bool)),P0))),s(fun(Q49088,fun(Q49087,fun(Q49068,bool))),F0))),s(fun(Q49068,bool),GENR_PVARR_31)))) <-> (exists X exists Y p(s(bool,i(s(fun(fun(Q49068,bool),bool),i(s(fun(bool,fun(fun(Q49068,bool),bool)),i(s(fun(fun(Q49068,bool),fun(bool,fun(fun(Q49068,bool),bool))),setspec),s(fun(Q49068,bool),GENR_PVARR_31))),s(bool,i(s(fun(Q49087,bool),i(s(fun(Q49088,fun(Q49087,bool)),P0),s(Q49088,X))),s(Q49087,Y))))),s(fun(Q49068,bool),i(s(fun(Q49087,fun(Q49068,bool)),i(s(fun(Q49088,fun(Q49087,fun(Q49068,bool))),F0),s(Q49088,X))),s(Q49087,Y))))))))) -> (all P0 all F0 s(fun(Q49068,bool),i(s(fun(fun(Q49068,bool),fun(Q49068,bool)),gspec),s(fun(Q49068,bool),i(s(fun(fun(Q49088,fun(Q49087,fun(Q49068,bool))),fun(Q49068,bool)),i(s(fun(fun(Q49088,fun(Q49087,bool)),fun(fun(Q49088,fun(Q49087,fun(Q49068,bool))),fun(Q49068,bool))),U_1),s(fun(Q49088,fun(Q49087,bool)),P0))),s(fun(Q49088,fun(Q49087,fun(Q49068,bool))),F0))))) = s(fun(Q49068,bool),i(s(fun(fun(fun(Q49068,bool),bool),fun(Q49068,bool)),unions),s(fun(fun(Q49068,bool),bool),i(s(fun(fun(fun(Q49068,bool),bool),fun(fun(Q49068,bool),bool)),gspec),s(fun(fun(Q49068,bool),bool),i(s(fun(fun(Q49088,fun(Q49087,fun(Q49068,bool))),fun(fun(Q49068,bool),bool)),i(s(fun(fun(Q49088,fun(Q49087,bool)),fun(fun(Q49088,fun(Q49087,fun(Q49068,bool))),fun(fun(Q49068,bool),bool))),U_0),s(fun(Q49088,fun(Q49087,bool)),P0))),s(fun(Q49088,fun(Q49087,fun(Q49068,bool))),F0)))))))))))) # label(aUNIONSu_GSPECu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1513 (all A all S0 all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),unions),s(fun(fun(A,bool),bool),S0)))))) <-> (exists T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T0))),s(fun(fun(A,bool),bool),S0)))))))) # label(aINu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1514 (all A5 all B0 all C0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,A5))),s(int,B0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,B0))),s(int,C0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,A5))),s(int,C0)))) # label(aINTu_SUBu_TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1515 (all B all A all T0 all S0 all F0 ((all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,i(s(fun(A,B),F0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,Y) = s(A,X))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0)))))) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(fun(B,bool),bool))),inj),s(fun(A,B),F0))),s(fun(A,bool),S0))),s(fun(B,bool),T0)))))) # label(aINJ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1516 (all S0 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) & s(fun(real,bool),empty) != s(fun(real,bool),S0) -> (exists B0 (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,B0))),s(fun(real,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))))))) # label(aSUPu_FINITEu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1517 (all B all A all F0 all G0 (s(fun(A,B),F0) = s(fun(A,B),G0) <-> (all X s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),G0),s(A,X)))))) # label(aFUNu_EQu_THM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1518 (all A all B all P0 ((all X ((all Y all XI_ (p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y)))) & p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,XI_)))) -> s(B,XI_) = s(B,Y))) & (exists Y p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y))))))) <-> (exists F0 all X all Y (p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y)))) <-> s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y))))) # label(aUNIQUEu_SKOLEMu_ALT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.52 1519 (all Q18985 all Q18984 all Q18983 s(Q18983,i(s(fun(Q18983,Q18983),i(s(fun(list(Q18984),fun(Q18983,Q18983)),i(s(fun(list(Q18985),fun(list(Q18984),fun(Q18983,Q18983))),i(s(fun(fun(Q18985,fun(Q18984,fun(Q18983,Q18983))),fun(list(Q18985),fun(list(Q18984),fun(Q18983,Q18983)))),itlist2),s(fun(Q18985,fun(Q18984,fun(Q18983,Q18983))),f))),s(list(Q18985),i(s(fun(list(Q18985),list(Q18985)),i(s(fun(Q18985,fun(list(Q18985),list(Q18985))),cons),s(Q18985,h1))),s(list(Q18985),t1))))),s(list(Q18984),i(s(fun(list(Q18984),list(Q18984)),i(s(fun(Q18984,fun(list(Q18984),list(Q18984))),cons),s(Q18984,h2))),s(list(Q18984),t2))))),s(Q18983,b0))) = s(Q18983,i(s(fun(Q18983,Q18983),i(s(fun(Q18984,fun(Q18983,Q18983)),i(s(fun(Q18985,fun(Q18984,fun(Q18983,Q18983))),f),s(Q18985,h1))),s(Q18984,h2))),s(Q18983,i(s(fun(Q18983,Q18983),i(s(fun(list(Q18984),fun(Q18983,Q18983)),i(s(fun(list(Q18985),fun(list(Q18984),fun(Q18983,Q18983))),i(s(fun(fun(Q18985,fun(Q18984,fun(Q18983,Q18983))),fun(list(Q18985),fun(list(Q18984),fun(Q18983,Q18983)))),itlist2),s(fun(Q18985,fun(Q18984,fun(Q18983,Q18983))),f))),s(list(Q18985),t1))),s(list(Q18984),t2))),s(Q18983,b0)))))) # label(aITLIST2u_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1520 (all B all A all S0 all T0 all F0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,bool),T0)))) & s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) -> ((all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> (exists X (s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))))) <-> (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) -> s(A,Y) = s(A,X)))))) # label(aSURJECTIVEu_IFFu_INJECTIVEu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1521 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,M0))),s(num,N0))))))),s(num,P0)))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0)))))))) # label(aDISTu_LEu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1522 (all X all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Y))),s(real,Z0)))))) # label(aREALu_LTu_RADD) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1523 (all P0 ((all A01 all A10 all A20 all A30 all A40 all A5 all A6 all A7 p(s(bool,i(s(fun(char,bool),P0),s(char,i(s(fun(bool,char),i(s(fun(bool,fun(bool,char)),i(s(fun(bool,fun(bool,fun(bool,char))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,char)))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,char))))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,char)))))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,char))))))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,char)))))))),ascii),s(bool,A01))),s(bool,A10))),s(bool,A20))),s(bool,A30))),s(bool,A40))),s(bool,A5))),s(bool,A6))),s(bool,A7))))))) -> (all X p(s(bool,i(s(fun(char,bool),P0),s(char,X))))))) # label(acharu_INDUCT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1524 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),i(s(fun(bool,fun(int,fun(int,int))),cond),s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y))))),s(int,Y))),s(int,X)))) # label(aINTu_MAX) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1525 (all A all B all U_2 ((all T0 all R0 all I0 all GENR_PVARR_164 (p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),i(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,fun(B,bool)))),U_2),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0))),s(B,GENR_PVARR_164)))) <-> (exists J0 exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),R0),s(A,I0))),s(B,J0))))) & p(s(bool,i(s(fun(B,bool),i(s(fun(bool,fun(B,bool)),i(s(fun(B,fun(bool,fun(B,bool))),setspec),s(B,GENR_PVARR_164))),s(bool,V))),s(B,J0)))))))) -> (all U_1 ((all T0 all R0 all I0 s(num,i(s(fun(A,num),i(s(fun(fun(A,fun(B,bool)),fun(A,num)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,num))),U_1),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0))) = s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),gspec),s(fun(B,bool),i(s(fun(A,fun(B,bool)),i(s(fun(fun(A,fun(B,bool)),fun(A,fun(B,bool))),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,fun(B,bool)))),U_2),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))),s(A,I0)))))))) -> (all U_0 ((all S0 all R0 all J0 all GENR_PVARR_163 (p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,fun(B,bool)),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(B,fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),R0))),s(B,J0))),s(A,GENR_PVARR_163)))) <-> (exists I0 exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),R0),s(A,I0))),s(B,J0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_163))),s(bool,V))),s(A,I0)))))))) -> (all R0 all S0 all T0 all K0 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & (all J0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),T0)))) -> s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,fun(B,bool)),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(B,fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),R0))),s(B,J0))))))) = s(num,K0))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,K0))),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(fun(A,fun(B,bool)),fun(A,num)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,bool)),fun(A,num))),U_1),s(fun(B,bool),T0))),s(fun(A,fun(B,bool)),R0))))))))))))) # label(aNSUMu_MULTICOUNT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1526 (all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,u_0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,u_0))),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_GEu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1527 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aMULTu_SUC) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1528 (all M0 all N0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> (exists Q0 exists R0 (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,Q0))),s(num,N0))))),s(num,R0))) = s(num,M0) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,R0))),s(num,N0)))))))) # label(aDIVMODu_EXIST) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1529 (all Q50345 all Q50349 all Q50350 all P0 all F0 all G0 ((all X all Y (s(Q50349,i(s(fun(Q50350,Q50349),G0),s(Q50350,X))) = s(Q50349,i(s(fun(Q50350,Q50349),G0),s(Q50350,Y))) & p(s(bool,i(s(fun(Q50350,bool),P0),s(Q50350,Y)))) & p(s(bool,i(s(fun(Q50350,bool),P0),s(Q50350,X)))) -> s(Q50345,i(s(fun(Q50350,Q50345),F0),s(Q50350,X))) = s(Q50345,i(s(fun(Q50350,Q50345),F0),s(Q50350,Y))))) <-> (exists H0 all X (p(s(bool,i(s(fun(Q50350,bool),P0),s(Q50350,X)))) -> s(Q50345,i(s(fun(Q50349,Q50345),H0),s(Q50349,i(s(fun(Q50350,Q50349),G0),s(Q50350,X))))) = s(Q50345,i(s(fun(Q50350,Q50345),F0),s(Q50350,X))))))) # label(aFUNCTIONu_FACTORSu_LEFTu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1530 (all A all N all X all Y (s(cart(A,N),Y) = s(cart(A,N),X) <-> (all I0 s(A,i(s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),d_),s(cart(A,N),X))),s(num,I0))) = s(A,i(s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),d_),s(cart(A,N),Y))),s(num,I0)))))) # label(aCARTu_EQu_FULL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1531 (all A s(recspace(A),i(s(fun(fun(num,fun(A,bool)),recspace(A)),u_mku_rec),s(fun(num,fun(A,bool)),zbot))) = s(recspace(A),bottom)) # label(aBOTTOM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1532 (all M0 all N0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,i(s(fun(num,real),realu_ofu_num),s(num,M0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),min),s(num,M0))),s(num,N0)))))) # label(aREALu_OFu_NUMu_MIN) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1533 (all X all Y (s(real,i(s(fun(real,real),realu_inv),s(real,X))) = s(real,i(s(fun(real,real),realu_inv),s(real,Y))) <-> s(real,Y) = s(real,X))) # label(aREALu_EQu_INV2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1534 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) | s(num,N0) = s(num,M0))) # label(aSsrnato_lequ_eqVlt) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1535 (all C all A all B all OP (p(s(bool,i(s(fun(fun(C,fun(C,C)),bool),monoidal),s(fun(C,fun(C,C)),OP)))) -> (all F0 all G0 all S0 ((all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,X) = s(A,Y))) -> s(C,i(s(fun(fun(B,C),C),i(s(fun(fun(B,bool),fun(fun(B,C),C)),i(s(fun(fun(C,fun(C,C)),fun(fun(B,bool),fun(fun(B,C),C))),iterate),s(fun(C,fun(C,C)),OP))),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,C),G0))) = s(C,i(s(fun(fun(A,C),C),i(s(fun(fun(A,bool),fun(fun(A,C),C)),i(s(fun(fun(C,fun(C,C)),fun(fun(A,bool),fun(fun(A,C),C))),iterate),s(fun(C,fun(C,C)),OP))),s(fun(A,bool),S0))),s(fun(A,C),i(s(fun(fun(A,B),fun(A,C)),i(s(fun(fun(B,C),fun(fun(A,B),fun(A,C))),o),s(fun(B,C),G0))),s(fun(A,B),F0))))))))) # label(aITERATEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1536 (all M0 all N0 all Q0 all R0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,R0))),s(num,N0)))) & s(num,M0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,Q0))),s(num,N0))))),s(num,R0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))) = s(num,R0) & s(num,Q0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))))) # label(aDIVMODu_UNIQ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1537 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,N0)))))) # label(aEXPu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1538 (all Q79444 all Q79442 all Q79441 all Q79451 all U_0 ((all Y s(bool,t) = s(bool,i(s(fun(Q79451,bool),U_0),s(Q79451,Y)))) -> (all CLAUSES all C0 all X (s(Q79451,i(s(fun(Q79441,Q79451),i(s(fun(Q79442,fun(Q79441,Q79451)),i(s(fun(list(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),fun(Q79442,fun(Q79441,Q79451))),casewise),s(list(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),CLAUSES))),s(Q79442,C0))),s(Q79441,X))) = s(Q79451,i(s(fun(fun(Q79451,bool),Q79451),h_),s(fun(Q79451,bool),U_0))) & -(exists S0 exists T0 exists A5 (s(Q79441,i(s(fun(Q79444,Q79441),S0),s(Q79444,A5))) = s(Q79441,X) & p(s(bool,i(s(fun(list(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),bool),i(s(fun(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451))),fun(list(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),bool)),mem),s(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451))),i(s(fun(fun(Q79442,fun(Q79444,Q79451)),prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),i(s(fun(fun(Q79444,Q79441),fun(fun(Q79442,fun(Q79444,Q79451)),prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451))))),c_),s(fun(Q79444,Q79441),S0))),s(fun(Q79442,fun(Q79444,Q79451)),T0))))),s(list(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),CLAUSES)))))) | (exists S0 exists T0 exists A5 (s(Q79451,i(s(fun(Q79444,Q79451),i(s(fun(Q79442,fun(Q79444,Q79451)),T0),s(Q79442,C0))),s(Q79444,A5))) = s(Q79451,i(s(fun(Q79441,Q79451),i(s(fun(Q79442,fun(Q79441,Q79451)),i(s(fun(list(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),fun(Q79442,fun(Q79441,Q79451))),casewise),s(list(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),CLAUSES))),s(Q79442,C0))),s(Q79441,X))) & s(Q79441,X) = s(Q79441,i(s(fun(Q79444,Q79441),S0),s(Q79444,A5))) & p(s(bool,i(s(fun(list(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),bool),i(s(fun(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451))),fun(list(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),bool)),mem),s(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451))),i(s(fun(fun(Q79442,fun(Q79444,Q79451)),prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),i(s(fun(fun(Q79444,Q79441),fun(fun(Q79442,fun(Q79444,Q79451)),prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451))))),c_),s(fun(Q79444,Q79441),S0))),s(fun(Q79442,fun(Q79444,Q79451)),T0))))),s(list(prod(fun(Q79444,Q79441),fun(Q79442,fun(Q79444,Q79451)))),CLAUSES)))))))))) # label(aCASEWISEu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1539 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,X)))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))))) # label(aINTu_LTEu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1540 (all U_0 ((all F0 all G0 all I0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),F0),s(num,I0))))),s(real,i(s(fun(num,real),G0),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),i(s(fun(fun(num,real),fun(fun(num,real),fun(num,real))),U_0),s(fun(num,real),F0))),s(fun(num,real),G0))),s(num,I0)))) -> (all F0 all G0 all M0 all N0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),G0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),i(s(fun(fun(num,real),fun(fun(num,real),fun(num,real))),U_0),s(fun(num,real),F0))),s(fun(num,real),G0)))))))) # label(aSUMu_ADDu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1541 (all Q46638 s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),p1))),s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),q))),s(fun(Q46638,bool),r0))))) = s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),p1))),s(fun(Q46638,bool),q))))),s(fun(Q46638,bool),r0)))) # label(aINTERu_ACIu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1542 (all Q4784 all Q4783 all U_0 ((all P0 all F0 (p(s(bool,i(s(fun(fun(prod(Q4784,Q4783),bool),bool),i(s(fun(fun(Q4784,fun(Q4783,bool)),fun(fun(prod(Q4784,Q4783),bool),bool)),U_0),s(fun(Q4784,fun(Q4783,bool)),P0))),s(fun(prod(Q4784,Q4783),bool),F0)))) <-> (all X all Y p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(Q4784,Q4783),bool),F0),s(prod(Q4784,Q4783),i(s(fun(Q4783,prod(Q4784,Q4783)),i(s(fun(Q4784,fun(Q4783,prod(Q4784,Q4783))),c_),s(Q4784,X))),s(Q4783,Y))))))),s(bool,i(s(fun(Q4783,bool),i(s(fun(Q4784,fun(Q4783,bool)),P0),s(Q4784,X))),s(Q4783,Y))))))))) -> (all P0 ((all X all Y p(s(bool,i(s(fun(Q4783,bool),i(s(fun(Q4784,fun(Q4783,bool)),P0),s(Q4784,X))),s(Q4783,Y))))) <-> p(s(bool,i(s(fun(fun(prod(Q4784,Q4783),bool),bool),e_),s(fun(prod(Q4784,Q4783),bool),i(s(fun(fun(fun(prod(Q4784,Q4783),bool),bool),fun(prod(Q4784,Q4783),bool)),gabs),s(fun(fun(prod(Q4784,Q4783),bool),bool),i(s(fun(fun(Q4784,fun(Q4783,bool)),fun(fun(prod(Q4784,Q4783),bool),bool)),U_0),s(fun(Q4784,fun(Q4783,bool)),P0)))))))))))) # label(aFORALLu_PAIREDu_THM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1543 (all Q70911 s(fun(fun(Q70911,bool),fun(fun(Q70911,real),real)),sum) = s(fun(fun(Q70911,bool),fun(fun(Q70911,real),real)),i(s(fun(fun(real,fun(real,real)),fun(fun(Q70911,bool),fun(fun(Q70911,real),real))),iterate),s(fun(real,fun(real,real)),realu_add)))) # label(asum) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1544 (all A all U_0 ((all F0 all N0 all I0 s(num,i(s(fun(A,num),i(s(fun(num,fun(A,num)),i(s(fun(fun(A,num),fun(num,fun(A,num))),U_0),s(fun(A,num),F0))),s(num,N0))),s(A,I0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(A,num),F0),s(A,I0))))),s(num,N0)))) -> (all F0 all N0 all S0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(num,fun(A,num)),i(s(fun(fun(A,num),fun(num,fun(A,num))),U_0),s(fun(A,num),F0))),s(num,N0))))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))))),s(num,N0))))))) # label(aMODu_NSUMu_MOD) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1545 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) # label(aARITHu_LEu_conjunct7) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1546 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,i(s(fun(real,real),realu_neg),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y)))) # label(aREALu_NEGu_MUL2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1547 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0))))))) # label(aREALu_LEu_RMULu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1548 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) <-> (exists X (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))),s(fun(A,bool),T0)))))))) # label(aPSUBSETu_INSERTu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1549 (all Y all X (-p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,X)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))))) # label(arealu_lt) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1550 (all P0 ((exists N0 ((all M0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> -p(s(bool,i(s(fun(num,bool),P0),s(num,M0)))))) & p(s(bool,i(s(fun(num,bool),P0),s(num,N0)))))) <-> (exists N0 p(s(bool,i(s(fun(num,bool),P0),s(num,N0))))))) # label(anumu_WOP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1551 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) <-> s(real,X) = s(real,i(s(fun(real,real),realu_abs),s(real,X))))) # label(aREALu_ABSu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1552 (all X1 all Y1 all X2 all Y2 (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),numpair),s(num,X2))),s(num,Y2))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),numpair),s(num,X1))),s(num,Y1))) <-> s(num,Y1) = s(num,Y2) & s(num,X2) = s(num,X1))) # label(aNUMPAIRu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1553 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,Y))) = s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),i(s(fun(real,fun(fun(real,bool),fun(real,bool))),insert),s(real,X))),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),i(s(fun(real,fun(fun(real,bool),fun(real,bool))),insert),s(real,Y))),s(fun(real,bool),empty)))))))) # label(aREALu_MINu_INF) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1554 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Z0))))),s(real,Y))))) # label(aREALu_LTu_LDIVu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1555 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Z0)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,Y))))),s(real,Z0)))))) # label(aREALu_MAXu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1556 (all Q71020 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q71020,bool),bool),finite),s(fun(Q71020,bool),S0)))) & p(s(bool,i(s(fun(fun(Q71020,bool),bool),i(s(fun(fun(Q71020,bool),fun(fun(Q71020,bool),bool)),disjoint),s(fun(Q71020,bool),S0))),s(fun(Q71020,bool),T0)))) & p(s(bool,i(s(fun(fun(Q71020,bool),bool),finite),s(fun(Q71020,bool),T0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(Q71020,real),real),i(s(fun(fun(Q71020,bool),fun(fun(Q71020,real),real)),sum),s(fun(Q71020,bool),S0))),s(fun(Q71020,real),F0))))),s(real,i(s(fun(fun(Q71020,real),real),i(s(fun(fun(Q71020,bool),fun(fun(Q71020,real),real)),sum),s(fun(Q71020,bool),T0))),s(fun(Q71020,real),F0))))) = s(real,i(s(fun(fun(Q71020,real),real),i(s(fun(fun(Q71020,bool),fun(fun(Q71020,real),real)),sum),s(fun(Q71020,bool),i(s(fun(fun(Q71020,bool),fun(Q71020,bool)),i(s(fun(fun(Q71020,bool),fun(fun(Q71020,bool),fun(Q71020,bool))),union),s(fun(Q71020,bool),S0))),s(fun(Q71020,bool),T0))))),s(fun(Q71020,real),F0))))) # label(aSUMu_UNION) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1557 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))) = s(int,Y)) # label(aINTu_SUBu_SUB2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1558 (all X all Y (s(prod(hreal,hreal),X) = s(prod(hreal,hreal),Y) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))))) # label(aTREALu_EQu_AP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1559 (all A all U_0 ((all S0 all T0 all GENR_PVARR_4 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,bool),T0))),s(A,GENR_PVARR_4)))) <-> (exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_4))),s(bool,V))),s(A,X)))) & (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) <-> p(s(bool,V))))))) -> (all S0 all T0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),T0))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))))) # label(aDIFF) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1560 (all M0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,N0) <-> s(num,M0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))) # label(aEQu_ADDu_LCANCELu_0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.53 1561 (all A all U_2 ((all P0 all X (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_2),s(fun(A,bool),P0))),s(A,X)))) <-> -p(s(bool,i(s(fun(A,bool),P0),s(A,X)))))) -> (all U_1 ((all S0 all P0 all GENR_PVARR_189 ((exists X exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_189))),s(bool,V))),s(A,X)))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),P0))),s(A,GENR_PVARR_189)))))) -> (all U_0 ((all P0 all F0 all G0 all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(A,bool),P0),s(A,X))))),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,i(s(fun(A,real),G0),s(A,X))))) = s(real,i(s(fun(A,real),i(s(fun(fun(A,real),fun(A,real)),i(s(fun(fun(A,real),fun(fun(A,real),fun(A,real))),i(s(fun(fun(A,bool),fun(fun(A,real),fun(fun(A,real),fun(A,real)))),U_0),s(fun(A,bool),P0))),s(fun(A,real),F0))),s(fun(A,real),G0))),s(A,X)))) -> (all S0 all P0 all F0 all G0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),P0))))))),s(fun(A,real),F0))))),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_2),s(fun(A,bool),P0))))))))),s(fun(A,real),G0))))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(fun(A,real),fun(A,real)),i(s(fun(fun(A,real),fun(fun(A,real),fun(A,real))),i(s(fun(fun(A,bool),fun(fun(A,real),fun(fun(A,real),fun(A,real)))),U_0),s(fun(A,bool),P0))),s(fun(A,real),F0))),s(fun(A,real),G0))))))))))))) # label(aSUMu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1562 (all X all Y (s(int,Y) = s(int,X) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))))) # label(aINTu_LEu_LT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1563 (all E0 ((exists N0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))))),s(real,E0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))))))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))))) # label(aREALu_ARCHu_INV) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1564 (all M0 all D0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,D0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(num,i(s(fun(fun(num,bool),num),card),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,D0)))))))) # label(aCARDu_NUMSEGu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1565 (all A all L all M0 s(list(A),i(s(fun(list(A),list(A)),reverse),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),L))),s(list(A),M0))))) = s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),i(s(fun(list(A),list(A)),reverse),s(list(A),M0))))),s(list(A),i(s(fun(list(A),list(A)),reverse),s(list(A),L)))))) # label(aREVERSEu_APPEND) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1566 (all U_0 ((all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),U_0),s(real,X))),s(real,Y)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,X))) -> (all X s(real,i(s(fun(fun(real,bool),real),h_),s(fun(real,bool),i(s(fun(real,fun(real,bool)),U_0),s(real,X))))) = s(real,i(s(fun(real,real),sqrt),s(real,X)))))) # label(asqrt) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1567 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))),s(int,Y))) = s(int,X)) # label(aINTu_SUBu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1568 (all M0 all N0 s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,M0))))),s(num,i(s(fun(num,num),numeral),s(num,N0)))))) # label(aARITHu_MULTu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1569 (all A all X all S0 (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> (all T0 s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),T0))))) = s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aSUBSETu_INSERT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1570 (all A all M0 all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),L))),s(fun(prod(A,A),bool),M0)))) <-> (all X all Y (p(s(bool,i(s(fun(prod(A,A),bool),M0),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,Y)))) <-> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))))))) # label(ainseg) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1571 (all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,i(s(fun(real,real),realu_neg),s(real,X)))))) # label(aREALu_ADDu_RINV) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1572 (all X1 all X2 all Y1 all Y2 s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X1))),s(hreal,X2))))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,Y1))),s(hreal,Y2))))) = s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,X1))),s(hreal,Y1))))),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,X2))),s(hreal,Y2)))))) # label(atrealu_add) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1573 (all B all A all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),T0))),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0)))))) <-> (exists SI_ (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),SI_))),s(fun(A,bool),S0)))) & s(fun(B,bool),T0) = s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),SI_))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),SI_)))))))) # label(aFINITEu_SUBSETu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1574 (all F0 all N0 s(real,i(s(fun(num,real),F0),s(num,N0))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,N0))),s(num,N0))))),s(fun(num,real),F0)))) # label(aSUMu_SINGu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1575 (all X (s(int,X) != s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),intu_abs),s(int,X)))))))) # label(aINTu_ABSu_NZ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1576 (exists H0 exists R0 ((all X s(hreal,i(s(fun(real,hreal),H0),s(real,i(s(fun(hreal,real),R0),s(hreal,X))))) = s(hreal,X)) & (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> s(real,X) = s(real,i(s(fun(hreal,real),R0),s(hreal,i(s(fun(real,hreal),H0),s(real,X))))))) & (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(hreal,real),R0),s(hreal,X))))))) & (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(hreal,real),R0),s(hreal,X))))),s(real,i(s(fun(hreal,real),R0),s(hreal,Y))))) = s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,Y)))))) # label(aREALu_HREALu_LEMMA2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1577 (all M0 all N0 s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),realu_ofu_num),s(num,M0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))))) # label(aREALu_OFu_NUMu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1578 (all N all A all U_0 ((all L all I0 s(A,i(s(fun(num,A),i(s(fun(list(A),fun(num,A)),U_0),s(list(A),L))),s(num,I0))) = s(A,i(s(fun(list(A),A),i(s(fun(num,fun(list(A),A)),el),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,I0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(list(A),L)))) -> (all L s(cart(A,N),i(s(fun(list(A),cart(A,N)),vector),s(list(A),L))) = s(cart(A,N),i(s(fun(fun(num,A),cart(A,N)),lambda),s(fun(num,A),i(s(fun(list(A),fun(num,A)),U_0),s(list(A),L)))))))) # label(avector) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1579 (all A all S0 (s(fun(A,bool),S0) != s(fun(A,bool),empty) <-> (exists X p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))))) # label(aMEMBERu_NOTu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1580 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,Z0)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0)))))))) # label(aINTu_LEu_LADDu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1581 (all A all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),univ))) = s(fun(A,bool),S0)) # label(aINTERu_UNIVu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1582 (all M0 all N0 ((exists D0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,D0))) = s(num,N0)) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))))) # label(aLEu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1583 (all B all P all A all U_1 ((all T0 all F0 all X s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,A)),fun(fun(A,B),fun(P,B))),U_1),s(fun(fun(A,B),fun(P,A)),T0))),s(fun(A,B),F0))),s(P,X))) = s(B,i(s(fun(A,B),F0),s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),T0),s(fun(A,B),F0))),s(P,X)))))) -> (all U_0 ((all T0 all F0 s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,A)),fun(fun(A,B),fun(P,B))),U_1),s(fun(fun(A,B),fun(P,A)),T0))),s(fun(A,B),F0))) = s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,A)),fun(fun(A,B),fun(P,B))),U_0),s(fun(fun(A,B),fun(P,A)),T0))),s(fun(A,B),F0)))) -> (all L_L_ all P0 all S0 all T0 (p(s(bool,i(s(fun(fun(fun(A,B),fun(P,A)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,A)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,A)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,A)),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,A)),T0)))) & (all F0 all A5 (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,A5)))) -> (all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,i(s(fun(P,A),i(s(fun(fun(A,B),fun(P,A)),T0),s(fun(A,B),F0))),s(P,A5)))))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),L_L_),s(A,Y))),s(A,i(s(fun(P,A),S0),s(P,A5)))))))))) -> p(s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),superadmissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,A)),fun(fun(A,B),fun(P,B))),U_0),s(fun(fun(A,B),fun(P,A)),T0)))))))))))) # label(aSUPERADMISSIBLEu_TAIL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1584 (all U_0 ((all K0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),U_0),s(num,K0))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,K0))),s(num,N0)))) -> (all K0 s(nadd,i(s(fun(fun(num,num),nadd),mku_nadd),s(fun(num,num),i(s(fun(num,fun(num,num)),U_0),s(num,K0))))) = s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,K0)))))) # label(anaddu_ofu_num) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1585 (all M0 all N0 all P0 s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,M0))),s(hreal,P0))))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,N0))),s(hreal,P0))))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,M0))),s(hreal,N0))))),s(hreal,P0)))) # label(aHREALu_ADDu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1586 (all A all A5 exists X s(A,A5) = s(A,X)) # label(aEXISTSu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1587 (all A5 s(int,i(s(fun(real,int),intu_ofu_real),s(real,i(s(fun(int,real),realu_ofu_int),s(int,A5))))) = s(int,A5)) # label(aintu_tybiju_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1588 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0)))))) # label(aCOUNTABLEu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1589 (all D0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D0)))) -> (exists E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,E0))),s(real,D0)))))))) # label(aREALu_DOWN) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1590 (all Q89012 all Q89013 all S0 all T0 (p(s(bool,i(s(fun(fun(Q89013,bool),bool),i(s(fun(fun(Q89012,bool),fun(fun(Q89013,bool),bool)),l_a_u_c),s(fun(Q89012,bool),S0))),s(fun(Q89013,bool),T0)))) <-> p(s(bool,i(s(fun(fun(Q89013,bool),bool),i(s(fun(fun(Q89012,bool),fun(fun(Q89013,bool),bool)),a_u_c),s(fun(Q89012,bool),S0))),s(fun(Q89013,bool),T0)))) | p(s(bool,i(s(fun(fun(Q89013,bool),bool),i(s(fun(fun(Q89012,bool),fun(fun(Q89013,bool),bool)),l_u_c),s(fun(Q89012,bool),S0))),s(fun(Q89013,bool),T0)))))) # label(aCARDu_LEu_LT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1591 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all X all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,Y)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) -> s(A,X) = s(A,Y) | p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) | p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))))))) # label(aWOSETu_TOTALu_LT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1592 (all Q58289 all Q58291 all F0 all L s(fun(Q58289,bool),i(s(fun(fun(Q58291,bool),fun(Q58289,bool)),i(s(fun(fun(Q58291,Q58289),fun(fun(Q58291,bool),fun(Q58289,bool))),image),s(fun(Q58291,Q58289),F0))),s(fun(Q58291,bool),i(s(fun(list(Q58291),fun(Q58291,bool)),setu_ofu_list),s(list(Q58291),L))))) = s(fun(Q58289,bool),i(s(fun(list(Q58289),fun(Q58289,bool)),setu_ofu_list),s(list(Q58289),i(s(fun(list(Q58291),list(Q58289)),i(s(fun(fun(Q58291,Q58289),fun(list(Q58291),list(Q58289))),map0),s(fun(Q58291,Q58289),F0))),s(list(Q58291),L)))))) # label(aSETu_OFu_LISTu_MAP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1593 (all U_1 ((all C0 all X all I0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_1),s(fun(num,real),C0))),s(real,X))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),C0),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0)))))) -> (all U_0 ((all N0 all C0 all GENR_PVARR_202 (p(s(bool,i(s(fun(real,bool),i(s(fun(fun(num,real),fun(real,bool)),i(s(fun(num,fun(fun(num,real),fun(real,bool))),U_0),s(num,N0))),s(fun(num,real),C0))),s(real,GENR_PVARR_202)))) <-> (exists X exists V (p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_202))),s(bool,V))),s(real,X)))) & (p(s(bool,V)) <-> s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_1),s(fun(num,real),C0))),s(real,X))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) -> (all N0 all C0 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(fun(num,real),fun(real,bool)),i(s(fun(num,fun(fun(num,real),fun(real,bool))),U_0),s(num,N0))),s(fun(num,real),C0)))))))) <-> (exists I0 (p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,I0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))))) & s(real,i(s(fun(num,real),C0),s(num,I0))) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))))))) # label(aREALu_POLYFUNu_FINITEu_ROOTS) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1594 (all X p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,X))))))) # label(aINTu_LEu_SQUARE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1595 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,X))) # label(aPOWu_2u_SQRT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1596 (all Q48928 all Q48912 all U_0 ((all S0 all F0 all GENR_PVARR_27 (p(s(bool,i(s(fun(Q48912,bool),i(s(fun(fun(Q48928,fun(Q48912,bool)),fun(Q48912,bool)),i(s(fun(fun(Q48928,bool),fun(fun(Q48928,fun(Q48912,bool)),fun(Q48912,bool))),U_0),s(fun(Q48928,bool),S0))),s(fun(Q48928,fun(Q48912,bool)),F0))),s(Q48912,GENR_PVARR_27)))) <-> (exists Y exists V (p(s(bool,i(s(fun(Q48912,bool),i(s(fun(bool,fun(Q48912,bool)),i(s(fun(Q48912,fun(bool,fun(Q48912,bool))),setspec),s(Q48912,GENR_PVARR_27))),s(bool,V))),s(Q48912,Y)))) & ((exists X (p(s(bool,i(s(fun(fun(Q48928,bool),bool),i(s(fun(Q48928,fun(fun(Q48928,bool),bool)),in),s(Q48928,X))),s(fun(Q48928,bool),S0)))) & p(s(bool,i(s(fun(fun(Q48912,bool),bool),i(s(fun(Q48912,fun(fun(Q48912,bool),bool)),in),s(Q48912,Y))),s(fun(Q48912,bool),i(s(fun(Q48928,fun(Q48912,bool)),F0),s(Q48928,X)))))))) <-> p(s(bool,V))))))) -> (all F0 all S0 s(fun(Q48912,bool),i(s(fun(fun(fun(Q48912,bool),bool),fun(Q48912,bool)),unions),s(fun(fun(Q48912,bool),bool),i(s(fun(fun(Q48928,bool),fun(fun(Q48912,bool),bool)),i(s(fun(fun(Q48928,fun(Q48912,bool)),fun(fun(Q48928,bool),fun(fun(Q48912,bool),bool))),image),s(fun(Q48928,fun(Q48912,bool)),F0))),s(fun(Q48928,bool),S0))))) = s(fun(Q48912,bool),i(s(fun(fun(Q48912,bool),fun(Q48912,bool)),gspec),s(fun(Q48912,bool),i(s(fun(fun(Q48928,fun(Q48912,bool)),fun(Q48912,bool)),i(s(fun(fun(Q48928,bool),fun(fun(Q48928,fun(Q48912,bool)),fun(Q48912,bool))),U_0),s(fun(Q48928,bool),S0))),s(fun(Q48928,fun(Q48912,bool)),F0)))))))) # label(aUNIONSu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1597 (all A all S0 s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),S0))) != s(num,i(s(fun(num,num),numeral),s(num,u_0)))) # label(aDIMINDEXu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1598 (all X all Y (s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,X) | s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,Y) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y)))))))) # label(aINTu_MULu_POSu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1599 (all A all F0 all U all V (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),V)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) & -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V)))) -> s(real,i(s(fun(A,real),F0),s(A,X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) -> s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),V))),s(fun(A,real),F0))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),U))),s(fun(A,bool),V))))),s(fun(A,real),F0))))) # label(aSUMu_UNIONu_LZERO) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1600 (all U_0 ((all N0 all GENR_PVARR_112 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))),s(num,GENR_PVARR_112)))) <-> (exists M0 p(s(bool,i(s(fun(num,bool),i(s(fun(bool,fun(num,bool)),i(s(fun(num,fun(bool,fun(num,bool))),setspec),s(num,GENR_PVARR_112))),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(num,M0))))))) -> (all N0 s(num,i(s(fun(fun(num,bool),num),card),s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),gspec),s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aCARDu_NUMSEGu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1601 (all A all B all C all S0 all T0 all U p(s(bool,i(s(fun(fun(sum0(sum0(A,B),C),bool),bool),i(s(fun(fun(sum0(A,sum0(B,C)),bool),fun(fun(sum0(sum0(A,B),C),bool),bool)),a_u_c),s(fun(sum0(A,sum0(B,C)),bool),i(s(fun(fun(sum0(B,C),bool),fun(sum0(A,sum0(B,C)),bool)),i(s(fun(fun(A,bool),fun(fun(sum0(B,C),bool),fun(sum0(A,sum0(B,C)),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(sum0(B,C),bool),i(s(fun(fun(C,bool),fun(sum0(B,C),bool)),i(s(fun(fun(B,bool),fun(fun(C,bool),fun(sum0(B,C),bool))),p_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U))))))),s(fun(sum0(sum0(A,B),C),bool),i(s(fun(fun(C,bool),fun(sum0(sum0(A,B),C),bool)),i(s(fun(fun(sum0(A,B),bool),fun(fun(C,bool),fun(sum0(sum0(A,B),C),bool))),p_u_c),s(fun(sum0(A,B),bool),i(s(fun(fun(B,bool),fun(sum0(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(sum0(A,B),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(C,bool),U))))))) # label(aCARDu_ADDu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1602 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0)))))))) # label(aREALu_LEu_LADDu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1603 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),poset),s(fun(prod(A,A),bool),L)))) -> (all X s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X))) = s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,X)))))))) # label(aPOSETu_FLEQ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1604 (all A all B all C all P all U_7 ((all T0 all F0 all X all U s(bool,i(s(fun(P,bool),i(s(fun(C,fun(P,bool)),i(s(fun(fun(A,B),fun(C,fun(P,bool))),T0),s(fun(A,B),F0))),s(C,U))),s(P,X))) = s(bool,i(s(fun(C,bool),i(s(fun(P,fun(C,bool)),i(s(fun(fun(A,B),fun(P,fun(C,bool))),i(s(fun(fun(fun(A,B),fun(C,fun(P,bool))),fun(fun(A,B),fun(P,fun(C,bool)))),U_7),s(fun(fun(A,B),fun(C,fun(P,bool))),T0))),s(fun(A,B),F0))),s(P,X))),s(C,U)))) -> (all U_6 ((all T0 all F0 all X s(fun(C,bool),i(s(fun(P,fun(C,bool)),i(s(fun(fun(A,B),fun(P,fun(C,bool))),i(s(fun(fun(fun(A,B),fun(C,fun(P,bool))),fun(fun(A,B),fun(P,fun(C,bool)))),U_6),s(fun(fun(A,B),fun(C,fun(P,bool))),T0))),s(fun(A,B),F0))),s(P,X))) = s(fun(C,bool),i(s(fun(P,fun(C,bool)),i(s(fun(fun(A,B),fun(P,fun(C,bool))),i(s(fun(fun(fun(A,B),fun(C,fun(P,bool))),fun(fun(A,B),fun(P,fun(C,bool)))),U_7),s(fun(fun(A,B),fun(C,fun(P,bool))),T0))),s(fun(A,B),F0))),s(P,X)))) -> (all U_5 ((all T0 all F0 s(fun(P,fun(C,bool)),i(s(fun(fun(A,B),fun(P,fun(C,bool))),i(s(fun(fun(fun(A,B),fun(C,fun(P,bool))),fun(fun(A,B),fun(P,fun(C,bool)))),U_6),s(fun(fun(A,B),fun(C,fun(P,bool))),T0))),s(fun(A,B),F0))) = s(fun(P,fun(C,bool)),i(s(fun(fun(A,B),fun(P,fun(C,bool))),i(s(fun(fun(fun(A,B),fun(C,fun(P,bool))),fun(fun(A,B),fun(P,fun(C,bool)))),U_5),s(fun(fun(A,B),fun(C,fun(P,bool))),T0))),s(fun(A,B),F0)))) -> (all U_4 ((all T0 all F0 all F1 (p(s(bool,i(s(fun(fun(prod(C,P),bool),bool),i(s(fun(fun(A,B),fun(fun(prod(C,P),bool),bool)),i(s(fun(fun(fun(A,B),fun(C,fun(P,bool))),fun(fun(A,B),fun(fun(prod(C,P),bool),bool))),U_4),s(fun(fun(A,B),fun(C,fun(P,bool))),T0))),s(fun(A,B),F0))),s(fun(prod(C,P),bool),F1)))) <-> (all U all X p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(C,P),bool),F1),s(prod(C,P),i(s(fun(P,prod(C,P)),i(s(fun(C,fun(P,prod(C,P))),c_),s(C,U))),s(P,X))))))),s(bool,i(s(fun(P,bool),i(s(fun(C,fun(P,bool)),i(s(fun(fun(A,B),fun(C,fun(P,bool))),T0),s(fun(A,B),F0))),s(C,U))),s(P,X))))))))) -> (all U_3 ((all T0 all F0 s(fun(prod(C,P),bool),i(s(fun(fun(fun(prod(C,P),bool),bool),fun(prod(C,P),bool)),gabs),s(fun(fun(prod(C,P),bool),bool),i(s(fun(fun(A,B),fun(fun(prod(C,P),bool),bool)),i(s(fun(fun(fun(A,B),fun(C,fun(P,bool))),fun(fun(A,B),fun(fun(prod(C,P),bool),bool))),U_4),s(fun(fun(A,B),fun(C,fun(P,bool))),T0))),s(fun(A,B),F0))))) = s(fun(prod(C,P),bool),i(s(fun(fun(A,B),fun(prod(C,P),bool)),i(s(fun(fun(fun(A,B),fun(C,fun(P,bool))),fun(fun(A,B),fun(prod(C,P),bool))),U_3),s(fun(fun(A,B),fun(C,fun(P,bool))),T0))),s(fun(A,B),F0)))) -> (all U_2 ((all S0 all F0 (p(s(bool,i(s(fun(fun(prod(C,P),A),bool),i(s(fun(fun(P,A),fun(fun(prod(C,P),A),bool)),U_2),s(fun(P,A),S0))),s(fun(prod(C,P),A),F0)))) <-> (all U all X p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),geq),s(A,i(s(fun(prod(C,P),A),F0),s(prod(C,P),i(s(fun(P,prod(C,P)),i(s(fun(C,fun(P,prod(C,P))),c_),s(C,U))),s(P,X))))))),s(A,i(s(fun(P,A),S0),s(P,X))))))))) -> (all U_1 ((all P0 all F0 all F1 ((all U all X p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(C,P),bool),F1),s(prod(C,P),i(s(fun(P,prod(C,P)),i(s(fun(C,fun(P,prod(C,P))),c_),s(C,U))),s(P,X))))))),s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,X))))))) <-> p(s(bool,i(s(fun(fun(prod(C,P),bool),bool),i(s(fun(fun(A,B),fun(fun(prod(C,P),bool),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(fun(prod(C,P),bool),bool))),U_1),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(A,B),F0))),s(fun(prod(C,P),bool),F1)))))) -> (all U_0 ((all P0 all F0 s(fun(prod(C,P),bool),i(s(fun(fun(fun(prod(C,P),bool),bool),fun(prod(C,P),bool)),gabs),s(fun(fun(prod(C,P),bool),bool),i(s(fun(fun(A,B),fun(fun(prod(C,P),bool),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(fun(prod(C,P),bool),bool))),U_1),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(A,B),F0))))) = s(fun(prod(C,P),bool),i(s(fun(fun(A,B),fun(prod(C,P),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(prod(C,P),bool))),U_0),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(A,B),F0)))) -> (all L_L_ all P0 all S0 all T0 (p(s(bool,i(s(fun(fun(fun(A,B),fun(prod(C,P),bool)),bool),i(s(fun(fun(prod(C,P),A),fun(fun(fun(A,B),fun(prod(C,P),bool)),bool)),i(s(fun(fun(fun(A,B),fun(prod(C,P),bool)),fun(fun(prod(C,P),A),fun(fun(fun(A,B),fun(prod(C,P),bool)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(prod(C,P),bool)),fun(fun(prod(C,P),A),fun(fun(fun(A,B),fun(prod(C,P),bool)),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(prod(C,P),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(prod(C,P),bool))),U_0),s(fun(fun(A,B),fun(P,bool)),P0))))),s(fun(prod(C,P),A),i(s(fun(fun(fun(prod(C,P),A),bool),fun(prod(C,P),A)),gabs),s(fun(fun(prod(C,P),A),bool),i(s(fun(fun(P,A),fun(fun(prod(C,P),A),bool)),U_2),s(fun(P,A),S0))))))),s(fun(fun(A,B),fun(prod(C,P),bool)),i(s(fun(fun(fun(A,B),fun(C,fun(P,bool))),fun(fun(A,B),fun(prod(C,P),bool))),U_3),s(fun(fun(A,B),fun(C,fun(P,bool))),T0)))))) -> p(s(bool,i(s(fun(fun(fun(A,B),fun(P,fun(C,bool))),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,fun(C,bool))),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,fun(C,bool))),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,fun(C,bool))),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,fun(C,bool))),i(s(fun(fun(fun(A,B),fun(C,fun(P,bool))),fun(fun(A,B),fun(P,fun(C,bool)))),U_5),s(fun(fun(A,B),fun(C,fun(P,bool))),T0)))))))))))))))))))))))) # label(aADMISSIBLEu_LAMBDA) # label(axiom) # label(non_clause). [assumption]. 14.50/14.54 1605 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) <-> (all P0 ((all X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))))) & (exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) -> (exists Y (p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))) & (all Z0 (p(s(bool,i(s(fun(A,bool),P0),s(A,Z0)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,Z0)))))))))))) & (all X all Y (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))) -> s(A,Y) = s(A,X))))) # label(aWOSET) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1606 (all A all B all S0 all T0 p(s(bool,i(s(fun(fun(sum0(A,B),bool),bool),i(s(fun(fun(A,bool),fun(fun(sum0(A,B),bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(sum0(A,B),bool),i(s(fun(fun(B,bool),fun(sum0(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(sum0(A,B),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))))) # label(aCARDu_LEu_ADDR) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1607 (all B all A all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),T0))),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0)))))) -> (exists SI_ (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),SI_))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),T0))),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),SI_)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),SI_)))))))) # label(aFINITEu_SUBSETu_IMAGEu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1608 (all B all A all P0 all G0 all H0 ((all F0 all X all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Y))),s(A,i(s(fun(A,A),i(s(fun(fun(A,B),fun(A,A)),G0),s(fun(A,B),F0))),s(A,X)))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),P0),s(fun(A,B),F0))),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Y))),s(A,X)))))) & (all F0 all G1 all X ((all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Z0))),s(A,X)))) -> s(B,i(s(fun(A,B),G1),s(A,Z0))) = s(B,i(s(fun(A,B),F0),s(A,Z0))))) -> s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),G1))),s(A,X))))) & (all F0 all G1 all X ((all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Z0))),s(A,X)))) -> s(B,i(s(fun(A,B),G1),s(A,Z0))) = s(B,i(s(fun(A,B),F0),s(A,Z0))))) -> s(A,i(s(fun(A,A),i(s(fun(fun(A,B),fun(A,A)),G0),s(fun(A,B),G1))),s(A,X))) = s(A,i(s(fun(A,A),i(s(fun(fun(A,B),fun(A,A)),G0),s(fun(A,B),F0))),s(A,X))) & s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),G1))),s(A,X))) & s(bool,i(s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),P0),s(fun(A,B),G1))),s(A,X))) = s(bool,i(s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),P0),s(fun(A,B),F0))),s(A,X))))) & p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))) -> (exists F0 all X s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,i(s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),P0),s(fun(A,B),F0))),s(A,X))))),s(B,i(s(fun(A,B),F0),s(A,i(s(fun(A,A),i(s(fun(fun(A,B),fun(A,A)),G0),s(fun(A,B),F0))),s(A,X))))))),s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X))))) = s(B,i(s(fun(A,B),F0),s(A,X)))))) # label(aWFu_RECu_TAILu_GENERAL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1609 (all U_0 ((all A5 all B0 all GENR_PVARR_127 ((exists X exists V (p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_127))),s(bool,V))),s(real,X)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,B0))))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),i(s(fun(real,fun(real,fun(real,bool))),U_0),s(real,A5))),s(real,B0))),s(real,GENR_PVARR_127)))))) -> (all A5 all B0 s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(real,fun(real,bool)),i(s(fun(real,fun(real,fun(real,bool))),U_0),s(real,A5))),s(real,B0))))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,A5)))))) # label(aFINITEu_REALu_INTERVALu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1610 (all P0 all Q0 all R0 ((p(s(bool,Q0)) | p(s(bool,R0))) & p(s(bool,P0)) <-> p(s(bool,Q0)) & p(s(bool,P0)) | p(s(bool,P0)) & p(s(bool,R0)))) # label(aLEFTu_ORu_DISTRIB) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1611 (all Q67516 all U_0 ((all C0 all N0 s(num,C0) = s(num,i(s(fun(Q67516,num),i(s(fun(num,fun(Q67516,num)),U_0),s(num,C0))),s(Q67516,N0)))) -> (all C0 all S0 (p(s(bool,i(s(fun(fun(Q67516,bool),bool),finite),s(fun(Q67516,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(fun(Q67516,bool),num),card),s(fun(Q67516,bool),S0))))),s(num,C0))) = s(num,i(s(fun(fun(Q67516,num),num),i(s(fun(fun(Q67516,bool),fun(fun(Q67516,num),num)),nsum),s(fun(Q67516,bool),S0))),s(fun(Q67516,num),i(s(fun(num,fun(Q67516,num)),U_0),s(num,C0))))))))) # label(aNSUMu_CONST) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1612 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),realu_neg),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aREALu_LEu_RNEG) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1613 (all A all A5 all B0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),A5))),s(fun(A,bool),B0)))) & s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),B0))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),A5))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),B0)))) -> s(fun(A,bool),A5) = s(fun(A,bool),B0))) # label(aCARDu_SUBSETu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1614 (all N0 s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,N0)) # label(aDISTu_RZERO) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1615 (all X all Y s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,Y)))) # label(aINTu_SUBu_LNEG) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1616 (all A5 s(n10,i(s(fun(bool,n10),oneu_abs),s(bool,i(s(fun(n10,bool),oneu_rep),s(n10,A5))))) = s(n10,A5)) # label(aoneu_tydefu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1617 (all A all B all S0 all T0 all F0 all G0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0)))) & s(A,i(s(fun(B,A),G0),s(B,i(s(fun(A,B),F0),s(A,X))))) = s(A,X))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,n)))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(B,A),G0),s(B,Y))))),s(fun(A,bool),S0)))) & s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,i(s(fun(B,A),G0),s(B,Y))))))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(B,bool),fun(num,bool)),hasu_size),s(fun(B,bool),T0))),s(num,n)))))) # label(aBIJECTIONSu_HASu_SIZE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1618 (all X exists B0 all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,M0))),s(num,N0))))))))))) # label(aNADDu_DIST) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1619 (all X all P0 all M0 all N0 (s(num,P0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,P0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),min),s(num,M0))),s(num,N0))))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,P0))),s(num,M0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,P0))),s(num,N0))))))) # label(aMODu_MODu_EXPu_MIN) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1620 (all C all B all A all F0 all G0 all X s(C,i(s(fun(B,C),F0),s(B,i(s(fun(A,B),G0),s(A,X))))) = s(C,i(s(fun(A,C),i(s(fun(fun(A,B),fun(A,C)),i(s(fun(fun(B,C),fun(fun(A,B),fun(A,C))),o),s(fun(B,C),F0))),s(fun(A,B),G0))),s(A,X)))) # label(aou_THM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1621 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,i(s(fun(real,real),realu_abs),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aREALu_LTu_SQUAREu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1622 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),T0)))))))))) # label(aCARDu_UNIONu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1623 (all A all P0 ((exists X p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),X))))) & (all C0 ((exists X p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),X))),s(fun(fun(A,bool),bool),C0))))) & (all X all Y (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),Y))),s(fun(fun(A,bool),bool),C0)))) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),X))),s(fun(fun(A,bool),bool),C0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),Y))),s(fun(A,bool),X)))) | p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),X))),s(fun(A,bool),Y)))))) & (all X (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),X))),s(fun(fun(A,bool),bool),C0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),X)))))) -> p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),unions),s(fun(fun(A,bool),bool),C0)))))))) -> (exists A5 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),X)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),A5))),s(fun(A,bool),X)))) -> s(fun(A,bool),X) = s(fun(A,bool),A5))) & p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),A5)))))))) # label(aZLu_SUBSETSu_UNIONSu_NONEMPTY) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1624 (all M0 all N0 all P0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) # label(aLEu_ADDu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1625 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,i(s(fun(num,num),bit1),s(num,N0))))),s(num,u_0))))) # label(aARITHu_GEu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1626 (all U_0 ((all N0 all GENR_PVARR_273 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))),s(num,GENR_PVARR_273)))) <-> (exists M0 p(s(bool,i(s(fun(num,bool),i(s(fun(bool,fun(num,bool)),i(s(fun(num,fun(bool,fun(num,bool))),setspec),s(num,GENR_PVARR_273))),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0))))),s(num,M0))))))) -> (all N0 s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),gspec),s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))))) = s(fun(num,bool),i(s(fun(num,fun(num,bool)),from),s(num,N0)))))) # label(afrom) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1627 (all U_0 ((all N0 s(num,i(s(fun(num,num),U_0),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))) -> (all X s(fun(num,num),i(s(fun(fun(num,num),fun(num,num)),i(s(fun(fun(num,num),fun(fun(num,num),fun(num,num))),i(s(fun(bool,fun(fun(num,num),fun(fun(num,num),fun(num,num)))),cond),s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))),s(fun(num,num),U_0))),s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))))) = s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,i(s(fun(nadd,nadd),naddu_inv),s(nadd,X)))))))) # label(aNADDu_INV) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1628 (all A all A5 all B0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),B0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),A5))),s(fun(A,bool),B0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),A5))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),B0)))))))) # label(aCARDu_PSUBSET) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1629 (all X (s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,X) <-> s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,i(s(fun(int,int),intu_abs),s(int,X))))) # label(aINTu_ABSu_ZERO) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1630 (all U_1 ((all C0 all X all I0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_1),s(fun(num,real),C0))),s(real,X))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),C0),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0)))))) -> (all U_0 ((all N0 all C0 all GENR_PVARR_199 ((exists X exists V ((p(s(bool,V)) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_1),s(fun(num,real),C0))),s(real,X)))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_199))),s(bool,V))),s(real,X)))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(fun(num,real),fun(real,bool)),i(s(fun(num,fun(fun(num,real),fun(real,bool))),U_0),s(num,N0))),s(fun(num,real),C0))),s(real,GENR_PVARR_199)))))) -> (all N0 all C0 (-(all I0 (p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,I0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(num,real),C0),s(num,I0))))) -> p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(fun(num,real),fun(real,bool)),i(s(fun(num,fun(fun(num,real),fun(real,bool))),U_0),s(num,N0))),s(fun(num,real),C0)))))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(real,bool),num),card),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(fun(num,real),fun(real,bool)),i(s(fun(num,fun(fun(num,real),fun(real,bool))),U_0),s(num,N0))),s(fun(num,real),C0))))))))),s(num,N0)))))))))) # label(aREALu_POLYFUNu_ROOTBOUND) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1631 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,i(s(fun(real,real),realu_inv),s(real,Y)))))) # label(arealu_div) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1632 (all A all H1 all H2 all T1 all T2 (s(A,H1) = s(A,H2) & s(list(A),T1) = s(list(A),T2) <-> s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,H2))),s(list(A),T2))) = s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,H1))),s(list(A),T1))))) # label(aCONSu_11) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1633 (all Q53685 all S0 all T0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53685,bool),fun(num,bool)),hasu_size),s(fun(Q53685,bool),T0))),s(num,N0)))) & p(s(bool,i(s(fun(fun(Q53685,bool),bool),i(s(fun(fun(Q53685,bool),fun(fun(Q53685,bool),bool)),subset),s(fun(Q53685,bool),T0))),s(fun(Q53685,bool),S0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53685,bool),fun(num,bool)),hasu_size),s(fun(Q53685,bool),S0))),s(num,M0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53685,bool),fun(num,bool)),hasu_size),s(fun(Q53685,bool),i(s(fun(fun(Q53685,bool),fun(Q53685,bool)),i(s(fun(fun(Q53685,bool),fun(fun(Q53685,bool),fun(Q53685,bool))),diff),s(fun(Q53685,bool),S0))),s(fun(Q53685,bool),T0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0)))))))) # label(aHASu_SIZEu_DIFF) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1634 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))))))) # label(aARITHu_MULTu_conjunct7) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1635 (all X s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(int,int),intu_neg),s(int,X))))) = s(int,X)) # label(aINTu_NEGu_NEG) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1636 (all A all X all Y all S0 s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(A,Y))) = s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,Y))))),s(A,X)))) # label(aDELETEu_COMM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1637 (all X p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,X))))) # label(aNADDu_LEu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1638 (all X s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(hreal,X))) = s(hreal,X)) # label(aHREALu_MULu_LID) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1639 (all X -p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,X))))) # label(aINTu_LTu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1640 (all U_2 ((all F0 all J0 all I0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),F0),s(num,I0))),s(num,J0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(fun(num,fun(num,num)),fun(num,fun(num,num))),U_2),s(fun(num,fun(num,num)),F0))),s(num,J0))),s(num,I0)))) -> (all U_1 ((all F0 all J0 s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(fun(num,fun(num,num)),fun(num,fun(num,num))),U_2),s(fun(num,fun(num,num)),F0))),s(num,J0))) = s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(fun(num,fun(num,num)),fun(num,fun(num,num))),U_1),s(fun(num,fun(num,num)),F0))),s(num,J0)))) -> (all U_0 ((all C0 all D0 all F0 all I0 s(num,i(s(fun(num,num),i(s(fun(fun(num,fun(num,num)),fun(num,num)),i(s(fun(num,fun(fun(num,fun(num,num)),fun(num,num))),i(s(fun(num,fun(num,fun(fun(num,fun(num,num)),fun(num,num)))),U_0),s(num,C0))),s(num,D0))),s(fun(num,fun(num,num)),F0))),s(num,I0))) = s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,C0))),s(num,D0))))),s(fun(num,num),i(s(fun(num,fun(num,num)),F0),s(num,I0)))))) -> (all A5 all B0 all C0 all D0 all F0 s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,C0))),s(num,D0))))),s(fun(num,num),i(s(fun(fun(num,fun(num,num)),fun(num,num)),i(s(fun(num,fun(fun(num,fun(num,num)),fun(num,num))),i(s(fun(num,fun(num,fun(fun(num,fun(num,num)),fun(num,num)))),U_0),s(num,A5))),s(num,B0))),s(fun(num,fun(num,num)),i(s(fun(fun(num,fun(num,num)),fun(num,fun(num,num))),U_1),s(fun(num,fun(num,num)),F0))))))) = s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,A5))),s(num,B0))))),s(fun(num,num),i(s(fun(fun(num,fun(num,num)),fun(num,num)),i(s(fun(num,fun(fun(num,fun(num,num)),fun(num,num))),i(s(fun(num,fun(num,fun(fun(num,fun(num,num)),fun(num,num)))),U_0),s(num,C0))),s(num,D0))),s(fun(num,fun(num,num)),F0)))))))))))) # label(aNSUMu_SWAPu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1641 (all A all P0 ((all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),P0),s(fun(prod(A,A),bool),L)))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),L)))))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),i(s(fun(fun(fun(prod(A,A),bool),bool),fun(prod(A,A),bool)),unions),s(fun(fun(prod(A,A),bool),bool),P0)))))))) # label(aORDINALu_UNION) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1642 (all A all X all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0)))) # label(aINSERTu_INSERT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1643 (all X (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),realu_neg),s(real,X))) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,X))) # label(aREALu_NEGu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1644 (all A all X all Y (s(A,Y) = s(A,X) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,Y))),s(fun(A,bool),empty)))))))) # label(aINu_SING) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1645 (all X s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_neg),s(real,X))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aREALu_NEGu_GT0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1646 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,M0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))))) # label(aREALu_OFu_NUMu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1647 (all Q56919 all U_0 ((all GENR_PVARR_100 (p(s(bool,i(s(fun(fun(Q56919,bool),bool),U_0),s(fun(Q56919,bool),GENR_PVARR_100)))) <-> (exists S0 p(s(bool,i(s(fun(fun(Q56919,bool),bool),i(s(fun(bool,fun(fun(Q56919,bool),bool)),i(s(fun(fun(Q56919,bool),fun(bool,fun(fun(Q56919,bool),bool))),setspec),s(fun(Q56919,bool),GENR_PVARR_100))),s(bool,i(s(fun(fun(Q56919,bool),bool),i(s(fun(fun(Q56919,bool),fun(fun(Q56919,bool),bool)),subset),s(fun(Q56919,bool),S0))),s(fun(Q56919,bool),empty))))),s(fun(Q56919,bool),S0))))))) -> s(fun(fun(Q56919,bool),bool),i(s(fun(fun(fun(Q56919,bool),bool),fun(fun(Q56919,bool),bool)),gspec),s(fun(fun(Q56919,bool),bool),U_0))) = s(fun(fun(Q56919,bool),bool),i(s(fun(fun(fun(Q56919,bool),bool),fun(fun(Q56919,bool),bool)),i(s(fun(fun(Q56919,bool),fun(fun(fun(Q56919,bool),bool),fun(fun(Q56919,bool),bool))),insert),s(fun(Q56919,bool),empty))),s(fun(fun(Q56919,bool),bool),empty))))) # label(aPOWERSETu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1648 (all Q63934 all Q63943 all U_0 ((all A5 all F0 all OP all X exists V ((p(s(bool,V)) <-> s(Q63943,X) = s(Q63943,A5)) & s(Q63934,i(s(fun(Q63943,Q63934),i(s(fun(fun(Q63934,fun(Q63934,Q63934)),fun(Q63943,Q63934)),i(s(fun(fun(Q63943,Q63934),fun(fun(Q63934,fun(Q63934,Q63934)),fun(Q63943,Q63934))),i(s(fun(Q63943,fun(fun(Q63943,Q63934),fun(fun(Q63934,fun(Q63934,Q63934)),fun(Q63943,Q63934)))),U_0),s(Q63943,A5))),s(fun(Q63943,Q63934),F0))),s(fun(Q63934,fun(Q63934,Q63934)),OP))),s(Q63943,X))) = s(Q63934,i(s(fun(Q63934,Q63934),i(s(fun(Q63934,fun(Q63934,Q63934)),i(s(fun(bool,fun(Q63934,fun(Q63934,Q63934))),cond),s(bool,V))),s(Q63934,i(s(fun(Q63943,Q63934),F0),s(Q63943,X))))),s(Q63934,i(s(fun(fun(Q63934,fun(Q63934,Q63934)),Q63934),neutral),s(fun(Q63934,fun(Q63934,Q63934)),OP))))))) -> (all OP all F0 all A5 p(s(bool,i(s(fun(fun(Q63943,bool),bool),finite),s(fun(Q63943,bool),i(s(fun(fun(Q63943,bool),fun(Q63943,bool)),i(s(fun(fun(Q63943,Q63934),fun(fun(Q63943,bool),fun(Q63943,bool))),i(s(fun(fun(Q63934,fun(Q63934,Q63934)),fun(fun(Q63943,Q63934),fun(fun(Q63943,bool),fun(Q63943,bool)))),support),s(fun(Q63934,fun(Q63934,Q63934)),OP))),s(fun(Q63943,Q63934),i(s(fun(fun(Q63934,fun(Q63934,Q63934)),fun(Q63943,Q63934)),i(s(fun(fun(Q63943,Q63934),fun(fun(Q63934,fun(Q63934,Q63934)),fun(Q63943,Q63934))),i(s(fun(Q63943,fun(fun(Q63943,Q63934),fun(fun(Q63934,fun(Q63934,Q63934)),fun(Q63943,Q63934)))),U_0),s(Q63943,A5))),s(fun(Q63943,Q63934),F0))),s(fun(Q63934,fun(Q63934,Q63934)),OP))))),s(fun(Q63943,bool),s0))))))))) # label(aFINITEu_SUPPORTu_DELTA) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1649 (all X all Y all Z0 (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0))) & s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(real,Z0) -> s(real,X) = s(real,Y))) # label(aREALu_EQu_RCANCELu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1650 (all S0 all A5 (s(fun(real,bool),empty) != s(fun(real,bool),S0) & p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) -> ((exists X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,A5)))) & p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))),s(real,A5))))))) # label(aREALu_INFu_LTu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1651 (all A all X s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),empty))),s(A,X))) = s(fun(A,bool),empty)) # label(aEMPTYu_DELETE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1652 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & s(real,X) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) -> s(real,i(s(fun(real,real),sqrt),s(real,X))) = s(real,Y))) # label(aSQRTu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1653 (all A all U_0 ((all S0 all X s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_0),s(fun(A,bool),S0))),s(A,X))) = s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> (all S0 s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_0),s(fun(A,bool),S0))))) = s(A,i(s(fun(fun(A,bool),A),choice0),s(fun(A,bool),S0)))))) # label(aCHOICE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1654 (all A all U_0 ((all S0 all GENR_PVARR_259 ((exists L exists V (p(s(bool,i(s(fun(list(A),bool),i(s(fun(bool,fun(list(A),bool)),i(s(fun(list(A),fun(bool,fun(list(A),bool))),setspec),s(list(A),GENR_PVARR_259))),s(bool,V))),s(list(A),L)))) & (p(s(bool,V)) <-> (all X (p(s(bool,i(s(fun(list(A),bool),i(s(fun(A,fun(list(A),bool)),mem),s(A,X))),s(list(A),L)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))))))) <-> p(s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,bool),fun(list(A),bool)),U_0),s(fun(A,bool),S0))),s(list(A),GENR_PVARR_259)))))) -> (all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(list(A),bool),bool),countable),s(fun(list(A),bool),i(s(fun(fun(list(A),bool),fun(list(A),bool)),gspec),s(fun(list(A),bool),i(s(fun(fun(A,bool),fun(list(A),bool)),U_0),s(fun(A,bool),S0)))))))))))) # label(aCOUNTABLEu_LISTu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1655 (all B all A all S0 all T0 (-p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(B,bool),fun(fun(A,bool),bool)),l_u_c),s(fun(B,bool),T0))),s(fun(A,bool),S0)))))) # label(aCARDu_NOTu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1656 (all A all X all S0 (s(fun(A,bool),S0) = s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))) <-> -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))) # label(aDELETEu_NONu_ELEMENT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1657 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(num,fun(fun(num,bool),fun(num,bool))),insert),s(num,M0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))) = s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))) # label(aNUMSEGu_LREC) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1658 (all U_0 ((all K0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),f),s(num,K0))))),s(real,i(s(fun(num,real),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(num,real),U_0),s(num,K0)))) -> (all M0 all N0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),U_0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),f),s(num,M0))))),s(real,i(s(fun(num,real),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) # label(aSUMu_DIFFS) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1659 (all X all Y (-p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,X)))))) # label(aREALu_NOTu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1660 (all Q49829 all Q49834 all F0 ((all X all Y (s(Q49829,i(s(fun(Q49834,Q49829),F0),s(Q49834,X))) = s(Q49829,i(s(fun(Q49834,Q49829),F0),s(Q49834,Y))) -> s(Q49834,Y) = s(Q49834,X))) <-> (all X all Y (s(Q49834,X) = s(Q49834,Y) <-> s(Q49829,i(s(fun(Q49834,Q49829),F0),s(Q49834,Y))) = s(Q49829,i(s(fun(Q49834,Q49829),F0),s(Q49834,X))))))) # label(aINJECTIVEu_ALT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1661 (all B all A all Y all S0 all F0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0)))))) <-> (exists X (s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))))) # label(aINu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1662 (all B all A (p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))) -> (all H0 all S0 ((all F0 all G0 all X ((all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Z0))),s(A,X)))) -> s(B,i(s(fun(A,B),F0),s(A,Z0))) = s(B,i(s(fun(A,B),G0),s(A,Z0))) & p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),S0),s(A,Z0))),s(B,i(s(fun(A,B),F0),s(A,Z0)))))))) -> s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),G0))),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X))) & p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),S0),s(A,X))),s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X)))))))) -> (exists F0 all X s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X)))))))) # label(aWFu_RECu_INVARIANT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1663 (all Q18919 all Q18913 exists V ((p(s(bool,V)) <-> s(Q18919,a0) = s(Q18919,i(s(fun(prod(Q18919,Q18913),Q18919),fst),s(prod(Q18919,Q18913),h0)))) & s(Q18913,i(s(fun(list(prod(Q18919,Q18913)),Q18913),i(s(fun(Q18919,fun(list(prod(Q18919,Q18913)),Q18913)),assoc),s(Q18919,a0))),s(list(prod(Q18919,Q18913)),i(s(fun(list(prod(Q18919,Q18913)),list(prod(Q18919,Q18913))),i(s(fun(prod(Q18919,Q18913),fun(list(prod(Q18919,Q18913)),list(prod(Q18919,Q18913)))),cons),s(prod(Q18919,Q18913),h0))),s(list(prod(Q18919,Q18913)),t0))))) = s(Q18913,i(s(fun(Q18913,Q18913),i(s(fun(Q18913,fun(Q18913,Q18913)),i(s(fun(bool,fun(Q18913,fun(Q18913,Q18913))),cond),s(bool,V))),s(Q18913,i(s(fun(prod(Q18919,Q18913),Q18913),snd),s(prod(Q18919,Q18913),h0))))),s(Q18913,i(s(fun(list(prod(Q18919,Q18913)),Q18913),i(s(fun(Q18919,fun(list(prod(Q18919,Q18913)),Q18913)),assoc),s(Q18919,a0))),s(list(prod(Q18919,Q18913)),t0))))))) # label(aASSOC) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1664 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,X))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_gt),s(int,X))),s(int,Y)))) # label(aINTu_GT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1665 (all X all M0 all N0 exists V ((s(num,X) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) <-> p(s(bool,V))) & (exists VI_ ((exists VI_I_ ((s(num,X) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> p(s(bool,VI_I_))) & s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,VI_I_))),s(bool,VI_))),s(bool,V))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0))))))) & (p(s(bool,VI_)) <-> (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,M0) -> s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) # label(aLEu_EXP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1666 (all X (p(s(bool,i(s(fun(real,bool),integer),s(real,X)))) <-> (exists N0 s(real,i(s(fun(real,real),realu_abs),s(real,X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))))) # label(ainteger) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1667 (all X all Y all Z0 s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Y))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Z0))))) = s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,Y))),s(nadd,Z0)))) # label(aNADDu_LEu_LADD) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1668 (all A all H0 ((all F0 all G0 all N0 ((all M0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> s(A,i(s(fun(num,A),F0),s(num,M0))) = s(A,i(s(fun(num,A),G0),s(num,M0))))) -> s(A,i(s(fun(num,A),i(s(fun(fun(num,A),fun(num,A)),H0),s(fun(num,A),G0))),s(num,N0))) = s(A,i(s(fun(num,A),i(s(fun(fun(num,A),fun(num,A)),H0),s(fun(num,A),F0))),s(num,N0))))) -> (exists F0 all N0 s(A,i(s(fun(num,A),F0),s(num,N0))) = s(A,i(s(fun(num,A),i(s(fun(fun(num,A),fun(num,A)),H0),s(fun(num,A),F0))),s(num,N0)))))) # label(aWFu_RECu_num) # label(axiom) # label(non_clause). [assumption]. 14.50/14.55 1669 (all X all M0 all N0 ((exists V (((s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))) <-> p(s(bool,V))) & (exists VI_ ((p(s(bool,VI_)) <-> s(num,X) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))) & (exists VI_I_ (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,VI_))),s(bool,V))),s(bool,VI_I_)))) & (p(s(bool,VI_I_)) <-> s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) = s(num,X) | s(num,N0) = s(num,M0)))))))) <-> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,M0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0))))) # label(aEQu_EXP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1670 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,X))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y)))) # label(aREALu_MULu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1671 (all N0 (p(s(bool,i(s(fun(num,bool),odd),s(num,i(s(fun(num,num),suc),s(num,N0)))))) <-> -p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))))) # label(aODDu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1672 (all M0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) & p(s(bool,i(s(fun(num,bool),even),s(num,M0)))) <-> p(s(bool,i(s(fun(num,bool),even),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,N0)))))))) # label(aEVENu_EXP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1673 (all W all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,W))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,W))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0)))))))) # label(aREALu_LTu_ADD2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1674 (all X (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) <-> s(int,X) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(int,num),numu_ofu_int),s(int,X))))))) # label(aNUMu_OFu_INT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1675 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) <-> s(num,N0) = s(num,M0))) # label(aSsrnato_eqnu_leq) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1676 (all P0 (p(s(bool,i(s(fun(n10,bool),P0),s(n10,one)))) -> (all X p(s(bool,i(s(fun(n10,bool),P0),s(n10,X))))))) # label(aoneu_INDUCT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1677 (all A all S0 all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,Y)))))) <-> s(A,X) != s(A,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))) # label(aINu_DELETE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1678 (all Q92923 p(s(bool,i(s(fun(fun(Q92923,bool),bool),countable),s(fun(Q92923,bool),empty))))) # label(aCOUNTABLEu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1679 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y)))))) # label(aINTu_LEu_ADDR) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1680 (all Q82421 all Q82424 all P0 all G0 all H0 all HI_ (p(s(bool,i(s(fun(fun(Q82424,fun(Q82424,bool)),bool),wf),s(fun(Q82424,fun(Q82424,bool)),l_l_)))) & (all F0 all G1 all X ((all Z0 (p(s(bool,i(s(fun(Q82424,bool),i(s(fun(Q82424,fun(Q82424,bool)),l_l_),s(Q82424,Z0))),s(Q82424,X)))) -> s(Q82421,i(s(fun(Q82424,Q82421),G1),s(Q82424,Z0))) = s(Q82421,i(s(fun(Q82424,Q82421),F0),s(Q82424,Z0))))) -> s(Q82424,i(s(fun(Q82424,Q82424),i(s(fun(fun(Q82424,Q82421),fun(Q82424,Q82424)),G0),s(fun(Q82424,Q82421),G1))),s(Q82424,X))) = s(Q82424,i(s(fun(Q82424,Q82424),i(s(fun(fun(Q82424,Q82421),fun(Q82424,Q82424)),G0),s(fun(Q82424,Q82421),F0))),s(Q82424,X))) & s(Q82421,i(s(fun(Q82424,Q82421),i(s(fun(fun(Q82424,Q82421),fun(Q82424,Q82421)),HI_),s(fun(Q82424,Q82421),F0))),s(Q82424,X))) = s(Q82421,i(s(fun(Q82424,Q82421),i(s(fun(fun(Q82424,Q82421),fun(Q82424,Q82421)),HI_),s(fun(Q82424,Q82421),G1))),s(Q82424,X))) & s(bool,i(s(fun(Q82424,bool),i(s(fun(fun(Q82424,Q82421),fun(Q82424,bool)),P0),s(fun(Q82424,Q82421),F0))),s(Q82424,X))) = s(bool,i(s(fun(Q82424,bool),i(s(fun(fun(Q82424,Q82421),fun(Q82424,bool)),P0),s(fun(Q82424,Q82421),G1))),s(Q82424,X))))) & (all F0 all X all Y (p(s(bool,i(s(fun(Q82424,bool),i(s(fun(fun(Q82424,Q82421),fun(Q82424,bool)),P0),s(fun(Q82424,Q82421),F0))),s(Q82424,X)))) & p(s(bool,i(s(fun(Q82424,bool),i(s(fun(Q82424,fun(Q82424,bool)),l_l_),s(Q82424,Y))),s(Q82424,i(s(fun(Q82424,Q82424),i(s(fun(fun(Q82424,Q82421),fun(Q82424,Q82424)),G0),s(fun(Q82424,Q82421),F0))),s(Q82424,X)))))) -> p(s(bool,i(s(fun(Q82424,bool),i(s(fun(Q82424,fun(Q82424,bool)),l_l_),s(Q82424,Y))),s(Q82424,X)))))) & (all F0 all X s(Q82421,i(s(fun(Q82424,Q82421),i(s(fun(fun(Q82424,Q82421),fun(Q82424,Q82421)),H0),s(fun(Q82424,Q82421),F0))),s(Q82424,X))) = s(Q82421,i(s(fun(Q82421,Q82421),i(s(fun(Q82421,fun(Q82421,Q82421)),i(s(fun(bool,fun(Q82421,fun(Q82421,Q82421))),cond),s(bool,i(s(fun(Q82424,bool),i(s(fun(fun(Q82424,Q82421),fun(Q82424,bool)),P0),s(fun(Q82424,Q82421),F0))),s(Q82424,X))))),s(Q82421,i(s(fun(Q82424,Q82421),F0),s(Q82424,i(s(fun(Q82424,Q82424),i(s(fun(fun(Q82424,Q82421),fun(Q82424,Q82424)),G0),s(fun(Q82424,Q82421),F0))),s(Q82424,X))))))),s(Q82421,i(s(fun(Q82424,Q82421),i(s(fun(fun(Q82424,Q82421),fun(Q82424,Q82421)),HI_),s(fun(Q82424,Q82421),F0))),s(Q82424,X)))))) -> (exists F0 all X s(Q82421,i(s(fun(Q82424,Q82421),F0),s(Q82424,X))) = s(Q82421,i(s(fun(Q82424,Q82421),i(s(fun(fun(Q82424,Q82421),fun(Q82424,Q82421)),H0),s(fun(Q82424,Q82421),F0))),s(Q82424,X)))))) # label(aWFu_RECu_TAILu_GENERALi_) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1681 (all Q71060 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q71060,bool),bool),i(s(fun(fun(Q71060,bool),fun(fun(Q71060,bool),bool)),subset),s(fun(Q71060,bool),T0))),s(fun(Q71060,bool),S0)))) & p(s(bool,i(s(fun(fun(Q71060,bool),bool),finite),s(fun(Q71060,bool),S0)))) -> s(real,i(s(fun(fun(Q71060,real),real),i(s(fun(fun(Q71060,bool),fun(fun(Q71060,real),real)),sum),s(fun(Q71060,bool),i(s(fun(fun(Q71060,bool),fun(Q71060,bool)),i(s(fun(fun(Q71060,bool),fun(fun(Q71060,bool),fun(Q71060,bool))),diff),s(fun(Q71060,bool),S0))),s(fun(Q71060,bool),T0))))),s(fun(Q71060,real),F0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(fun(Q71060,real),real),i(s(fun(fun(Q71060,bool),fun(fun(Q71060,real),real)),sum),s(fun(Q71060,bool),S0))),s(fun(Q71060,real),F0))))),s(real,i(s(fun(fun(Q71060,real),real),i(s(fun(fun(Q71060,bool),fun(fun(Q71060,real),real)),sum),s(fun(Q71060,bool),T0))),s(fun(Q71060,real),F0))))))) # label(aSUMu_DIFF) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1682 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y)))))) <-> s(real,Y) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) | s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,X))) # label(aREALu_MULu_POSu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1683 (all X all K0 ((all N0 p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,N0))))),s(nadd,X))))),s(nadd,K0))))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) # label(aNADDu_ARCHu_ZERO) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1684 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),infinite),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(sum0(A,B),bool),fun(fun(B,bool),bool)),a_u_c),s(fun(sum0(A,B),bool),i(s(fun(fun(B,bool),fun(sum0(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(sum0(A,B),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(B,bool),T0)))))) # label(aCARDu_ADDu_ABSORB) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1685 (all X all Y all Z0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,Z0))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0)))))) # label(aINTu_LTu_LADD) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1686 (all A all P0 all Q0 ((exists X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> p(s(bool,Q0)))) <-> ((all X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) -> p(s(bool,Q0))))) # label(aLEFTu_IMPu_FORALLu_THM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1687 (all T0 (p(s(bool,T0)) <-> --p(s(bool,T0)))) # label(aNOTu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1688 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Y))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) # label(aINTu_LTu_ADD1) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1689 (all M0 all N0 exists V ((p(s(bool,V)) <-> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) & s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))) = s(num,M0)) & (exists VI_ ((p(s(bool,VI_)) <-> s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))) & (exists VI_I_ (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,VI_))),s(bool,V))),s(bool,VI_I_)))) & (p(s(bool,VI_I_)) <-> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))) = s(num,M0) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))),s(num,N0))))))))))) # label(aDIVISIONu_0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1690 (all A all B all U_1 ((all T0 all GENR_PVARR_247 ((exists L exists V (p(s(bool,i(s(fun(list(B),bool),i(s(fun(bool,fun(list(B),bool)),i(s(fun(list(B),fun(bool,fun(list(B),bool))),setspec),s(list(B),GENR_PVARR_247))),s(bool,V))),s(list(B),L)))) & (p(s(bool,V)) <-> (all X (p(s(bool,i(s(fun(list(B),bool),i(s(fun(B,fun(list(B),bool)),mem),s(B,X))),s(list(B),L)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,X))),s(fun(B,bool),T0))))))))) <-> p(s(bool,i(s(fun(list(B),bool),i(s(fun(fun(B,bool),fun(list(B),bool)),U_1),s(fun(B,bool),T0))),s(list(B),GENR_PVARR_247)))))) -> (all U_0 ((all S0 all GENR_PVARR_246 (p(s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,bool),fun(list(A),bool)),U_0),s(fun(A,bool),S0))),s(list(A),GENR_PVARR_246)))) <-> (exists L exists V (p(s(bool,i(s(fun(list(A),bool),i(s(fun(bool,fun(list(A),bool)),i(s(fun(list(A),fun(bool,fun(list(A),bool))),setspec),s(list(A),GENR_PVARR_246))),s(bool,V))),s(list(A),L)))) & (p(s(bool,V)) <-> (all X (p(s(bool,i(s(fun(list(A),bool),i(s(fun(A,fun(list(A),bool)),mem),s(A,X))),s(list(A),L)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))))))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(list(B),bool),bool),i(s(fun(fun(list(A),bool),fun(fun(list(B),bool),bool)),l_a_u_c),s(fun(list(A),bool),i(s(fun(fun(list(A),bool),fun(list(A),bool)),gspec),s(fun(list(A),bool),i(s(fun(fun(A,bool),fun(list(A),bool)),U_0),s(fun(A,bool),S0))))))),s(fun(list(B),bool),i(s(fun(fun(list(B),bool),fun(list(B),bool)),gspec),s(fun(list(B),bool),i(s(fun(fun(B,bool),fun(list(B),bool)),U_1),s(fun(B,bool),T0)))))))))))))) # label(aCARDu_LEu_LIST) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1691 (all A all X s(bool,i(s(fun(A,bool),empty),s(A,X))) = s(bool,f0)) # label(aEMPTY) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1692 (all A all S0 all F0 all B0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(A,real),F0),s(A,X))))))),s(real,B0)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))))),s(real,B0)))))))) # label(aSUMu_ABSu_BOUND) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1693 (all Q90344 all Q90347 all S0 all T0 all X all Y (p(s(bool,i(s(fun(fun(Q90344,bool),bool),i(s(fun(Q90344,fun(fun(Q90344,bool),bool)),in),s(Q90344,X))),s(fun(Q90344,bool),S0)))) & p(s(bool,i(s(fun(fun(Q90347,bool),bool),i(s(fun(Q90347,fun(fun(Q90347,bool),bool)),in),s(Q90347,Y))),s(fun(Q90347,bool),T0)))) <-> p(s(bool,i(s(fun(fun(prod(Q90344,Q90347),bool),bool),i(s(fun(prod(Q90344,Q90347),fun(fun(prod(Q90344,Q90347),bool),bool)),in),s(prod(Q90344,Q90347),i(s(fun(Q90347,prod(Q90344,Q90347)),i(s(fun(Q90344,fun(Q90347,prod(Q90344,Q90347))),c_),s(Q90344,X))),s(Q90347,Y))))),s(fun(prod(Q90344,Q90347),bool),i(s(fun(fun(Q90347,bool),fun(prod(Q90344,Q90347),bool)),i(s(fun(fun(Q90344,bool),fun(fun(Q90347,bool),fun(prod(Q90344,Q90347),bool))),t_u_c),s(fun(Q90344,bool),S0))),s(fun(Q90347,bool),T0)))))))) # label(aINu_CARDu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1694 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))) # label(aARITHu_ADDu_conjunct7) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1695 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,Y))),s(real,X)))) # label(aREALu_MINu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1696 (all A all P0 all Q0 ((all X (p(s(bool,P0)) -> p(s(bool,Q0)))) <-> ((exists X p(s(bool,P0))) -> (all X p(s(bool,Q0)))))) # label(aTRIVu_FORALLu_IMPu_THM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1697 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0))))) = s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))))) # label(aARITHu_MULTu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1698 (all A all P all B all U_5 ((all P0 all H0 all K0 all F0 all X s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B))),i(s(fun(fun(fun(A,B),fun(P,B)),fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,B)),fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B))))),U_5),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,B)),H0))),s(fun(fun(A,B),fun(P,B)),K0))),s(fun(A,B),F0))),s(P,X))) = s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,X))))),s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),H0),s(fun(A,B),F0))),s(P,X))))),s(B,i(s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),K0),s(fun(A,B),F0))),s(P,X)))))) -> (all U_4 ((all P0 all H0 all K0 all F0 s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B))),i(s(fun(fun(fun(A,B),fun(P,B)),fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,B)),fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B))))),U_5),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,B)),H0))),s(fun(fun(A,B),fun(P,B)),K0))),s(fun(A,B),F0))) = s(fun(P,B),i(s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B))),i(s(fun(fun(fun(A,B),fun(P,B)),fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,B)),fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B))))),U_4),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,B)),H0))),s(fun(fun(A,B),fun(P,B)),K0))),s(fun(A,B),F0)))) -> (all U_3 ((all P0 all F0 all X (-p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool))),U_3),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(A,B),F0))),s(P,X)))))) -> (all U_2 ((all P0 all F0 s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool))),U_3),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(A,B),F0))) = s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool))),U_2),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(A,B),F0)))) -> (all U_1 ((all P0 all P1 all F0 all X (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool)))),U_1),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,bool)),P1))),s(fun(A,B),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P1),s(fun(A,B),F0))),s(P,X)))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),P0),s(fun(A,B),F0))),s(P,X)))))) -> (all U_0 ((all P0 all P1 all F0 s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool)))),U_1),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,bool)),P1))),s(fun(A,B),F0))) = s(fun(P,bool),i(s(fun(fun(A,B),fun(P,bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool)))),U_0),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,bool)),P1))),s(fun(A,B),F0)))) -> (all L_L_ all P0 all P1 all S0 all H0 all K0 (p(s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),superadmissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool)))),U_0),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool))),U_2),s(fun(fun(A,B),fun(P,bool)),P1))))))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),K0)))) & p(s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),superadmissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(A,B),fun(P,bool)))),U_0),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(fun(A,B),fun(P,bool)),P1))))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),H0)))) & p(s(bool,i(s(fun(fun(fun(A,B),fun(P,bool)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,bool)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,bool)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,bool)),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,bool)),P1)))) -> p(s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),superadmissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),i(s(fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B))),i(s(fun(fun(fun(A,B),fun(P,B)),fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B)))),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(fun(A,B),fun(P,B)),fun(fun(fun(A,B),fun(P,B)),fun(fun(A,B),fun(P,B))))),U_4),s(fun(fun(A,B),fun(P,bool)),P1))),s(fun(fun(A,B),fun(P,B)),H0))),s(fun(fun(A,B),fun(P,B)),K0)))))))))))))))))))) # label(aSUPERADMISSIBLEu_COND) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1699 (all A all S0 -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(A,bool),S0))))) # label(aCARDu_LTu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1700 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y)))))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y)))))))) # label(aINTu_MAXu_MAX) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1701 (all N0 p(s(bool,i(s(fun(num,bool),even),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))))) # label(aEVENu_DOUBLE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1702 (all X all Y all Z0 p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),Z0))))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y))))),s(prod(hreal,hreal),Z0))))))) # label(aTREALu_ADDu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1703 (all N all A all M all X all Y s(cart(A,M),i(s(fun(cart(A,finite_sum(M,N)),cart(A,M)),fstcart),s(cart(A,finite_sum(M,N)),i(s(fun(cart(A,N),cart(A,finite_sum(M,N))),i(s(fun(cart(A,M),fun(cart(A,N),cart(A,finite_sum(M,N)))),pastecart),s(cart(A,M),X))),s(cart(A,N),Y))))) = s(cart(A,M),X)) # label(aFSTCARTu_PASTECART) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1704 (all U_0 ((all F0 all I0 s(num,i(s(fun(num,num),i(s(fun(fun(num,num),fun(num,num)),U_0),s(fun(num,num),F0))),s(num,I0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))))),s(num,i(s(fun(num,num),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) -> (all F0 all M0 all N0 s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),i(s(fun(fun(num,num),fun(num,num)),U_0),s(fun(num,num),F0))))) = s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,num),F0)))))) # label(aNSUMu_PAIR) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1705 (all Q63584 all Q63585 all OP all F0 all S0 p(s(bool,i(s(fun(fun(Q63585,bool),bool),i(s(fun(fun(Q63585,bool),fun(fun(Q63585,bool),bool)),subset),s(fun(Q63585,bool),i(s(fun(fun(Q63585,bool),fun(Q63585,bool)),i(s(fun(fun(Q63585,Q63584),fun(fun(Q63585,bool),fun(Q63585,bool))),i(s(fun(fun(Q63584,fun(Q63584,Q63584)),fun(fun(Q63585,Q63584),fun(fun(Q63585,bool),fun(Q63585,bool)))),support),s(fun(Q63584,fun(Q63584,Q63584)),OP))),s(fun(Q63585,Q63584),F0))),s(fun(Q63585,bool),S0))))),s(fun(Q63585,bool),S0))))) # label(aSUPPORTu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1706 (all A all E0 ((all FN all XI_ (s(A,i(s(fun(n10,A),FN),s(n10,one))) = s(A,E0) & s(A,E0) = s(A,i(s(fun(n10,A),XI_),s(n10,one))) -> s(fun(n10,A),FN) = s(fun(n10,A),XI_))) & (exists FN s(A,i(s(fun(n10,A),FN),s(n10,one))) = s(A,E0)))) # label(aoneu_Axiom) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1707 (all B all A all F0 ((all X all Y (s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) -> s(A,X) = s(A,Y))) -> (all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),infinite),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0)))))))))) # label(aINFINITEu_IMAGEu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1708 (all X s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) # label(aREALu_POLYu_CLAUSESu_conjunct8) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1709 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,i(s(fun(int,int),intu_neg),s(int,Y))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y)))) # label(aINTu_SUBu_RNEG) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1710 (all Q63859 all Q63707 all F0 all X all S0 s(fun(Q63707,bool),i(s(fun(fun(Q63707,bool),fun(Q63707,bool)),i(s(fun(fun(Q63707,Q63859),fun(fun(Q63707,bool),fun(Q63707,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63707,Q63859),fun(fun(Q63707,bool),fun(Q63707,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63707,Q63859),F0))),s(fun(Q63707,bool),i(s(fun(Q63707,fun(Q63707,bool)),i(s(fun(fun(Q63707,bool),fun(Q63707,fun(Q63707,bool))),delete),s(fun(Q63707,bool),S0))),s(Q63707,X))))) = s(fun(Q63707,bool),i(s(fun(Q63707,fun(Q63707,bool)),i(s(fun(fun(Q63707,bool),fun(Q63707,fun(Q63707,bool))),delete),s(fun(Q63707,bool),i(s(fun(fun(Q63707,bool),fun(Q63707,bool)),i(s(fun(fun(Q63707,Q63859),fun(fun(Q63707,bool),fun(Q63707,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63707,Q63859),fun(fun(Q63707,bool),fun(Q63707,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63707,Q63859),F0))),s(fun(Q63707,bool),S0))))),s(Q63707,X)))) # label(aSUPPORTu_CLAUSESu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1711 (all X all Y s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,i(s(fun(real,real),realu_abs),s(real,Y)))))) # label(aREALu_ABSu_DIV) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1712 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0)))))))) # label(aREALu_LTu_RMUL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1713 (all D all C all A all B all F0 all G0 all H0 s(fun(A,D),i(s(fun(fun(A,C),fun(A,D)),i(s(fun(fun(C,D),fun(fun(A,C),fun(A,D))),o),s(fun(C,D),F0))),s(fun(A,C),i(s(fun(fun(A,B),fun(A,C)),i(s(fun(fun(B,C),fun(fun(A,B),fun(A,C))),o),s(fun(B,C),G0))),s(fun(A,B),H0))))) = s(fun(A,D),i(s(fun(fun(A,B),fun(A,D)),i(s(fun(fun(B,D),fun(fun(A,B),fun(A,D))),o),s(fun(B,D),i(s(fun(fun(B,C),fun(B,D)),i(s(fun(fun(C,D),fun(fun(B,C),fun(B,D))),o),s(fun(C,D),F0))),s(fun(B,C),G0))))),s(fun(A,B),H0)))) # label(aou_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1714 (all X all N0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))),s(real,X))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X))))),s(num,N0)))))))) # label(aREALu_POWu_LBOUND) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1715 (all A all S0 -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),S0))))) # label(aPSUBSETu_IRREFL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.56 1716 (all A all P0 all Q0 ((all X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) & p(s(bool,Q0)))) <-> (all X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) & p(s(bool,Q0)))) # label(aLEFTu_ANDu_FORALLu_THM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1717 (all Q49989 all Q49986 all F0 all S0 ((exists G0 all X (p(s(bool,i(s(fun(fun(Q49986,bool),bool),i(s(fun(Q49986,fun(fun(Q49986,bool),bool)),in),s(Q49986,X))),s(fun(Q49986,bool),S0)))) -> s(Q49986,i(s(fun(Q49989,Q49986),G0),s(Q49989,i(s(fun(Q49986,Q49989),F0),s(Q49986,X))))) = s(Q49986,X))) <-> (all X all Y (p(s(bool,i(s(fun(fun(Q49986,bool),bool),i(s(fun(Q49986,fun(fun(Q49986,bool),bool)),in),s(Q49986,X))),s(fun(Q49986,bool),S0)))) & p(s(bool,i(s(fun(fun(Q49986,bool),bool),i(s(fun(Q49986,fun(fun(Q49986,bool),bool)),in),s(Q49986,Y))),s(fun(Q49986,bool),S0)))) & s(Q49989,i(s(fun(Q49986,Q49989),F0),s(Q49986,X))) = s(Q49989,i(s(fun(Q49986,Q49989),F0),s(Q49986,Y))) -> s(Q49986,X) = s(Q49986,Y))))) # label(aINJECTIVEu_ONu_LEFTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1718 (all P0 (p(s(bool,i(s(fun(bool,bool),P0),s(bool,f0)))) & p(s(bool,i(s(fun(bool,bool),P0),s(bool,t)))) -> (all X p(s(bool,i(s(fun(bool,bool),P0),s(bool,X))))))) # label(aboolu_INDUCT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1719 (all X s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aINTu_MULu_RZERO) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1720 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Z0)))))) # label(aREALu_LTu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1721 (all X all Y (s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(int,X) = s(int,i(s(fun(int,int),intu_neg),s(int,Y))))) # label(aINTu_LNEGu_UNIQ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1722 (all M0 all N0 (s(bool,i(s(fun(num,bool),odd),s(num,M0))) != s(bool,i(s(fun(num,bool),odd),s(num,N0))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))) <-> p(s(bool,i(s(fun(num,bool),odd),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0)))))))) # label(aODDu_SUB) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1723 (all Q20354 all L all X ((exists I0 (s(Q20354,X) = s(Q20354,i(s(fun(list(Q20354),Q20354),i(s(fun(num,fun(list(Q20354),Q20354)),el),s(num,I0))),s(list(Q20354),L))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,I0))),s(num,i(s(fun(list(Q20354),num),length),s(list(Q20354),L)))))))) <-> p(s(bool,i(s(fun(list(Q20354),bool),i(s(fun(Q20354,fun(list(Q20354),bool)),mem),s(Q20354,X))),s(list(Q20354),L)))))) # label(aMEMu_EXISTSu_EL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1724 (all X exists B0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))))))))),s(num,B0))))) # label(aNADDu_SUC) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1725 (all A all P0 ((all C0 ((all X all Y (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),X))),s(fun(fun(A,bool),bool),C0)))) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),Y))),s(fun(fun(A,bool),bool),C0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),Y))),s(fun(A,bool),X)))) | p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),X))),s(fun(A,bool),Y)))))) & (all X (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),X))),s(fun(fun(A,bool),bool),C0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),X)))))) -> p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),unions),s(fun(fun(A,bool),bool),C0)))))))) -> (exists A5 (p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),A5)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),X)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),A5))),s(fun(A,bool),X)))) -> s(fun(A,bool),X) = s(fun(A,bool),A5))))))) # label(aZLu_SUBSETSu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1726 (all Q18767 all Q18766 (p(s(bool,i(s(fun(list(Q18766),bool),i(s(fun(list(Q18767),fun(list(Q18766),bool)),i(s(fun(fun(Q18767,fun(Q18766,bool)),fun(list(Q18767),fun(list(Q18766),bool))),all2),s(fun(Q18767,fun(Q18766,bool)),p0))),s(list(Q18767),i(s(fun(list(Q18767),list(Q18767)),i(s(fun(Q18767,fun(list(Q18767),list(Q18767))),cons),s(Q18767,h1))),s(list(Q18767),t1))))),s(list(Q18766),i(s(fun(list(Q18766),list(Q18766)),i(s(fun(Q18766,fun(list(Q18766),list(Q18766))),cons),s(Q18766,h2))),s(list(Q18766),t2)))))) <-> p(s(bool,i(s(fun(list(Q18766),bool),i(s(fun(list(Q18767),fun(list(Q18766),bool)),i(s(fun(fun(Q18767,fun(Q18766,bool)),fun(list(Q18767),fun(list(Q18766),bool))),all2),s(fun(Q18767,fun(Q18766,bool)),p0))),s(list(Q18767),t1))),s(list(Q18766),t2)))) & p(s(bool,i(s(fun(Q18766,bool),i(s(fun(Q18767,fun(Q18766,bool)),p0),s(Q18767,h1))),s(Q18766,h2)))))) # label(aALL2u_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1727 (all Q71149 all F0 all S0 s(real,i(s(fun(fun(Q71149,real),real),i(s(fun(fun(Q71149,bool),fun(fun(Q71149,real),real)),sum),s(fun(Q71149,bool),S0))),s(fun(Q71149,real),F0))) = s(real,i(s(fun(fun(Q71149,real),real),i(s(fun(fun(Q71149,bool),fun(fun(Q71149,real),real)),sum),s(fun(Q71149,bool),i(s(fun(fun(Q71149,bool),fun(Q71149,bool)),i(s(fun(fun(Q71149,real),fun(fun(Q71149,bool),fun(Q71149,bool))),i(s(fun(fun(real,fun(real,real)),fun(fun(Q71149,real),fun(fun(Q71149,bool),fun(Q71149,bool)))),support),s(fun(real,fun(real,real)),realu_add))),s(fun(Q71149,real),F0))),s(fun(Q71149,bool),S0))))),s(fun(Q71149,real),F0)))) # label(aSUMu_SUPPORT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1728 (all X all Y s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),X))) = s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))) # label(aTREALu_EQu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1729 (all M0 all N0 p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,M0))))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,N0))))))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))))))) # label(aNADDu_OFu_NUMu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1730 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),poset),s(fun(prod(A,A),bool),L)))) -> (all X all Y (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) -> s(A,X) = s(A,Y))))) # label(aPOSETu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1731 (all Q45300 all S0 all X s(bool,i(s(fun(fun(Q45300,bool),bool),i(s(fun(Q45300,fun(fun(Q45300,bool),bool)),in),s(Q45300,X))),s(fun(Q45300,bool),S0))) = s(bool,i(s(fun(fun(Q45300,bool),bool),i(s(fun(fun(Q45300,bool),fun(fun(Q45300,bool),bool)),subset),s(fun(Q45300,bool),i(s(fun(fun(Q45300,bool),fun(Q45300,bool)),i(s(fun(Q45300,fun(fun(Q45300,bool),fun(Q45300,bool))),insert),s(Q45300,X))),s(fun(Q45300,bool),empty))))),s(fun(Q45300,bool),S0)))) # label(aSINGu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1732 (all M0 all N0 s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))) # label(aADDu_SUBR) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1733 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),p0),s(real,X))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),p0),s(real,Y))),s(real,X)))) & (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),p0),s(real,X))),s(real,Y)))))) -> (all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),p0),s(real,X))),s(real,Y))))) # label(aREALu_WLOGu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1734 (all S0 (p(s(bool,i(s(fun(fun(num,bool),bool),finite),s(fun(num,bool),S0)))) -> (exists A5 -p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,A5))),s(fun(num,bool),S0))))))) # label(anumu_FINITEu_AVOID) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1735 (all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,u_0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,u_0)))) # label(aARITHu_LEu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1736 (all Z all A all NONEI_ all SOMEI_ exists FN ((all A5 s(Z,i(s(fun(option(A),Z),FN),s(option(A),i(s(fun(A,option(A)),some),s(A,A5))))) = s(Z,i(s(fun(A,Z),SOMEI_),s(A,A5)))) & s(Z,NONEI_) = s(Z,i(s(fun(option(A),Z),FN),s(option(A),none))))) # label(aoptionu_RECURSION) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1737 (all A all B all S0 all T0 all F0 all G0 all H0 all K0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),H0),s(A,X))))),s(fun(B,bool),T0)))) & s(A,i(s(fun(B,A),K0),s(B,i(s(fun(A,B),H0),s(A,X))))) = s(A,X) & s(real,i(s(fun(B,real),G0),s(B,i(s(fun(A,B),H0),s(A,X))))) = s(real,i(s(fun(A,real),F0),s(A,X))))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> s(B,i(s(fun(A,B),H0),s(A,i(s(fun(B,A),K0),s(B,Y))))) = s(B,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(B,A),K0),s(B,Y))))),s(fun(A,bool),S0)))))) -> s(real,i(s(fun(fun(B,real),real),i(s(fun(fun(B,bool),fun(fun(B,real),real)),sum),s(fun(B,bool),T0))),s(fun(B,real),G0))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))) # label(aSUMu_EQu_GENERALu_INVERSES) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1738 (all N0 all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))) & s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,N0)))))))) # label(aINTu_POWu_LT2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1739 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),bit1),s(num,N0))))),s(num,u_0))) = s(num,i(s(fun(num,num),bit1),s(num,N0)))) # label(aARITHu_ADDu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1740 (all M0 all N0 s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),max),s(num,M0))),s(num,N0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,i(s(fun(num,real),realu_ofu_num),s(num,M0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))))) # label(aREALu_OFu_NUMu_MAX) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1741 (all X p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(nadd,X))))),s(nadd,X))))) # label(aNADDu_MULu_LID) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1742 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aCARDu_LEu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1743 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Z0))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y)))))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Z0))),s(int,Y)))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Z0))),s(int,X)))))) # label(aINTu_LEu_MAX) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1744 (all X all Y all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,Y))),s(num,N0)))))) <-> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,N0) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,X))),s(num,Y)))))) # label(aEXPu_MONOu_LE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1745 (all X all Y p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(int,int),intu_abs),s(int,X))))),s(int,i(s(fun(int,int),intu_abs),s(int,Y))))))),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))))))) # label(aINTu_SUBu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1746 (all M0 all N0 all X (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,M0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0)))))))) # label(aREALu_POWu_MONOu_INV) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1747 (all M0 all N0 p(s(bool,i(s(fun(fun(num,bool),bool),finite),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))))) # label(aFINITEu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1748 (all Q20471 all Q20470 all U_1 ((all P0 all Q0 all X all Y (p(s(bool,i(s(fun(Q20470,bool),i(s(fun(Q20471,fun(Q20470,bool)),i(s(fun(fun(Q20471,fun(Q20470,bool)),fun(Q20471,fun(Q20470,bool))),i(s(fun(fun(Q20471,fun(Q20470,bool)),fun(fun(Q20471,fun(Q20470,bool)),fun(Q20471,fun(Q20470,bool)))),U_1),s(fun(Q20471,fun(Q20470,bool)),P0))),s(fun(Q20471,fun(Q20470,bool)),Q0))),s(Q20471,X))),s(Q20470,Y)))) <-> p(s(bool,i(s(fun(Q20470,bool),i(s(fun(Q20471,fun(Q20470,bool)),P0),s(Q20471,X))),s(Q20470,Y)))) & p(s(bool,i(s(fun(Q20470,bool),i(s(fun(Q20471,fun(Q20470,bool)),Q0),s(Q20471,X))),s(Q20470,Y)))))) -> (all U_0 ((all P0 all Q0 all X s(fun(Q20470,bool),i(s(fun(Q20471,fun(Q20470,bool)),i(s(fun(fun(Q20471,fun(Q20470,bool)),fun(Q20471,fun(Q20470,bool))),i(s(fun(fun(Q20471,fun(Q20470,bool)),fun(fun(Q20471,fun(Q20470,bool)),fun(Q20471,fun(Q20470,bool)))),U_0),s(fun(Q20471,fun(Q20470,bool)),P0))),s(fun(Q20471,fun(Q20470,bool)),Q0))),s(Q20471,X))) = s(fun(Q20470,bool),i(s(fun(Q20471,fun(Q20470,bool)),i(s(fun(fun(Q20471,fun(Q20470,bool)),fun(Q20471,fun(Q20470,bool))),i(s(fun(fun(Q20471,fun(Q20470,bool)),fun(fun(Q20471,fun(Q20470,bool)),fun(Q20471,fun(Q20470,bool)))),U_1),s(fun(Q20471,fun(Q20470,bool)),P0))),s(fun(Q20471,fun(Q20470,bool)),Q0))),s(Q20471,X)))) -> (all P0 all Q0 all L all M0 (p(s(bool,i(s(fun(list(Q20470),bool),i(s(fun(list(Q20471),fun(list(Q20470),bool)),i(s(fun(fun(Q20471,fun(Q20470,bool)),fun(list(Q20471),fun(list(Q20470),bool))),all2),s(fun(Q20471,fun(Q20470,bool)),Q0))),s(list(Q20471),L))),s(list(Q20470),M0)))) & p(s(bool,i(s(fun(list(Q20470),bool),i(s(fun(list(Q20471),fun(list(Q20470),bool)),i(s(fun(fun(Q20471,fun(Q20470,bool)),fun(list(Q20471),fun(list(Q20470),bool))),all2),s(fun(Q20471,fun(Q20470,bool)),P0))),s(list(Q20471),L))),s(list(Q20470),M0)))) <-> p(s(bool,i(s(fun(list(Q20470),bool),i(s(fun(list(Q20471),fun(list(Q20470),bool)),i(s(fun(fun(Q20471,fun(Q20470,bool)),fun(list(Q20471),fun(list(Q20470),bool))),all2),s(fun(Q20471,fun(Q20470,bool)),i(s(fun(fun(Q20471,fun(Q20470,bool)),fun(Q20471,fun(Q20470,bool))),i(s(fun(fun(Q20471,fun(Q20470,bool)),fun(fun(Q20471,fun(Q20470,bool)),fun(Q20471,fun(Q20470,bool)))),U_0),s(fun(Q20471,fun(Q20470,bool)),P0))),s(fun(Q20471,fun(Q20470,bool)),Q0))))),s(list(Q20471),L))),s(list(Q20470),M0)))))))))) # label(aANDu_ALL2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1749 (all Q53649 all S0 all T0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53649,bool),fun(num,bool)),hasu_size),s(fun(Q53649,bool),S0))),s(num,M0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53649,bool),fun(num,bool)),hasu_size),s(fun(Q53649,bool),T0))),s(num,N0)))) & p(s(bool,i(s(fun(fun(Q53649,bool),bool),i(s(fun(fun(Q53649,bool),fun(fun(Q53649,bool),bool)),disjoint),s(fun(Q53649,bool),S0))),s(fun(Q53649,bool),T0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53649,bool),fun(num,bool)),hasu_size),s(fun(Q53649,bool),i(s(fun(fun(Q53649,bool),fun(Q53649,bool)),i(s(fun(fun(Q53649,bool),fun(fun(Q53649,bool),fun(Q53649,bool))),union),s(fun(Q53649,bool),S0))),s(fun(Q53649,bool),T0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))))) # label(aHASu_SIZEu_UNION) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1750 (all A all U_1 ((all L all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),U_1),s(fun(prod(A,A),bool),L))),s(A,Y)))) <-> -p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,Y)))))) -> (all U_0 ((all L all F0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),U_0),s(fun(prod(A,A),bool),L))),s(fun(prod(A,A),bool),F0)))) <-> (all X all Y exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(A,A),bool),F0),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y))))))),s(bool,V)))) & (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) | (s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),U_1),s(fun(prod(A,A),bool),L))))) = s(A,X) | p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X))))) & s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),U_1),s(fun(prod(A,A),bool),L))))) = s(A,Y) <-> p(s(bool,V))))))) -> (all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),L)))) & (exists X -p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X))))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),i(s(fun(fun(fun(prod(A,A),bool),bool),fun(prod(A,A),bool)),gabs),s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),U_0),s(fun(prod(A,A),bool),L)))))))))))))) # label(aORDINALu_SUC) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1751 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) <-> s(num,M0) = s(num,N0))) # label(aLEu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1752 (all M0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(num,M0)) # label(aSUBu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1753 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),poset),s(fun(prod(A,A),bool),L)))) -> (all C0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(A,bool),bool)),chain),s(fun(prod(A,A),bool),L))),s(fun(A,bool),C0)))) -> (exists P0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),C0))),s(fun(A,bool),P0)))) & (all R0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),P0))),s(fun(A,bool),R0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(A,bool),bool)),chain),s(fun(prod(A,A),bool),L))),s(fun(A,bool),R0)))) -> s(fun(A,bool),P0) = s(fun(A,bool),R0))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(A,bool),bool)),chain),s(fun(prod(A,A),bool),L))),s(fun(A,bool),P0)))))))))) # label(aKL) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1754 (all M0 all N0 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,M0))))),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,N0)))))) <-> s(num,N0) = s(num,M0))) # label(aTREALu_OFu_NUMu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1755 (all A s(fun(A,bool),i(s(fun(list(A),fun(A,bool)),setu_ofu_list),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,h0))),s(list(A),t0))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,h0))),s(fun(A,bool),i(s(fun(list(A),fun(A,bool)),setu_ofu_list),s(list(A),t0)))))) # label(asetu_ofu_listu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1756 (all A all U_1 ((all P0 all F0 all X s(num,i(s(fun(A,num),i(s(fun(fun(A,num),fun(A,num)),i(s(fun(fun(A,bool),fun(fun(A,num),fun(A,num))),U_1),s(fun(A,bool),P0))),s(fun(A,num),F0))),s(A,X))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(A,bool),P0),s(A,X))))),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) -> (all U_0 ((all S0 all P0 all GENR_PVARR_157 ((exists X exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_157))),s(bool,V))),s(A,X)))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,bool),P0))),s(A,GENR_PVARR_157)))))) -> (all P0 all S0 all F0 s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(fun(A,num),fun(A,num)),i(s(fun(fun(A,bool),fun(fun(A,num),fun(A,num))),U_1),s(fun(A,bool),P0))),s(fun(A,num),F0))))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,bool),P0))))))),s(fun(A,num),F0)))))))) # label(aNSUMu_RESTRICTu_SET) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1757 (all Q50396 all Q50395 all Q50375 all F0 all G0 ((all X all Y (s(Q50375,i(s(fun(Q50395,Q50375),G0),s(Q50395,X))) = s(Q50375,i(s(fun(Q50395,Q50375),G0),s(Q50395,Y))) -> s(Q50396,i(s(fun(Q50395,Q50396),F0),s(Q50395,X))) = s(Q50396,i(s(fun(Q50395,Q50396),F0),s(Q50395,Y))))) <-> (exists H0 s(fun(Q50395,Q50396),F0) = s(fun(Q50395,Q50396),i(s(fun(fun(Q50395,Q50375),fun(Q50395,Q50396)),i(s(fun(fun(Q50375,Q50396),fun(fun(Q50395,Q50375),fun(Q50395,Q50396))),o),s(fun(Q50375,Q50396),H0))),s(fun(Q50395,Q50375),G0)))))) # label(aFUNCTIONu_FACTORSu_LEFT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1758 (all X all Y (s(num,i(s(fun(num,num),numfst),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),numpair),s(num,X))),s(num,Y))))) = s(num,X) & s(num,Y) = s(num,i(s(fun(num,num),numsnd),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),numpair),s(num,X))),s(num,Y))))))) # label(aNUMPAIRu_DEST) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1759 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,Y))) = s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),i(s(fun(real,fun(fun(real,bool),fun(real,bool))),insert),s(real,X))),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),i(s(fun(real,fun(fun(real,bool),fun(real,bool))),insert),s(real,Y))),s(fun(real,bool),empty)))))))) # label(aREALu_MAXu_SUP) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1760 (all A all U_0 ((all S0 all P0 all GENR_PVARR_67 ((exists X exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_67))),s(bool,V))),s(A,X)))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,bool),P0))),s(A,GENR_PVARR_67)))))) -> (all S0 all P0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,bool),P0)))))))))))) # label(aFINITEu_RESTRICT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1761 (all A all P0 ((all X -p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) <-> -(exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) # label(aNOTu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1762 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) # label(aARITHu_LTu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1763 (all B all A all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),T0))),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0)))))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(B,bool),fun(fun(A,bool),bool)),l_a_u_c),s(fun(B,bool),T0))),s(fun(A,bool),S0)))))) # label(aCARDu_LEu_IMAGEu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1764 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (exists A5 exists N0 all N1 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,N1)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N1))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N1)))))))))))) # label(aNADDu_LBOUND) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1765 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))))) = s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))) # label(aCARDu_LTu_CARD) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1766 (all B all A all G0 all F0 (p(s(bool,i(s(fun(fun(B,A),bool),i(s(fun(fun(A,B),fun(fun(B,A),bool)),iso0),s(fun(A,B),F0))),s(fun(B,A),G0)))) <-> (all X s(B,X) = s(B,i(s(fun(A,B),F0),s(A,i(s(fun(B,A),G0),s(B,X)))))) & (all Y s(A,Y) = s(A,i(s(fun(B,A),G0),s(B,i(s(fun(A,B),F0),s(A,Y)))))))) # label(aISO) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1767 (all N0 exists V (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,V))),s(num,u_0))),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),pre),s(num,N0))))))) = s(num,i(s(fun(num,num),pre),s(num,i(s(fun(num,num),bit0),s(num,N0))))) & (p(s(bool,V)) <-> s(num,N0) = s(num,u_0)))) # label(aARITHu_PREu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1768 (all M0 all N0 all X (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(int,X)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,M0))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0)))))))) # label(aINTu_POWu_MONOu_LT) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1769 (all A all A5 all B0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),B0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),A5))),s(fun(A,bool),B0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),A5))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),B0)))))))) # label(aCARDu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1770 (all Q88517 all Q88521 all S0 (s(fun(Q88521,bool),S0) = s(fun(Q88521,bool),empty) <-> p(s(bool,i(s(fun(fun(Q88517,bool),bool),i(s(fun(fun(Q88521,bool),fun(fun(Q88517,bool),bool)),a_u_c),s(fun(Q88521,bool),S0))),s(fun(Q88517,bool),empty)))))) # label(aCARDu_EQu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1771 (all Q58502 all Q58505 all U_1 ((all R0 all X all F0 all Y ((s(Q58502,i(s(fun(Q58505,Q58502),F0),s(Q58505,X))) != s(Q58502,i(s(fun(Q58505,Q58502),F0),s(Q58505,Y))) -> p(s(bool,i(s(fun(Q58502,bool),i(s(fun(Q58502,fun(Q58502,bool)),R0),s(Q58502,i(s(fun(Q58505,Q58502),F0),s(Q58505,X))))),s(Q58502,i(s(fun(Q58505,Q58502),F0),s(Q58505,Y))))))) <-> p(s(bool,i(s(fun(Q58505,bool),i(s(fun(fun(Q58505,Q58502),fun(Q58505,bool)),i(s(fun(Q58505,fun(fun(Q58505,Q58502),fun(Q58505,bool))),i(s(fun(fun(Q58502,fun(Q58502,bool)),fun(Q58505,fun(fun(Q58505,Q58502),fun(Q58505,bool)))),U_1),s(fun(Q58502,fun(Q58502,bool)),R0))),s(Q58505,X))),s(fun(Q58505,Q58502),F0))),s(Q58505,Y)))))) -> (all U_0 ((all R0 all F0 all X s(fun(Q58505,bool),i(s(fun(Q58505,fun(Q58505,bool)),i(s(fun(fun(Q58505,Q58502),fun(Q58505,fun(Q58505,bool))),i(s(fun(fun(Q58502,fun(Q58502,bool)),fun(fun(Q58505,Q58502),fun(Q58505,fun(Q58505,bool)))),U_0),s(fun(Q58502,fun(Q58502,bool)),R0))),s(fun(Q58505,Q58502),F0))),s(Q58505,X))) = s(fun(Q58505,bool),i(s(fun(fun(Q58505,Q58502),fun(Q58505,bool)),i(s(fun(Q58505,fun(fun(Q58505,Q58502),fun(Q58505,bool))),i(s(fun(fun(Q58502,fun(Q58502,bool)),fun(Q58505,fun(fun(Q58505,Q58502),fun(Q58505,bool)))),U_1),s(fun(Q58502,fun(Q58502,bool)),R0))),s(Q58505,X))),s(fun(Q58505,Q58502),F0)))) -> (all R0 all F0 s(bool,i(s(fun(fun(Q58505,bool),bool),i(s(fun(fun(Q58505,fun(Q58505,bool)),fun(fun(Q58505,bool),bool)),pairwise),s(fun(Q58505,fun(Q58505,bool)),i(s(fun(fun(Q58505,Q58502),fun(Q58505,fun(Q58505,bool))),i(s(fun(fun(Q58502,fun(Q58502,bool)),fun(fun(Q58505,Q58502),fun(Q58505,fun(Q58505,bool)))),U_0),s(fun(Q58502,fun(Q58502,bool)),R0))),s(fun(Q58505,Q58502),F0))))),s(fun(Q58505,bool),s0))) = s(bool,i(s(fun(fun(Q58502,bool),bool),i(s(fun(fun(Q58502,fun(Q58502,bool)),fun(fun(Q58502,bool),bool)),pairwise),s(fun(Q58502,fun(Q58502,bool)),R0))),s(fun(Q58502,bool),i(s(fun(fun(Q58505,bool),fun(Q58502,bool)),i(s(fun(fun(Q58505,Q58502),fun(fun(Q58505,bool),fun(Q58502,bool))),image),s(fun(Q58505,Q58502),F0))),s(fun(Q58505,bool),s0)))))))))) # label(aPAIRWISEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1772 (all B all A all F0 all S0 ((all X all Y (s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,Y) = s(A,X))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(B,bool),fun(fun(A,bool),bool)),a_u_c),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(A,bool),S0)))))) # label(aCARDu_EQu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1773 (all A all B (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),univ)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),univ)))) -> p(s(bool,i(s(fun(fun(fun(A,B),bool),bool),finite),s(fun(fun(A,B),bool),univ)))))) # label(aFINITEu_FUNSPACEu_UNIV) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1774 (all X p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(prod(hreal,hreal),X))))),s(prod(hreal,hreal),X))))) # label(aTREALu_ADDu_LID) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1775 (all A5 all B0 ((all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,N0))))),s(num,B0))))) <-> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,A5))) # label(aBOUNDSu_LINEARu_0) # label(axiom) # label(non_clause). [assumption]. 14.50/14.57 1776 (all A all B all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,bool),fun(A,bool)))),support),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,bool),fun(A,bool)))),support),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,bool),T0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,bool),fun(A,bool)))),support),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,bool),T0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,bool),fun(A,bool)))),support),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,bool),S0)))))) -> s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,B),F0))) = s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),OP),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))))),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),T0))),s(fun(A,B),F0))))))))) # label(aITERATEu_UNIONu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1777 (all Q19367 all L all N0 ((exists H0 exists T0 (s(list(Q19367),L) = s(list(Q19367),i(s(fun(list(Q19367),list(Q19367)),i(s(fun(Q19367,fun(list(Q19367),list(Q19367))),cons),s(Q19367,H0))),s(list(Q19367),T0))) & s(num,i(s(fun(list(Q19367),num),length),s(list(Q19367),T0))) = s(num,N0))) <-> s(num,i(s(fun(num,num),suc),s(num,N0))) = s(num,i(s(fun(list(Q19367),num),length),s(list(Q19367),L))))) # label(aLENGTHu_EQu_CONS) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1778 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Z0))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y)))))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Z0))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Z0))),s(int,X)))))) # label(aINTu_LTu_MIN) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1779 (all A all B all U_2 ((all X all F0 (p(s(bool,i(s(fun(fun(prod(A,B),real),bool),i(s(fun(fun(A,fun(B,real)),fun(fun(prod(A,B),real),bool)),U_2),s(fun(A,fun(B,real)),X))),s(fun(prod(A,B),real),F0)))) <-> (all I0 all J0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),geq),s(real,i(s(fun(prod(A,B),real),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,I0))),s(B,J0))))))),s(real,i(s(fun(B,real),i(s(fun(A,fun(B,real)),X),s(A,I0))),s(B,J0))))))))) -> (all U_1 ((all S0 all T0 all GENR_PVARR_188 ((exists I0 exists J0 exists V (p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(bool,fun(prod(A,B),bool)),i(s(fun(prod(A,B),fun(bool,fun(prod(A,B),bool))),setspec),s(prod(A,B),GENR_PVARR_188))),s(bool,V))),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,I0))),s(B,J0)))))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0))))))) <-> p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(prod(A,B),GENR_PVARR_188)))))) -> (all U_0 ((all T0 all X all I0 s(real,i(s(fun(fun(B,real),real),i(s(fun(fun(B,bool),fun(fun(B,real),real)),sum),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0))))),s(fun(B,real),i(s(fun(A,fun(B,real)),X),s(A,I0))))) = s(real,i(s(fun(A,real),i(s(fun(fun(A,fun(B,real)),fun(A,real)),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,real)),fun(A,real))),U_0),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,real)),X))),s(A,I0)))) -> (all S0 all T0 all X (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all I0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0)))))))) -> s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(fun(A,fun(B,real)),fun(A,real)),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,real)),fun(A,real))),U_0),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,real)),X))))) = s(real,i(s(fun(fun(prod(A,B),real),real),i(s(fun(fun(prod(A,B),bool),fun(fun(prod(A,B),real),real)),sum),s(fun(prod(A,B),bool),i(s(fun(fun(prod(A,B),bool),fun(prod(A,B),bool)),gspec),s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))))))),s(fun(prod(A,B),real),i(s(fun(fun(fun(prod(A,B),real),bool),fun(prod(A,B),real)),gabs),s(fun(fun(prod(A,B),real),bool),i(s(fun(fun(A,fun(B,real)),fun(fun(prod(A,B),real),bool)),U_2),s(fun(A,fun(B,real)),X))))))))))))))) # label(aSUMu_SUMu_PRODUCT) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1780 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,X))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_ge),s(int,X))),s(int,Y)))) # label(aINTu_GE) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1781 (all Q48184 all Q48180 all U_0 ((all S0 all F0 all GENR_PVARR_11 (p(s(bool,i(s(fun(Q48184,bool),i(s(fun(fun(Q48180,Q48184),fun(Q48184,bool)),i(s(fun(fun(Q48180,bool),fun(fun(Q48180,Q48184),fun(Q48184,bool))),U_0),s(fun(Q48180,bool),S0))),s(fun(Q48180,Q48184),F0))),s(Q48184,GENR_PVARR_11)))) <-> (exists X p(s(bool,i(s(fun(Q48184,bool),i(s(fun(bool,fun(Q48184,bool)),i(s(fun(Q48184,fun(bool,fun(Q48184,bool))),setspec),s(Q48184,GENR_PVARR_11))),s(bool,i(s(fun(fun(Q48180,bool),bool),i(s(fun(Q48180,fun(fun(Q48180,bool),bool)),in),s(Q48180,X))),s(fun(Q48180,bool),S0))))),s(Q48184,i(s(fun(Q48180,Q48184),F0),s(Q48180,X))))))))) -> (all F0 all S0 s(fun(Q48184,bool),i(s(fun(fun(Q48180,bool),fun(Q48184,bool)),i(s(fun(fun(Q48180,Q48184),fun(fun(Q48180,bool),fun(Q48184,bool))),image),s(fun(Q48180,Q48184),F0))),s(fun(Q48180,bool),S0))) = s(fun(Q48184,bool),i(s(fun(fun(Q48184,bool),fun(Q48184,bool)),gspec),s(fun(Q48184,bool),i(s(fun(fun(Q48180,Q48184),fun(Q48184,bool)),i(s(fun(fun(Q48180,bool),fun(fun(Q48180,Q48184),fun(Q48184,bool))),U_0),s(fun(Q48180,bool),S0))),s(fun(Q48180,Q48184),F0)))))))) # label(aSIMPLEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1782 (all N0 (p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))) | p(s(bool,i(s(fun(num,bool),even),s(num,N0)))))) # label(aEVENu_ORu_ODD) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1783 (all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,X)) # label(aREALu_ADDu_RID) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1784 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Z0))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,Y)))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Z0))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Z0))),s(real,Y)))))) # label(aREALu_LEu_MIN) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1785 (all A all P0 all Q0 ((all X p(s(bool,P0))) | (all X p(s(bool,Q0))) <-> (all X (p(s(bool,Q0)) | p(s(bool,P0)))))) # label(aTRIVu_FORALLu_ORu_THM) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1786 p(s(bool,p1)) | p(s(bool,q)) <-> p(s(bool,p1)) | p(s(bool,q)) # label(aDISJu_ACIu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1787 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,X)))) <-> -p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))))) # label(aREALu_NOTu_LT) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1788 (all N0 all X all Y (p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))) # label(aREALu_POWu_LT2u_ODDu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1789 (all B all A (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),univ)))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),univ)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),univ))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),univ))))) = s(num,i(s(fun(fun(fun(A,B),bool),num),card),s(fun(fun(A,B),bool),univ))))) # label(aCARDu_FUNSPACEu_UNIV) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1790 (all B all A all L all F0 s(num,i(s(fun(list(A),num),length),s(list(A),L))) = s(num,i(s(fun(list(B),num),length),s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),L)))))) # label(aLENGTHu_MAP) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1791 (all A all P0 ((all C0 all I0 all R0 ((all N0 p(s(bool,i(s(fun(recspace(A),bool),P0),s(recspace(A),i(s(fun(num,recspace(A)),R0),s(num,N0))))))) -> p(s(bool,i(s(fun(recspace(A),bool),P0),s(recspace(A),i(s(fun(fun(num,recspace(A)),recspace(A)),i(s(fun(A,fun(fun(num,recspace(A)),recspace(A))),i(s(fun(num,fun(A,fun(fun(num,recspace(A)),recspace(A)))),constr),s(num,C0))),s(A,I0))),s(fun(num,recspace(A)),R0)))))))) & p(s(bool,i(s(fun(recspace(A),bool),P0),s(recspace(A),bottom)))) -> (all X p(s(bool,i(s(fun(recspace(A),bool),P0),s(recspace(A),X))))))) # label(aCONSTRu_IND) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1792 (all X all C0 ((all M0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,M0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,M0))))),s(real,X))))),s(real,C0)))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,C0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aREALu_ARCHu_RDIVu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1793 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))) -> s(int,X) != s(int,Y))) # label(aINTu_LTu_IMPu_NE) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1794 (all A all B all X s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,i(s(fun(prod(A,B),A),fst),s(prod(A,B),X))))),s(B,i(s(fun(prod(A,B),B),snd),s(prod(A,B),X))))) = s(prod(A,B),X)) # label(aPAIR) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1795 (all A all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) -> s(real,i(s(fun(A,real),F0),s(A,X))) = s(real,i(s(fun(A,real),g),s(A,X))))) & (all X (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(A,real),F0),s(A,X))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0)))) -> s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),T0))),s(fun(A,real),g))))) # label(aSUMu_EQu_SUPERSET) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1796 (all N0 all X (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aREALu_POWu_1u_LT) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1797 (all T0 ((-p(s(bool,T0)) <-> s(bool,T0) = s(bool,f0)) & (-p(s(bool,T0)) <-> s(bool,f0) = s(bool,T0)) & (s(bool,t) = s(bool,T0) <-> p(s(bool,T0))) & (s(bool,T0) = s(bool,t) <-> p(s(bool,T0))))) # label(aEQu_CLAUSES) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1798 (all Q63971 all Q63959 all OP all F0 all S0 s(Q63959,i(s(fun(fun(Q63971,Q63959),Q63959),i(s(fun(fun(Q63971,bool),fun(fun(Q63971,Q63959),Q63959)),i(s(fun(fun(Q63959,fun(Q63959,Q63959)),fun(fun(Q63971,bool),fun(fun(Q63971,Q63959),Q63959))),iterate),s(fun(Q63959,fun(Q63959,Q63959)),OP))),s(fun(Q63971,bool),i(s(fun(fun(Q63971,bool),fun(Q63971,bool)),i(s(fun(fun(Q63971,Q63959),fun(fun(Q63971,bool),fun(Q63971,bool))),i(s(fun(fun(Q63959,fun(Q63959,Q63959)),fun(fun(Q63971,Q63959),fun(fun(Q63971,bool),fun(Q63971,bool)))),support),s(fun(Q63959,fun(Q63959,Q63959)),OP))),s(fun(Q63971,Q63959),F0))),s(fun(Q63971,bool),S0))))),s(fun(Q63971,Q63959),F0))) = s(Q63959,i(s(fun(fun(Q63971,Q63959),Q63959),i(s(fun(fun(Q63971,bool),fun(fun(Q63971,Q63959),Q63959)),i(s(fun(fun(Q63959,fun(Q63959,Q63959)),fun(fun(Q63971,bool),fun(fun(Q63971,Q63959),Q63959))),iterate),s(fun(Q63959,fun(Q63959,Q63959)),OP))),s(fun(Q63971,bool),S0))),s(fun(Q63971,Q63959),F0)))) # label(aITERATEu_SUPPORT) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1799 (all A all B all U_2 ((all F0 all J0 all I0 s(real,i(s(fun(B,real),i(s(fun(A,fun(B,real)),F0),s(A,I0))),s(B,J0))) = s(real,i(s(fun(A,real),i(s(fun(B,fun(A,real)),i(s(fun(fun(A,fun(B,real)),fun(B,fun(A,real))),U_2),s(fun(A,fun(B,real)),F0))),s(B,J0))),s(A,I0)))) -> (all U_1 ((all S0 all F0 all J0 s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(B,fun(A,real)),i(s(fun(fun(A,fun(B,real)),fun(B,fun(A,real))),U_2),s(fun(A,fun(B,real)),F0))),s(B,J0))))) = s(real,i(s(fun(B,real),i(s(fun(fun(A,fun(B,real)),fun(B,real)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,real)),fun(B,real))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,real)),F0))),s(B,J0)))) -> (all U_0 ((all T0 all F0 all I0 s(real,i(s(fun(fun(B,real),real),i(s(fun(fun(B,bool),fun(fun(B,real),real)),sum),s(fun(B,bool),T0))),s(fun(B,real),i(s(fun(A,fun(B,real)),F0),s(A,I0))))) = s(real,i(s(fun(A,real),i(s(fun(fun(A,fun(B,real)),fun(A,real)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,real)),fun(A,real))),U_0),s(fun(B,bool),T0))),s(fun(A,fun(B,real)),F0))),s(A,I0)))) -> (all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) -> s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(fun(A,fun(B,real)),fun(A,real)),i(s(fun(fun(B,bool),fun(fun(A,fun(B,real)),fun(A,real))),U_0),s(fun(B,bool),T0))),s(fun(A,fun(B,real)),F0))))) = s(real,i(s(fun(fun(B,real),real),i(s(fun(fun(B,bool),fun(fun(B,real),real)),sum),s(fun(B,bool),T0))),s(fun(B,real),i(s(fun(fun(A,fun(B,real)),fun(B,real)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,real)),fun(B,real))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,real)),F0))))))))))))) # label(aSUMu_SWAP) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1800 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) <-> s(fun(A,bool),T0) = s(fun(A,bool),S0))) # label(aSUBSETu_ANTISYMu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1801 (all X all Y s(int,i(s(fun(real,int),intu_ofu_real),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y))))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y)))) # label(aintu_min) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1802 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y))) = s(int,i(s(fun(real,int),intu_ofu_real),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y)))))))) # label(aintu_max) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1803 (all Q58114 all U_0 ((all S0 all L (s(num,i(s(fun(fun(Q58114,bool),num),card),s(fun(Q58114,bool),S0))) = s(num,i(s(fun(list(Q58114),num),length),s(list(Q58114),L))) & s(fun(Q58114,bool),S0) = s(fun(Q58114,bool),i(s(fun(list(Q58114),fun(Q58114,bool)),setu_ofu_list),s(list(Q58114),L))) <-> p(s(bool,i(s(fun(list(Q58114),bool),i(s(fun(fun(Q58114,bool),fun(list(Q58114),bool)),U_0),s(fun(Q58114,bool),S0))),s(list(Q58114),L)))))) -> (all S0 s(list(Q58114),i(s(fun(fun(list(Q58114),bool),list(Q58114)),h_),s(fun(list(Q58114),bool),i(s(fun(fun(Q58114,bool),fun(list(Q58114),bool)),U_0),s(fun(Q58114,bool),S0))))) = s(list(Q58114),i(s(fun(fun(Q58114,bool),list(Q58114)),listu_ofu_set),s(fun(Q58114,bool),S0)))))) # label(alistu_ofu_set) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1804 (all U_0 ((all N0 s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(num,num),U_0),s(num,N0)))) -> p(s(bool,i(s(fun(fun(num,num),bool),isu_nadd),s(fun(num,num),U_0)))))) # label(aisu_naddu_0) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1805 (all X all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Z0))),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))),s(real,Z0)))) # label(aREALu_LEu_SUBu_RADD) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1806 (all A all U_0 ((all Q0 all P0 all X ((p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),Q0))),s(fun(A,bool),P0))),s(A,X)))))) -> (all P0 all Q0 all L s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,bool),fun(list(A),bool)),all0),s(fun(A,bool),P0))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(fun(A,bool),fun(list(A),list(A))),filter0),s(fun(A,bool),Q0))),s(list(A),L))))) = s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,bool),fun(list(A),bool)),all0),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),Q0))),s(fun(A,bool),P0))))),s(list(A),L)))))) # label(aALLu_FILTER) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1807 (all U_0 ((all M0 all N0 all GENR_PVARR_134 ((exists X exists V ((p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,X)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,X))),s(num,N0)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(num,bool),i(s(fun(bool,fun(num,bool)),i(s(fun(num,fun(bool,fun(num,bool))),setspec),s(num,GENR_PVARR_134))),s(bool,V))),s(num,X)))))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),U_0),s(num,M0))),s(num,N0))),s(num,GENR_PVARR_134)))))) -> (all M0 all N0 s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))) = s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),gspec),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),U_0),s(num,M0))),s(num,N0)))))))) # label(anumseg) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1808 (all U_0 ((all F0 all I0 s(real,i(s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),U_0),s(fun(num,real),F0))),s(num,I0))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),F0),s(num,I0)))))) -> (all F0 all M0 all N0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),U_0),s(fun(num,real),F0))))))))))) # label(aSUMu_ABSu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1809 (all X all Y p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Y))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,Y))),s(nadd,X))))))) # label(aNADDu_ADDu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1810 (all X all N0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aREALu_POLYu_CLAUSESu_conjunct9) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1811 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,Z0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Z0)))))) # label(aINTu_LTEu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1812 (all Q93303 all S0 (p(s(bool,i(s(fun(fun(Q93303,bool),bool),infinite),s(fun(Q93303,bool),S0)))) & p(s(bool,i(s(fun(fun(Q93303,bool),bool),countable),s(fun(Q93303,bool),S0)))) -> (exists F0 (s(fun(Q93303,bool),i(s(fun(fun(num,bool),fun(Q93303,bool)),i(s(fun(fun(num,Q93303),fun(fun(num,bool),fun(Q93303,bool))),image),s(fun(num,Q93303),F0))),s(fun(num,bool),univ))) = s(fun(Q93303,bool),S0) & (all M0 all N0 (s(Q93303,i(s(fun(num,Q93303),F0),s(num,N0))) = s(Q93303,i(s(fun(num,Q93303),F0),s(num,M0))) -> s(num,M0) = s(num,N0))))))) # label(aCOUNTABLEu_ASu_INJECTIVEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1813 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y))))) # label(aINTu_LEu_MULu_EQu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1814 (all Q63492 all Q63489 all OP all F0 all X all S0 (p(s(bool,i(s(fun(fun(Q63492,bool),bool),i(s(fun(Q63492,fun(fun(Q63492,bool),bool)),in),s(Q63492,X))),s(fun(Q63492,bool),S0)))) & s(Q63489,i(s(fun(Q63492,Q63489),F0),s(Q63492,X))) != s(Q63489,i(s(fun(fun(Q63489,fun(Q63489,Q63489)),Q63489),neutral),s(fun(Q63489,fun(Q63489,Q63489)),OP))) <-> p(s(bool,i(s(fun(fun(Q63492,bool),bool),i(s(fun(Q63492,fun(fun(Q63492,bool),bool)),in),s(Q63492,X))),s(fun(Q63492,bool),i(s(fun(fun(Q63492,bool),fun(Q63492,bool)),i(s(fun(fun(Q63492,Q63489),fun(fun(Q63492,bool),fun(Q63492,bool))),i(s(fun(fun(Q63489,fun(Q63489,Q63489)),fun(fun(Q63492,Q63489),fun(fun(Q63492,bool),fun(Q63492,bool)))),support),s(fun(Q63489,fun(Q63489,Q63489)),OP))),s(fun(Q63492,Q63489),F0))),s(fun(Q63492,bool),S0)))))))) # label(aINu_SUPPORT) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1815 (all Q46704 s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),q))),s(fun(Q46704,bool),p1))) = s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),p1))),s(fun(Q46704,bool),q)))) # label(aUNIONu_ACIu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1816 (all Q51578 all S0 (p(s(bool,i(s(fun(fun(Q51578,bool),bool),infinite),s(fun(Q51578,bool),S0)))) -> s(fun(Q51578,bool),empty) != s(fun(Q51578,bool),S0))) # label(aINFINITEu_NONEMPTY) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1817 (all Q46638 s(fun(Q46638,bool),i(s(fun(fun(Q46638,bool),fun(Q46638,bool)),i(s(fun(fun(Q46638,bool),fun(fun(Q46638,bool),fun(Q46638,bool))),inter),s(fun(Q46638,bool),p1))),s(fun(Q46638,bool),p1))) = s(fun(Q46638,bool),p1)) # label(aINTERu_ACIu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1818 (all U_0 ((all X all Y all D0 (s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,Y))),s(hreal,D0))) = s(hreal,X) <-> p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),i(s(fun(hreal,fun(hreal,fun(hreal,bool))),U_0),s(hreal,X))),s(hreal,Y))),s(hreal,D0)))))) -> (all Y all X exists V (s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),i(s(fun(bool,fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal)))),cond),s(bool,V))),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),i(s(fun(bool,fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal)))),cond),s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,Y))),s(hreal,X))))),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,i(s(fun(hreal,hreal),hrealu_inv),s(hreal,i(s(fun(fun(hreal,bool),hreal),h_),s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),i(s(fun(hreal,fun(hreal,fun(hreal,bool))),U_0),s(hreal,X))),s(hreal,Y))))))))),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(hreal,i(s(fun(hreal,hreal),hrealu_inv),s(hreal,i(s(fun(fun(hreal,bool),hreal),h_),s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),i(s(fun(hreal,fun(hreal,fun(hreal,bool))),U_0),s(hreal,Y))),s(hreal,X))))))))))))) = s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),trealu_inv),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,X))),s(hreal,Y))))) & (p(s(bool,V)) <-> s(hreal,X) = s(hreal,Y)))))) # label(atrealu_inv) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1819 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) -> -p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,X)))))) # label(aREALu_LTu_GT) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1820 (all A all F1 all F1I_ all F2 all F2I_ (s(fun(num,fun(A,bool)),F2) = s(fun(num,fun(A,bool)),F2I_) & s(fun(num,fun(A,bool)),F1) = s(fun(num,fun(A,bool)),F1I_) <-> s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(A,bool)),fun(num,fun(A,bool))),i(s(fun(fun(num,fun(A,bool)),fun(fun(num,fun(A,bool)),fun(num,fun(A,bool)))),injp),s(fun(num,fun(A,bool)),F1I_))),s(fun(num,fun(A,bool)),F2I_))) = s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(A,bool)),fun(num,fun(A,bool))),i(s(fun(fun(num,fun(A,bool)),fun(fun(num,fun(A,bool)),fun(num,fun(A,bool)))),injp),s(fun(num,fun(A,bool)),F1))),s(fun(num,fun(A,bool)),F2))))) # label(aINJPu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1821 (all N0 all X all Y (p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0)))))))) # label(aREALu_POWu_LE2u_ODD) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1822 (all X s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),realu_sgn),s(real,X))))) = s(real,i(s(fun(real,real),realu_sgn),s(real,i(s(fun(real,real),realu_neg),s(real,X)))))) # label(aREALu_SGNu_NEG) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1823 (all A all B all C p(s(bool,i(s(fun(fun(fun(prod(A,B),C),bool),bool),i(s(fun(fun(fun(A,fun(B,C)),bool),fun(fun(fun(prod(A,B),C),bool),bool)),a_u_c),s(fun(fun(A,fun(B,C)),bool),univ))),s(fun(fun(prod(A,B),C),bool),univ))))) # label(aCARDu_FUNSPACEu_CURRY) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1824 (all Q18583 s(bool,i(s(fun(list(Q18583),bool),null),s(list(Q18583),nil))) = s(bool,t)) # label(aNULLu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1825 (all B all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0)))))) -> (exists F0 ((all X all Y (s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,i(s(fun(A,B),F0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,Y) = s(A,X))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,bool),T0)))))))) # label(aCARDu_LEu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1826 (all A all E0 exists FN s(A,i(s(fun(n10,A),FN),s(n10,one))) = s(A,E0)) # label(aoneu_RECURSION) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1827 (all Q48678 all Q48557 all U_0 ((all P0 all F0 all GENR_PVARR_21 (p(s(bool,i(s(fun(Q48678,bool),i(s(fun(fun(Q48557,Q48678),fun(Q48678,bool)),i(s(fun(fun(Q48557,bool),fun(fun(Q48557,Q48678),fun(Q48678,bool))),U_0),s(fun(Q48557,bool),P0))),s(fun(Q48557,Q48678),F0))),s(Q48678,GENR_PVARR_21)))) <-> (exists X p(s(bool,i(s(fun(Q48678,bool),i(s(fun(bool,fun(Q48678,bool)),i(s(fun(Q48678,fun(bool,fun(Q48678,bool))),setspec),s(Q48678,GENR_PVARR_21))),s(bool,i(s(fun(Q48557,bool),P0),s(Q48557,X))))),s(Q48678,i(s(fun(Q48557,Q48678),F0),s(Q48557,X))))))))) -> (all P0 all F0 ((all X (p(s(bool,i(s(fun(Q48557,bool),P0),s(Q48557,X)))) -> p(s(bool,i(s(fun(Q48678,bool),q0),s(Q48678,i(s(fun(Q48557,Q48678),F0),s(Q48557,X)))))))) <-> (all Z0 (p(s(bool,i(s(fun(fun(Q48678,bool),bool),i(s(fun(Q48678,fun(fun(Q48678,bool),bool)),in),s(Q48678,Z0))),s(fun(Q48678,bool),i(s(fun(fun(Q48678,bool),fun(Q48678,bool)),gspec),s(fun(Q48678,bool),i(s(fun(fun(Q48557,Q48678),fun(Q48678,bool)),i(s(fun(fun(Q48557,bool),fun(fun(Q48557,Q48678),fun(Q48678,bool))),U_0),s(fun(Q48557,bool),P0))),s(fun(Q48557,Q48678),F0)))))))) -> p(s(bool,i(s(fun(Q48678,bool),q0),s(Q48678,Z0)))))))))) # label(aFORALLu_INu_GSPECu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1828 (all D1 all D2 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D2)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D1)))) -> (exists E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,E0))),s(real,D2)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,E0))),s(real,D1)))))))) # label(aREALu_DOWN2) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1829 (all Q79580 all Q79588 all Q79587 all Q79583 all Q79593 all P0 all L_L_ all S0 all T0 (p(s(bool,i(s(fun(fun(fun(Q79587,Q79583),fun(Q79593,Q79588)),bool),i(s(fun(fun(Q79593,Q79580),fun(fun(fun(Q79587,Q79583),fun(Q79593,Q79588)),bool)),i(s(fun(fun(fun(Q79587,Q79583),fun(Q79593,bool)),fun(fun(Q79593,Q79580),fun(fun(fun(Q79587,Q79583),fun(Q79593,Q79588)),bool))),i(s(fun(fun(Q79587,fun(Q79580,bool)),fun(fun(fun(Q79587,Q79583),fun(Q79593,bool)),fun(fun(Q79593,Q79580),fun(fun(fun(Q79587,Q79583),fun(Q79593,Q79588)),bool)))),admissible),s(fun(Q79587,fun(Q79580,bool)),L_L_))),s(fun(fun(Q79587,Q79583),fun(Q79593,bool)),P0))),s(fun(Q79593,Q79580),S0))),s(fun(fun(Q79587,Q79583),fun(Q79593,Q79588)),T0)))) <-> (all F0 all G0 all A5 (p(s(bool,i(s(fun(Q79593,bool),i(s(fun(fun(Q79587,Q79583),fun(Q79593,bool)),P0),s(fun(Q79587,Q79583),G0))),s(Q79593,A5)))) & (all Z0 (p(s(bool,i(s(fun(Q79580,bool),i(s(fun(Q79587,fun(Q79580,bool)),L_L_),s(Q79587,Z0))),s(Q79580,i(s(fun(Q79593,Q79580),S0),s(Q79593,A5)))))) -> s(Q79583,i(s(fun(Q79587,Q79583),G0),s(Q79587,Z0))) = s(Q79583,i(s(fun(Q79587,Q79583),F0),s(Q79587,Z0))))) & p(s(bool,i(s(fun(Q79593,bool),i(s(fun(fun(Q79587,Q79583),fun(Q79593,bool)),P0),s(fun(Q79587,Q79583),F0))),s(Q79593,A5)))) -> s(Q79588,i(s(fun(Q79593,Q79588),i(s(fun(fun(Q79587,Q79583),fun(Q79593,Q79588)),T0),s(fun(Q79587,Q79583),G0))),s(Q79593,A5))) = s(Q79588,i(s(fun(Q79593,Q79588),i(s(fun(fun(Q79587,Q79583),fun(Q79593,Q79588)),T0),s(fun(Q79587,Q79583),F0))),s(Q79593,A5))))))) # label(aadmissible) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1830 (all W all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,W))),s(int,X)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,Z0)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,W))),s(int,Y))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0)))))))) # label(aINTu_LEu_ADD2) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1831 (all A all U_0 ((all P0 all L all F0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),i(s(fun(fun(A,bool),fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool))),U_0),s(fun(A,bool),P0))),s(fun(prod(A,A),bool),L))),s(fun(prod(A,A),bool),F0)))) <-> (all X all Y exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(A,A),bool),F0),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y))))))),s(bool,V)))))))) -> (all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all P0 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,x)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,x)))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),i(s(fun(fun(fun(prod(A,A),bool),bool),fun(prod(A,A),bool)),gabs),s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),i(s(fun(fun(A,bool),fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool))),U_0),s(fun(A,bool),P0))),s(fun(prod(A,A),bool),L))))))),s(A,x)))))))))) # label(aFLu_RESTRICT) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1832 (all M0 all N0 all Q0 all R0 (s(num,M0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,Q0))),s(num,N0))))),s(num,R0))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,R0))),s(num,N0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))) = s(num,Q0))) # label(aDIVu_UNIQ) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1833 (all Q82753 all B all A all U_2 ((all A5 s(bool,i(s(fun(Q82753,bool),U_2),s(Q82753,A5))) = s(bool,t)) -> (all U_1 ((all F0 s(fun(Q82753,bool),U_2) = s(fun(Q82753,bool),i(s(fun(fun(A,B),fun(Q82753,bool)),U_1),s(fun(A,B),F0)))) -> (all U_0 ((all L_L_ all F0 ((all S0 all T0 p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))),bool),F0),s(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))),i(s(fun(fun(fun(A,B),fun(Q82753,B)),prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B)))),i(s(fun(fun(Q82753,A),fun(fun(fun(A,B),fun(Q82753,B)),prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))))),c_),s(fun(Q82753,A),S0))),s(fun(fun(A,B),fun(Q82753,B)),T0))))))),s(bool,i(s(fun(fun(fun(A,B),fun(Q82753,B)),bool),i(s(fun(fun(Q82753,A),fun(fun(fun(A,B),fun(Q82753,B)),bool)),i(s(fun(fun(fun(A,B),fun(Q82753,bool)),fun(fun(Q82753,A),fun(fun(fun(A,B),fun(Q82753,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(Q82753,bool)),fun(fun(Q82753,A),fun(fun(fun(A,B),fun(Q82753,B)),bool)))),tailadmissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(Q82753,bool)),U_1))),s(fun(Q82753,A),S0))),s(fun(fun(A,B),fun(Q82753,B)),T0))))))) <-> p(s(bool,i(s(fun(fun(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))),bool),bool),i(s(fun(fun(A,fun(A,bool)),fun(fun(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))),bool),bool)),U_0),s(fun(A,fun(A,bool)),L_L_))),s(fun(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))),bool),F0)))))) -> (all L_L_ all CLAUSES (p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),L_L_)))) & p(s(bool,i(s(fun(list(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B)))),bool),i(s(fun(fun(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))),bool),fun(list(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B)))),bool)),all0),s(fun(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))),bool),i(s(fun(fun(fun(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))),bool),bool),fun(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))),bool)),gabs),s(fun(fun(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))),bool),bool),i(s(fun(fun(A,fun(A,bool)),fun(fun(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B))),bool),bool)),U_0),s(fun(A,fun(A,bool)),L_L_))))))),s(list(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B)))),CLAUSES)))) -> (exists F0 all X s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),i(s(fun(list(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B)))),fun(fun(A,B),fun(A,B))),casewise),s(list(prod(fun(Q82753,A),fun(fun(A,B),fun(Q82753,B)))),CLAUSES))),s(fun(A,B),F0))),s(A,X)))))))))))) # label(aWFu_RECu_CASESi_) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1834 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))) <-> -p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))))) # label(aNOTu_LE) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1835 (all Q47352 all F0 all T0 (p(s(bool,i(s(fun(fun(Q47352,bool),bool),i(s(fun(fun(Q47352,bool),fun(fun(Q47352,bool),bool)),subset),s(fun(Q47352,bool),i(s(fun(fun(fun(Q47352,bool),bool),fun(Q47352,bool)),unions),s(fun(fun(Q47352,bool),bool),F0))))),s(fun(Q47352,bool),T0)))) <-> (all S0 (p(s(bool,i(s(fun(fun(fun(Q47352,bool),bool),bool),i(s(fun(fun(Q47352,bool),fun(fun(fun(Q47352,bool),bool),bool)),in),s(fun(Q47352,bool),S0))),s(fun(fun(Q47352,bool),bool),F0)))) -> p(s(bool,i(s(fun(fun(Q47352,bool),bool),i(s(fun(fun(Q47352,bool),fun(fun(Q47352,bool),bool)),subset),s(fun(Q47352,bool),S0))),s(fun(Q47352,bool),T0)))))))) # label(aUNIONSu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.59/14.58 1836 (all N0 s(num,u_0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,u_0))),s(num,i(s(fun(num,num),bit1),s(num,N0)))))) # label(aARITHu_EXPu_conjunct7) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1837 (all A all S0 s(num,i(s(fun(fun(finite_image(A),bool),num),card),s(fun(finite_image(A),bool),univ))) = s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),S0)))) # label(aCARDu_FINITEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1838 (all A all B all X all Y s(B,i(s(fun(prod(A,B),B),snd),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y))))) = s(B,Y)) # label(aSND) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1839 (all B all A (p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))) -> (all H0 ((all F0 all G0 all X ((all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Z0))),s(A,X)))) -> s(B,i(s(fun(A,B),F0),s(A,Z0))) = s(B,i(s(fun(A,B),G0),s(A,Z0))))) -> s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),G0))),s(A,X))))) -> (exists F0 all X s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X)))))))) # label(aWFu_REC) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1840 (all A all F0 ((all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),F0),s(fun(A,bool),S0))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),F0),s(fun(A,bool),T0)))))))) -> (exists S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),F0),s(fun(A,bool),S0))) = s(fun(A,bool),S0)))) # label(aTARSKIu_SET) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1841 (all Q72954 all S0 all F0 all B0 (s(fun(Q72954,bool),empty) != s(fun(Q72954,bool),S0) & (all X (p(s(bool,i(s(fun(fun(Q72954,bool),bool),i(s(fun(Q72954,fun(fun(Q72954,bool),bool)),in),s(Q72954,X))),s(fun(Q72954,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(Q72954,real),F0),s(Q72954,X))))),s(real,B0)))))) & p(s(bool,i(s(fun(fun(Q72954,bool),bool),finite),s(fun(Q72954,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(fun(Q72954,real),real),i(s(fun(fun(Q72954,bool),fun(fun(Q72954,real),real)),sum),s(fun(Q72954,bool),S0))),s(fun(Q72954,real),F0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(Q72954,bool),num),card),s(fun(Q72954,bool),S0))))))),s(real,B0)))))))) # label(aSUMu_BOUNDu_LTu_ALL) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1842 (all Q21004 all Q21006 all F0 all L s(list(Q21004),i(s(fun(list(Q21006),list(Q21004)),i(s(fun(fun(Q21006,Q21004),fun(list(Q21006),list(Q21004))),map0),s(fun(Q21006,Q21004),F0))),s(list(Q21006),i(s(fun(list(Q21006),list(Q21006)),reverse),s(list(Q21006),L))))) = s(list(Q21004),i(s(fun(list(Q21004),list(Q21004)),reverse),s(list(Q21004),i(s(fun(list(Q21006),list(Q21004)),i(s(fun(fun(Q21006,Q21004),fun(list(Q21006),list(Q21004))),map0),s(fun(Q21006,Q21004),F0))),s(list(Q21006),L)))))) # label(aMAPu_REVERSE) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1843 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))))) # label(aREALu_LEu_MULu_EQu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1844 (all Q63384 all OP (p(s(bool,i(s(fun(fun(Q63384,fun(Q63384,Q63384)),bool),monoidal),s(fun(Q63384,fun(Q63384,Q63384)),OP)))) -> (all A5 all B0 all C0 s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,A5))),s(Q63384,B0))))),s(Q63384,C0))) = s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,A5))),s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,B0))),s(Q63384,C0)))))) & (all A5 all B0 all C0 s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,A5))),s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,B0))),s(Q63384,C0))))) = s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,B0))),s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,A5))),s(Q63384,C0)))))) & (all A5 all B0 s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,A5))),s(Q63384,B0))) = s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,B0))),s(Q63384,A5)))) & (all A5 s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,A5))),s(Q63384,i(s(fun(fun(Q63384,fun(Q63384,Q63384)),Q63384),neutral),s(fun(Q63384,fun(Q63384,Q63384)),OP))))) = s(Q63384,A5)) & (all A5 s(Q63384,A5) = s(Q63384,i(s(fun(Q63384,Q63384),i(s(fun(Q63384,fun(Q63384,Q63384)),OP),s(Q63384,i(s(fun(fun(Q63384,fun(Q63384,Q63384)),Q63384),neutral),s(fun(Q63384,fun(Q63384,Q63384)),OP))))),s(Q63384,A5)))))) # label(aMONOIDALu_AC) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1845 (all A all U_0 ((all X s(A,i(s(fun(A,A),U_0),s(A,X))) = s(A,X)) -> p(s(bool,i(s(fun(fun(A,A),bool),i(s(fun(fun(A,A),fun(fun(A,A),bool)),iso0),s(fun(A,A),U_0))),s(fun(A,A),U_0)))))) # label(aISOu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1846 (all Q20835 all N0 s(Q20835,i(s(fun(list(Q20835),Q20835),i(s(fun(num,fun(list(Q20835),Q20835)),el),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(list(Q20835),l0))) = s(Q20835,i(s(fun(list(Q20835),Q20835),i(s(fun(num,fun(list(Q20835),Q20835)),el),s(num,N0))),s(list(Q20835),i(s(fun(list(Q20835),list(Q20835)),tl),s(list(Q20835),l0)))))) # label(aELu_TL) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1847 (all N0 all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0)))))))) # label(aREALu_POWu_LEu_1) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1848 p(s(bool,i(s(fun(num,bool),p0),s(num,i(s(fun(num,num),pre),s(num,n)))))) <-> (all M0 (s(num,i(s(fun(num,num),suc),s(num,M0))) = s(num,n) | s(num,n) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) & s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,M0) -> p(s(bool,i(s(fun(num,bool),p0),s(num,M0)))))) # label(aPREu_ELIMu_THM) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1849 (all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))) -> s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aLEu_1u_conjunct5) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1850 (all A all P0 all X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> p(s(bool,i(s(fun(A,bool),P0),s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),P0)))))))) # label(aSELECTu_AX) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1851 (all B all A all C all S0 all T0 all U (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(B,bool),fun(fun(C,bool),bool)),l_a_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U)))) -> p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(A,bool),fun(fun(C,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(C,bool),U)))))) # label(aCARDu_LTEu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1852 (all P0 all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,P0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,N0))),s(num,P0)))))) # label(aMULTu_EXP) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1853 (all N0 s(num,N0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))) # label(aMULTu_CLAUSESu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1854 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))))) # label(aREALu_LETu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1855 (all X s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),realu_inv),s(real,X))))) = s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(real,real),realu_neg),s(real,X)))))) # label(aREALu_INVu_NEG) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1856 (all A all B all U_0 ((all P0 all X ((exists Y s(prod(A,B),P0) = s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(prod(A,B),fun(A,bool)),U_0),s(prod(A,B),P0))),s(A,X)))))) -> (all P0 s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),i(s(fun(prod(A,B),fun(A,bool)),U_0),s(prod(A,B),P0))))) = s(A,i(s(fun(prod(A,B),A),fst),s(prod(A,B),P0)))))) # label(aFSTu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1857 (all Q48364 all U_0 ((all GENR_PVARR_15 (p(s(bool,i(s(fun(Q48364,bool),U_0),s(Q48364,GENR_PVARR_15)))) <-> (exists X p(s(bool,i(s(fun(Q48364,bool),i(s(fun(bool,fun(Q48364,bool)),i(s(fun(Q48364,fun(bool,fun(Q48364,bool))),setspec),s(Q48364,GENR_PVARR_15))),s(bool,t))),s(Q48364,X))))))) -> s(fun(Q48364,bool),i(s(fun(fun(Q48364,bool),fun(Q48364,bool)),gspec),s(fun(Q48364,bool),U_0))) = s(fun(Q48364,bool),univ))) # label(aUNIVu_GSPEC) # label(axiom) # label(non_clause). [assumption]. 14.59/14.59 1858 (all A all B all U_1 ((all F0 all T0 all GENR_PVARR_63 ((exists X p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_63))),s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0))))),s(A,X))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),U_1),s(fun(A,B),F0))),s(fun(B,bool),T0))),s(A,GENR_PVARR_63)))))) -> (all U_0 ((all F0 all Y all GENR_PVARR_62 (p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),U_0),s(fun(A,B),F0))),s(B,Y))),s(A,GENR_PVARR_62)))) <-> (exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_62))),s(bool,V))),s(A,X)))) & (p(s(bool,V)) <-> s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X)))))))) -> (all F0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),U_0),s(fun(A,B),F0))),s(B,Y)))))))))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),U_1),s(fun(A,B),F0))),s(fun(B,bool),T0)))))))))))))) # label(aFINITEu_FINITEu_PREIMAGE) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1859 (all U_0 ((all K0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),f),s(num,K0))))) = s(real,i(s(fun(num,real),U_0),s(num,K0)))) -> (all M0 all N0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),f),s(num,M0))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),U_0)))))) # label(aSUMu_DIFFSu_ALT) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1860 (all A all F0 all G0 all S0 ((exists X (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,i(s(fun(A,num),G0),s(A,X)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,i(s(fun(A,num),G0),s(A,X)))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))))),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),G0)))))))) # label(aNSUMu_LT) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1861 (all R0 (p(s(bool,i(s(fun(real,bool),integer),s(real,R0)))) <-> s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(real,int),intu_ofu_real),s(real,R0))))) = s(real,R0))) # label(aintu_tybiju_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1862 (all A s(A,h0) = s(A,i(s(fun(list(A),A),hd),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,h0))),s(list(A),t0)))))) # label(aHD) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1863 (all A all P0 all X ((all Y (s(A,X) = s(A,Y) <-> p(s(bool,i(s(fun(A,bool),P0),s(A,Y)))))) -> s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),P0))) = s(A,X))) # label(aSELECTu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1864 (all Q79285 all Q79249 all Q79290 all Q79289 all U_0 ((all Y (p(s(bool,i(s(fun(Q79285,bool),U_0),s(Q79285,Y)))) <-> s(Q79289,i(s(fun(Q79285,Q79289),i(s(fun(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249))),fun(Q79285,Q79289)),fst),s(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249))),h0))),s(Q79285,Y))) = s(Q79289,x))) -> (exists V (s(Q79249,i(s(fun(Q79289,Q79249),i(s(fun(Q79290,fun(Q79289,Q79249)),i(s(fun(list(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249)))),fun(Q79290,fun(Q79289,Q79249))),casewise),s(list(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249)))),i(s(fun(list(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249)))),list(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249))))),i(s(fun(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249))),fun(list(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249)))),list(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249)))))),cons),s(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249))),h0))),s(list(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249)))),t0))))),s(Q79290,f))),s(Q79289,x))) = s(Q79249,i(s(fun(Q79249,Q79249),i(s(fun(Q79249,fun(Q79249,Q79249)),i(s(fun(bool,fun(Q79249,fun(Q79249,Q79249))),cond),s(bool,V))),s(Q79249,i(s(fun(Q79285,Q79249),i(s(fun(Q79290,fun(Q79285,Q79249)),i(s(fun(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249))),fun(Q79290,fun(Q79285,Q79249))),snd),s(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249))),h0))),s(Q79290,f))),s(Q79285,i(s(fun(fun(Q79285,bool),Q79285),h_),s(fun(Q79285,bool),U_0))))))),s(Q79249,i(s(fun(Q79289,Q79249),i(s(fun(Q79290,fun(Q79289,Q79249)),i(s(fun(list(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249)))),fun(Q79290,fun(Q79289,Q79249))),casewise),s(list(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249)))),t0))),s(Q79290,f))),s(Q79289,x))))) & (p(s(bool,V)) <-> (exists Y s(Q79289,x) = s(Q79289,i(s(fun(Q79285,Q79289),i(s(fun(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249))),fun(Q79285,Q79289)),fst),s(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249))),h0))),s(Q79285,Y))))))))) # label(aCASEWISEu_DEFu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1865 (all Q68605 all U_0 ((all X s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) = s(num,i(s(fun(Q68605,num),U_0),s(Q68605,X)))) -> (all S0 (p(s(bool,i(s(fun(fun(Q68605,bool),bool),finite),s(fun(Q68605,bool),S0)))) -> s(num,i(s(fun(fun(Q68605,num),num),i(s(fun(fun(Q68605,bool),fun(fun(Q68605,num),num)),nsum),s(fun(Q68605,bool),S0))),s(fun(Q68605,num),U_0))) = s(num,i(s(fun(fun(Q68605,bool),num),card),s(fun(Q68605,bool),S0))))))) # label(aCARDu_EQu_NSUM) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1866 (all X exists B0 all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,M0))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))))) # label(aNADDu_CAUCHY) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1867 (all M0 all N0 s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),numeral),s(num,M0))))),s(num,i(s(fun(num,num),numeral),s(num,N0)))))) # label(aARITHu_EXPu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1868 (all S0 all A5 (s(fun(real,bool),empty) != s(fun(real,bool),S0) & (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,A5)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))))),s(real,A5)))))) # label(aREALu_ABSu_INFu_LE) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1869 (all Q68329 all S0 all T0 all U (s(fun(Q68329,bool),empty) = s(fun(Q68329,bool),i(s(fun(fun(Q68329,bool),fun(Q68329,bool)),i(s(fun(fun(Q68329,bool),fun(fun(Q68329,bool),fun(Q68329,bool))),inter),s(fun(Q68329,bool),S0))),s(fun(Q68329,bool),T0))) & s(fun(Q68329,bool),U) = s(fun(Q68329,bool),i(s(fun(fun(Q68329,bool),fun(Q68329,bool)),i(s(fun(fun(Q68329,bool),fun(fun(Q68329,bool),fun(Q68329,bool))),union),s(fun(Q68329,bool),S0))),s(fun(Q68329,bool),T0))) & p(s(bool,i(s(fun(fun(Q68329,bool),bool),finite),s(fun(Q68329,bool),U)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(Q68329,num),num),i(s(fun(fun(Q68329,bool),fun(fun(Q68329,num),num)),nsum),s(fun(Q68329,bool),S0))),s(fun(Q68329,num),f))))),s(num,i(s(fun(fun(Q68329,num),num),i(s(fun(fun(Q68329,bool),fun(fun(Q68329,num),num)),nsum),s(fun(Q68329,bool),T0))),s(fun(Q68329,num),f))))) = s(num,i(s(fun(fun(Q68329,num),num),i(s(fun(fun(Q68329,bool),fun(fun(Q68329,num),num)),nsum),s(fun(Q68329,bool),U))),s(fun(Q68329,num),f))))) # label(aNSUMu_UNIONu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1870 (all A all B all AP all BP (p(s(bool,i(s(fun(fun(AP,bool),bool),i(s(fun(fun(A,bool),fun(fun(AP,bool),bool)),a_u_c),s(fun(A,bool),univ))),s(fun(AP,bool),univ)))) & p(s(bool,i(s(fun(fun(BP,bool),bool),i(s(fun(fun(B,bool),fun(fun(BP,bool),bool)),a_u_c),s(fun(B,bool),univ))),s(fun(BP,bool),univ)))) -> p(s(bool,i(s(fun(fun(fun(AP,BP),bool),bool),i(s(fun(fun(fun(A,B),bool),fun(fun(fun(AP,BP),bool),bool)),a_u_c),s(fun(fun(A,B),bool),univ))),s(fun(fun(AP,BP),bool),univ)))))) # label(aCARDu_FUNSPACEu_CONG) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1871 (all Q58377 all R0 s(bool,i(s(fun(fun(Q58377,bool),bool),i(s(fun(fun(Q58377,fun(Q58377,bool)),fun(fun(Q58377,bool),bool)),pairwise),s(fun(Q58377,fun(Q58377,bool)),R0))),s(fun(Q58377,bool),empty))) = s(bool,t)) # label(aPAIRWISEu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1872 (all A all B all N all I0 exists K0 ((all Y s(B,i(s(fun(num,B),i(s(fun(cart(B,N),fun(num,B)),d_),s(cart(B,N),Y))),s(num,I0))) = s(B,i(s(fun(num,B),i(s(fun(cart(B,N),fun(num,B)),d_),s(cart(B,N),Y))),s(num,K0)))) & (all X s(A,i(s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),d_),s(cart(A,N),X))),s(num,I0))) = s(A,i(s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),d_),s(cart(A,N),X))),s(num,K0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0)))))) # label(aFINITEu_INDEXu_INRANGEu_2) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1873 (all Q19015 all Q19023 s(list(prod(Q19015,Q19023)),i(s(fun(list(prod(Q19015,Q19023)),list(prod(Q19015,Q19023))),i(s(fun(prod(Q19015,Q19023),fun(list(prod(Q19015,Q19023)),list(prod(Q19015,Q19023)))),cons),s(prod(Q19015,Q19023),i(s(fun(Q19023,prod(Q19015,Q19023)),i(s(fun(Q19015,fun(Q19023,prod(Q19015,Q19023))),c_),s(Q19015,h1))),s(Q19023,i(s(fun(list(Q19023),Q19023),hd),s(list(Q19023),l2))))))),s(list(prod(Q19015,Q19023)),i(s(fun(list(Q19023),list(prod(Q19015,Q19023))),i(s(fun(list(Q19015),fun(list(Q19023),list(prod(Q19015,Q19023)))),zip0),s(list(Q19015),t1))),s(list(Q19023),i(s(fun(list(Q19023),list(Q19023)),tl),s(list(Q19023),l2))))))) = s(list(prod(Q19015,Q19023)),i(s(fun(list(Q19023),list(prod(Q19015,Q19023))),i(s(fun(list(Q19015),fun(list(Q19023),list(prod(Q19015,Q19023)))),zip0),s(list(Q19015),i(s(fun(list(Q19015),list(Q19015)),i(s(fun(Q19015,fun(list(Q19015),list(Q19015))),cons),s(Q19015,h1))),s(list(Q19015),t1))))),s(list(Q19023),l2)))) # label(aZIPu_DEFu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1874 (all Q18672 (p(s(bool,i(s(fun(list(Q18672),bool),i(s(fun(Q18672,fun(list(Q18672),bool)),mem),s(Q18672,x))),s(list(Q18672),i(s(fun(list(Q18672),list(Q18672)),i(s(fun(Q18672,fun(list(Q18672),list(Q18672))),cons),s(Q18672,h0))),s(list(Q18672),t0)))))) <-> p(s(bool,i(s(fun(list(Q18672),bool),i(s(fun(Q18672,fun(list(Q18672),bool)),mem),s(Q18672,x))),s(list(Q18672),t0)))) | s(Q18672,x) = s(Q18672,h0))) # label(aMEMu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1875 (all N0 s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))) = s(int,i(s(fun(real,int),intu_ofu_real),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))))) # label(aintu_ofu_num) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1876 (all X all Y s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),X))) = s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))) # label(aTREALu_ADDu_SYMu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1877 (all Q54766 all S0 all T0 (p(s(bool,i(s(fun(fun(Q54766,bool),bool),finite),s(fun(Q54766,bool),S0)))) & p(s(bool,i(s(fun(fun(Q54766,bool),bool),finite),s(fun(Q54766,bool),T0)))) -> (s(fun(Q54766,bool),i(s(fun(fun(Q54766,bool),fun(Q54766,bool)),i(s(fun(fun(Q54766,bool),fun(fun(Q54766,bool),fun(Q54766,bool))),inter),s(fun(Q54766,bool),S0))),s(fun(Q54766,bool),T0))) = s(fun(Q54766,bool),empty) <-> s(num,i(s(fun(fun(Q54766,bool),num),card),s(fun(Q54766,bool),i(s(fun(fun(Q54766,bool),fun(Q54766,bool)),i(s(fun(fun(Q54766,bool),fun(fun(Q54766,bool),fun(Q54766,bool))),union),s(fun(Q54766,bool),S0))),s(fun(Q54766,bool),T0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(Q54766,bool),num),card),s(fun(Q54766,bool),S0))))),s(num,i(s(fun(fun(Q54766,bool),num),card),s(fun(Q54766,bool),T0)))))))) # label(aCARDu_UNIONu_OVERLAPu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1878 (all Q47598 all Q47602 s(fun(Q47602,bool),empty) = s(fun(Q47602,bool),i(s(fun(fun(Q47598,bool),fun(Q47602,bool)),i(s(fun(fun(Q47598,Q47602),fun(fun(Q47598,bool),fun(Q47602,bool))),image),s(fun(Q47598,Q47602),f))),s(fun(Q47598,bool),empty)))) # label(aIMAGEu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1879 (all X1 all X2 all Y1 all Y2 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),X2)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),Y1))),s(prod(hreal,hreal),Y2)))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),Y1))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),X2))),s(prod(hreal,hreal),Y2)))))))) # label(aTREALu_ADDu_WELLDEF) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1880 (all X all M0 all N0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,M0))))),s(num,N0)))) # label(aREALu_POWu_POW) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1881 (all X all Y s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))) = s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y))),s(int,X)))))) # label(aINTu_ABSu_SUB) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1882 (all Q96848 all P0 all S0 s(fun(Q96848,bool),i(s(fun(fun(Q96848,bool),fun(Q96848,bool)),i(s(fun(fun(fun(Q96848,bool),bool),fun(fun(Q96848,bool),fun(Q96848,bool))),hull),s(fun(fun(Q96848,bool),bool),P0))),s(fun(Q96848,bool),S0))) = s(fun(Q96848,bool),i(s(fun(fun(Q96848,bool),fun(Q96848,bool)),i(s(fun(fun(fun(Q96848,bool),bool),fun(fun(Q96848,bool),fun(Q96848,bool))),hull),s(fun(fun(Q96848,bool),bool),P0))),s(fun(Q96848,bool),i(s(fun(fun(Q96848,bool),fun(Q96848,bool)),i(s(fun(fun(fun(Q96848,bool),bool),fun(fun(Q96848,bool),fun(Q96848,bool))),hull),s(fun(fun(Q96848,bool),bool),P0))),s(fun(Q96848,bool),S0)))))) # label(aHULLu_HULL) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1883 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))))) # label(aREALu_LTu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1884 (all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),F0))))),s(real,i(s(fun(num,real),F0),s(num,N0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))))) # label(aSUMu_CLAUSESu_RIGHT) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1885 (all X s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),i(s(fun(bool,fun(int,fun(int,int))),cond),s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),i(s(fun(bool,fun(int,fun(int,int))),cond),s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))),s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) = s(int,i(s(fun(int,int),intu_sgn),s(int,X)))) # label(aINTu_SGN) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1886 (all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,N0))),s(num,N0))))) # label(aDIVu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1887 (all B all A all F0 all S0 exists T0 ((all X all Y (s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,i(s(fun(A,B),F0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) -> s(A,X) = s(A,Y))) & s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))) = s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),T0))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0)))))) # label(aIMAGEu_INJECTIVEu_IMAGEu_OFu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1888 (all Q58875 all S0 all F0 (p(s(bool,i(s(fun(fun(Q58875,bool),bool),finite),s(fun(Q58875,bool),S0)))) & s(fun(Q58875,bool),S0) = s(fun(Q58875,bool),i(s(fun(fun(Q58875,bool),fun(Q58875,bool)),i(s(fun(fun(Q58875,Q58875),fun(fun(Q58875,bool),fun(Q58875,bool))),image),s(fun(Q58875,Q58875),F0))),s(fun(Q58875,bool),S0))) -> (all X all Y (p(s(bool,i(s(fun(fun(Q58875,bool),bool),i(s(fun(Q58875,fun(fun(Q58875,bool),bool)),in),s(Q58875,X))),s(fun(Q58875,bool),S0)))) & s(Q58875,i(s(fun(Q58875,Q58875),F0),s(Q58875,X))) = s(Q58875,i(s(fun(Q58875,Q58875),F0),s(Q58875,Y))) & p(s(bool,i(s(fun(fun(Q58875,bool),bool),i(s(fun(Q58875,fun(fun(Q58875,bool),bool)),in),s(Q58875,Y))),s(fun(Q58875,bool),S0)))) -> s(Q58875,X) = s(Q58875,Y))))) # label(aIMAGEu_IMPu_INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1889 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),suc),s(num,M0))))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) # label(aLEu_SUCu_LT) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1890 (all A all S0 all T0 all F0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,num),F0))))),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,num),F0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))))),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),T0))),s(fun(A,num),F0))))))) # label(aNSUMu_INCLu_EXCL) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1891 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,N0))),s(num,M0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,i(s(fun(num,num),bit1),s(num,N0))))),s(num,i(s(fun(num,num),bit1),s(num,M0)))))) # label(aARITHu_GTu_conjunct9) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1892 (all X p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),intu_abs),s(int,X))))))) # label(aINTu_ABSu_POS) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1893 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0))))) = s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))) # label(aARITHu_ADDu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1894 (all X1 all Y2 all Y1 all X2 s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,X1))),s(hreal,X2))))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,Y1))),s(hreal,Y2))))))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,X1))),s(hreal,Y2))))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,Y1))),s(hreal,X2))))))) = s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,X1))),s(hreal,Y1))))),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,X2))),s(hreal,Y2)))))) # label(atrealu_mul) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1895 (all X all Y s(real,i(s(fun(real,real),realu_neg),s(real,Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))) # label(aREALu_ADDu_SUB2) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1896 (all Q18943 all Q18951 all Q18941 s(Q18941,i(s(fun(Q18941,Q18941),i(s(fun(Q18951,fun(Q18941,Q18941)),i(s(fun(Q18943,fun(Q18951,fun(Q18941,Q18941))),f),s(Q18943,h1))),s(Q18951,i(s(fun(list(Q18951),Q18951),hd),s(list(Q18951),l2))))),s(Q18941,i(s(fun(Q18941,Q18941),i(s(fun(list(Q18951),fun(Q18941,Q18941)),i(s(fun(list(Q18943),fun(list(Q18951),fun(Q18941,Q18941))),i(s(fun(fun(Q18943,fun(Q18951,fun(Q18941,Q18941))),fun(list(Q18943),fun(list(Q18951),fun(Q18941,Q18941)))),itlist2),s(fun(Q18943,fun(Q18951,fun(Q18941,Q18941))),f))),s(list(Q18943),t1))),s(list(Q18951),i(s(fun(list(Q18951),list(Q18951)),tl),s(list(Q18951),l2))))),s(Q18941,b0))))) = s(Q18941,i(s(fun(Q18941,Q18941),i(s(fun(list(Q18951),fun(Q18941,Q18941)),i(s(fun(list(Q18943),fun(list(Q18951),fun(Q18941,Q18941))),i(s(fun(fun(Q18943,fun(Q18951,fun(Q18941,Q18941))),fun(list(Q18943),fun(list(Q18951),fun(Q18941,Q18941)))),itlist2),s(fun(Q18943,fun(Q18951,fun(Q18941,Q18941))),f))),s(list(Q18943),i(s(fun(list(Q18943),list(Q18943)),i(s(fun(Q18943,fun(list(Q18943),list(Q18943))),cons),s(Q18943,h1))),s(list(Q18943),t1))))),s(list(Q18951),l2))),s(Q18941,b0)))) # label(aITLIST2u_DEFu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1897 (all X s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(real,real),realu_inv),s(real,X))))) = s(real,X)) # label(aREALu_INVu_INV) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1898 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))))),s(int,i(s(fun(int,int),intu_neg),s(int,Y)))))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) # label(aINTu_ABSu_SIGN2) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1899 (all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))) -> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),F0))))) # label(aNSUMu_TRIVu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1900 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y)))))))) # label(aREALu_MULu_POSu_LT) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1901 (all Q47235 all P0 all S0 ((exists X (p(s(bool,i(s(fun(Q47235,bool),P0),s(Q47235,X)))) & p(s(bool,i(s(fun(fun(Q47235,bool),bool),i(s(fun(Q47235,fun(fun(Q47235,bool),bool)),in),s(Q47235,X))),s(fun(Q47235,bool),i(s(fun(fun(fun(Q47235,bool),bool),fun(Q47235,bool)),unions),s(fun(fun(Q47235,bool),bool),S0)))))))) <-> (exists T0 exists X (p(s(bool,i(s(fun(fun(fun(Q47235,bool),bool),bool),i(s(fun(fun(Q47235,bool),fun(fun(fun(Q47235,bool),bool),bool)),in),s(fun(Q47235,bool),T0))),s(fun(fun(Q47235,bool),bool),S0)))) & p(s(bool,i(s(fun(Q47235,bool),P0),s(Q47235,X)))) & p(s(bool,i(s(fun(fun(Q47235,bool),bool),i(s(fun(Q47235,fun(fun(Q47235,bool),bool)),in),s(Q47235,X))),s(fun(Q47235,bool),T0)))))))) # label(aEXISTSu_INu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1902 (all Q96890 all P0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q96890,bool),bool),i(s(fun(fun(Q96890,bool),fun(fun(Q96890,bool),bool)),subset),s(fun(Q96890,bool),S0))),s(fun(Q96890,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q96890,bool),bool),i(s(fun(fun(Q96890,bool),fun(fun(Q96890,bool),bool)),subset),s(fun(Q96890,bool),i(s(fun(fun(Q96890,bool),fun(Q96890,bool)),i(s(fun(fun(fun(Q96890,bool),bool),fun(fun(Q96890,bool),fun(Q96890,bool))),hull),s(fun(fun(Q96890,bool),bool),P0))),s(fun(Q96890,bool),S0))))),s(fun(Q96890,bool),i(s(fun(fun(Q96890,bool),fun(Q96890,bool)),i(s(fun(fun(fun(Q96890,bool),bool),fun(fun(Q96890,bool),fun(Q96890,bool))),hull),s(fun(fun(Q96890,bool),bool),P0))),s(fun(Q96890,bool),T0)))))))) # label(aHULLu_MONO) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1903 (all A all S0 s(fun(A,bool),univ) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),univ)))) # label(aUNIONu_UNIVu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1904 (all Q51988 all Q51987 all F0 all B0 all S0 all A5 (p(s(bool,i(s(fun(num,bool),i(s(fun(Q51987,fun(num,bool)),i(s(fun(fun(Q51988,bool),fun(Q51987,fun(num,bool))),i(s(fun(Q51987,fun(fun(Q51988,bool),fun(Q51987,fun(num,bool)))),i(s(fun(fun(Q51988,fun(Q51987,Q51987)),fun(Q51987,fun(fun(Q51988,bool),fun(Q51987,fun(num,bool))))),finrec),s(fun(Q51988,fun(Q51987,Q51987)),F0))),s(Q51987,B0))),s(fun(Q51988,bool),S0))),s(Q51987,A5))),s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) <-> (exists X (s(fun(Q51988,bool),S0) = s(fun(Q51988,bool),i(s(fun(fun(Q51988,bool),fun(Q51988,bool)),i(s(fun(Q51988,fun(fun(Q51988,bool),fun(Q51988,bool))),insert),s(Q51988,X))),s(fun(Q51988,bool),empty))) & s(Q51987,i(s(fun(Q51987,Q51987),i(s(fun(Q51988,fun(Q51987,Q51987)),F0),s(Q51988,X))),s(Q51987,B0))) = s(Q51987,A5))))) # label(aFINRECu_1u_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1905 (all M0 all N0 all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,M0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0)))))))) # label(aREALu_POWu_MONO) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1906 (all A all A5 all B0 exists F0 (s(A,i(s(fun(bool,A),F0),s(bool,t))) = s(A,B0) & s(A,A5) = s(A,i(s(fun(bool,A),F0),s(bool,f0))))) # label(aboolu_RECURSION) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1907 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))))),s(real,i(s(fun(real,real),realu_neg),s(real,Y)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) # label(aREALu_ABSu_SIGN2) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1908 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,Y)))) # label(aREALu_LTu_LNEG) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1909 (all Q63859 all Q63821 all F0 all S0 all T0 s(fun(Q63821,bool),i(s(fun(fun(Q63821,bool),fun(Q63821,bool)),i(s(fun(fun(Q63821,bool),fun(fun(Q63821,bool),fun(Q63821,bool))),diff),s(fun(Q63821,bool),i(s(fun(fun(Q63821,bool),fun(Q63821,bool)),i(s(fun(fun(Q63821,Q63859),fun(fun(Q63821,bool),fun(Q63821,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63821,Q63859),fun(fun(Q63821,bool),fun(Q63821,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63821,Q63859),F0))),s(fun(Q63821,bool),S0))))),s(fun(Q63821,bool),i(s(fun(fun(Q63821,bool),fun(Q63821,bool)),i(s(fun(fun(Q63821,Q63859),fun(fun(Q63821,bool),fun(Q63821,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63821,Q63859),fun(fun(Q63821,bool),fun(Q63821,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63821,Q63859),F0))),s(fun(Q63821,bool),T0))))) = s(fun(Q63821,bool),i(s(fun(fun(Q63821,bool),fun(Q63821,bool)),i(s(fun(fun(Q63821,Q63859),fun(fun(Q63821,bool),fun(Q63821,bool))),i(s(fun(fun(Q63859,fun(Q63859,Q63859)),fun(fun(Q63821,Q63859),fun(fun(Q63821,bool),fun(Q63821,bool)))),support),s(fun(Q63859,fun(Q63859,Q63859)),op))),s(fun(Q63821,Q63859),F0))),s(fun(Q63821,bool),i(s(fun(fun(Q63821,bool),fun(Q63821,bool)),i(s(fun(fun(Q63821,bool),fun(fun(Q63821,bool),fun(Q63821,bool))),diff),s(fun(Q63821,bool),S0))),s(fun(Q63821,bool),T0)))))) # label(aSUPPORTu_CLAUSESu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1910 (all Y all X s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),trealu_neg),s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,X))),s(hreal,Y))))) = s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,Y))),s(hreal,X)))) # label(atrealu_neg) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1911 (all N0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))))) # label(aLEu_1u_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1912 (all Q90519 all Q90521 all S0 all T0 (p(s(bool,i(s(fun(fun(Q90519,bool),bool),finite),s(fun(Q90519,bool),S0)))) & p(s(bool,i(s(fun(fun(Q90521,bool),bool),finite),s(fun(Q90521,bool),T0)))) -> s(num,i(s(fun(fun(sum0(Q90519,Q90521),bool),num),card),s(fun(sum0(Q90519,Q90521),bool),i(s(fun(fun(Q90521,bool),fun(sum0(Q90519,Q90521),bool)),i(s(fun(fun(Q90519,bool),fun(fun(Q90521,bool),fun(sum0(Q90519,Q90521),bool))),p_u_c),s(fun(Q90519,bool),S0))),s(fun(Q90521,bool),T0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(Q90519,bool),num),card),s(fun(Q90519,bool),S0))))),s(num,i(s(fun(fun(Q90521,bool),num),card),s(fun(Q90521,bool),T0))))))) # label(aCARDu_ADDu_C) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1913 (all X s(real,i(s(fun(real,real),realu_abs),s(real,X))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),realu_neg),s(real,X)))))) # label(aREALu_ABSu_NEG) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1914 (all N0 s(num,i(s(fun(num,num),bit0),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,u_0)))) # label(aARITHu_ADDu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1915 (all Q20144 all P0 all L all X (p(s(bool,i(s(fun(Q20144,bool),P0),s(Q20144,X)))) & p(s(bool,i(s(fun(list(Q20144),bool),i(s(fun(Q20144,fun(list(Q20144),bool)),mem),s(Q20144,X))),s(list(Q20144),L)))) <-> p(s(bool,i(s(fun(list(Q20144),bool),i(s(fun(Q20144,fun(list(Q20144),bool)),mem),s(Q20144,X))),s(list(Q20144),i(s(fun(list(Q20144),list(Q20144)),i(s(fun(fun(Q20144,bool),fun(list(Q20144),list(Q20144))),filter0),s(fun(Q20144,bool),P0))),s(list(Q20144),L)))))))) # label(aMEMu_FILTER) # label(axiom) # label(non_clause). [assumption]. 14.61/14.59 1916 (all X all Y all Z0 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),Z0)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Z0)))))) # label(aTREALu_LEu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1917 (all Q87220 all U_0 ((all P0 all F0 (p(s(bool,i(s(fun(fun(prod(fun(Q87220,bool),fun(Q87220,bool)),bool),bool),i(s(fun(fun(fun(Q87220,bool),bool),fun(fun(prod(fun(Q87220,bool),fun(Q87220,bool)),bool),bool)),U_0),s(fun(fun(Q87220,bool),bool),P0))),s(fun(prod(fun(Q87220,bool),fun(Q87220,bool)),bool),F0)))) <-> (all X all Y exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(Q87220,bool),fun(Q87220,bool)),bool),F0),s(prod(fun(Q87220,bool),fun(Q87220,bool)),i(s(fun(fun(Q87220,bool),prod(fun(Q87220,bool),fun(Q87220,bool))),i(s(fun(fun(Q87220,bool),fun(fun(Q87220,bool),prod(fun(Q87220,bool),fun(Q87220,bool)))),c_),s(fun(Q87220,bool),X))),s(fun(Q87220,bool),Y))))))),s(bool,V)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(Q87220,bool),bool),P0),s(fun(Q87220,bool),X)))) & p(s(bool,i(s(fun(fun(Q87220,bool),bool),i(s(fun(fun(Q87220,bool),fun(fun(Q87220,bool),bool)),subset),s(fun(Q87220,bool),X))),s(fun(Q87220,bool),Y)))) & p(s(bool,i(s(fun(fun(Q87220,bool),bool),P0),s(fun(Q87220,bool),Y))))))))) -> (all P0 p(s(bool,i(s(fun(fun(prod(fun(Q87220,bool),fun(Q87220,bool)),bool),bool),poset),s(fun(prod(fun(Q87220,bool),fun(Q87220,bool)),bool),i(s(fun(fun(fun(prod(fun(Q87220,bool),fun(Q87220,bool)),bool),bool),fun(prod(fun(Q87220,bool),fun(Q87220,bool)),bool)),gabs),s(fun(fun(prod(fun(Q87220,bool),fun(Q87220,bool)),bool),bool),i(s(fun(fun(fun(Q87220,bool),bool),fun(fun(prod(fun(Q87220,bool),fun(Q87220,bool)),bool),bool)),U_0),s(fun(fun(Q87220,bool),bool),P0))))))))))) # label(aPOSETu_RESTRICTEDu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1918 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_abs),s(real,X)))))) <-> s(real,X) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aREALu_ABSu_NZ) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1919 (all A all P0 all Q0 ((all X (p(s(bool,P0)) & p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))) <-> (all X p(s(bool,i(s(fun(A,bool),Q0),s(A,X))))) & p(s(bool,P0)))) # label(aRIGHTu_ANDu_FORALLu_THM) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1920 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,y2)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,y1)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,x1))),s(real,y1))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,x2))),s(real,y2))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x1))),s(real,y2))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x2))),s(real,y1))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_inv),s(real,y1))))),s(real,i(s(fun(real,real),realu_inv),s(real,y2))))))) # label(aRATu_LEMMA3) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1921 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0)))))))) # label(aREALu_LTu_LADDu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1922 (all U_0 ((all X all I0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0)))) -> (all X all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) # label(aREALu_SUBu_POWu_R1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1923 (all Q97302 all P0 all S0 all X (p(s(bool,i(s(fun(fun(Q97302,bool),bool),i(s(fun(Q97302,fun(fun(Q97302,bool),bool)),in),s(Q97302,X))),s(fun(Q97302,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q97302,bool),bool),i(s(fun(Q97302,fun(fun(Q97302,bool),bool)),in),s(Q97302,X))),s(fun(Q97302,bool),i(s(fun(fun(Q97302,bool),fun(Q97302,bool)),i(s(fun(fun(fun(Q97302,bool),bool),fun(fun(Q97302,bool),fun(Q97302,bool))),hull),s(fun(fun(Q97302,bool),bool),P0))),s(fun(Q97302,bool),S0)))))))) # label(aHULLu_INC) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1924 (all Q92717 all S0 (p(s(bool,i(s(fun(fun(Q92717,bool),bool),finite),s(fun(Q92717,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q92717,bool),bool),countable),s(fun(Q92717,bool),S0)))))) # label(aFINITEu_IMPu_COUNTABLE) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1925 (all X all N0 (s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) | s(num,X) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) <-> s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0))))) # label(aEXPu_EQu_1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1926 (all X s(ind0,indu_0) != s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,X)))) # label(aINDu_SUCu_0) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1927 (all N0 s(bool,t) = s(bool,i(s(fun(num,bool),even),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_EVENu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1928 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all X all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,Y)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) | p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))))))) # label(aWOSETu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1929 (all X all Y all N0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))),s(num,N0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0)))))) # label(aREALu_POWu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1930 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,P0))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,P0))))),s(num,N0)))) # label(aMODu_MULTu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1931 (all Q18767 all Q18766 s(bool,i(s(fun(list(Q18766),bool),i(s(fun(list(Q18767),fun(list(Q18766),bool)),i(s(fun(fun(Q18767,fun(Q18766,bool)),fun(list(Q18767),fun(list(Q18766),bool))),all2),s(fun(Q18767,fun(Q18766,bool)),p0))),s(list(Q18767),i(s(fun(list(Q18767),list(Q18767)),i(s(fun(Q18767,fun(list(Q18767),list(Q18767))),cons),s(Q18767,h1))),s(list(Q18767),t1))))),s(list(Q18766),nil))) = s(bool,f0)) # label(aALL2u_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1932 (all X all Y all D0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))))),s(int,D0)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,D0)))))))) # label(aINTu_ABSu_BOUND) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1933 (all Q47692 all Q47696 all Q47687 all F0 all G0 all S0 s(fun(Q47692,bool),i(s(fun(fun(Q47687,bool),fun(Q47692,bool)),i(s(fun(fun(Q47687,Q47692),fun(fun(Q47687,bool),fun(Q47692,bool))),image),s(fun(Q47687,Q47692),i(s(fun(fun(Q47687,Q47696),fun(Q47687,Q47692)),i(s(fun(fun(Q47696,Q47692),fun(fun(Q47687,Q47696),fun(Q47687,Q47692))),o),s(fun(Q47696,Q47692),F0))),s(fun(Q47687,Q47696),G0))))),s(fun(Q47687,bool),S0))) = s(fun(Q47692,bool),i(s(fun(fun(Q47696,bool),fun(Q47692,bool)),i(s(fun(fun(Q47696,Q47692),fun(fun(Q47696,bool),fun(Q47692,bool))),image),s(fun(Q47696,Q47692),F0))),s(fun(Q47696,bool),i(s(fun(fun(Q47687,bool),fun(Q47696,bool)),i(s(fun(fun(Q47687,Q47696),fun(fun(Q47687,bool),fun(Q47696,bool))),image),s(fun(Q47687,Q47696),G0))),s(fun(Q47687,bool),S0)))))) # label(aIMAGEu_o) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1934 (all B all A all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0)))))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> (exists X (s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))) & (all X all XI_ (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0)))) & s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,XI_))) & s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y) -> s(A,XI_) = s(A,X))))) -> s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))) = s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))))) # label(aCARDu_IMAGEu_INJu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.61/14.60 1935 (all Q79780 all Q79773 exists V ((p(s(bool,V)) <-> (exists Y p(s(bool,i(s(fun(Q79773,bool),i(s(fun(Q79780,fun(Q79773,bool)),r0),s(Q79780,x))),s(Q79773,Y)))))) & s(Q79773,i(s(fun(Q79773,Q79773),i(s(fun(Q79773,fun(Q79773,Q79773)),i(s(fun(bool,fun(Q79773,fun(Q79773,Q79773))),cond),s(bool,V))),s(Q79773,i(s(fun(fun(Q79780,fun(Q79773,bool)),Q79773),i(s(fun(Q79780,fun(fun(Q79780,fun(Q79773,bool)),Q79773)),u_match),s(Q79780,x))),s(fun(Q79780,fun(Q79773,bool)),r0))))),s(Q79773,i(s(fun(fun(Q79780,fun(Q79773,bool)),Q79773),i(s(fun(Q79780,fun(fun(Q79780,fun(Q79773,bool)),Q79773)),u_match),s(Q79780,x))),s(fun(Q79780,fun(Q79773,bool)),s0))))) = s(Q79773,i(s(fun(fun(Q79780,fun(Q79773,bool)),Q79773),i(s(fun(Q79780,fun(fun(Q79780,fun(Q79773,bool)),Q79773)),u_match),s(Q79780,x))),s(fun(Q79780,fun(Q79773,bool)),i(s(fun(fun(Q79780,fun(Q79773,bool)),fun(Q79780,fun(Q79773,bool))),i(s(fun(fun(Q79780,fun(Q79773,bool)),fun(fun(Q79780,fun(Q79773,bool)),fun(Q79780,fun(Q79773,bool)))),u_seqpattern),s(fun(Q79780,fun(Q79773,bool)),r0))),s(fun(Q79780,fun(Q79773,bool)),s0))))))) # label(aMATCHu_SEQPATTERN) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1936 (all X all Y (s(int,Y) = s(int,X) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,X)))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))))) # label(aINTu_LTu_TOTAL) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1937 (all X all XI_ (p(s(bool,XI_)) & p(s(bool,X)) <-> p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),u_unguardedu_pattern),s(bool,X))),s(bool,XI_)))))) # label(au_UNGUARDEDu_PATTERN) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1938 (all B1 all X1 all B2 all X2 (s(num,X1) = s(num,X2) & s(bool,B2) = s(bool,B1) <-> s(num,i(s(fun(num,num),i(s(fun(bool,fun(num,num)),numsum),s(bool,B1))),s(num,X1))) = s(num,i(s(fun(num,num),i(s(fun(bool,fun(num,num)),numsum),s(bool,B2))),s(num,X2))))) # label(aNUMSUMu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1939 (all Q18547 exists V (s(list(Q18547),i(s(fun(list(Q18547),list(Q18547)),butlast),s(list(Q18547),i(s(fun(list(Q18547),list(Q18547)),i(s(fun(Q18547,fun(list(Q18547),list(Q18547))),cons),s(Q18547,h0))),s(list(Q18547),t0))))) = s(list(Q18547),i(s(fun(list(Q18547),list(Q18547)),i(s(fun(list(Q18547),fun(list(Q18547),list(Q18547))),i(s(fun(bool,fun(list(Q18547),fun(list(Q18547),list(Q18547)))),cond),s(bool,V))),s(list(Q18547),nil))),s(list(Q18547),i(s(fun(list(Q18547),list(Q18547)),i(s(fun(Q18547,fun(list(Q18547),list(Q18547))),cons),s(Q18547,h0))),s(list(Q18547),i(s(fun(list(Q18547),list(Q18547)),butlast),s(list(Q18547),t0))))))) & (p(s(bool,V)) <-> s(list(Q18547),nil) = s(list(Q18547),t0)))) # label(aBUTLASTu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1940 (all W all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,Z0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,W))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,W))),s(int,Y))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0)))))))) # label(aINTu_LTEu_ADD2) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1941 (all A all B all C all P all U_6 ((all A5 all B0 all H0 all F0 all X s(num,i(s(fun(P,num),i(s(fun(fun(B,C),fun(P,num)),i(s(fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num))))),U_6),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,fun(num,num))),H0))),s(fun(B,C),F0))),s(P,X))) = s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(P,num),A5),s(P,X))))),s(num,i(s(fun(P,num),B0),s(P,X))))))),s(fun(num,num),i(s(fun(P,fun(num,num)),i(s(fun(fun(B,C),fun(P,fun(num,num))),H0),s(fun(B,C),F0))),s(P,X)))))) -> (all U_5 ((all A5 all B0 all H0 all F0 s(fun(P,num),i(s(fun(fun(B,C),fun(P,num)),i(s(fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num))))),U_5),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,fun(num,num))),H0))),s(fun(B,C),F0))) = s(fun(P,num),i(s(fun(fun(B,C),fun(P,num)),i(s(fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num))))),U_6),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,fun(num,num))),H0))),s(fun(B,C),F0)))) -> (all U_4 ((all H0 all F0 all F1 ((all K0 all X p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),geq),s(num,i(s(fun(prod(num,P),num),F1),s(prod(num,P),i(s(fun(P,prod(num,P)),i(s(fun(num,fun(P,prod(num,P))),c_),s(num,K0))),s(P,X))))))),s(num,i(s(fun(num,num),i(s(fun(P,fun(num,num)),i(s(fun(fun(B,C),fun(P,fun(num,num))),H0),s(fun(B,C),F0))),s(P,X))),s(num,K0))))))) <-> p(s(bool,i(s(fun(fun(prod(num,P),num),bool),i(s(fun(fun(B,C),fun(fun(prod(num,P),num),bool)),i(s(fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(fun(prod(num,P),num),bool))),U_4),s(fun(fun(B,C),fun(P,fun(num,num))),H0))),s(fun(B,C),F0))),s(fun(prod(num,P),num),F1)))))) -> (all U_3 ((all H0 all F0 s(fun(prod(num,P),num),i(s(fun(fun(fun(prod(num,P),num),bool),fun(prod(num,P),num)),gabs),s(fun(fun(prod(num,P),num),bool),i(s(fun(fun(B,C),fun(fun(prod(num,P),num),bool)),i(s(fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(fun(prod(num,P),num),bool))),U_4),s(fun(fun(B,C),fun(P,fun(num,num))),H0))),s(fun(B,C),F0))))) = s(fun(prod(num,P),num),i(s(fun(fun(B,C),fun(prod(num,P),num)),i(s(fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(prod(num,P),num))),U_3),s(fun(fun(B,C),fun(P,fun(num,num))),H0))),s(fun(B,C),F0)))) -> (all U_2 ((all S0 all F0 ((all K0 all X p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),geq),s(A,i(s(fun(prod(num,P),A),F0),s(prod(num,P),i(s(fun(P,prod(num,P)),i(s(fun(num,fun(P,prod(num,P))),c_),s(num,K0))),s(P,X))))))),s(A,i(s(fun(P,A),S0),s(P,X))))))) <-> p(s(bool,i(s(fun(fun(prod(num,P),A),bool),i(s(fun(fun(P,A),fun(fun(prod(num,P),A),bool)),U_2),s(fun(P,A),S0))),s(fun(prod(num,P),A),F0)))))) -> (all U_1 ((all A5 all B0 all P0 all F0 all F1 ((all K0 all X exists V ((p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(P,num),B0),s(P,X)))))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(B,C),fun(P,bool)),P0),s(fun(B,C),F0))),s(P,X)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(P,num),A5),s(P,X))))),s(num,K0)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(num,P),bool),F1),s(prod(num,P),i(s(fun(P,prod(num,P)),i(s(fun(num,fun(P,prod(num,P))),c_),s(num,K0))),s(P,X))))))),s(bool,V)))))) <-> p(s(bool,i(s(fun(fun(prod(num,P),bool),bool),i(s(fun(fun(B,C),fun(fun(prod(num,P),bool),bool)),i(s(fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool))))),U_1),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,bool)),P0))),s(fun(B,C),F0))),s(fun(prod(num,P),bool),F1)))))) -> (all U_0 ((all A5 all B0 all P0 all F0 s(fun(prod(num,P),bool),i(s(fun(fun(B,C),fun(prod(num,P),bool)),i(s(fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool))))),U_0),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,bool)),P0))),s(fun(B,C),F0))) = s(fun(prod(num,P),bool),i(s(fun(fun(fun(prod(num,P),bool),bool),fun(prod(num,P),bool)),gabs),s(fun(fun(prod(num,P),bool),bool),i(s(fun(fun(B,C),fun(fun(prod(num,P),bool),bool)),i(s(fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(fun(prod(num,P),bool),bool))))),U_1),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,bool)),P0))),s(fun(B,C),F0)))))) -> (all L_L_ all P0 all S0 all H0 all A5 all B0 (p(s(bool,i(s(fun(fun(fun(B,C),fun(prod(num,P),num)),bool),i(s(fun(fun(prod(num,P),A),fun(fun(fun(B,C),fun(prod(num,P),num)),bool)),i(s(fun(fun(fun(B,C),fun(prod(num,P),bool)),fun(fun(prod(num,P),A),fun(fun(fun(B,C),fun(prod(num,P),num)),bool))),i(s(fun(fun(B,fun(A,bool)),fun(fun(fun(B,C),fun(prod(num,P),bool)),fun(fun(prod(num,P),A),fun(fun(fun(B,C),fun(prod(num,P),num)),bool)))),admissible),s(fun(B,fun(A,bool)),L_L_))),s(fun(fun(B,C),fun(prod(num,P),bool)),i(s(fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,bool)),fun(fun(B,C),fun(prod(num,P),bool))))),U_0),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,bool)),P0))))),s(fun(prod(num,P),A),i(s(fun(fun(fun(prod(num,P),A),bool),fun(prod(num,P),A)),gabs),s(fun(fun(prod(num,P),A),bool),i(s(fun(fun(P,A),fun(fun(prod(num,P),A),bool)),U_2),s(fun(P,A),S0))))))),s(fun(fun(B,C),fun(prod(num,P),num)),i(s(fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(prod(num,P),num))),U_3),s(fun(fun(B,C),fun(P,fun(num,num))),H0)))))) -> p(s(bool,i(s(fun(fun(fun(B,C),fun(P,num)),bool),i(s(fun(fun(P,A),fun(fun(fun(B,C),fun(P,num)),bool)),i(s(fun(fun(fun(B,C),fun(P,bool)),fun(fun(P,A),fun(fun(fun(B,C),fun(P,num)),bool))),i(s(fun(fun(B,fun(A,bool)),fun(fun(fun(B,C),fun(P,bool)),fun(fun(P,A),fun(fun(fun(B,C),fun(P,num)),bool)))),admissible),s(fun(B,fun(A,bool)),L_L_))),s(fun(fun(B,C),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(B,C),fun(P,num)),i(s(fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num))),i(s(fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num)))),i(s(fun(fun(P,num),fun(fun(P,num),fun(fun(fun(B,C),fun(P,fun(num,num))),fun(fun(B,C),fun(P,num))))),U_5),s(fun(P,num),A5))),s(fun(P,num),B0))),s(fun(fun(B,C),fun(P,fun(num,num))),H0)))))))))))))))))))))) # label(aADMISSIBLEu_NSUM) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1942 (all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),bit1),s(num,N0))))),s(num,u_0))) = s(bool,f0)) # label(aARITHu_LEu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1943 (all X all Y all Z0 (s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) | s(real,Y) = s(real,Z0) <-> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))) # label(aREALu_EQu_MULu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1944 (all Q87245 all U_0 ((all P0 all F0 (p(s(bool,i(s(fun(fun(prod(fun(Q87245,bool),fun(Q87245,bool)),bool),bool),i(s(fun(fun(fun(Q87245,bool),bool),fun(fun(prod(fun(Q87245,bool),fun(Q87245,bool)),bool),bool)),U_0),s(fun(fun(Q87245,bool),bool),P0))),s(fun(prod(fun(Q87245,bool),fun(Q87245,bool)),bool),F0)))) <-> (all X all Y exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(Q87245,bool),fun(Q87245,bool)),bool),F0),s(prod(fun(Q87245,bool),fun(Q87245,bool)),i(s(fun(fun(Q87245,bool),prod(fun(Q87245,bool),fun(Q87245,bool))),i(s(fun(fun(Q87245,bool),fun(fun(Q87245,bool),prod(fun(Q87245,bool),fun(Q87245,bool)))),c_),s(fun(Q87245,bool),X))),s(fun(Q87245,bool),Y))))))),s(bool,V)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(Q87245,bool),bool),P0),s(fun(Q87245,bool),X)))) & p(s(bool,i(s(fun(fun(Q87245,bool),bool),P0),s(fun(Q87245,bool),Y)))) & p(s(bool,i(s(fun(fun(Q87245,bool),bool),i(s(fun(fun(Q87245,bool),fun(fun(Q87245,bool),bool)),subset),s(fun(Q87245,bool),X))),s(fun(Q87245,bool),Y))))))))) -> (all P0 s(fun(fun(Q87245,bool),bool),P0) = s(fun(fun(Q87245,bool),bool),i(s(fun(fun(prod(fun(Q87245,bool),fun(Q87245,bool)),bool),fun(fun(Q87245,bool),bool)),fl),s(fun(prod(fun(Q87245,bool),fun(Q87245,bool)),bool),i(s(fun(fun(fun(prod(fun(Q87245,bool),fun(Q87245,bool)),bool),bool),fun(prod(fun(Q87245,bool),fun(Q87245,bool)),bool)),gabs),s(fun(fun(prod(fun(Q87245,bool),fun(Q87245,bool)),bool),bool),i(s(fun(fun(fun(Q87245,bool),bool),fun(fun(prod(fun(Q87245,bool),fun(Q87245,bool)),bool),bool)),U_0),s(fun(fun(Q87245,bool),bool),P0)))))))))) # label(aFLu_RESTRICTEDu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1945 (all M0 all N0 s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(fun(num,num),f))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),f))))),s(num,i(s(fun(num,num),f),s(num,i(s(fun(num,num),suc),s(num,N0))))))))),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),f)))))) # label(aNSUMu_CLAUSESu_NUMSEGu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1946 (all A all X all S0 all T0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))),s(fun(A,bool),T0))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),i(s(fun(bool,fun(fun(A,bool),fun(fun(A,bool),fun(A,bool)))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aINSERTu_INTER) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1947 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0)))))) # label(aARITHu_LTu_conjunct7) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1948 (all X all Y all X0 s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Y))))),s(num,X0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,X0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,Y))),s(num,X0)))))) # label(aNADDu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1949 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0)))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0)))))) # label(aREALu_LTu_LCANCELu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1950 (all Q70953 all F0 s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(fun(Q70953,real),real),i(s(fun(fun(Q70953,bool),fun(fun(Q70953,real),real)),sum),s(fun(Q70953,bool),empty))),s(fun(Q70953,real),F0)))) # label(aSUMu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1951 (all X all Y p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X))),s(hreal,Y))))))) # label(aHREALu_LEu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1952 (all A all U_0 ((all S0 all GENR_PVARR_245 ((exists T0 exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_245))),s(bool,V))),s(fun(A,bool),T0)))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))),s(fun(A,bool),GENR_PVARR_245)))))) -> (all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),a_u_c),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))))))),s(fun(A,bool),S0)))))))) # label(aCARDu_EQu_FINITEu_SUBSETS) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1953 (all B0 (s(fun(real,bool),empty) != s(fun(real,bool),s0) & (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),s0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),s0))))),s(real,B0)))))) # label(aREALu_SUPu_LE) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1954 (all X all Y (s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(int,i(s(fun(int,int),intu_abs),s(int,X))) & s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(int,i(s(fun(int,int),intu_abs),s(int,Y))) <-> s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))))) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) # label(aINTu_ABSu_MULu_1) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1955 (all A all S0 ((exists F0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(num,bool),fun(A,bool)),i(s(fun(fun(num,A),fun(fun(num,bool),fun(A,bool))),image),s(fun(num,A),F0))),s(fun(num,bool),univ))))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0)))))) # label(aCOUNTABLEu_ASu_IMAGEu_SUBSETu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1956 (all A exists L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),L)))) & (all X p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X))))))) # label(aLEMMA) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1957 (all N0 all X all Y (s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))) & p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))) -> s(real,X) = s(real,Y))) # label(aREALu_POWu_EQu_ODD) # label(axiom) # label(non_clause). [assumption]. 14.61/14.61 1958 (all A all S0 all T0 all X s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),T0))),s(A,X))))),s(fun(A,bool),S0))) = s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(fun(A,bool),T0)))) # label(aDISJOINTu_DELETEu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1959 (all A all B all S0 all T0 p(s(bool,i(s(fun(fun(sum0(A,B),bool),bool),i(s(fun(fun(B,bool),fun(fun(sum0(A,B),bool),bool)),l_a_u_c),s(fun(B,bool),T0))),s(fun(sum0(A,B),bool),i(s(fun(fun(B,bool),fun(sum0(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(sum0(A,B),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))))) # label(aCARDu_LEu_ADDL) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1960 (all A all S0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(A,bool),S0))))) # label(aCARDu_LEu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1961 (all A all S0 p(s(bool,i(s(fun(num,bool),i(s(fun(fun(finite_image(A),bool),fun(num,bool)),hasu_size),s(fun(finite_image(A),bool),univ))),s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),S0))))))) # label(aHASu_SIZEu_FINITEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1962 (all A all S0 (s(fun(A,bool),S0) = s(fun(A,bool),empty) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),empty)))))) # label(aSUBSETu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1963 (all X p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,i(s(fun(int,int),intu_abs),s(int,X))))))) # label(aINTu_ABSu_LE) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1964 (all Q58267 all L1 all L2 s(fun(Q58267,bool),i(s(fun(fun(Q58267,bool),fun(Q58267,bool)),i(s(fun(fun(Q58267,bool),fun(fun(Q58267,bool),fun(Q58267,bool))),union),s(fun(Q58267,bool),i(s(fun(list(Q58267),fun(Q58267,bool)),setu_ofu_list),s(list(Q58267),L1))))),s(fun(Q58267,bool),i(s(fun(list(Q58267),fun(Q58267,bool)),setu_ofu_list),s(list(Q58267),L2))))) = s(fun(Q58267,bool),i(s(fun(list(Q58267),fun(Q58267,bool)),setu_ofu_list),s(list(Q58267),i(s(fun(list(Q58267),list(Q58267)),i(s(fun(list(Q58267),fun(list(Q58267),list(Q58267))),append),s(list(Q58267),L1))),s(list(Q58267),L2)))))) # label(aSETu_OFu_LISTu_APPEND) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1965 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all X all Y (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,Y)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) | p(s(bool,i(s(fun(prod(A,A),bool),i(s(fun(fun(prod(A,A),bool),fun(prod(A,A),bool)),less),s(fun(prod(A,A),bool),L))),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))))))) # label(aWOSETu_TOTALu_LE) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1966 (all Q20049 all Q20052 all F0 all Y all L ((exists X (s(Q20049,Y) = s(Q20049,i(s(fun(Q20052,Q20049),F0),s(Q20052,X))) & p(s(bool,i(s(fun(list(Q20052),bool),i(s(fun(Q20052,fun(list(Q20052),bool)),mem),s(Q20052,X))),s(list(Q20052),L)))))) <-> p(s(bool,i(s(fun(list(Q20049),bool),i(s(fun(Q20049,fun(list(Q20049),bool)),mem),s(Q20049,Y))),s(list(Q20049),i(s(fun(list(Q20052),list(Q20049)),i(s(fun(fun(Q20052,Q20049),fun(list(Q20052),list(Q20049))),map0),s(fun(Q20052,Q20049),F0))),s(list(Q20052),L)))))))) # label(aMEMu_MAP) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1967 (all A all B all U_1 ((all T0 all GENR_PVARR_253 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),U_1),s(fun(B,bool),T0))),s(fun(B,bool),GENR_PVARR_253)))) <-> (exists V exists V0 ((p(s(bool,V0)) <-> p(s(bool,i(s(fun(fun(B,bool),bool),countable),s(fun(B,bool),V)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),V))),s(fun(B,bool),T0))))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(bool,fun(fun(B,bool),bool)),i(s(fun(fun(B,bool),fun(bool,fun(fun(B,bool),bool))),setspec),s(fun(B,bool),GENR_PVARR_253))),s(bool,V0))),s(fun(B,bool),V)))))))) -> (all U_0 ((all S0 all GENR_PVARR_252 ((exists U exists V (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_252))),s(bool,V))),s(fun(A,bool),U)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),U))),s(fun(A,bool),S0))))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))),s(fun(A,bool),GENR_PVARR_252)))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(fun(B,bool),bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(fun(B,bool),bool),bool)),l_a_u_c),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))))))),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),gspec),s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),U_1),s(fun(B,bool),T0)))))))))))))) # label(aCARDu_LEu_COUNTABLEu_SUBSETS) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1968 (all Q78477 all Q78476 all Q78478 ((all P0 p(s(bool,i(s(fun(cart(Q78476,finite_sum(Q78477,Q78478)),bool),p0),s(cart(Q78476,finite_sum(Q78477,Q78478)),P0))))) <-> (all X all Y p(s(bool,i(s(fun(cart(Q78476,finite_sum(Q78477,Q78478)),bool),p0),s(cart(Q78476,finite_sum(Q78477,Q78478)),i(s(fun(cart(Q78476,Q78478),cart(Q78476,finite_sum(Q78477,Q78478))),i(s(fun(cart(Q78476,Q78477),fun(cart(Q78476,Q78478),cart(Q78476,finite_sum(Q78477,Q78478)))),pastecart),s(cart(Q78476,Q78477),X))),s(cart(Q78476,Q78478),Y))))))))) # label(aFORALLu_PASTECART) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1969 (all N0 -p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,u_0))),s(num,i(s(fun(num,num),bit1),s(num,N0))))))) # label(aARITHu_GEu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1970 (all A all U_0 ((all L all A5 all F0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(A,fun(fun(prod(A,A),bool),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(fun(prod(A,A),bool),bool))),U_0),s(fun(prod(A,A),bool),L))),s(A,A5))),s(fun(prod(A,A),bool),F0)))) <-> (all X all Y exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(A,A),bool),F0),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y))))))),s(bool,V)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,A5)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y))))))))))) -> (all L all A5 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,A5)))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),i(s(fun(fun(fun(prod(A,A),bool),bool),fun(prod(A,A),bool)),gabs),s(fun(fun(prod(A,A),bool),bool),i(s(fun(A,fun(fun(prod(A,A),bool),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(fun(prod(A,A),bool),bool))),U_0),s(fun(prod(A,A),bool),L))),s(A,A5))))))),s(fun(prod(A,A),bool),L)))))))) # label(aEXTENDu_INSEG) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1971 (all N0 s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),bit0),s(num,N0))))) = s(num,i(s(fun(num,num),bit1),s(num,N0)))) # label(aARITHu_SUCu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1972 (all A all B all X ((exists A5 s(sum0(A,B),i(s(fun(B,sum0(A,B)),inr),s(B,A5))) = s(sum0(A,B),X)) | (exists A5 s(sum0(A,B),X) = s(sum0(A,B),i(s(fun(A,sum0(A,B)),inl),s(A,A5)))))) # label(asumu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1973 (all A all B all U_0 ((all OP all F0 all G0 all X s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),OP),s(B,i(s(fun(A,B),F0),s(A,X))))),s(B,i(s(fun(A,B),G0),s(A,X))))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),i(s(fun(fun(A,B),fun(fun(A,B),fun(A,B))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,B),fun(A,B)))),U_0),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,B),G0))),s(A,X)))) -> (all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,bool),fun(A,bool)))),support),s(fun(B,fun(B,B)),OP))),s(fun(A,B),G0))),s(fun(A,bool),S0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(A,bool))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,bool),fun(A,bool)))),support),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,bool),S0)))))) -> s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),i(s(fun(fun(A,B),fun(fun(A,B),fun(A,B))),i(s(fun(fun(B,fun(B,B)),fun(fun(A,B),fun(fun(A,B),fun(A,B)))),U_0),s(fun(B,fun(B,B)),OP))),s(fun(A,B),F0))),s(fun(A,B),G0))))) = s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),OP),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))))),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),G0))))))))))) # label(aITERATEu_OPu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1974 (all X s(int,X) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aINTu_ADDu_RID) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1975 (all A all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0)))) & s(fun(A,bool),empty) != s(fun(A,bool),S0) -> (exists F0 s(fun(A,bool),i(s(fun(fun(num,bool),fun(A,bool)),i(s(fun(fun(num,A),fun(fun(num,bool),fun(A,bool))),image),s(fun(num,A),F0))),s(fun(num,bool),univ))) = s(fun(A,bool),S0)))) # label(aCOUNTABLEu_ASu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1976 (all M0 s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(hreal,M0))) = s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aHREALu_MULu_LZERO) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1977 (all A all B all S0 all T0 all F0 all G0 ((p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) | p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,i(s(fun(B,A),G0),s(B,i(s(fun(A,B),F0),s(A,X))))) = s(A,X) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0)))))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,i(s(fun(B,A),G0),s(B,Y))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(B,A),G0),s(B,Y))))),s(fun(A,bool),S0)))))) -> s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))) = s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))))) # label(aBIJECTIONSu_CARDu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1978 (all A all C0 all I0 all R0 s(recspace(A),i(s(fun(fun(num,recspace(A)),recspace(A)),i(s(fun(A,fun(fun(num,recspace(A)),recspace(A))),i(s(fun(num,fun(A,fun(fun(num,recspace(A)),recspace(A)))),constr),s(num,C0))),s(A,I0))),s(fun(num,recspace(A)),R0))) != s(recspace(A),bottom)) # label(aCONSTRu_BOT) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1979 (all K0 all X s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,K0))),s(num,X))) = s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,K0))))),s(num,X)))) # label(aNADDu_OFu_NUM) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1980 (all U_0 ((all C0 all X all I0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),C0),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),C0))),s(real,X))),s(num,I0)))) -> (all N0 all C0 all K0 ((all X s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),C0))),s(real,X))))) = s(real,K0)) <-> s(real,K0) = s(real,i(s(fun(num,real),C0),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & (all I0 (p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,I0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(num,real),C0),s(num,I0))))))))) # label(aREALu_POLYFUNu_EQu_CONST) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1981 (all Q79800 all Q79801 all Q79802 all Q79803 all Q79804 all U_0 ((all C0 all F0 s(fun(Q79803,Q79804),i(s(fun(fun(Q79801,Q79802),fun(Q79803,Q79804)),i(s(fun(fun(Q79803,Q79804),fun(fun(Q79801,Q79802),fun(Q79803,Q79804))),U_0),s(fun(Q79803,Q79804),C0))),s(fun(Q79801,Q79802),F0))) = s(fun(Q79803,Q79804),C0)) -> (all P0 all S0 all C0 p(s(bool,i(s(fun(fun(fun(Q79801,Q79802),fun(Q79803,Q79804)),bool),i(s(fun(fun(Q79803,Q79800),fun(fun(fun(Q79801,Q79802),fun(Q79803,Q79804)),bool)),i(s(fun(fun(fun(Q79801,Q79802),fun(Q79803,bool)),fun(fun(Q79803,Q79800),fun(fun(fun(Q79801,Q79802),fun(Q79803,Q79804)),bool))),i(s(fun(fun(Q79801,fun(Q79800,bool)),fun(fun(fun(Q79801,Q79802),fun(Q79803,bool)),fun(fun(Q79803,Q79800),fun(fun(fun(Q79801,Q79802),fun(Q79803,Q79804)),bool)))),admissible),s(fun(Q79801,fun(Q79800,bool)),l_l_))),s(fun(fun(Q79801,Q79802),fun(Q79803,bool)),P0))),s(fun(Q79803,Q79800),S0))),s(fun(fun(Q79801,Q79802),fun(Q79803,Q79804)),i(s(fun(fun(Q79803,Q79804),fun(fun(Q79801,Q79802),fun(Q79803,Q79804))),U_0),s(fun(Q79803,Q79804),C0))))))))) # label(aADMISSIBLEu_CONST) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1982 (all A all U_0 ((all N0 s(real,i(s(fun(A,real),U_0),s(A,N0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) -> (all S0 s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),U_0)))))) # label(aSUMu_0) # label(axiom) # label(non_clause). [assumption]. 14.63/14.61 1983 (all X all Y (s(hreal,Y) = s(hreal,X) <-> p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,Y))),s(hreal,X)))) & p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,X))),s(hreal,Y)))))) # label(aHREALu_LEu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1984 (all N0 s(bool,f0) = s(bool,i(s(fun(num,bool),odd),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_ODDu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1985 (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,X))))) # label(aREALu_LEu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1986 (all Q48971 all Q48955 all U_0 ((all S0 all F0 all GENR_PVARR_28 ((exists Y exists V (p(s(bool,i(s(fun(Q48955,bool),i(s(fun(bool,fun(Q48955,bool)),i(s(fun(Q48955,fun(bool,fun(Q48955,bool))),setspec),s(Q48955,GENR_PVARR_28))),s(bool,V))),s(Q48955,Y)))) & ((all X (p(s(bool,i(s(fun(fun(Q48971,bool),bool),i(s(fun(Q48971,fun(fun(Q48971,bool),bool)),in),s(Q48971,X))),s(fun(Q48971,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q48955,bool),bool),i(s(fun(Q48955,fun(fun(Q48955,bool),bool)),in),s(Q48955,Y))),s(fun(Q48955,bool),i(s(fun(Q48971,fun(Q48955,bool)),F0),s(Q48971,X)))))))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(Q48955,bool),i(s(fun(fun(Q48971,fun(Q48955,bool)),fun(Q48955,bool)),i(s(fun(fun(Q48971,bool),fun(fun(Q48971,fun(Q48955,bool)),fun(Q48955,bool))),U_0),s(fun(Q48971,bool),S0))),s(fun(Q48971,fun(Q48955,bool)),F0))),s(Q48955,GENR_PVARR_28)))))) -> (all F0 all S0 s(fun(Q48955,bool),i(s(fun(fun(fun(Q48955,bool),bool),fun(Q48955,bool)),inters),s(fun(fun(Q48955,bool),bool),i(s(fun(fun(Q48971,bool),fun(fun(Q48955,bool),bool)),i(s(fun(fun(Q48971,fun(Q48955,bool)),fun(fun(Q48971,bool),fun(fun(Q48955,bool),bool))),image),s(fun(Q48971,fun(Q48955,bool)),F0))),s(fun(Q48971,bool),S0))))) = s(fun(Q48955,bool),i(s(fun(fun(Q48955,bool),fun(Q48955,bool)),gspec),s(fun(Q48955,bool),i(s(fun(fun(Q48971,fun(Q48955,bool)),fun(Q48955,bool)),i(s(fun(fun(Q48971,bool),fun(fun(Q48971,fun(Q48955,bool)),fun(Q48955,bool))),U_0),s(fun(Q48971,bool),S0))),s(fun(Q48971,fun(Q48955,bool)),F0)))))))) # label(aINTERSu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1987 (all A all U_0 ((all S0 all GENR_PVARR_262 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))),s(fun(A,bool),GENR_PVARR_262)))) <-> (exists T0 exists V (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_262))),s(bool,V))),s(fun(A,bool),T0)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0))))))))) -> (all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),countable),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0)))))))))))) # label(aCOUNTABLEu_FINITEu_SUBSETS) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1988 (all P0 ((all I0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,I0)))) -> p(s(bool,i(s(fun(int,bool),P0),s(int,I0)))))) <-> (all N0 p(s(bool,i(s(fun(int,bool),P0),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))))))) # label(aINTu_FORALLu_POS) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1989 (all X (-p(s(bool,X)) <-> (p(s(bool,X)) -> p(s(bool,f0))))) # label(aNOTu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1990 (all A all B all P0 ((all X ((all Y all XI_ (p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,XI_)))) & p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y)))) -> s(B,Y) = s(B,XI_))) & (exists Y p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y))))))) <-> (exists F0 all X p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,i(s(fun(A,B),F0),s(A,X))))))) & (all F0 all XI_ ((all X p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,i(s(fun(A,B),F0),s(A,X))))))) & (all X p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,i(s(fun(A,B),XI_),s(A,X))))))) -> s(fun(A,B),XI_) = s(fun(A,B),F0))))) # label(aUNIQUEu_SKOLEMu_THM) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1991 (all X all Y all Z0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y))),s(int,Z0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Z0)))))) # label(aINTu_SUBu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1992 (all X all Y all Z0 (s(real,Z0) = s(real,Y) <-> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0))))) # label(aREALu_EQu_ADDu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1993 (all X all Y all Z0 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),Z0)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Z0)))))) # label(aTREALu_EQu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1994 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) & s(num,P0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0)))))))) # label(aLTu_MULTu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1995 (all X all Y (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,Y)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y)))))) # label(aNADDu_EQu_IMPu_LE) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1996 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))))) # label(aREALu_LEu_RCANCELu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1997 (all X s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),realu_inv),s(real,X))))) = s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(real,real),realu_abs),s(real,X)))))) # label(aREALu_ABSu_INV) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1998 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) <-> s(real,Y) = s(real,X) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))))) # label(aREALu_LEu_LT) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 1999 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,M0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,M0))))))) # label(aREALu_OFu_NUMu_SUB) # label(axiom) # label(non_clause). [assumption]. 14.63/14.62 2000 (all A all L all X (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))) <-> (exists Y (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))) | p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))))))) # label(afl) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2001 (p(s(bool,c0)) -> p(s(bool,d0))) & (p(s(bool,b)) -> p(s(bool,a))) -> ((p(s(bool,a)) -> p(s(bool,c0))) -> (p(s(bool,b)) -> p(s(bool,d0)))) # label(aMONOu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2002 (all U_0 ((all B0 all GENR_PVARR_124 ((exists X p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_124))),s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,B0))))),s(real,X))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),U_0),s(real,B0))),s(real,GENR_PVARR_124)))))) -> (all B0 -p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(real,fun(real,bool)),U_0),s(real,B0))))))))))) # label(aFINITEu_REALu_INTERVALu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2003 (all N0 s(num,N0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) # label(aDIVu_1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2004 (all M0 all N0 all P0 s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,M0))),s(hreal,N0))) = s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,M0))),s(hreal,P0))))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,N0))),s(hreal,P0)))))) # label(aHREALu_LEu_ADDu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2005 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),poset),s(fun(prod(A,A),bool),L)))) & (all P0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(A,bool),bool)),chain),s(fun(prod(A,A),bool),L))),s(fun(A,bool),P0)))) -> (exists Y ((all X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,Y)))))))) -> (exists Y (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,Y)))) & (all X (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,X)))))) -> s(A,Y) = s(A,X))))))) # label(aZL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2006 (p(s(bool,p1)) & p(s(bool,q)) -> p(s(bool,r0))) <-> (p(s(bool,p1)) -> (p(s(bool,q)) -> p(s(bool,r0)))) # label(aIMPu_CONJ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2007 (all M0 all N0 (s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,M0))) = s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,N0))) <-> s(num,N0) = s(num,M0))) # label(aHREALu_OFu_NUMu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2008 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_LEu_conjunct8) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2009 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,y2)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,y1)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,x1))),s(real,y1))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,x2))),s(real,y2))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x1))),s(real,y2))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x2))),s(real,y1))))) # label(aRATu_LEMMA4) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2010 (all Q18647 all Q18646 s(Q18646,i(s(fun(Q18646,Q18646),i(s(fun(Q18647,fun(Q18646,Q18646)),f),s(Q18647,h0))),s(Q18646,i(s(fun(Q18646,Q18646),i(s(fun(list(Q18647),fun(Q18646,Q18646)),i(s(fun(fun(Q18647,fun(Q18646,Q18646)),fun(list(Q18647),fun(Q18646,Q18646))),itlist),s(fun(Q18647,fun(Q18646,Q18646)),f))),s(list(Q18647),t0))),s(Q18646,b0))))) = s(Q18646,i(s(fun(Q18646,Q18646),i(s(fun(list(Q18647),fun(Q18646,Q18646)),i(s(fun(fun(Q18647,fun(Q18646,Q18646)),fun(list(Q18647),fun(Q18646,Q18646))),itlist),s(fun(Q18647,fun(Q18646,Q18646)),f))),s(list(Q18647),i(s(fun(list(Q18647),list(Q18647)),i(s(fun(Q18647,fun(list(Q18647),list(Q18647))),cons),s(Q18647,h0))),s(list(Q18647),t0))))),s(Q18646,b0)))) # label(aITLISTu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2011 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,Y))),s(real,Z0))))))) # label(aREALu_LEu_RDIVu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2012 (all A all P0 all Q0 ((exists X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) & p(s(bool,Q0)))) <-> p(s(bool,Q0)) & (exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) # label(aLEFTu_EXISTSu_ANDu_THM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2013 (all M0 all N0 all P0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))))),s(num,P0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0))))))),s(num,N0))))) # label(aDIVu_MOD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2014 (all A all N (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),univ)))) -> p(s(bool,i(s(fun(fun(cart(A,N),bool),bool),finite),s(fun(cart(A,N),bool),univ)))))) # label(aFINITEu_CARTu_UNIV) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2015 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,M0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))))) # label(aINu_NUMSEGu_0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2016 (all X all Y all Z0 (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,Y)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,Y))),s(nadd,Z0)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,Z0)))))) # label(aNADDu_EQu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2017 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,y2)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,y1)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,x1))),s(real,y1))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,x2))),s(real,y2))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x1))),s(real,y2))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x2))),s(real,y1))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_inv),s(real,y1))))),s(real,i(s(fun(real,real),realu_inv),s(real,y2))))))) # label(aRATu_LEMMA2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2018 (all M0 all N0 (p(s(bool,f0)) <-> s(num,i(s(fun(num,num),bit0),s(num,M0))) = s(num,i(s(fun(num,num),bit1),s(num,N0))))) # label(aARITHu_EQu_conjunct7) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2019 (all X all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,Z0))),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,i(s(fun(real,real),realu_neg),s(real,Y))))))),s(real,Z0)))) # label(aREALu_LTu_ADDNEG2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2020 (all X1 all Y1 all X2 all Y2 (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),numpair),s(num,X1))),s(num,Y1))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),numpair),s(num,X2))),s(num,Y2))) -> s(num,X1) = s(num,X2))) # label(aNUMPAIRu_INJu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2021 (all X all Y p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),X))))))) # label(aTREALu_MULu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2022 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,M0)))) # label(aLTu_ADDR) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2023 (all M0 all N0 s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,M0))))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,N0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) # label(aNADDu_OFu_NUMu_LE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2024 (all Q18647 all Q18646 s(Q18646,i(s(fun(Q18646,Q18646),i(s(fun(list(Q18647),fun(Q18646,Q18646)),i(s(fun(fun(Q18647,fun(Q18646,Q18646)),fun(list(Q18647),fun(Q18646,Q18646))),itlist),s(fun(Q18647,fun(Q18646,Q18646)),f))),s(list(Q18647),nil))),s(Q18646,b0))) = s(Q18646,b0)) # label(aITLISTu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2025 (all X all XI_ all Y all YI_ (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,Y))),s(nadd,YI_)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,XI_)))) -> s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,XI_))),s(nadd,YI_))) = s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y))))) # label(aNADDu_LEu_WELLDEF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2026 (all X exists B0 all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N0))))))))))),s(num,B0))))) # label(aNADDu_ADDITIVE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2027 (all X all Y (s(real,i(s(fun(real,real),realu_abs),s(real,X))) = s(real,i(s(fun(real,real),realu_abs),s(real,Y))) <-> s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) # label(aREALu_EQu_SQUAREu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2028 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_inv),s(real,Y))))),s(real,i(s(fun(real,real),realu_inv),s(real,X)))))))) # label(aREALu_LTu_INV2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2029 (all U_0 ((all F0 all G0 all I0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),F0),s(num,I0))))),s(real,i(s(fun(num,real),G0),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),i(s(fun(fun(num,real),fun(fun(num,real),fun(num,real))),U_0),s(fun(num,real),F0))),s(fun(num,real),G0))),s(num,I0)))) -> (all F0 all G0 all M0 all N0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),i(s(fun(fun(num,real),fun(fun(num,real),fun(num,real))),U_0),s(fun(num,real),F0))),s(fun(num,real),G0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),G0)))))))) # label(aSUMu_SUBu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2030 (all X s(int,i(s(fun(int,int),intu_abs),s(int,X))) = s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),intu_neg),s(int,X)))))) # label(aINTu_ABSu_NEG) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2031 (all X all Y (s(real,Y) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))) <-> s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aREALu_EQu_ADDu_RCANCELu_0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2032 (all N0 s(hreal,N0) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,N0))),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aHREALu_ADDu_RID) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2033 (all Q18767 all Q18766 s(bool,i(s(fun(list(Q18766),bool),i(s(fun(list(Q18767),fun(list(Q18766),bool)),i(s(fun(fun(Q18767,fun(Q18766,bool)),fun(list(Q18767),fun(list(Q18766),bool))),all2),s(fun(Q18767,fun(Q18766,bool)),p0))),s(list(Q18767),nil))),s(list(Q18766),i(s(fun(list(Q18766),list(Q18766)),i(s(fun(Q18766,fun(list(Q18766),list(Q18766))),cons),s(Q18766,h2))),s(list(Q18766),t2))))) = s(bool,f0)) # label(aALL2u_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2034 (all M0 ((exists N0 s(num,i(s(fun(num,num),suc),s(num,N0))) = s(num,M0)) | s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(anumu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2035 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) <-> (exists D0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,D0))))) = s(num,N0)))) # label(aLTu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2036 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,i(s(fun(int,int),intu_neg),s(int,Y)))))) # label(aINTu_NEGu_MUL2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2037 (all B all A all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))))) # label(aCARDu_LEu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2038 (all A all B all S0 all T0 all N0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(B,bool),fun(num,bool)),hasu_size),s(fun(B,bool),T0))),s(num,N0)))))) # label(aCARDu_HASu_SIZEu_CONG) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2039 (all U_0 ((all P0 all N0 ((all M0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> -p(s(bool,i(s(fun(num,bool),P0),s(num,M0)))))) & p(s(bool,i(s(fun(num,bool),P0),s(num,N0)))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),U_0),s(fun(num,bool),P0))),s(num,N0)))))) -> (all P0 s(num,i(s(fun(fun(num,bool),num),h_),s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),U_0),s(fun(num,bool),P0))))) = s(num,i(s(fun(fun(num,bool),num),minimal),s(fun(num,bool),P0)))))) # label(aminimal) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2040 (all X s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,X))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) # label(aINTu_LEu_NEGL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2041 (all V s(n10,V) = s(n10,one)) # label(aone) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2042 (all Q20187 all Q20185 all L1 all L2 (s(num,i(s(fun(list(Q20187),num),length),s(list(Q20187),L2))) = s(num,i(s(fun(list(Q20185),num),length),s(list(Q20185),L1))) -> s(list(Q20185),L1) = s(list(Q20185),i(s(fun(list(prod(Q20185,Q20187)),list(Q20185)),i(s(fun(fun(prod(Q20185,Q20187),Q20185),fun(list(prod(Q20185,Q20187)),list(Q20185))),map0),s(fun(prod(Q20185,Q20187),Q20185),fst))),s(list(prod(Q20185,Q20187)),i(s(fun(list(Q20187),list(prod(Q20185,Q20187))),i(s(fun(list(Q20185),fun(list(Q20187),list(prod(Q20185,Q20187)))),zip0),s(list(Q20185),L1))),s(list(Q20187),L2))))))) # label(aMAPu_FSTu_ZIP) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2043 (all A all B all F0 all B0 ((all X all Y all S0 (s(A,Y) != s(A,X) -> s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,S0))))) = s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,S0))))))) -> (all N0 all S0 all Z0 (p(s(bool,i(s(fun(num,bool),i(s(fun(B,fun(num,bool)),i(s(fun(fun(A,bool),fun(B,fun(num,bool))),i(s(fun(B,fun(fun(A,bool),fun(B,fun(num,bool)))),i(s(fun(fun(A,fun(B,B)),fun(B,fun(fun(A,bool),fun(B,fun(num,bool))))),finrec),s(fun(A,fun(B,B)),F0))),s(B,B0))),s(fun(A,bool),S0))),s(B,Z0))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) -> (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> (exists W (s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,W))) = s(B,Z0) & p(s(bool,i(s(fun(num,bool),i(s(fun(B,fun(num,bool)),i(s(fun(fun(A,bool),fun(B,fun(num,bool))),i(s(fun(B,fun(fun(A,bool),fun(B,fun(num,bool)))),i(s(fun(fun(A,fun(B,B)),fun(B,fun(fun(A,bool),fun(B,fun(num,bool))))),finrec),s(fun(A,fun(B,B)),F0))),s(B,B0))),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(B,W))),s(num,N0)))))))))))) # label(aFINRECu_SUCu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2044 (all X all N0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0)))))))) # label(aREALu_POWu_LE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2045 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0)))))) # label(aLEFTu_ADDu_DISTRIB) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2046 (all X all Y (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) -> s(real,i(s(fun(real,real),realu_inv),s(real,X))) = s(real,Y))) # label(aREALu_MULu_RINVu_UNIQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2047 (all Q97046 all P0 all S0 all T0 p(s(bool,i(s(fun(fun(Q97046,bool),bool),i(s(fun(fun(Q97046,bool),fun(fun(Q97046,bool),bool)),subset),s(fun(Q97046,bool),i(s(fun(fun(Q97046,bool),fun(Q97046,bool)),i(s(fun(fun(Q97046,bool),fun(fun(Q97046,bool),fun(Q97046,bool))),union),s(fun(Q97046,bool),i(s(fun(fun(Q97046,bool),fun(Q97046,bool)),i(s(fun(fun(fun(Q97046,bool),bool),fun(fun(Q97046,bool),fun(Q97046,bool))),hull),s(fun(fun(Q97046,bool),bool),P0))),s(fun(Q97046,bool),S0))))),s(fun(Q97046,bool),i(s(fun(fun(Q97046,bool),fun(Q97046,bool)),i(s(fun(fun(fun(Q97046,bool),bool),fun(fun(Q97046,bool),fun(Q97046,bool))),hull),s(fun(fun(Q97046,bool),bool),P0))),s(fun(Q97046,bool),T0))))))),s(fun(Q97046,bool),i(s(fun(fun(Q97046,bool),fun(Q97046,bool)),i(s(fun(fun(fun(Q97046,bool),bool),fun(fun(Q97046,bool),fun(Q97046,bool))),hull),s(fun(fun(Q97046,bool),bool),P0))),s(fun(Q97046,bool),i(s(fun(fun(Q97046,bool),fun(Q97046,bool)),i(s(fun(fun(Q97046,bool),fun(fun(Q97046,bool),fun(Q97046,bool))),union),s(fun(Q97046,bool),S0))),s(fun(Q97046,bool),T0))))))))) # label(aHULLu_UNIONu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2048 (all M0 all N0 all P0 all Q0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,P0))),s(num,Q0))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,M0))),s(num,P0))))))),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,N0))),s(num,Q0))))))))))) # label(aDISTu_ADD2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2049 (all M0 all N0 s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(num,int),intu_ofu_num),s(num,M0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0)))))) # label(aINTu_OFu_NUMu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2050 (all A all X (p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))) -> -p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,X))),s(A,X)))))) # label(aWFu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2051 (all A all A5 ((all X all XI_ (s(A,A5) = s(A,X) & s(A,A5) = s(A,XI_) -> s(A,X) = s(A,XI_))) & (exists X s(A,A5) = s(A,X)))) # label(aEXISTSu_UNIQUEu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2052 (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),realu_abs),s(real,X))))))) # label(aREALu_ABSu_LE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2053 (all X all Y (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))) <-> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),X)))))) # label(aTREALu_LEu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2054 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_inv),s(real,X)))))))) # label(aREALu_LTu_INV) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2055 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),p0),s(real,X))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),p0),s(real,Y))),s(real,X)))) & (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),p0),s(real,X))),s(real,Y)))))) & (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),p0),s(real,X))),s(real,X))))) -> (all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),p0),s(real,X))),s(real,Y))))) # label(aREALu_WLOGu_LT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2056 (all M0 all N0 all P0 (s(num,N0) = s(num,P0) <-> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))) # label(aEQu_ADDu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2057 (all A all S0 all X s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))) = s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) # label(aFINITEu_INSERT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2058 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_abs),s(real,X)))))) | s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,X))) # label(aREALu_ABSu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2059 (all B all A all P0 ((all X exists Y p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,Y))))) <-> (exists Y all X p(s(bool,i(s(fun(B,bool),i(s(fun(A,fun(B,bool)),P0),s(A,X))),s(B,i(s(fun(A,B),Y),s(A,X))))))))) # label(aSKOLEMu_THM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2060 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,Z0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Z0)))))))) # label(aINTu_LEu_LMUL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2061 (all Q53951 (s(fun(Q53951,bool),s0) = s(fun(Q53951,bool),empty) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53951,bool),fun(num,bool)),hasu_size),s(fun(Q53951,bool),s0))),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aHASu_SIZEu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2062 (all N0 all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_divides),s(int,N0))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),i(s(fun(int,fun(int,fun(int,bool))),intu_mod),s(int,N0))),s(int,X))),s(int,Y)))) # label(aintu_mod) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2063 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,N0))))),s(num,P0)))) # label(aEXPu_MULT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2064 (all U_0 ((all X all Y all N0 s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),i(s(fun(nadd,fun(nadd,fun(num,num))),U_0),s(nadd,X))),s(nadd,Y))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,Y))),s(num,N0)))))) -> (all X all Y s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Y))) = s(nadd,i(s(fun(fun(num,num),nadd),mku_nadd),s(fun(num,num),i(s(fun(nadd,fun(num,num)),i(s(fun(nadd,fun(nadd,fun(num,num))),U_0),s(nadd,X))),s(nadd,Y)))))))) # label(anaddu_mul) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2065 (p(s(bool,c0)) -> p(s(bool,d0))) & (p(s(bool,a)) -> p(s(bool,b))) -> (p(s(bool,c0)) | p(s(bool,a)) -> p(s(bool,b)) | p(s(bool,d0))) # label(aMONOu_OR) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2066 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Y))),s(int,X)))) # label(aINTu_ADDu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2067 (all N0 all X all Y s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),numu_mod),s(num,N0))),s(num,X))),s(num,Y))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),i(s(fun(int,fun(int,fun(int,bool))),intu_mod),s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,X))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,Y)))))) # label(anumu_mod) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2068 (all A all L (s(list(A),L) = s(list(A),nil) <-> s(num,i(s(fun(list(A),num),length),s(list(A),L))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aLENGTHu_EQu_NIL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2069 (all P0 all Q0 ((exists B0 all I0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),P0),s(num,I0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),Q0),s(num,I0))))),s(num,B0))))))) <-> (exists B0 exists N0 all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,I0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),P0),s(num,I0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),Q0),s(num,I0))))),s(num,B0)))))))))) # label(aBOUNDSu_IGNORE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2070 (all Q71274 all U_1 ((all F0 all G0 all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(Q71274,real),F0),s(Q71274,X))))),s(real,i(s(fun(Q71274,real),G0),s(Q71274,X))))) = s(real,i(s(fun(Q71274,real),i(s(fun(fun(Q71274,real),fun(Q71274,real)),i(s(fun(fun(Q71274,real),fun(fun(Q71274,real),fun(Q71274,real))),U_1),s(fun(Q71274,real),F0))),s(fun(Q71274,real),G0))),s(Q71274,X)))) -> (all U_0 ((all S0 all F0 all GENR_PVARR_174 (p(s(bool,i(s(fun(Q71274,bool),i(s(fun(fun(Q71274,real),fun(Q71274,bool)),i(s(fun(fun(Q71274,bool),fun(fun(Q71274,real),fun(Q71274,bool))),U_0),s(fun(Q71274,bool),S0))),s(fun(Q71274,real),F0))),s(Q71274,GENR_PVARR_174)))) <-> (exists X exists V (p(s(bool,i(s(fun(Q71274,bool),i(s(fun(bool,fun(Q71274,bool)),i(s(fun(Q71274,fun(bool,fun(Q71274,bool))),setspec),s(Q71274,GENR_PVARR_174))),s(bool,V))),s(Q71274,X)))) & (p(s(bool,i(s(fun(fun(Q71274,bool),bool),i(s(fun(Q71274,fun(fun(Q71274,bool),bool)),in),s(Q71274,X))),s(fun(Q71274,bool),S0)))) & s(real,i(s(fun(Q71274,real),F0),s(Q71274,X))) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> p(s(bool,V))))))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q71274,bool),bool),finite),s(fun(Q71274,bool),i(s(fun(fun(Q71274,bool),fun(Q71274,bool)),gspec),s(fun(Q71274,bool),i(s(fun(fun(Q71274,real),fun(Q71274,bool)),i(s(fun(fun(Q71274,bool),fun(fun(Q71274,real),fun(Q71274,bool))),U_0),s(fun(Q71274,bool),S0))),s(fun(Q71274,real),F0)))))))) & p(s(bool,i(s(fun(fun(Q71274,bool),bool),finite),s(fun(Q71274,bool),i(s(fun(fun(Q71274,bool),fun(Q71274,bool)),gspec),s(fun(Q71274,bool),i(s(fun(fun(Q71274,real),fun(Q71274,bool)),i(s(fun(fun(Q71274,bool),fun(fun(Q71274,real),fun(Q71274,bool))),U_0),s(fun(Q71274,bool),S0))),s(fun(Q71274,real),G0)))))))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(Q71274,real),real),i(s(fun(fun(Q71274,bool),fun(fun(Q71274,real),real)),sum),s(fun(Q71274,bool),S0))),s(fun(Q71274,real),F0))))),s(real,i(s(fun(fun(Q71274,real),real),i(s(fun(fun(Q71274,bool),fun(fun(Q71274,real),real)),sum),s(fun(Q71274,bool),S0))),s(fun(Q71274,real),G0))))) = s(real,i(s(fun(fun(Q71274,real),real),i(s(fun(fun(Q71274,bool),fun(fun(Q71274,real),real)),sum),s(fun(Q71274,bool),S0))),s(fun(Q71274,real),i(s(fun(fun(Q71274,real),fun(Q71274,real)),i(s(fun(fun(Q71274,real),fun(fun(Q71274,real),fun(Q71274,real))),U_1),s(fun(Q71274,real),F0))),s(fun(Q71274,real),G0))))))))))) # label(aSUMu_ADDu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2071 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,i(s(fun(real,real),realu_neg),s(real,Y)))))) # label(arealu_sub) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2072 (all A all H0 all T0 all L s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,H0))),s(list(A),T0))))),s(list(A),L))) = s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,H0))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),T0))),s(list(A),L)))))) # label(aAPPENDu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2073 (all A all X all S0 s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))) = s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(A,X)))) # label(aDELETEu_DELETE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.62 2074 (all M0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(num,M0)) # label(aMULTu_CLAUSESu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2075 (all Q47636 all Q47625 all F0 all S0 all T0 s(fun(Q47636,bool),i(s(fun(fun(Q47625,bool),fun(Q47636,bool)),i(s(fun(fun(Q47625,Q47636),fun(fun(Q47625,bool),fun(Q47636,bool))),image),s(fun(Q47625,Q47636),F0))),s(fun(Q47625,bool),i(s(fun(fun(Q47625,bool),fun(Q47625,bool)),i(s(fun(fun(Q47625,bool),fun(fun(Q47625,bool),fun(Q47625,bool))),union),s(fun(Q47625,bool),S0))),s(fun(Q47625,bool),T0))))) = s(fun(Q47636,bool),i(s(fun(fun(Q47636,bool),fun(Q47636,bool)),i(s(fun(fun(Q47636,bool),fun(fun(Q47636,bool),fun(Q47636,bool))),union),s(fun(Q47636,bool),i(s(fun(fun(Q47625,bool),fun(Q47636,bool)),i(s(fun(fun(Q47625,Q47636),fun(fun(Q47625,bool),fun(Q47636,bool))),image),s(fun(Q47625,Q47636),F0))),s(fun(Q47625,bool),S0))))),s(fun(Q47636,bool),i(s(fun(fun(Q47625,bool),fun(Q47636,bool)),i(s(fun(fun(Q47625,Q47636),fun(fun(Q47625,bool),fun(Q47636,bool))),image),s(fun(Q47625,Q47636),F0))),s(fun(Q47625,bool),T0)))))) # label(aIMAGEu_UNION) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2076 (all Q20522 all L all M0 (s(list(Q20522),nil) = s(list(Q20522),i(s(fun(list(Q20522),list(Q20522)),i(s(fun(list(Q20522),fun(list(Q20522),list(Q20522))),append),s(list(Q20522),L))),s(list(Q20522),M0))) <-> s(list(Q20522),M0) = s(list(Q20522),nil) & s(list(Q20522),nil) = s(list(Q20522),L))) # label(aAPPENDu_EQu_NIL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2077 (all A p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),zrecspace),s(fun(num,fun(A,bool)),zbot))))) # label(aZRECSPACEu_RULESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2078 (all A all A5 all F0 all N0 s(A,i(s(fun(num,A),i(s(fun(fun(num,A),fun(num,A)),i(s(fun(A,fun(fun(num,A),fun(num,A))),fcons),s(A,A5))),s(fun(num,A),F0))),s(num,i(s(fun(num,num),suc),s(num,N0))))) = s(A,i(s(fun(num,A),F0),s(num,N0)))) # label(aFCONSu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2079 (all Q80660 all Q80776 all Q80661 all Q80738 all P all Q80785 all U_5 ((all PAT all E0 all Q0 all T0 all Y all F0 all X s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool)))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))))))),U_5),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0))),s(fun(fun(Q80661,Q80738),fun(P,Q80785)),T0))),s(fun(fun(Q80661,Q80738),fun(P,Q80785)),Y))),s(fun(Q80661,Q80738),F0))),s(P,X))) = s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),u_guardedu_pattern),s(bool,i(s(fun(Q80776,bool),i(s(fun(Q80776,fun(Q80776,bool)),geq),s(Q80776,i(s(fun(P,Q80776),i(s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT),s(fun(Q80661,Q80738),F0))),s(P,X))))),s(Q80776,i(s(fun(P,Q80776),i(s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0),s(fun(Q80661,Q80738),F0))),s(P,X))))))),s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0),s(fun(Q80661,Q80738),F0))),s(P,X))))),s(bool,i(s(fun(Q80785,bool),i(s(fun(Q80785,fun(Q80785,bool)),geq),s(Q80785,i(s(fun(P,Q80785),i(s(fun(fun(Q80661,Q80738),fun(P,Q80785)),T0),s(fun(Q80661,Q80738),F0))),s(P,X))))),s(Q80785,i(s(fun(P,Q80785),i(s(fun(fun(Q80661,Q80738),fun(P,Q80785)),Y),s(fun(Q80661,Q80738),F0))),s(P,X)))))))) -> (all U_4 ((all PAT all E0 all Q0 all T0 all Y all F0 s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool)))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))))))),U_4),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0))),s(fun(fun(Q80661,Q80738),fun(P,Q80785)),T0))),s(fun(fun(Q80661,Q80738),fun(P,Q80785)),Y))),s(fun(Q80661,Q80738),F0))) = s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool)))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))))))),U_5),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0))),s(fun(fun(Q80661,Q80738),fun(P,Q80785)),T0))),s(fun(fun(Q80661,Q80738),fun(P,Q80785)),Y))),s(fun(Q80661,Q80738),F0)))) -> (all U_3 ((all P0 all PAT all E0 all F0 all X (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool))))),U_3),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(Q80661,Q80738),F0))),s(P,X)))) <-> s(Q80776,i(s(fun(P,Q80776),i(s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT),s(fun(Q80661,Q80738),F0))),s(P,X))) = s(Q80776,i(s(fun(P,Q80776),i(s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0),s(fun(Q80661,Q80738),F0))),s(P,X))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),P0),s(fun(Q80661,Q80738),F0))),s(P,X)))))) -> (all U_2 ((all P0 all PAT all E0 all F0 s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool))))),U_2),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(Q80661,Q80738),F0))) = s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool))))),U_3),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(Q80661,Q80738),F0)))) -> (all U_1 ((all P0 all PAT all E0 all Q0 all F0 all X (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool)))))),U_1),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0))),s(fun(Q80661,Q80738),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),P0),s(fun(Q80661,Q80738),F0))),s(P,X)))) & s(Q80776,i(s(fun(P,Q80776),i(s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT),s(fun(Q80661,Q80738),F0))),s(P,X))) = s(Q80776,i(s(fun(P,Q80776),i(s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0),s(fun(Q80661,Q80738),F0))),s(P,X))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0),s(fun(Q80661,Q80738),F0))),s(P,X)))))) -> (all U_0 ((all P0 all PAT all E0 all Q0 all F0 s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool)))))),U_1),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0))),s(fun(Q80661,Q80738),F0))) = s(fun(P,bool),i(s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool)))))),U_0),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0))),s(fun(Q80661,Q80738),F0)))) -> (all L_L_ all P0 all S0 all PAT all Q0 all E0 all T0 all Y (p(s(bool,i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),bool),i(s(fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),bool))),i(s(fun(fun(Q80661,fun(Q80660,bool)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),bool)))),admissible),s(fun(Q80661,fun(Q80660,bool)),L_L_))),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(P,Q80660),S0))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0)))) & p(s(bool,i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),bool),i(s(fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),bool))),i(s(fun(fun(Q80661,fun(Q80660,bool)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),bool)))),admissible),s(fun(Q80661,fun(Q80660,bool)),L_L_))),s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool)))))),U_0),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0))))),s(fun(P,Q80660),S0))),s(fun(fun(Q80661,Q80738),fun(P,Q80785)),Y)))) & p(s(bool,i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),bool),i(s(fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,bool)),bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,bool)),bool))),i(s(fun(fun(Q80661,fun(Q80660,bool)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,bool)),bool)))),admissible),s(fun(Q80661,fun(Q80660,bool)),L_L_))),s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(Q80661,Q80738),fun(P,bool))))),U_2),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))))),s(fun(P,Q80660),S0))),s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0)))) & p(s(bool,i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),bool),i(s(fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),bool))),i(s(fun(fun(Q80661,fun(Q80660,bool)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),bool)))),admissible),s(fun(Q80661,fun(Q80660,bool)),L_L_))),s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(Q80661,Q80738),fun(P,bool)))))),U_0),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0))))),s(fun(P,Q80660),S0))),s(fun(fun(Q80661,Q80738),fun(P,Q80785)),T0)))) & p(s(bool,i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),bool),i(s(fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),bool))),i(s(fun(fun(Q80661,fun(Q80660,bool)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),bool)))),admissible),s(fun(Q80661,fun(Q80660,bool)),L_L_))),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(P,Q80660),S0))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT)))) -> p(s(bool,i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),bool),i(s(fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,bool)),bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,bool)),bool))),i(s(fun(fun(Q80661,fun(Q80660,bool)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(P,Q80660),fun(fun(fun(Q80661,Q80738),fun(P,bool)),bool)))),admissible),s(fun(Q80661,fun(Q80660,bool)),L_L_))),s(fun(fun(Q80661,Q80738),fun(P,bool)),P0))),s(fun(P,Q80660),S0))),s(fun(fun(Q80661,Q80738),fun(P,bool)),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool)))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool)))))),i(s(fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,Q80776)),fun(fun(fun(Q80661,Q80738),fun(P,bool)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(fun(Q80661,Q80738),fun(P,Q80785)),fun(fun(Q80661,Q80738),fun(P,bool))))))),U_4),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),PAT))),s(fun(fun(Q80661,Q80738),fun(P,Q80776)),E0))),s(fun(fun(Q80661,Q80738),fun(P,bool)),Q0))),s(fun(fun(Q80661,Q80738),fun(P,Q80785)),T0))),s(fun(fun(Q80661,Q80738),fun(P,Q80785)),Y)))))))))))))))))))) # label(aADMISSIBLEu_GUARDEDu_PATTERN) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2080 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y))))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y))))),s(int,X)))))) # label(aINTu_MINu_MIN) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2081 (all X all Y all Z0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,Y))))),s(real,Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,Y))),s(real,Z0)))))) # label(aREALu_MINu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2082 (all A all U_0 ((all S0 all GENR_PVARR_99 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))),s(fun(A,bool),GENR_PVARR_99)))) <-> (exists T0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_99))),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0))))),s(fun(A,bool),T0))))))) -> (all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),finite),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0)))))))))))) # label(aFINITEu_POWERSET) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2083 (all A all Q92609 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(Q92609,bool),fun(fun(A,bool),bool)),l_a_u_c),s(fun(Q92609,bool),S0))),s(fun(A,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q92609,bool),bool),countable),s(fun(Q92609,bool),S0)))))) # label(aCARDu_LEu_COUNTABLE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2084 (all M0 all N0 all P0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))),s(num,P0))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))),s(num,N0))))) # label(aMODu_MULTu_LMOD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2085 (all F0 all M0 all N0 (s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),F0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,I0)))) -> s(num,i(s(fun(num,num),F0),s(num,I0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aNSUMu_EQu_0u_IFFu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2086 (all Q53951 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53951,bool),fun(num,bool)),hasu_size),s(fun(Q53951,bool),s0))),s(num,i(s(fun(num,num),suc),s(num,n)))))) <-> (exists A5 exists T0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(Q53951,bool),fun(num,bool)),hasu_size),s(fun(Q53951,bool),T0))),s(num,n)))) & s(fun(Q53951,bool),i(s(fun(fun(Q53951,bool),fun(Q53951,bool)),i(s(fun(Q53951,fun(fun(Q53951,bool),fun(Q53951,bool))),insert),s(Q53951,A5))),s(fun(Q53951,bool),T0))) = s(fun(Q53951,bool),s0) & -p(s(bool,i(s(fun(fun(Q53951,bool),bool),i(s(fun(Q53951,fun(fun(Q53951,bool),bool)),in),s(Q53951,A5))),s(fun(Q53951,bool),T0)))))))) # label(aHASu_SIZEu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2087 (all A5 all B0 ((exists X exists Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,A5))),s(int,X))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,B0))),s(int,Y))))) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) <-> p(s(bool,i(s(fun(prod(int,int),bool),intu_coprime),s(prod(int,int),i(s(fun(int,prod(int,int)),i(s(fun(int,fun(int,prod(int,int))),c_),s(int,A5))),s(int,B0)))))))) # label(aintu_coprime) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2088 (all M0 all P0 all N0 s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))))) = s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,N0))),s(num,P0)))))) # label(aDISTu_LADD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2089 (all X s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_inv),s(real,X)))))) # label(aREALu_LTu_INVu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2090 (all U_0 ((all C0 all N0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,C0))),s(num,N0))) = s(real,C0)) -> (all C0 all M0 all N0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))))),s(real,C0))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,C0)))))))) # label(aSUMu_CONSTu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2091 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_inv),s(real,Y))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_inv),s(real,X))))),s(real,Y)))))) # label(aREALu_LEu_LINV) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2092 (all Q64144 all Q64188 all Q64186 all OP (p(s(bool,i(s(fun(fun(Q64186,fun(Q64186,Q64186)),bool),monoidal),s(fun(Q64186,fun(Q64186,Q64186)),OP)))) -> (all F0 s(Q64186,i(s(fun(fun(Q64186,fun(Q64186,Q64186)),Q64186),neutral),s(fun(Q64186,fun(Q64186,Q64186)),OP))) = s(Q64186,i(s(fun(fun(Q64144,Q64186),Q64186),i(s(fun(fun(Q64144,bool),fun(fun(Q64144,Q64186),Q64186)),i(s(fun(fun(Q64186,fun(Q64186,Q64186)),fun(fun(Q64144,bool),fun(fun(Q64144,Q64186),Q64186))),iterate),s(fun(Q64186,fun(Q64186,Q64186)),OP))),s(fun(Q64144,bool),empty))),s(fun(Q64144,Q64186),F0)))) & (all F0 all X all S0 (p(s(bool,i(s(fun(fun(Q64188,bool),bool),finite),s(fun(Q64188,bool),S0)))) -> s(Q64186,i(s(fun(fun(Q64188,Q64186),Q64186),i(s(fun(fun(Q64188,bool),fun(fun(Q64188,Q64186),Q64186)),i(s(fun(fun(Q64186,fun(Q64186,Q64186)),fun(fun(Q64188,bool),fun(fun(Q64188,Q64186),Q64186))),iterate),s(fun(Q64186,fun(Q64186,Q64186)),OP))),s(fun(Q64188,bool),i(s(fun(fun(Q64188,bool),fun(Q64188,bool)),i(s(fun(Q64188,fun(fun(Q64188,bool),fun(Q64188,bool))),insert),s(Q64188,X))),s(fun(Q64188,bool),S0))))),s(fun(Q64188,Q64186),F0))) = s(Q64186,i(s(fun(Q64186,Q64186),i(s(fun(Q64186,fun(Q64186,Q64186)),i(s(fun(bool,fun(Q64186,fun(Q64186,Q64186))),cond),s(bool,i(s(fun(fun(Q64188,bool),bool),i(s(fun(Q64188,fun(fun(Q64188,bool),bool)),in),s(Q64188,X))),s(fun(Q64188,bool),S0))))),s(Q64186,i(s(fun(fun(Q64188,Q64186),Q64186),i(s(fun(fun(Q64188,bool),fun(fun(Q64188,Q64186),Q64186)),i(s(fun(fun(Q64186,fun(Q64186,Q64186)),fun(fun(Q64188,bool),fun(fun(Q64188,Q64186),Q64186))),iterate),s(fun(Q64186,fun(Q64186,Q64186)),OP))),s(fun(Q64188,bool),S0))),s(fun(Q64188,Q64186),F0))))),s(Q64186,i(s(fun(Q64186,Q64186),i(s(fun(Q64186,fun(Q64186,Q64186)),OP),s(Q64186,i(s(fun(Q64188,Q64186),F0),s(Q64188,X))))),s(Q64186,i(s(fun(fun(Q64188,Q64186),Q64186),i(s(fun(fun(Q64188,bool),fun(fun(Q64188,Q64186),Q64186)),i(s(fun(fun(Q64186,fun(Q64186,Q64186)),fun(fun(Q64188,bool),fun(fun(Q64188,Q64186),Q64186))),iterate),s(fun(Q64186,fun(Q64186,Q64186)),OP))),s(fun(Q64188,bool),S0))),s(fun(Q64188,Q64186),F0))))))))))) # label(aITERATEu_CLAUSES) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2093 (all X (s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(hreal,X) -> s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,i(s(fun(hreal,hreal),hrealu_inv),s(hreal,X))))),s(hreal,X))))) # label(aHREALu_MULu_LINV) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2094 (all Q58179 all S0 (p(s(bool,i(s(fun(fun(Q58179,bool),bool),finite),s(fun(Q58179,bool),S0)))) -> s(num,i(s(fun(fun(Q58179,bool),num),card),s(fun(Q58179,bool),S0))) = s(num,i(s(fun(list(Q58179),num),length),s(list(Q58179),i(s(fun(fun(Q58179,bool),list(Q58179)),listu_ofu_set),s(fun(Q58179,bool),S0))))))) # label(aLENGTHu_LISTu_OFu_SET) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2095 (all Q50725 p(s(bool,i(s(fun(fun(Q50725,bool),bool),finite),s(fun(Q50725,bool),empty))))) # label(aFINITEu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2096 (all S0 all A5 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) & s(fun(real,bool),empty) != s(fun(real,bool),S0) -> (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,A5))),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0)))))) <-> (exists X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,A5))),s(real,X)))) & p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0))))))))) # label(aREALu_LTu_SUPu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2097 (all A p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),empty))))) # label(aFINITEu_RULESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2098 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,i(s(fun(nadd,nadd),naddu_inv),s(nadd,X))))),s(nadd,X))))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aNADDu_MULu_LINV) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2099 (all A all X all Y (s(recspace(A),i(s(fun(fun(num,fun(A,bool)),recspace(A)),u_mku_rec),s(fun(num,fun(A,bool)),Y))) = s(recspace(A),i(s(fun(fun(num,fun(A,bool)),recspace(A)),u_mku_rec),s(fun(num,fun(A,bool)),X))) -> (p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),zrecspace),s(fun(num,fun(A,bool)),Y)))) & p(s(bool,i(s(fun(fun(num,fun(A,bool)),bool),zrecspace),s(fun(num,fun(A,bool)),X)))) -> s(fun(num,fun(A,bool)),X) = s(fun(num,fun(A,bool)),Y)))) # label(aMKu_RECu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2100 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all X all Y all Z0 (p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,Z0)))))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Z0)))))))))) # label(aWOSETu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2101 (all N0 all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0)))))))) # label(aREALu_POWu_LT2u_ODD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2102 (p(s(bool,b)) -> p(s(bool,a))) -> (-p(s(bool,a)) -> -p(s(bool,b))) # label(aMONOu_NOT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2103 (all Q21057 all H0 all T0 s(list(Q21057),i(s(fun(list(Q21057),list(Q21057)),i(s(fun(list(Q21057),fun(list(Q21057),list(Q21057))),append),s(list(Q21057),i(s(fun(list(Q21057),list(Q21057)),i(s(fun(Q21057,fun(list(Q21057),list(Q21057))),cons),s(Q21057,H0))),s(list(Q21057),nil))))),s(list(Q21057),T0))) = s(list(Q21057),i(s(fun(list(Q21057),list(Q21057)),i(s(fun(Q21057,fun(list(Q21057),list(Q21057))),cons),s(Q21057,H0))),s(list(Q21057),T0)))) # label(aAPPENDu_SING) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2104 (all U_0 ((all S0 all A5 (p(s(bool,i(s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),U_0),s(fun(real,bool),S0))),s(real,A5)))) <-> (all B0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,B0)))))) & (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,A5)))))))) -> (all S0 s(real,i(s(fun(fun(real,bool),real),h_),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),U_0),s(fun(real,bool),S0))))) = s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0)))))) # label(asup) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2105 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,i(s(fun(real,real),realu_neg),s(real,Y)))))) # label(aREALu_LEu_NEG2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2106 (all Q50148 all Q50145 ((all Y exists X s(Q50145,i(s(fun(Q50148,Q50145),f),s(Q50148,X))) = s(Q50145,Y)) <-> (exists G0 all Y s(Q50145,i(s(fun(Q50148,Q50145),f),s(Q50148,i(s(fun(Q50145,Q50148),G0),s(Q50145,Y))))) = s(Q50145,Y)))) # label(aSURJECTIVEu_RIGHTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2107 (all N all A (p(s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),univ)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(cart(A,N),bool),fun(fun(A,bool),bool)),a_u_c),s(fun(cart(A,N),bool),univ))),s(fun(A,bool),univ)))))) # label(aCARDu_EQu_CART) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2108 (all X all Y (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),trealu_inv),s(prod(hreal,hreal),X))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),trealu_inv),s(prod(hreal,hreal),Y)))))))) # label(aTREALu_INVu_WELLDEF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2109 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) -> s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))))))) # label(aINTu_LTu_MULu_EQu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2110 (all X all X0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,X0))),s(num,X0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,X0))))) = s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,X0)))) # label(anaddu_rinv) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2111 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,X))),s(int,Y))))),s(int,Z0)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,Z0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Z0)))))) # label(aINTu_MAXu_LE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2112 (all Q0 all R0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,n) & s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,Q0) & s(num,m) = s(num,R0) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,R0))),s(num,n)))) & s(num,m) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,Q0))),s(num,n))))),s(num,R0))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,Q0))),s(num,R0)))))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,m))),s(num,n))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,m))),s(num,n)))))) # label(aDIVMODu_ELIMu_THM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2113 (all Q93123 all S0 all T0 (p(s(bool,i(s(fun(fun(Q93123,bool),bool),finite),s(fun(Q93123,bool),S0)))) -> s(bool,i(s(fun(fun(Q93123,bool),bool),countable),s(fun(Q93123,bool),i(s(fun(fun(Q93123,bool),fun(Q93123,bool)),i(s(fun(fun(Q93123,bool),fun(fun(Q93123,bool),fun(Q93123,bool))),diff),s(fun(Q93123,bool),T0))),s(fun(Q93123,bool),S0))))) = s(bool,i(s(fun(fun(Q93123,bool),bool),countable),s(fun(Q93123,bool),T0))))) # label(aCOUNTABLEu_DIFFu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2114 (all A (p(s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,fun(A,bool)),fun(list(A),bool)),pairwise0),s(fun(A,fun(A,bool)),r0))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,h0))),s(list(A),t0)))))) <-> p(s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,bool),fun(list(A),bool)),all0),s(fun(A,bool),i(s(fun(A,fun(A,bool)),r0),s(A,h0))))),s(list(A),t0)))) & p(s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,fun(A,bool)),fun(list(A),bool)),pairwise0),s(fun(A,fun(A,bool)),r0))),s(list(A),t0)))))) # label(aPAIRWISEu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2115 (all Q47300 all U_0 ((all S0 all T0 all GENR_PVARR_8 (p(s(bool,i(s(fun(fun(Q47300,bool),bool),i(s(fun(fun(Q47300,bool),fun(fun(Q47300,bool),bool)),i(s(fun(fun(fun(Q47300,bool),bool),fun(fun(Q47300,bool),fun(fun(Q47300,bool),bool))),U_0),s(fun(fun(Q47300,bool),bool),S0))),s(fun(Q47300,bool),T0))),s(fun(Q47300,bool),GENR_PVARR_8)))) <-> (exists X p(s(bool,i(s(fun(fun(Q47300,bool),bool),i(s(fun(bool,fun(fun(Q47300,bool),bool)),i(s(fun(fun(Q47300,bool),fun(bool,fun(fun(Q47300,bool),bool))),setspec),s(fun(Q47300,bool),GENR_PVARR_8))),s(bool,i(s(fun(fun(fun(Q47300,bool),bool),bool),i(s(fun(fun(Q47300,bool),fun(fun(fun(Q47300,bool),bool),bool)),in),s(fun(Q47300,bool),X))),s(fun(fun(Q47300,bool),bool),S0))))),s(fun(Q47300,bool),i(s(fun(fun(Q47300,bool),fun(Q47300,bool)),i(s(fun(fun(Q47300,bool),fun(fun(Q47300,bool),fun(Q47300,bool))),inter),s(fun(Q47300,bool),X))),s(fun(Q47300,bool),T0))))))))) -> (all S0 all T0 s(fun(Q47300,bool),i(s(fun(fun(Q47300,bool),fun(Q47300,bool)),i(s(fun(fun(Q47300,bool),fun(fun(Q47300,bool),fun(Q47300,bool))),inter),s(fun(Q47300,bool),i(s(fun(fun(fun(Q47300,bool),bool),fun(Q47300,bool)),unions),s(fun(fun(Q47300,bool),bool),S0))))),s(fun(Q47300,bool),T0))) = s(fun(Q47300,bool),i(s(fun(fun(fun(Q47300,bool),bool),fun(Q47300,bool)),unions),s(fun(fun(Q47300,bool),bool),i(s(fun(fun(fun(Q47300,bool),bool),fun(fun(Q47300,bool),bool)),gspec),s(fun(fun(Q47300,bool),bool),i(s(fun(fun(Q47300,bool),fun(fun(Q47300,bool),bool)),i(s(fun(fun(fun(Q47300,bool),bool),fun(fun(Q47300,bool),fun(fun(Q47300,bool),bool))),U_0),s(fun(fun(Q47300,bool),bool),S0))),s(fun(Q47300,bool),T0)))))))))) # label(aINTERu_UNIONSu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2116 (all X (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (exists B0 exists N0 all M0 all N1 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,N1)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N1))))))),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,N1))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N1))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),naddu_rinv),s(nadd,X))),s(num,M0))))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N1))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N1)))))))))))))) # label(aNADDu_MULu_LINVu_LEMMA5) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2117 p(s(bool,p1)) <-> p(s(bool,p1)) & p(s(bool,p1)) # label(aCONJu_ACIu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2118 (all X s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X))) = s(int,X)) # label(aINTu_ADDu_LID) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2119 (all X p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(nadd,X))))),s(nadd,X))))) # label(aNADDu_ADDu_LID) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2120 (all Q18624 s(bool,i(s(fun(list(Q18624),bool),i(s(fun(fun(Q18624,bool),fun(list(Q18624),bool)),ex0),s(fun(Q18624,bool),p0))),s(list(Q18624),nil))) = s(bool,f0)) # label(aEXu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2121 (all A all N all M0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),univ))),s(num,M0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(A,N),bool),fun(num,bool)),hasu_size),s(fun(cart(A,N),bool),univ))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))))))) # label(aHASu_SIZEu_CARTu_UNIV) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2122 (all X s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) # label(aINTu_NEGu_LE0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2123 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Z0))),s(real,X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Z0))),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))) # label(aREALu_LTu_LMULu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2124 (all Q97643 all P0 all S0 all T0 ((all F0 ((all S0 (p(s(bool,i(s(fun(fun(fun(Q97643,bool),bool),bool),i(s(fun(fun(Q97643,bool),fun(fun(fun(Q97643,bool),bool),bool)),in),s(fun(Q97643,bool),S0))),s(fun(fun(Q97643,bool),bool),F0)))) -> p(s(bool,i(s(fun(fun(Q97643,bool),bool),P0),s(fun(Q97643,bool),S0)))))) -> p(s(bool,i(s(fun(fun(Q97643,bool),bool),P0),s(fun(Q97643,bool),i(s(fun(fun(fun(Q97643,bool),bool),fun(Q97643,bool)),inters),s(fun(fun(Q97643,bool),bool),F0)))))))) & p(s(bool,i(s(fun(fun(Q97643,bool),bool),i(s(fun(fun(Q97643,bool),fun(fun(Q97643,bool),bool)),subset),s(fun(Q97643,bool),T0))),s(fun(Q97643,bool),i(s(fun(fun(Q97643,bool),fun(Q97643,bool)),i(s(fun(fun(fun(Q97643,bool),bool),fun(fun(Q97643,bool),fun(Q97643,bool))),hull),s(fun(fun(Q97643,bool),bool),P0))),s(fun(Q97643,bool),S0)))))) & p(s(bool,i(s(fun(fun(Q97643,bool),bool),i(s(fun(fun(Q97643,bool),fun(fun(Q97643,bool),bool)),subset),s(fun(Q97643,bool),S0))),s(fun(Q97643,bool),i(s(fun(fun(Q97643,bool),fun(Q97643,bool)),i(s(fun(fun(fun(Q97643,bool),bool),fun(fun(Q97643,bool),fun(Q97643,bool))),hull),s(fun(fun(Q97643,bool),bool),P0))),s(fun(Q97643,bool),T0)))))) -> s(fun(Q97643,bool),i(s(fun(fun(Q97643,bool),fun(Q97643,bool)),i(s(fun(fun(fun(Q97643,bool),bool),fun(fun(Q97643,bool),fun(Q97643,bool))),hull),s(fun(fun(Q97643,bool),bool),P0))),s(fun(Q97643,bool),S0))) = s(fun(Q97643,bool),i(s(fun(fun(Q97643,bool),fun(Q97643,bool)),i(s(fun(fun(fun(Q97643,bool),bool),fun(fun(Q97643,bool),fun(Q97643,bool))),hull),s(fun(fun(Q97643,bool),bool),P0))),s(fun(Q97643,bool),T0))))) # label(aHULLSu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2125 (all Q67049 all U_0 ((all F0 all G0 all X s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(Q67049,num),F0),s(Q67049,X))))),s(num,i(s(fun(Q67049,num),G0),s(Q67049,X))))) = s(num,i(s(fun(Q67049,num),i(s(fun(fun(Q67049,num),fun(Q67049,num)),i(s(fun(fun(Q67049,num),fun(fun(Q67049,num),fun(Q67049,num))),U_0),s(fun(Q67049,num),F0))),s(fun(Q67049,num),G0))),s(Q67049,X)))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q67049,bool),bool),finite),s(fun(Q67049,bool),S0)))) -> s(num,i(s(fun(fun(Q67049,num),num),i(s(fun(fun(Q67049,bool),fun(fun(Q67049,num),num)),nsum),s(fun(Q67049,bool),S0))),s(fun(Q67049,num),i(s(fun(fun(Q67049,num),fun(Q67049,num)),i(s(fun(fun(Q67049,num),fun(fun(Q67049,num),fun(Q67049,num))),U_0),s(fun(Q67049,num),F0))),s(fun(Q67049,num),G0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(Q67049,num),num),i(s(fun(fun(Q67049,bool),fun(fun(Q67049,num),num)),nsum),s(fun(Q67049,bool),S0))),s(fun(Q67049,num),F0))))),s(num,i(s(fun(fun(Q67049,num),num),i(s(fun(fun(Q67049,bool),fun(fun(Q67049,num),num)),nsum),s(fun(Q67049,bool),S0))),s(fun(Q67049,num),G0))))))))) # label(aNSUMu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2126 (all A all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) <-> (exists F0 (s(fun(A,bool),i(s(fun(fun(num,bool),fun(A,bool)),i(s(fun(fun(num,A),fun(fun(num,bool),fun(A,bool))),image),s(fun(num,A),F0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))))) = s(fun(A,bool),S0) & (all I0 all J0 (p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,J0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0)))))))) & s(A,i(s(fun(num,A),F0),s(num,J0))) = s(A,i(s(fun(num,A),F0),s(num,I0))) & p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,I0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0)))))))) -> s(num,J0) = s(num,I0))))))) # label(aFINITEu_INDEXu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2127 (all X all Y all Z0 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),Y))),s(prod(hreal,hreal),Z0)))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y))))),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Z0)))))))) # label(aTREALu_LEu_LADDu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2128 (all U_0 ((all U ((exists X1 exists Y1 (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_add),s(prod(hreal,hreal),X1))),s(prod(hreal,hreal),Y1))))),s(prod(hreal,hreal),U)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(real,fun(prod(hreal,hreal),bool)),destu_real),s(real,y1))),s(prod(hreal,hreal),Y1)))) & p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(real,fun(prod(hreal,hreal),bool)),destu_real),s(real,x1))),s(prod(hreal,hreal),X1)))))) <-> p(s(bool,i(s(fun(prod(hreal,hreal),bool),U_0),s(prod(hreal,hreal),U)))))) -> s(real,i(s(fun(fun(prod(hreal,hreal),bool),real),mku_real),s(fun(prod(hreal,hreal),bool),U_0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,x1))),s(real,y1))))) # label(arealu_add) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2129 (all Q45857 all S0 all T0 all U (p(s(bool,i(s(fun(fun(Q45857,bool),bool),i(s(fun(fun(Q45857,bool),fun(fun(Q45857,bool),bool)),subset),s(fun(Q45857,bool),S0))),s(fun(Q45857,bool),U)))) & p(s(bool,i(s(fun(fun(Q45857,bool),bool),i(s(fun(fun(Q45857,bool),fun(fun(Q45857,bool),bool)),subset),s(fun(Q45857,bool),S0))),s(fun(Q45857,bool),T0)))) <-> p(s(bool,i(s(fun(fun(Q45857,bool),bool),i(s(fun(fun(Q45857,bool),fun(fun(Q45857,bool),bool)),subset),s(fun(Q45857,bool),S0))),s(fun(Q45857,bool),i(s(fun(fun(Q45857,bool),fun(Q45857,bool)),i(s(fun(fun(Q45857,bool),fun(fun(Q45857,bool),fun(Q45857,bool))),inter),s(fun(Q45857,bool),T0))),s(fun(Q45857,bool),U)))))))) # label(aSUBSETu_INTER) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2130 (all Q88986 all Q88987 all S0 all T0 (p(s(bool,i(s(fun(fun(Q88987,bool),bool),i(s(fun(fun(Q88986,bool),fun(fun(Q88987,bool),bool)),l_u_c),s(fun(Q88986,bool),S0))),s(fun(Q88987,bool),T0)))) <-> -p(s(bool,i(s(fun(fun(Q88987,bool),bool),i(s(fun(fun(Q88986,bool),fun(fun(Q88987,bool),bool)),a_u_c),s(fun(Q88986,bool),S0))),s(fun(Q88987,bool),T0)))) & p(s(bool,i(s(fun(fun(Q88987,bool),bool),i(s(fun(fun(Q88986,bool),fun(fun(Q88987,bool),bool)),l_a_u_c),s(fun(Q88986,bool),S0))),s(fun(Q88987,bool),T0)))))) # label(aCARDu_LTu_LE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2131 (all X p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,X))))) # label(aNADDu_EQu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2132 (all A all B all F0 all G0 ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(B,bool),num),dimindex),s(fun(B,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> s(A,i(s(fun(num,A),G0),s(num,I0))) = s(A,i(s(fun(num,A),i(s(fun(cart(A,B),fun(num,A)),d_),s(cart(A,B),F0))),s(num,I0))))) <-> s(cart(A,B),i(s(fun(fun(num,A),cart(A,B)),lambda),s(fun(num,A),G0))) = s(cart(A,B),F0))) # label(aLAMBDAu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2133 (all B all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) -> (exists F0 ((all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) -> s(A,Y) = s(A,X))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> (exists X (s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0)))))))))) # label(aCARDu_EQu_BIJECTION) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2134 (all A s(fun(finite_image(A),bool),i(s(fun(fun(num,bool),fun(finite_image(A),bool)),i(s(fun(fun(num,finite_image(A)),fun(fun(num,bool),fun(finite_image(A),bool))),image),s(fun(num,finite_image(A)),finiteu_index))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),univ))))))) = s(fun(finite_image(A),bool),univ)) # label(aFINITEu_IMAGEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2135 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))))) # label(aFINITEu_UNIONu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2136 (all A all P0 all A5 ((all X (s(A,X) = s(A,A5) -> p(s(bool,i(s(fun(A,bool),P0),s(A,X)))))) <-> p(s(bool,i(s(fun(A,bool),P0),s(A,A5)))))) # label(aFORALLu_UNWINDu_THM2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2137 (all Q68228 all S0 all F0 all B0 ((all X (p(s(bool,i(s(fun(fun(Q68228,bool),bool),i(s(fun(Q68228,fun(fun(Q68228,bool),bool)),in),s(Q68228,X))),s(fun(Q68228,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(Q68228,num),F0),s(Q68228,X))))),s(num,B0)))))) & s(fun(Q68228,bool),empty) != s(fun(Q68228,bool),S0) & p(s(bool,i(s(fun(fun(Q68228,bool),bool),finite),s(fun(Q68228,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(Q68228,num),num),i(s(fun(fun(Q68228,bool),fun(fun(Q68228,num),num)),nsum),s(fun(Q68228,bool),S0))),s(fun(Q68228,num),F0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(fun(Q68228,bool),num),card),s(fun(Q68228,bool),S0))))),s(num,B0)))))))) # label(aNSUMu_BOUNDu_LTu_ALL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2138 (all A all U_0 ((all GENR_PVARR_5 ((exists Y exists V ((p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),s0)))) | s(A,Y) = s(A,x) <-> p(s(bool,V))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_5))),s(bool,V))),s(A,Y)))))) <-> p(s(bool,i(s(fun(A,bool),U_0),s(A,GENR_PVARR_5)))))) -> s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,x))),s(fun(A,bool),s0))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),U_0))))) # label(aINSERT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2139 (all N0 s(num,N0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))) # label(aADDu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2140 (all Q59981 all Q59984 all T0 all S0 ((exists F0 ((all Y (p(s(bool,i(s(fun(fun(Q59981,bool),bool),i(s(fun(Q59981,fun(fun(Q59981,bool),bool)),in),s(Q59981,Y))),s(fun(Q59981,bool),T0)))) -> (all X all XI_ (p(s(bool,i(s(fun(fun(Q59984,bool),bool),i(s(fun(Q59984,fun(fun(Q59984,bool),bool)),in),s(Q59984,XI_))),s(fun(Q59984,bool),S0)))) & s(Q59981,i(s(fun(Q59984,Q59981),F0),s(Q59984,XI_))) = s(Q59981,Y) & s(Q59981,i(s(fun(Q59984,Q59981),F0),s(Q59984,X))) = s(Q59981,Y) & p(s(bool,i(s(fun(fun(Q59984,bool),bool),i(s(fun(Q59984,fun(fun(Q59984,bool),bool)),in),s(Q59984,X))),s(fun(Q59984,bool),S0)))) -> s(Q59984,X) = s(Q59984,XI_))) & (exists X (p(s(bool,i(s(fun(fun(Q59984,bool),bool),i(s(fun(Q59984,fun(fun(Q59984,bool),bool)),in),s(Q59984,X))),s(fun(Q59984,bool),S0)))) & s(Q59981,i(s(fun(Q59984,Q59981),F0),s(Q59984,X))) = s(Q59981,Y))))) & (all X (p(s(bool,i(s(fun(fun(Q59984,bool),bool),i(s(fun(Q59984,fun(fun(Q59984,bool),bool)),in),s(Q59984,X))),s(fun(Q59984,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q59981,bool),bool),i(s(fun(Q59981,fun(fun(Q59981,bool),bool)),in),s(Q59981,i(s(fun(Q59984,Q59981),F0),s(Q59984,X))))),s(fun(Q59981,bool),T0)))))))) <-> p(s(bool,i(s(fun(fun(Q59981,bool),bool),i(s(fun(fun(Q59984,bool),fun(fun(Q59981,bool),bool)),a_u_c),s(fun(Q59984,bool),S0))),s(fun(Q59981,bool),T0)))))) # label(aequ_c) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2141 (all M0 all N0 all P0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,M0) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,P0)))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0)))))))) # label(aLEu_MULTu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2142 (all X (s(real,X) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,X))))) # label(aREALu_DIVu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2143 (all X all Y (p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))) -> p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_le),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),Y)))))) # label(aTREALu_EQu_IMPu_LE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2144 (all X p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),X))),s(prod(hreal,hreal),X))))) # label(aTREALu_EQu_REFL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2145 (all X all Y s(int,i(s(fun(int,int),intu_neg),s(int,Y))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))),s(int,X)))) # label(aINTu_SUBu_SUB) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2146 (all Q20380 all P0 all L ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,I0))),s(num,i(s(fun(list(Q20380),num),length),s(list(Q20380),L)))))) -> p(s(bool,i(s(fun(Q20380,bool),P0),s(Q20380,i(s(fun(list(Q20380),Q20380),i(s(fun(num,fun(list(Q20380),Q20380)),el),s(num,I0))),s(list(Q20380),L)))))))) <-> p(s(bool,i(s(fun(list(Q20380),bool),i(s(fun(fun(Q20380,bool),fun(list(Q20380),bool)),all0),s(fun(Q20380,bool),P0))),s(list(Q20380),L)))))) # label(aALLu_EL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2147 (all M0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))) <-> s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) | s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aMULTu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2148 (all Q54685 all S0 all T0 (p(s(bool,i(s(fun(fun(Q54685,bool),bool),finite),s(fun(Q54685,bool),T0)))) & p(s(bool,i(s(fun(fun(Q54685,bool),bool),finite),s(fun(Q54685,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(Q54685,bool),num),card),s(fun(Q54685,bool),S0))))),s(num,i(s(fun(fun(Q54685,bool),num),card),s(fun(Q54685,bool),T0))))))),s(num,i(s(fun(fun(Q54685,bool),num),card),s(fun(Q54685,bool),i(s(fun(fun(Q54685,bool),fun(Q54685,bool)),i(s(fun(fun(Q54685,bool),fun(fun(Q54685,bool),fun(Q54685,bool))),inter),s(fun(Q54685,bool),S0))),s(fun(Q54685,bool),T0))))))) = s(num,i(s(fun(fun(Q54685,bool),num),card),s(fun(Q54685,bool),i(s(fun(fun(Q54685,bool),fun(Q54685,bool)),i(s(fun(fun(Q54685,bool),fun(fun(Q54685,bool),fun(Q54685,bool))),union),s(fun(Q54685,bool),S0))),s(fun(Q54685,bool),T0))))))) # label(aCARDu_UNIONu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.64/14.64 2149 (all A all S0 s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(fun(A,bool),fun(fun(num,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(num,bool),univ))) = s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) # label(aFINITEu_CARDu_LT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2150 (all Q80235 all Q80236 all Q80237 all P all Q80272 all Q80269 all U_3 ((all E0 all C0 all F0 all X s(Q80269,i(s(fun(P,Q80269),i(s(fun(fun(Q80236,Q80237),fun(P,Q80269)),i(s(fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(Q80236,Q80237),fun(P,Q80269))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(Q80236,Q80237),fun(P,Q80269)))),U_3),s(fun(fun(Q80236,Q80237),fun(P,Q80272)),E0))),s(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),C0))),s(fun(Q80236,Q80237),F0))),s(P,X))) = s(Q80269,i(s(fun(fun(Q80272,fun(Q80269,bool)),Q80269),i(s(fun(Q80272,fun(fun(Q80272,fun(Q80269,bool)),Q80269)),u_match),s(Q80272,i(s(fun(P,Q80272),i(s(fun(fun(Q80236,Q80237),fun(P,Q80272)),E0),s(fun(Q80236,Q80237),F0))),s(P,X))))),s(fun(Q80272,fun(Q80269,bool)),i(s(fun(P,fun(Q80272,fun(Q80269,bool))),i(s(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),C0),s(fun(Q80236,Q80237),F0))),s(P,X)))))) -> (all U_2 ((all E0 all C0 all F0 s(fun(P,Q80269),i(s(fun(fun(Q80236,Q80237),fun(P,Q80269)),i(s(fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(Q80236,Q80237),fun(P,Q80269))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(Q80236,Q80237),fun(P,Q80269)))),U_2),s(fun(fun(Q80236,Q80237),fun(P,Q80272)),E0))),s(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),C0))),s(fun(Q80236,Q80237),F0))) = s(fun(P,Q80269),i(s(fun(fun(Q80236,Q80237),fun(P,Q80269)),i(s(fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(Q80236,Q80237),fun(P,Q80269))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(Q80236,Q80237),fun(P,Q80269)))),U_3),s(fun(fun(Q80236,Q80237),fun(P,Q80272)),E0))),s(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),C0))),s(fun(Q80236,Q80237),F0)))) -> (all U_1 ((all C0 all E0 all F0 all X s(fun(Q80269,bool),i(s(fun(Q80272,fun(Q80269,bool)),i(s(fun(P,fun(Q80272,fun(Q80269,bool))),i(s(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),C0),s(fun(Q80236,Q80237),F0))),s(P,X))),s(Q80272,i(s(fun(P,Q80272),i(s(fun(fun(Q80236,Q80237),fun(P,Q80272)),E0),s(fun(Q80236,Q80237),F0))),s(P,X))))) = s(fun(Q80269,bool),i(s(fun(P,fun(Q80269,bool)),i(s(fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool)))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))))),U_1),s(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),C0))),s(fun(fun(Q80236,Q80237),fun(P,Q80272)),E0))),s(fun(Q80236,Q80237),F0))),s(P,X)))) -> (all U_0 ((all C0 all E0 all F0 s(fun(P,fun(Q80269,bool)),i(s(fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool)))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))))),U_0),s(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),C0))),s(fun(fun(Q80236,Q80237),fun(P,Q80272)),E0))),s(fun(Q80236,Q80237),F0))) = s(fun(P,fun(Q80269,bool)),i(s(fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool)))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))))),U_1),s(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),C0))),s(fun(fun(Q80236,Q80237),fun(P,Q80272)),E0))),s(fun(Q80236,Q80237),F0)))) -> (all L_L_ all P0 all S0 all E0 all C0 (p(s(bool,i(s(fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),bool),i(s(fun(fun(P,Q80235),fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),bool)),i(s(fun(fun(fun(Q80236,Q80237),fun(P,bool)),fun(fun(P,Q80235),fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),bool))),i(s(fun(fun(Q80236,fun(Q80235,bool)),fun(fun(fun(Q80236,Q80237),fun(P,bool)),fun(fun(P,Q80235),fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),bool)))),admissible),s(fun(Q80236,fun(Q80235,bool)),L_L_))),s(fun(fun(Q80236,Q80237),fun(P,bool)),P0))),s(fun(P,Q80235),S0))),s(fun(fun(Q80236,Q80237),fun(P,Q80272)),E0)))) & p(s(bool,i(s(fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))),bool),i(s(fun(fun(P,Q80235),fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))),bool)),i(s(fun(fun(fun(Q80236,Q80237),fun(P,bool)),fun(fun(P,Q80235),fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))),bool))),i(s(fun(fun(Q80236,fun(Q80235,bool)),fun(fun(fun(Q80236,Q80237),fun(P,bool)),fun(fun(P,Q80235),fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))),bool)))),admissible),s(fun(Q80236,fun(Q80235,bool)),L_L_))),s(fun(fun(Q80236,Q80237),fun(P,bool)),P0))),s(fun(P,Q80235),S0))),s(fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool)))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(Q80236,Q80237),fun(P,fun(Q80269,bool))))),U_0),s(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),C0))),s(fun(fun(Q80236,Q80237),fun(P,Q80272)),E0)))))) -> p(s(bool,i(s(fun(fun(fun(Q80236,Q80237),fun(P,Q80269)),bool),i(s(fun(fun(P,Q80235),fun(fun(fun(Q80236,Q80237),fun(P,Q80269)),bool)),i(s(fun(fun(fun(Q80236,Q80237),fun(P,bool)),fun(fun(P,Q80235),fun(fun(fun(Q80236,Q80237),fun(P,Q80269)),bool))),i(s(fun(fun(Q80236,fun(Q80235,bool)),fun(fun(fun(Q80236,Q80237),fun(P,bool)),fun(fun(P,Q80235),fun(fun(fun(Q80236,Q80237),fun(P,Q80269)),bool)))),admissible),s(fun(Q80236,fun(Q80235,bool)),L_L_))),s(fun(fun(Q80236,Q80237),fun(P,bool)),P0))),s(fun(P,Q80235),S0))),s(fun(fun(Q80236,Q80237),fun(P,Q80269)),i(s(fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(Q80236,Q80237),fun(P,Q80269))),i(s(fun(fun(fun(Q80236,Q80237),fun(P,Q80272)),fun(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),fun(fun(Q80236,Q80237),fun(P,Q80269)))),U_2),s(fun(fun(Q80236,Q80237),fun(P,Q80272)),E0))),s(fun(fun(Q80236,Q80237),fun(P,fun(Q80272,fun(Q80269,bool)))),C0)))))))))))))))) # label(aADMISSIBLEu_MATCH) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2151 (all Q47111 s(fun(Q47111,bool),i(s(fun(fun(fun(Q47111,bool),bool),fun(Q47111,bool)),unions),s(fun(fun(Q47111,bool),bool),empty))) = s(fun(Q47111,bool),empty)) # label(aUNIONSu_0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2152 (all X all Y (s(int,Y) != s(int,X) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,X)))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))))) # label(aINTu_NOTu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2153 (all U_0 ((all N0 all GENR_PVARR_110 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))),s(num,GENR_PVARR_110)))) <-> (exists M0 p(s(bool,i(s(fun(num,bool),i(s(fun(bool,fun(num,bool)),i(s(fun(num,fun(bool,fun(num,bool))),setspec),s(num,GENR_PVARR_110))),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(num,M0))))))) -> (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),hasu_size),s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),gspec),s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) # label(aHASu_SIZEu_NUMSEGu_LE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2154 (all T0 ((p(s(bool,T0)) <-> (p(s(bool,t)) -> p(s(bool,T0)))) & (p(s(bool,t)) <-> (p(s(bool,T0)) -> p(s(bool,T0)))) & ((p(s(bool,T0)) -> p(s(bool,f0))) <-> -p(s(bool,T0))) & (p(s(bool,t)) <-> (p(s(bool,f0)) -> p(s(bool,T0)))) & ((p(s(bool,T0)) -> p(s(bool,t))) <-> p(s(bool,t))))) # label(aIMPu_CLAUSES) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2155 (all A all B all X all Y s(fun(A,fun(B,bool)),i(s(fun(prod(A,B),fun(A,fun(B,bool))),repu_prod),s(prod(A,B),i(s(fun(fun(A,fun(B,bool)),prod(A,B)),absu_prod),s(fun(A,fun(B,bool)),i(s(fun(B,fun(A,fun(B,bool))),i(s(fun(A,fun(B,fun(A,fun(B,bool)))),mku_pair),s(A,X))),s(B,Y))))))) = s(fun(A,fun(B,bool)),i(s(fun(B,fun(A,fun(B,bool))),i(s(fun(A,fun(B,fun(A,fun(B,bool)))),mku_pair),s(A,X))),s(B,Y)))) # label(aREPu_ABSu_PAIR) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2156 (all A all B all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all R0 (p(s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),R0),s(B,i(s(fun(fun(B,fun(B,B)),B),neutral),s(fun(B,fun(B,B)),OP))))),s(B,i(s(fun(fun(B,fun(B,B)),B),neutral),s(fun(B,fun(B,B)),OP)))))) & (all X1 all Y1 all X2 all Y2 (p(s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),R0),s(B,Y1))),s(B,Y2)))) & p(s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),R0),s(B,X1))),s(B,X2)))) -> p(s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),R0),s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),OP),s(B,X1))),s(B,Y1))))),s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),OP),s(B,X2))),s(B,Y2)))))))) -> (all F0 all G0 all S0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),R0),s(B,i(s(fun(A,B),F0),s(A,X))))),s(B,i(s(fun(A,B),G0),s(A,X)))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(B,bool),i(s(fun(B,fun(B,bool)),R0),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))))),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),G0)))))))))))) # label(aITERATEu_RELATED) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2157 (all M0 all N0 (s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) <-> s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))) = s(num,N0) & s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) # label(aMULTu_EQu_1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2158 (all M0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))),s(num,N0)))) & s(num,M0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))))) # label(aDIVISION) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2159 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y)))))))) # label(aINTu_LTu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2160 (all A5 all B0 all C0 (p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,A5))),s(hreal,B0)))) -> p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,A5))),s(hreal,C0))))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,B0))),s(hreal,C0)))))))) # label(aHREALu_LEu_MULu_RCANCELu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2161 (all X all Y all Z0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Y))),s(int,Z0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))))),s(int,Z0)))) # label(aINTu_MULu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2162 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),poset),s(fun(prod(A,A),bool),L)))) -> (exists P0 ((all Q0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),P0))),s(fun(A,bool),Q0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(A,bool),bool)),chain),s(fun(prod(A,A),bool),L))),s(fun(A,bool),Q0)))) -> s(fun(A,bool),P0) = s(fun(A,bool),Q0))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(A,bool),bool)),chain),s(fun(prod(A,A),bool),L))),s(fun(A,bool),P0)))))))) # label(aHP) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2163 (all X s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(int,X)) # label(aINTu_POWu_1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2164 (all A all B all C all OP (p(s(bool,i(s(fun(fun(C,fun(C,C)),bool),monoidal),s(fun(C,fun(C,C)),OP)))) -> (all S0 all T0 all F0 all G0 all H0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(C,i(s(fun(B,C),G0),s(B,i(s(fun(A,B),H0),s(A,X))))) = s(C,i(s(fun(A,C),F0),s(A,X))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),H0),s(A,X))))),s(fun(B,bool),T0)))))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> (all X all XI_ (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),H0),s(A,XI_))) = s(B,Y) & s(B,i(s(fun(A,B),H0),s(A,X))) = s(B,Y) -> s(A,X) = s(A,XI_))) & (exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),H0),s(A,X))) = s(B,Y))))) -> s(C,i(s(fun(fun(B,C),C),i(s(fun(fun(B,bool),fun(fun(B,C),C)),i(s(fun(fun(C,fun(C,C)),fun(fun(B,bool),fun(fun(B,C),C))),iterate),s(fun(C,fun(C,C)),OP))),s(fun(B,bool),T0))),s(fun(B,C),G0))) = s(C,i(s(fun(fun(A,C),C),i(s(fun(fun(A,bool),fun(fun(A,C),C)),i(s(fun(fun(C,fun(C,C)),fun(fun(A,bool),fun(fun(A,C),C))),iterate),s(fun(C,fun(C,C)),OP))),s(fun(A,bool),S0))),s(fun(A,C),F0))))))) # label(aITERATEu_EQu_GENERAL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2165 (all M0 all N0 s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,M0))))),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,N0)))))) # label(aHREALu_OFu_NUMu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2166 (all Q47385 all F0 all G0 (p(s(bool,i(s(fun(fun(fun(Q47385,bool),bool),bool),i(s(fun(fun(fun(Q47385,bool),bool),fun(fun(fun(Q47385,bool),bool),bool)),subset),s(fun(fun(Q47385,bool),bool),F0))),s(fun(fun(Q47385,bool),bool),G0)))) -> p(s(bool,i(s(fun(fun(Q47385,bool),bool),i(s(fun(fun(Q47385,bool),fun(fun(Q47385,bool),bool)),subset),s(fun(Q47385,bool),i(s(fun(fun(fun(Q47385,bool),bool),fun(Q47385,bool)),unions),s(fun(fun(Q47385,bool),bool),F0))))),s(fun(Q47385,bool),i(s(fun(fun(fun(Q47385,bool),bool),fun(Q47385,bool)),unions),s(fun(fun(Q47385,bool),bool),G0)))))))) # label(aSUBSETu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2167 (all M all N p(s(bool,i(s(fun(num,bool),i(s(fun(fun(finite_sum(M,N),bool),fun(num,bool)),hasu_size),s(fun(finite_sum(M,N),bool),univ))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))))) # label(aDIMINDEXu_HASu_SIZEu_FINITEu_SUM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2168 (all Q18839 all Q18838 all Q18845 s(list(Q18845),i(s(fun(list(Q18838),list(Q18845)),i(s(fun(list(Q18839),fun(list(Q18838),list(Q18845))),i(s(fun(fun(Q18839,fun(Q18838,Q18845)),fun(list(Q18839),fun(list(Q18838),list(Q18845)))),map2),s(fun(Q18839,fun(Q18838,Q18845)),f))),s(list(Q18839),nil))),s(list(Q18838),nil))) = s(list(Q18845),nil)) # label(aMAP2u_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2169 (all N0 s(bool,i(s(fun(num,bool),even),s(num,i(s(fun(num,num),numeral),s(num,N0))))) = s(bool,i(s(fun(num,bool),even),s(num,N0)))) # label(aARITHu_EVENu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2170 (all A all S0 all F0 all B0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (exists X (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,B0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,B0)))))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,B0)))))))) # label(aNSUMu_BOUNDu_LT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2171 (all Q18603 (p(s(bool,i(s(fun(list(Q18603),bool),i(s(fun(fun(Q18603,bool),fun(list(Q18603),bool)),all0),s(fun(Q18603,bool),p0))),s(list(Q18603),t0)))) & p(s(bool,i(s(fun(Q18603,bool),p0),s(Q18603,h0)))) <-> p(s(bool,i(s(fun(list(Q18603),bool),i(s(fun(fun(Q18603,bool),fun(list(Q18603),bool)),all0),s(fun(Q18603,bool),p0))),s(list(Q18603),i(s(fun(list(Q18603),list(Q18603)),i(s(fun(Q18603,fun(list(Q18603),list(Q18603))),cons),s(Q18603,h0))),s(list(Q18603),t0)))))))) # label(aALLu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2172 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0)))))) # label(aARITHu_LEu_conjunct9) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2173 (all Q96863 all P0 all S0 p(s(bool,i(s(fun(fun(Q96863,bool),bool),i(s(fun(fun(Q96863,bool),fun(fun(Q96863,bool),bool)),subset),s(fun(Q96863,bool),S0))),s(fun(Q96863,bool),i(s(fun(fun(Q96863,bool),fun(Q96863,bool)),i(s(fun(fun(fun(Q96863,bool),bool),fun(fun(Q96863,bool),fun(Q96863,bool))),hull),s(fun(fun(Q96863,bool),bool),P0))),s(fun(Q96863,bool),S0))))))) # label(aHULLu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2174 (all A all P all B all L_L_ all P0 all S0 all T0 (p(s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),admissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),T0)))) -> p(s(bool,i(s(fun(fun(fun(A,B),fun(P,B)),bool),i(s(fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)),i(s(fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool))),i(s(fun(fun(A,fun(A,bool)),fun(fun(fun(A,B),fun(P,bool)),fun(fun(P,A),fun(fun(fun(A,B),fun(P,B)),bool)))),superadmissible),s(fun(A,fun(A,bool)),L_L_))),s(fun(fun(A,B),fun(P,bool)),P0))),s(fun(P,A),S0))),s(fun(fun(A,B),fun(P,B)),T0)))))) # label(aADMISSIBLEu_IMPu_SUPERADMISSIBLE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2175 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,i(s(fun(num,num),bit0),s(num,M0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,N0))),s(num,M0)))) # label(aARITHu_GTu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2176 (all Q48848 all Q48727 all U_0 ((all P0 all F0 all GENR_PVARR_24 ((exists X p(s(bool,i(s(fun(Q48848,bool),i(s(fun(bool,fun(Q48848,bool)),i(s(fun(Q48848,fun(bool,fun(Q48848,bool))),setspec),s(Q48848,GENR_PVARR_24))),s(bool,i(s(fun(Q48727,bool),P0),s(Q48727,X))))),s(Q48848,i(s(fun(Q48727,Q48848),F0),s(Q48727,X))))))) <-> p(s(bool,i(s(fun(Q48848,bool),i(s(fun(fun(Q48727,Q48848),fun(Q48848,bool)),i(s(fun(fun(Q48727,bool),fun(fun(Q48727,Q48848),fun(Q48848,bool))),U_0),s(fun(Q48727,bool),P0))),s(fun(Q48727,Q48848),F0))),s(Q48848,GENR_PVARR_24)))))) -> (all P0 all F0 ((exists X (p(s(bool,i(s(fun(Q48727,bool),P0),s(Q48727,X)))) & p(s(bool,i(s(fun(Q48848,bool),q0),s(Q48848,i(s(fun(Q48727,Q48848),F0),s(Q48727,X)))))))) <-> (exists Z0 (p(s(bool,i(s(fun(fun(Q48848,bool),bool),i(s(fun(Q48848,fun(fun(Q48848,bool),bool)),in),s(Q48848,Z0))),s(fun(Q48848,bool),i(s(fun(fun(Q48848,bool),fun(Q48848,bool)),gspec),s(fun(Q48848,bool),i(s(fun(fun(Q48727,Q48848),fun(Q48848,bool)),i(s(fun(fun(Q48727,bool),fun(fun(Q48727,Q48848),fun(Q48848,bool))),U_0),s(fun(Q48727,bool),P0))),s(fun(Q48727,Q48848),F0)))))))) & p(s(bool,i(s(fun(Q48848,bool),q0),s(Q48848,Z0)))))))))) # label(aEXISTSu_INu_GSPECu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2177 (all N0 s(bool,i(s(fun(num,bool),even),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(bool,f0)) # label(aARITHu_EVENu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2178 (all U_0 ((all N0 all GENR_PVARR_108 ((exists M0 p(s(bool,i(s(fun(num,bool),i(s(fun(bool,fun(num,bool)),i(s(fun(num,fun(bool,fun(num,bool))),setspec),s(num,GENR_PVARR_108))),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0))))),s(num,M0))))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0))),s(num,GENR_PVARR_108)))))) -> (all N0 s(num,N0) = s(num,i(s(fun(fun(num,bool),num),card),s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),gspec),s(fun(num,bool),i(s(fun(num,fun(num,bool)),U_0),s(num,N0)))))))))) # label(aCARDu_NUMSEGu_LT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2179 (all A (p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),univ)))) -> p(s(bool,i(s(fun(fun(list(A),bool),bool),countable),s(fun(list(A),bool),univ)))))) # label(aCOUNTABLEu_LIST) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2180 (all A all U_0 ((all L all F0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),U_0),s(fun(prod(A,A),bool),L))),s(fun(prod(A,A),bool),F0)))) <-> (all X all Y exists V ((p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,Y))),s(A,a0)))))) & p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(A,A),bool),F0),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y))))))),s(bool,V)))))))) -> (all L all X (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),i(s(fun(fun(fun(prod(A,A),bool),bool),fun(prod(A,A),bool)),gabs),s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),U_0),s(fun(prod(A,A),bool),L))))))),s(A,X))) = s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,a0))))))))) # label(aEXTENDu_FL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2181 (all N0 p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(num,N0))))))) # label(aINTu_LTu_POW2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2182 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,P0)))) # label(aMULTu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2183 (all A all X ((all Q0 ((all X0 (p(s(bool,i(s(fun(A,bool),X),s(A,X0)))) -> p(s(bool,Q0)))) -> p(s(bool,Q0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),q_),s(fun(A,bool),X)))))) # label(aEXISTSu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2184 (all Q18943 all Q18951 all Q18941 s(Q18941,i(s(fun(Q18941,Q18941),i(s(fun(list(Q18951),fun(Q18941,Q18941)),i(s(fun(list(Q18943),fun(list(Q18951),fun(Q18941,Q18941))),i(s(fun(fun(Q18943,fun(Q18951,fun(Q18941,Q18941))),fun(list(Q18943),fun(list(Q18951),fun(Q18941,Q18941)))),itlist2),s(fun(Q18943,fun(Q18951,fun(Q18941,Q18941))),f))),s(list(Q18943),nil))),s(list(Q18951),l2))),s(Q18941,b0))) = s(Q18941,b0)) # label(aITLIST2u_DEFu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2185 (all A all U_0 ((all C0 all F0 all X s(num,i(s(fun(A,num),i(s(fun(fun(A,num),fun(A,num)),i(s(fun(num,fun(fun(A,num),fun(A,num))),U_0),s(num,C0))),s(fun(A,num),F0))),s(A,X))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,C0))),s(num,i(s(fun(A,num),F0),s(A,X)))))) -> (all F0 all C0 all S0 s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),i(s(fun(fun(A,num),fun(A,num)),i(s(fun(num,fun(fun(A,num),fun(A,num))),U_0),s(num,C0))),s(fun(A,num),F0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,C0))),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0)))))))) # label(aNSUMu_LMUL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2186 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,N0)))))) # label(aARITHu_EXPu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2187 p(s(bool,i(s(fun(fun(num,num),bool),isu_nadd),s(fun(num,num),r0)))) <-> s(fun(num,num),r0) = s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,i(s(fun(fun(num,num),nadd),mku_nadd),s(fun(num,num),r0))))) # label(anaddu_rep) # label(axiom) # label(non_clause). [assumption]. 14.64/14.65 2188 (all Q52949 all Q52950 all S0 all F0 all G0 all B0 (p(s(bool,i(s(fun(fun(Q52949,bool),bool),finite),s(fun(Q52949,bool),S0)))) & (all X all Y all S1 (s(Q52949,X) != s(Q52949,Y) -> s(Q52950,i(s(fun(Q52950,Q52950),i(s(fun(Q52949,fun(Q52950,Q52950)),F0),s(Q52949,Y))),s(Q52950,i(s(fun(Q52950,Q52950),i(s(fun(Q52949,fun(Q52950,Q52950)),F0),s(Q52949,X))),s(Q52950,S1))))) = s(Q52950,i(s(fun(Q52950,Q52950),i(s(fun(Q52949,fun(Q52950,Q52950)),F0),s(Q52949,X))),s(Q52950,i(s(fun(Q52950,Q52950),i(s(fun(Q52949,fun(Q52950,Q52950)),F0),s(Q52949,Y))),s(Q52950,S1))))))) & (all X all Y all S1 (s(Q52949,Y) != s(Q52949,X) -> s(Q52950,i(s(fun(Q52950,Q52950),i(s(fun(Q52949,fun(Q52950,Q52950)),G0),s(Q52949,X))),s(Q52950,i(s(fun(Q52950,Q52950),i(s(fun(Q52949,fun(Q52950,Q52950)),G0),s(Q52949,Y))),s(Q52950,S1))))) = s(Q52950,i(s(fun(Q52950,Q52950),i(s(fun(Q52949,fun(Q52950,Q52950)),G0),s(Q52949,Y))),s(Q52950,i(s(fun(Q52950,Q52950),i(s(fun(Q52949,fun(Q52950,Q52950)),G0),s(Q52949,X))),s(Q52950,S1))))))) & (all X (p(s(bool,i(s(fun(fun(Q52949,bool),bool),i(s(fun(Q52949,fun(fun(Q52949,bool),bool)),in),s(Q52949,X))),s(fun(Q52949,bool),S0)))) -> s(fun(Q52950,Q52950),i(s(fun(Q52949,fun(Q52950,Q52950)),G0),s(Q52949,X))) = s(fun(Q52950,Q52950),i(s(fun(Q52949,fun(Q52950,Q52950)),F0),s(Q52949,X))))) -> s(Q52950,i(s(fun(Q52950,Q52950),i(s(fun(fun(Q52949,bool),fun(Q52950,Q52950)),i(s(fun(fun(Q52949,fun(Q52950,Q52950)),fun(fun(Q52949,bool),fun(Q52950,Q52950))),itset),s(fun(Q52949,fun(Q52950,Q52950)),F0))),s(fun(Q52949,bool),S0))),s(Q52950,B0))) = s(Q52950,i(s(fun(Q52950,Q52950),i(s(fun(fun(Q52949,bool),fun(Q52950,Q52950)),i(s(fun(fun(Q52949,fun(Q52950,Q52950)),fun(fun(Q52949,bool),fun(Q52950,Q52950))),itset),s(fun(Q52949,fun(Q52950,Q52950)),G0))),s(fun(Q52949,bool),S0))),s(Q52950,B0))))) # label(aITSETu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2189 (all Q51883 all S0 all T0 (p(s(bool,i(s(fun(fun(Q51883,bool),bool),i(s(fun(fun(Q51883,bool),fun(fun(Q51883,bool),bool)),subset),s(fun(Q51883,bool),S0))),s(fun(Q51883,bool),T0)))) & p(s(bool,i(s(fun(fun(Q51883,bool),bool),infinite),s(fun(Q51883,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q51883,bool),bool),infinite),s(fun(Q51883,bool),T0)))))) # label(aINFINITEu_SUPERSET) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2190 (all X all Y s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_ge),s(int,X))),s(int,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_ge),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y)))))) # label(aintu_ge) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2191 (all A (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),univ))),s(num,n)))) -> s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),univ))) = s(num,n))) # label(aDIMINDEXu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2192 p(s(bool,r0)) & p(s(bool,q)) & p(s(bool,p1)) <-> p(s(bool,r0)) & p(s(bool,q)) & p(s(bool,p1)) # label(aCONJu_ACIu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2193 (all B all A all C all S0 all T0 all U (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(B,bool),fun(fun(C,bool),bool)),l_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U)))) -> p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(A,bool),fun(fun(C,bool),bool)),l_u_c),s(fun(A,bool),S0))),s(fun(C,bool),U)))))) # label(aCARDu_LETu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2194 (all N0 all X all Y (s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))) = s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,N0))) & s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> s(int,i(s(fun(int,int),intu_abs),s(int,Y))) = s(int,i(s(fun(int,int),intu_abs),s(int,X))))) # label(aINTu_POWu_EQu_ABS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2195 (all Q81671 all P all Q81786 all Q81787 all U_9 ((all C1 all C2 all F0 all X s(fun(Q81786,fun(Q81787,bool)),i(s(fun(fun(Q81786,fun(Q81787,bool)),fun(Q81786,fun(Q81787,bool))),i(s(fun(fun(Q81786,fun(Q81787,bool)),fun(fun(Q81786,fun(Q81787,bool)),fun(Q81786,fun(Q81787,bool)))),u_seqpattern),s(fun(Q81786,fun(Q81787,bool)),i(s(fun(P,fun(Q81786,fun(Q81787,bool))),i(s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1),s(fun(Q81671,Q81787),F0))),s(P,X))))),s(fun(Q81786,fun(Q81787,bool)),i(s(fun(P,fun(Q81786,fun(Q81787,bool))),i(s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C2),s(fun(Q81671,Q81787),F0))),s(P,X))))) = s(fun(Q81786,fun(Q81787,bool)),i(s(fun(P,fun(Q81786,fun(Q81787,bool))),i(s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool))))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))))),U_9),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C2))),s(fun(Q81671,Q81787),F0))),s(P,X)))) -> (all U_8 ((all C1 all C2 all F0 s(fun(P,fun(Q81786,fun(Q81787,bool))),i(s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool))))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))))),U_9),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C2))),s(fun(Q81671,Q81787),F0))) = s(fun(P,fun(Q81786,fun(Q81787,bool))),i(s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool))))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))))),U_8),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C2))),s(fun(Q81671,Q81787),F0)))) -> (all U_7 ((all P0 all C1 all E0 all F0 all X (-(exists Y p(s(bool,i(s(fun(Q81787,bool),i(s(fun(Q81786,fun(Q81787,bool)),i(s(fun(P,fun(Q81786,fun(Q81787,bool))),i(s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1),s(fun(Q81671,Q81787),F0))),s(P,X))),s(Q81786,i(s(fun(P,Q81786),i(s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0),s(fun(Q81671,Q81787),F0))),s(P,X))))),s(Q81787,Y))))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q81671,Q81787),fun(P,bool)),P0),s(fun(Q81671,Q81787),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))))),U_7),s(fun(fun(Q81671,Q81787),fun(P,bool)),P0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(Q81671,Q81787),F0))),s(P,X)))))) -> (all U_6 ((all P0 all C1 all E0 all F0 s(fun(P,bool),i(s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))))),U_6),s(fun(fun(Q81671,Q81787),fun(P,bool)),P0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(Q81671,Q81787),F0))) = s(fun(P,bool),i(s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))))),U_7),s(fun(fun(Q81671,Q81787),fun(P,bool)),P0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(Q81671,Q81787),F0)))) -> (all U_5 ((all E0 all C1 all F0 all X s(Q81787,i(s(fun(fun(Q81786,fun(Q81787,bool)),Q81787),i(s(fun(Q81786,fun(fun(Q81786,fun(Q81787,bool)),Q81787)),u_match),s(Q81786,i(s(fun(P,Q81786),i(s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0),s(fun(Q81671,Q81787),F0))),s(P,X))))),s(fun(Q81786,fun(Q81787,bool)),i(s(fun(P,fun(Q81786,fun(Q81787,bool))),i(s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1),s(fun(Q81671,Q81787),F0))),s(P,X))))) = s(Q81787,i(s(fun(P,Q81787),i(s(fun(fun(Q81671,Q81787),fun(P,Q81787)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787)))),U_5),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(Q81671,Q81787),F0))),s(P,X)))) -> (all U_4 ((all E0 all C1 all F0 s(fun(P,Q81787),i(s(fun(fun(Q81671,Q81787),fun(P,Q81787)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787)))),U_4),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(Q81671,Q81787),F0))) = s(fun(P,Q81787),i(s(fun(fun(Q81671,Q81787),fun(P,Q81787)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787)))),U_5),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(Q81671,Q81787),F0)))) -> (all U_3 ((all P0 all C1 all E0 all F0 all X (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))))),U_3),s(fun(fun(Q81671,Q81787),fun(P,bool)),P0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(Q81671,Q81787),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q81671,Q81787),fun(P,bool)),P0),s(fun(Q81671,Q81787),F0))),s(P,X)))) & (exists Y p(s(bool,i(s(fun(Q81787,bool),i(s(fun(Q81786,fun(Q81787,bool)),i(s(fun(P,fun(Q81786,fun(Q81787,bool))),i(s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1),s(fun(Q81671,Q81787),F0))),s(P,X))),s(Q81786,i(s(fun(P,Q81786),i(s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0),s(fun(Q81671,Q81787),F0))),s(P,X))))),s(Q81787,Y))))))) -> (all U_2 ((all P0 all C1 all E0 all F0 s(fun(P,bool),i(s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))))),U_3),s(fun(fun(Q81671,Q81787),fun(P,bool)),P0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(Q81671,Q81787),F0))) = s(fun(P,bool),i(s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))))),U_2),s(fun(fun(Q81671,Q81787),fun(P,bool)),P0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(Q81671,Q81787),F0)))) -> (all U_1 ((all C1 all E0 all F0 all X (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),U_1),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(Q81671,Q81787),F0))),s(P,X)))) <-> (exists Y p(s(bool,i(s(fun(Q81787,bool),i(s(fun(Q81786,fun(Q81787,bool)),i(s(fun(P,fun(Q81786,fun(Q81787,bool))),i(s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1),s(fun(Q81671,Q81787),F0))),s(P,X))),s(Q81786,i(s(fun(P,Q81786),i(s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0),s(fun(Q81671,Q81787),F0))),s(P,X))))),s(Q81787,Y))))))) -> (all U_0 ((all C1 all E0 all F0 s(fun(P,bool),i(s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),U_0),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(Q81671,Q81787),F0))) = s(fun(P,bool),i(s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),U_1),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(Q81671,Q81787),F0)))) -> (all L_L_ all P0 all S0 all C1 all C2 all E0 (p(s(bool,i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),bool),i(s(fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,bool)),bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,bool)),bool))),i(s(fun(fun(Q81671,fun(Q81671,bool)),fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,bool)),bool)))),admissible),s(fun(Q81671,fun(Q81671,bool)),L_L_))),s(fun(fun(Q81671,Q81787),fun(P,bool)),P0))),s(fun(P,Q81671),S0))),s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),U_0),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0)))))) & p(s(bool,i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool),i(s(fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool))),i(s(fun(fun(Q81671,fun(Q81671,bool)),fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool)))),superadmissible),s(fun(Q81671,fun(Q81671,bool)),L_L_))),s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))))),U_6),s(fun(fun(Q81671,Q81787),fun(P,bool)),P0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))))),s(fun(P,Q81671),S0))),s(fun(fun(Q81671,Q81787),fun(P,Q81787)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787)))),U_4),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C2)))))) & p(s(bool,i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool),i(s(fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool))),i(s(fun(fun(Q81671,fun(Q81671,bool)),fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool)))),superadmissible),s(fun(Q81671,fun(Q81671,bool)),L_L_))),s(fun(fun(Q81671,Q81787),fun(P,bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(Q81671,Q81787),fun(P,bool))))),U_2),s(fun(fun(Q81671,Q81787),fun(P,bool)),P0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))))),s(fun(P,Q81671),S0))),s(fun(fun(Q81671,Q81787),fun(P,Q81787)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787)))),U_4),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1)))))) -> p(s(bool,i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool),i(s(fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool))),i(s(fun(fun(Q81671,fun(Q81671,bool)),fun(fun(fun(Q81671,Q81787),fun(P,bool)),fun(fun(P,Q81671),fun(fun(fun(Q81671,Q81787),fun(P,Q81787)),bool)))),superadmissible),s(fun(Q81671,fun(Q81671,bool)),L_L_))),s(fun(fun(Q81671,Q81787),fun(P,bool)),P0))),s(fun(P,Q81671),S0))),s(fun(fun(Q81671,Q81787),fun(P,Q81787)),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,Q81786)),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,Q81787)))),U_4),s(fun(fun(Q81671,Q81787),fun(P,Q81786)),E0))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool))))),i(s(fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))))),U_8),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C1))),s(fun(fun(Q81671,Q81787),fun(P,fun(Q81786,fun(Q81787,bool)))),C2)))))))))))))))))))))))))))))) # label(aSUPERADMISSIBLEu_MATCHu_SEQPATTERN) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2196 (all X s(hreal,X) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(hreal,X)))) # label(aHREALu_ADDu_LID) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2197 (all Q83140 all Q83146 all Q83142 all U_1 ((all X s(bool,t) = s(bool,i(s(fun(Q83146,bool),U_1),s(Q83146,X)))) -> (all U_0 ((all F0 s(fun(Q83146,bool),U_1) = s(fun(Q83146,bool),i(s(fun(fun(Q83140,Q83142),fun(Q83146,bool)),U_0),s(fun(Q83140,Q83142),F0)))) -> s(bool,i(s(fun(fun(fun(Q83140,Q83142),fun(Q83146,Q83142)),bool),i(s(fun(fun(Q83146,Q83140),fun(fun(fun(Q83140,Q83142),fun(Q83146,Q83142)),bool)),i(s(fun(fun(fun(Q83140,Q83142),fun(Q83146,bool)),fun(fun(Q83146,Q83140),fun(fun(fun(Q83140,Q83142),fun(Q83146,Q83142)),bool))),i(s(fun(fun(Q83140,fun(Q83140,bool)),fun(fun(fun(Q83140,Q83142),fun(Q83146,bool)),fun(fun(Q83146,Q83140),fun(fun(fun(Q83140,Q83142),fun(Q83146,Q83142)),bool)))),superadmissible),s(fun(Q83140,fun(Q83140,bool)),l_l_))),s(fun(fun(Q83140,Q83142),fun(Q83146,bool)),U_0))),s(fun(Q83146,Q83140),s0))),s(fun(fun(Q83140,Q83142),fun(Q83146,Q83142)),t0))) = s(bool,i(s(fun(fun(fun(Q83140,Q83142),fun(Q83146,Q83142)),bool),i(s(fun(fun(Q83146,Q83140),fun(fun(fun(Q83140,Q83142),fun(Q83146,Q83142)),bool)),i(s(fun(fun(fun(Q83140,Q83142),fun(Q83146,bool)),fun(fun(Q83146,Q83140),fun(fun(fun(Q83140,Q83142),fun(Q83146,Q83142)),bool))),i(s(fun(fun(Q83140,fun(Q83140,bool)),fun(fun(fun(Q83140,Q83142),fun(Q83146,bool)),fun(fun(Q83146,Q83140),fun(fun(fun(Q83140,Q83142),fun(Q83146,Q83142)),bool)))),tailadmissible),s(fun(Q83140,fun(Q83140,bool)),l_l_))),s(fun(fun(Q83140,Q83142),fun(Q83146,bool)),U_0))),s(fun(Q83146,Q83140),s0))),s(fun(fun(Q83140,Q83142),fun(Q83146,Q83142)),t0))))))) # label(aSUPERADMISSIBLEu_T) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2198 (all X all Y s(int,i(s(fun(real,int),intu_ofu_real),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y))))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y)))) # label(aintu_mul) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2199 (all A all X (s(A,X) = s(A,X) <-> p(s(bool,t)))) # label(aREFLu_CLAUSE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2200 (all M0 all N0 all P0 all Q0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,Q0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,P0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,P0))),s(num,Q0)))))))) # label(aLEu_ADD2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2201 (all X all Y all Z0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,Z0)))))) # label(aREALu_SUBu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2202 (all Q46571 s(fun(Q46571,bool),i(s(fun(fun(Q46571,bool),fun(Q46571,bool)),i(s(fun(Q46571,fun(fun(Q46571,bool),fun(Q46571,bool))),insert),s(Q46571,x))),s(fun(Q46571,bool),s0))) = s(fun(Q46571,bool),i(s(fun(fun(Q46571,bool),fun(Q46571,bool)),i(s(fun(Q46571,fun(fun(Q46571,bool),fun(Q46571,bool))),insert),s(Q46571,x))),s(fun(Q46571,bool),i(s(fun(fun(Q46571,bool),fun(Q46571,bool)),i(s(fun(Q46571,fun(fun(Q46571,bool),fun(Q46571,bool))),insert),s(Q46571,x))),s(fun(Q46571,bool),s0)))))) # label(aINSERTu_ACu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2203 (all A all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) -> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(A,num),F0),s(A,X))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) -> s(num,i(s(fun(A,num),g),s(A,X))) = s(num,i(s(fun(A,num),F0),s(A,X))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0)))) -> s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),T0))),s(fun(A,num),g))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))))) # label(aNSUMu_EQu_SUPERSET) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2204 (all A all K0 all L all M0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),L)))) & p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),ordinal),s(fun(prod(A,A),bool),M0)))) -> (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),K0))),s(fun(prod(A,A),bool),L)))) & p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),K0))),s(fun(prod(A,A),bool),M0)))) -> s(fun(prod(A,A),bool),L) = s(fun(prod(A,A),bool),K0) | (exists A5 (s(fun(prod(A,A),bool),K0) = s(fun(prod(A,A),bool),i(s(fun(A,fun(prod(A,A),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(prod(A,A),bool))),linseg),s(fun(prod(A,A),bool),M0))),s(A,A5))) & s(fun(prod(A,A),bool),K0) = s(fun(prod(A,A),bool),i(s(fun(A,fun(prod(A,A),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(prod(A,A),bool))),linseg),s(fun(prod(A,A),bool),L))),s(A,A5))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),M0))),s(A,A5)))) & p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,A5)))))) | s(fun(prod(A,A),bool),M0) = s(fun(prod(A,A),bool),K0)))) # label(aORDINALu_CHAINEDu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2205 (all X all Y all Z0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,Y))))),s(real,Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,Y))),s(real,Z0)))))) # label(aREALu_MAXu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2206 (all A all X (p(s(bool,i(s(fun(fun(A,bool),bool),e_),s(fun(A,bool),X)))) <-> (all X0 s(bool,t) = s(bool,i(s(fun(A,bool),X),s(A,X0)))))) # label(aFORALLu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2207 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,N0))),s(num,M0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,M0))),s(num,N0)))) & (all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,M0))),s(num,N0)))))) & (all M0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,M0))),s(num,M0))))) -> (all M0 all Y p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),p0),s(num,M0))),s(num,Y))))) # label(aWLOGu_LT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2208 (all M0 all N0 ((exists Q0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,Q0))) = s(num,M0)) <-> (exists V ((p(s(bool,V)) <-> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,M0)) & (exists VI_ ((exists VI_I_ ((p(s(bool,VI_I_)) <-> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0)))) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,VI_))),s(bool,V))),s(bool,VI_I_)))))) & (s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> p(s(bool,VI_))))))))) # label(aMODu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2209 (all X all Y all Z0 (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))) <-> s(real,Y) = s(real,X) | s(real,Z0) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aREALu_EQu_MULu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2210 (all C all A all B all PAIRI_ exists FN all A01 all A10 s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),PAIRI_),s(A,A01))),s(B,A10))) = s(C,i(s(fun(prod(A,B),C),FN),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,A01))),s(B,A10)))))) # label(apairu_RECURSION) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2211 (all X s(int,X) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(int,X)))) # label(aINTu_MULu_LID) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2212 (all Q44069 all P0 all V all T0 (p(s(bool,P0)) & s(Q44069,T0) = s(Q44069,V) <-> p(s(bool,i(s(fun(Q44069,bool),i(s(fun(bool,fun(Q44069,bool)),i(s(fun(Q44069,fun(bool,fun(Q44069,bool))),setspec),s(Q44069,V))),s(bool,P0))),s(Q44069,T0)))))) # label(aSETSPEC) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2213 (all A all S0 all T0 p(s(bool,i(s(fun(fun(sum0(A,A),bool),bool),i(s(fun(fun(A,bool),fun(fun(sum0(A,A),bool),bool)),l_a_u_c),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(sum0(A,A),bool),i(s(fun(fun(A,bool),fun(sum0(A,A),bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(sum0(A,A),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(A,bool),T0))))))) # label(aUNIONu_LEu_ADDu_C) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2214 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(num,N0))),s(num,M0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),max),s(num,M0))),s(num,N0)))) # label(aMAX) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2215 (all Q49353 all Q49352 all Q49351 all Q49327 all U_1 ((all P0 all F0 all GENR_PVARR_40 (p(s(bool,i(s(fun(Q49327,bool),i(s(fun(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),fun(Q49327,bool)),i(s(fun(fun(Q49353,fun(Q49352,fun(Q49351,bool))),fun(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),fun(Q49327,bool))),U_1),s(fun(Q49353,fun(Q49352,fun(Q49351,bool))),P0))),s(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),F0))),s(Q49327,GENR_PVARR_40)))) <-> (exists A5 exists V ((p(s(bool,V)) <-> (all X all Y all Z0 (p(s(bool,i(s(fun(Q49351,bool),i(s(fun(Q49352,fun(Q49351,bool)),i(s(fun(Q49353,fun(Q49352,fun(Q49351,bool))),P0),s(Q49353,X))),s(Q49352,Y))),s(Q49351,Z0)))) -> p(s(bool,i(s(fun(fun(Q49327,bool),bool),i(s(fun(Q49327,fun(fun(Q49327,bool),bool)),in),s(Q49327,A5))),s(fun(Q49327,bool),i(s(fun(Q49351,fun(Q49327,bool)),i(s(fun(Q49352,fun(Q49351,fun(Q49327,bool))),i(s(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),F0),s(Q49353,X))),s(Q49352,Y))),s(Q49351,Z0))))))))) & p(s(bool,i(s(fun(Q49327,bool),i(s(fun(bool,fun(Q49327,bool)),i(s(fun(Q49327,fun(bool,fun(Q49327,bool))),setspec),s(Q49327,GENR_PVARR_40))),s(bool,V))),s(Q49327,A5)))))))) -> (all U_0 ((all P0 all F0 all GENR_PVARR_39 ((exists X exists Y exists Z0 p(s(bool,i(s(fun(fun(Q49327,bool),bool),i(s(fun(bool,fun(fun(Q49327,bool),bool)),i(s(fun(fun(Q49327,bool),fun(bool,fun(fun(Q49327,bool),bool))),setspec),s(fun(Q49327,bool),GENR_PVARR_39))),s(bool,i(s(fun(Q49351,bool),i(s(fun(Q49352,fun(Q49351,bool)),i(s(fun(Q49353,fun(Q49352,fun(Q49351,bool))),P0),s(Q49353,X))),s(Q49352,Y))),s(Q49351,Z0))))),s(fun(Q49327,bool),i(s(fun(Q49351,fun(Q49327,bool)),i(s(fun(Q49352,fun(Q49351,fun(Q49327,bool))),i(s(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),F0),s(Q49353,X))),s(Q49352,Y))),s(Q49351,Z0))))))) <-> p(s(bool,i(s(fun(fun(Q49327,bool),bool),i(s(fun(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),fun(fun(Q49327,bool),bool)),i(s(fun(fun(Q49353,fun(Q49352,fun(Q49351,bool))),fun(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),fun(fun(Q49327,bool),bool))),U_0),s(fun(Q49353,fun(Q49352,fun(Q49351,bool))),P0))),s(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),F0))),s(fun(Q49327,bool),GENR_PVARR_39)))))) -> (all P0 all F0 s(fun(Q49327,bool),i(s(fun(fun(fun(Q49327,bool),bool),fun(Q49327,bool)),inters),s(fun(fun(Q49327,bool),bool),i(s(fun(fun(fun(Q49327,bool),bool),fun(fun(Q49327,bool),bool)),gspec),s(fun(fun(Q49327,bool),bool),i(s(fun(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),fun(fun(Q49327,bool),bool)),i(s(fun(fun(Q49353,fun(Q49352,fun(Q49351,bool))),fun(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),fun(fun(Q49327,bool),bool))),U_0),s(fun(Q49353,fun(Q49352,fun(Q49351,bool))),P0))),s(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),F0))))))) = s(fun(Q49327,bool),i(s(fun(fun(Q49327,bool),fun(Q49327,bool)),gspec),s(fun(Q49327,bool),i(s(fun(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),fun(Q49327,bool)),i(s(fun(fun(Q49353,fun(Q49352,fun(Q49351,bool))),fun(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),fun(Q49327,bool))),U_1),s(fun(Q49353,fun(Q49352,fun(Q49351,bool))),P0))),s(fun(Q49353,fun(Q49352,fun(Q49351,fun(Q49327,bool)))),F0)))))))))) # label(aINTERSu_GSPECu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2216 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) & s(fun(A,bool),empty) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),T0))))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))))) # label(aCARDu_UNION) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2217 (all B all A all B0 all F0 all G0 all X s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,B0))),s(B,i(s(fun(A,B),F0),s(A,X))))),s(B,i(s(fun(A,B),G0),s(A,X))))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),i(s(fun(fun(A,B),fun(fun(A,B),fun(A,B))),i(s(fun(bool,fun(fun(A,B),fun(fun(A,B),fun(A,B)))),cond),s(bool,B0))),s(fun(A,B),F0))),s(fun(A,B),G0))),s(A,X)))) # label(aCONDu_RATOR) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2218 (all F0 all G0 all M0 all N0 ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,I0)))) -> s(real,i(s(fun(num,real),G0),s(num,I0))) = s(real,i(s(fun(num,real),F0),s(num,I0))))) -> s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),G0))))) # label(aSUMu_EQu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2219 (all A all S0 (s(fun(A,bool),empty) != s(fun(A,bool),S0) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(fun(A,bool),A),choice0),s(fun(A,bool),S0))))),s(fun(A,bool),S0)))))) # label(aCHOICEu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2220 (all A all P0 s(A,i(s(fun(fun(A,bool),A),h_),s(fun(A,bool),P0))) = s(A,i(s(fun(fun(A,bool),A),gabs),s(fun(A,bool),P0)))) # label(aGABSu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2221 (all N0 s(bool,f0) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,u_0)))) # label(aARITHu_LTu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2222 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),suc),s(num,M0))))),s(num,N0)))) # label(aMULTu_CLAUSESu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2223 p(s(bool,p1)) | p(s(bool,q)) | p(s(bool,r0)) <-> p(s(bool,r0)) | p(s(bool,q)) | p(s(bool,p1)) # label(aDISJu_ACIu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2224 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,Z0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Z0)))))) # label(aINTu_LEu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2225 (all Q49497 all U_0 ((all S0 all T0 all GENR_PVARR_44 (p(s(bool,i(s(fun(fun(Q49497,bool),bool),i(s(fun(fun(Q49497,bool),fun(fun(Q49497,bool),bool)),i(s(fun(fun(fun(Q49497,bool),bool),fun(fun(Q49497,bool),fun(fun(Q49497,bool),bool))),U_0),s(fun(fun(Q49497,bool),bool),S0))),s(fun(Q49497,bool),T0))),s(fun(Q49497,bool),GENR_PVARR_44)))) <-> (exists X p(s(bool,i(s(fun(fun(Q49497,bool),bool),i(s(fun(bool,fun(fun(Q49497,bool),bool)),i(s(fun(fun(Q49497,bool),fun(bool,fun(fun(Q49497,bool),bool))),setspec),s(fun(Q49497,bool),GENR_PVARR_44))),s(bool,i(s(fun(fun(fun(Q49497,bool),bool),bool),i(s(fun(fun(Q49497,bool),fun(fun(fun(Q49497,bool),bool),bool)),in),s(fun(Q49497,bool),X))),s(fun(fun(Q49497,bool),bool),S0))))),s(fun(Q49497,bool),i(s(fun(fun(Q49497,bool),fun(Q49497,bool)),i(s(fun(fun(Q49497,bool),fun(fun(Q49497,bool),fun(Q49497,bool))),diff),s(fun(Q49497,bool),X))),s(fun(Q49497,bool),T0))))))))) -> (all S0 all T0 s(fun(Q49497,bool),i(s(fun(fun(fun(Q49497,bool),bool),fun(Q49497,bool)),unions),s(fun(fun(Q49497,bool),bool),i(s(fun(fun(fun(Q49497,bool),bool),fun(fun(Q49497,bool),bool)),gspec),s(fun(fun(Q49497,bool),bool),i(s(fun(fun(Q49497,bool),fun(fun(Q49497,bool),bool)),i(s(fun(fun(fun(Q49497,bool),bool),fun(fun(Q49497,bool),fun(fun(Q49497,bool),bool))),U_0),s(fun(fun(Q49497,bool),bool),S0))),s(fun(Q49497,bool),T0))))))) = s(fun(Q49497,bool),i(s(fun(fun(Q49497,bool),fun(Q49497,bool)),i(s(fun(fun(Q49497,bool),fun(fun(Q49497,bool),fun(Q49497,bool))),diff),s(fun(Q49497,bool),i(s(fun(fun(fun(Q49497,bool),bool),fun(Q49497,bool)),unions),s(fun(fun(Q49497,bool),bool),S0))))),s(fun(Q49497,bool),T0)))))) # label(aUNIONSu_DIFF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2226 (all U_0 ((all X all I0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))),s(num,I0)))) -> (all X all M0 all N0 exists V (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,M0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),suc),s(num,N0))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X))))))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))))) & (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,X) <-> p(s(bool,V))))))) # label(aSUMu_GP) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2227 (all X all Y s(int,i(s(fun(real,int),intu_ofu_real),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y))))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y)))) # label(aintu_sub) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2228 (all N0 s(num,i(s(fun(num,num),bit1),s(num,N0))) = s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,N0)))))) # label(aBIT1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2229 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,N0))),s(num,M0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,i(s(fun(num,num),bit1),s(num,M0)))))) # label(aARITHu_GTu_conjunct8) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2230 (all Q51863 all S0 all T0 (p(s(bool,i(s(fun(fun(Q51863,bool),bool),finite),s(fun(Q51863,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q51863,bool),bool),finite),s(fun(Q51863,bool),i(s(fun(fun(Q51863,bool),fun(Q51863,bool)),i(s(fun(fun(Q51863,bool),fun(fun(Q51863,bool),fun(Q51863,bool))),diff),s(fun(Q51863,bool),S0))),s(fun(Q51863,bool),T0)))))))) # label(aFINITEu_DIFF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2231 (all X all M0 all N0 (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(real,X) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,M0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))))))),s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,M0))))))))))) # label(aREALu_DIVu_POW2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2232 (all A all T0 s(A,T0) = s(A,i(s(fun(A,A),letu_end),s(A,T0)))) # label(aLETu_ENDu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2233 (all A s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),empty)))) # label(aCARDu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2234 (all A all B all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all P0 (p(s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(fun(B,fun(B,B)),B),neutral),s(fun(B,fun(B,B)),OP)))))) & (all X all Y (p(s(bool,i(s(fun(B,bool),P0),s(B,X)))) & p(s(bool,i(s(fun(B,bool),P0),s(B,Y)))) -> p(s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),OP),s(B,X))),s(B,Y)))))))) -> (all F0 all S0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,X))) != s(B,i(s(fun(fun(B,fun(B,B)),B),neutral),s(fun(B,fun(B,B)),OP))) -> p(s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(A,B),F0),s(A,X)))))))) -> p(s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0)))))))))))) # label(aITERATEu_CLOSED) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2235 (all X exists B0 all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,M0))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,N0))))))) # label(aNADDu_DISTu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2236 (all Q93047 all X all S0 s(bool,i(s(fun(fun(Q93047,bool),bool),countable),s(fun(Q93047,bool),i(s(fun(fun(Q93047,bool),fun(Q93047,bool)),i(s(fun(Q93047,fun(fun(Q93047,bool),fun(Q93047,bool))),insert),s(Q93047,X))),s(fun(Q93047,bool),S0))))) = s(bool,i(s(fun(fun(Q93047,bool),bool),countable),s(fun(Q93047,bool),S0)))) # label(aCOUNTABLEu_INSERT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2237 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,P0)))) # label(aADDu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2238 (all Q18603 s(bool,t) = s(bool,i(s(fun(list(Q18603),bool),i(s(fun(fun(Q18603,bool),fun(list(Q18603),bool)),all0),s(fun(Q18603,bool),p0))),s(list(Q18603),nil)))) # label(aALLu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2239 (all A all S0 all N0 ((all A5 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,A5))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,A5))))),s(num,N0)))))) & s(fun(A,bool),S0) != s(fun(A,bool),empty) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,i(s(fun(num,num),suc),s(num,N0)))))))) # label(aHASu_SIZEu_SUC) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2240 (all A all B all S0 all T0 all F0 all G0 all H0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),H0),s(A,X))))),s(fun(B,bool),T0)))) & s(real,i(s(fun(A,real),F0),s(A,X))) = s(real,i(s(fun(B,real),G0),s(B,i(s(fun(A,B),H0),s(A,X))))))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> (all X all XI_ (s(B,i(s(fun(A,B),H0),s(A,X))) = s(B,Y) & s(B,i(s(fun(A,B),H0),s(A,XI_))) = s(B,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,X) = s(A,XI_))) & (exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,Y) = s(B,i(s(fun(A,B),H0),s(A,X))))))) -> s(real,i(s(fun(fun(B,real),real),i(s(fun(fun(B,bool),fun(fun(B,real),real)),sum),s(fun(B,bool),T0))),s(fun(B,real),G0))) = s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))) # label(aSUMu_EQu_GENERAL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2241 (all X all K0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,K0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_neg),s(real,K0))))),s(real,X)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,X))))),s(real,K0)))))) # label(aREALu_ABSu_BOUNDS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2242 (all X all Y all N0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),i(s(fun(real,fun(real,fun(real,bool))),realu_mod),s(real,N0))),s(real,X))),s(real,Y)))) <-> (exists Q0 (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Q0))),s(real,N0))) & p(s(bool,i(s(fun(real,bool),integer),s(real,Q0)))))))) # label(arealu_mod) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2243 (all Q69646 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q69646,bool),bool),finite),s(fun(Q69646,bool),S0)))) & p(s(bool,i(s(fun(fun(Q69646,bool),bool),finite),s(fun(Q69646,bool),T0)))) & (all X (p(s(bool,i(s(fun(fun(Q69646,bool),bool),i(s(fun(Q69646,fun(fun(Q69646,bool),bool)),in),s(Q69646,X))),s(fun(Q69646,bool),i(s(fun(fun(Q69646,bool),fun(Q69646,bool)),i(s(fun(fun(Q69646,bool),fun(fun(Q69646,bool),fun(Q69646,bool))),inter),s(fun(Q69646,bool),S0))),s(fun(Q69646,bool),T0)))))) -> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(Q69646,num),F0),s(Q69646,X))))) -> s(num,i(s(fun(fun(Q69646,num),num),i(s(fun(fun(Q69646,bool),fun(fun(Q69646,num),num)),nsum),s(fun(Q69646,bool),i(s(fun(fun(Q69646,bool),fun(Q69646,bool)),i(s(fun(fun(Q69646,bool),fun(fun(Q69646,bool),fun(Q69646,bool))),union),s(fun(Q69646,bool),S0))),s(fun(Q69646,bool),T0))))),s(fun(Q69646,num),F0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(Q69646,num),num),i(s(fun(fun(Q69646,bool),fun(fun(Q69646,num),num)),nsum),s(fun(Q69646,bool),S0))),s(fun(Q69646,num),F0))))),s(num,i(s(fun(fun(Q69646,num),num),i(s(fun(fun(Q69646,bool),fun(fun(Q69646,num),num)),nsum),s(fun(Q69646,bool),T0))),s(fun(Q69646,num),F0))))))) # label(aNSUMu_UNIONu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2244 (all Q66926 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q66926,bool),bool),finite),s(fun(Q66926,bool),S0)))) & p(s(bool,i(s(fun(fun(Q66926,bool),bool),i(s(fun(fun(Q66926,bool),fun(fun(Q66926,bool),bool)),subset),s(fun(Q66926,bool),T0))),s(fun(Q66926,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(fun(Q66926,num),num),i(s(fun(fun(Q66926,bool),fun(fun(Q66926,num),num)),nsum),s(fun(Q66926,bool),S0))),s(fun(Q66926,num),F0))))),s(num,i(s(fun(fun(Q66926,num),num),i(s(fun(fun(Q66926,bool),fun(fun(Q66926,num),num)),nsum),s(fun(Q66926,bool),T0))),s(fun(Q66926,num),F0))))) = s(num,i(s(fun(fun(Q66926,num),num),i(s(fun(fun(Q66926,bool),fun(fun(Q66926,num),num)),nsum),s(fun(Q66926,bool),i(s(fun(fun(Q66926,bool),fun(Q66926,bool)),i(s(fun(fun(Q66926,bool),fun(fun(Q66926,bool),fun(Q66926,bool))),diff),s(fun(Q66926,bool),S0))),s(fun(Q66926,bool),T0))))),s(fun(Q66926,num),F0))))) # label(aNSUMu_DIFF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2245 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0))))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,Y))),s(real,Z0))))))) # label(aREALu_LTu_RDIVu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2246 (all Q79285 all Q79290 all Q79289 all Q79249 all U_0 ((all Y s(bool,i(s(fun(Q79249,bool),U_0),s(Q79249,Y))) = s(bool,t)) -> s(Q79249,i(s(fun(fun(Q79249,bool),Q79249),h_),s(fun(Q79249,bool),U_0))) = s(Q79249,i(s(fun(Q79289,Q79249),i(s(fun(Q79290,fun(Q79289,Q79249)),i(s(fun(list(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249)))),fun(Q79290,fun(Q79289,Q79249))),casewise),s(list(prod(fun(Q79285,Q79289),fun(Q79290,fun(Q79285,Q79249)))),nil))),s(Q79290,f))),s(Q79289,x))))) # label(aCASEWISEu_DEFu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2247 (all A all L all M0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) & p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),M0))),s(fun(prod(A,A),bool),L)))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),M0)))))) # label(aINSEGu_WOSET) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2248 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,Y))),s(real,X))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,Y)))) # label(aREALu_MAXu_SYM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2249 (all X all Y p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,Y))))))) # label(aNADDu_LEu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2250 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),realu_inv),s(real,Y)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,i(s(fun(real,real),realu_inv),s(real,X)))))))) # label(aREALu_LEu_RINV) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2251 (all Q93264 (p(s(bool,i(s(fun(fun(Q93264,bool),bool),p0),s(fun(Q93264,bool),empty)))) & (all F0 p(s(bool,i(s(fun(fun(Q93264,bool),bool),p0),s(fun(Q93264,bool),i(s(fun(fun(num,bool),fun(Q93264,bool)),i(s(fun(fun(num,Q93264),fun(fun(num,bool),fun(Q93264,bool))),image),s(fun(num,Q93264),F0))),s(fun(num,bool),univ))))))) <-> (all D0 (p(s(bool,i(s(fun(fun(Q93264,bool),bool),countable),s(fun(Q93264,bool),D0)))) -> p(s(bool,i(s(fun(fun(Q93264,bool),bool),p0),s(fun(Q93264,bool),D0)))))))) # label(aFORALLu_COUNTABLEu_ASu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2252 (all X all Y all Z0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))),s(int,Z0))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Z0))),s(int,Y)))))) # label(aINTu_LEu_SUBu_RADD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2253 (all S0 (p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) & s(fun(real,bool),empty) != s(fun(real,bool),S0) -> p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0))))),s(fun(real,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),S0)))))))))) # label(aSUPu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2254 (all Q19878 all P0 all L (p(s(bool,i(s(fun(list(Q19878),bool),i(s(fun(fun(Q19878,bool),fun(list(Q19878),bool)),all0),s(fun(Q19878,bool),P0))),s(list(Q19878),L)))) <-> (all X (p(s(bool,i(s(fun(list(Q19878),bool),i(s(fun(Q19878,fun(list(Q19878),bool)),mem),s(Q19878,X))),s(list(Q19878),L)))) -> p(s(bool,i(s(fun(Q19878,bool),P0),s(Q19878,X)))))))) # label(aALLu_MEM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2255 (all X all N0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0)))))))) # label(aINTu_POWu_LE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2256 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))))) # label(aFINITEu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2257 (all A all S0 all T0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),T0))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,bool),T0)))) # label(aDIFFu_DIFF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2258 (all Q97584 all P0 all S0 ((all F0 ((all S0 (p(s(bool,i(s(fun(fun(fun(Q97584,bool),bool),bool),i(s(fun(fun(Q97584,bool),fun(fun(fun(Q97584,bool),bool),bool)),in),s(fun(Q97584,bool),S0))),s(fun(fun(Q97584,bool),bool),F0)))) -> p(s(bool,i(s(fun(fun(Q97584,bool),bool),P0),s(fun(Q97584,bool),S0)))))) -> p(s(bool,i(s(fun(fun(Q97584,bool),bool),P0),s(fun(Q97584,bool),i(s(fun(fun(fun(Q97584,bool),bool),fun(Q97584,bool)),inters),s(fun(fun(Q97584,bool),bool),F0)))))))) -> (p(s(bool,i(s(fun(fun(Q97584,bool),bool),P0),s(fun(Q97584,bool),S0)))) <-> (exists T0 s(fun(Q97584,bool),S0) = s(fun(Q97584,bool),i(s(fun(fun(Q97584,bool),fun(Q97584,bool)),i(s(fun(fun(fun(Q97584,bool),bool),fun(fun(Q97584,bool),fun(Q97584,bool))),hull),s(fun(fun(Q97584,bool),bool),P0))),s(fun(Q97584,bool),T0))))))) # label(aISu_HULL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2259 (all Q20949 all L (s(list(Q20949),L) != s(list(Q20949),nil) -> s(list(Q20949),i(s(fun(list(Q20949),list(Q20949)),i(s(fun(Q20949,fun(list(Q20949),list(Q20949))),cons),s(Q20949,i(s(fun(list(Q20949),Q20949),hd),s(list(Q20949),L))))),s(list(Q20949),i(s(fun(list(Q20949),list(Q20949)),tl),s(list(Q20949),L))))) = s(list(Q20949),L))) # label(aCONSu_HDu_TL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2260 (all Q4047 all Q4051 all U_0 ((all Z0 s(bool,f0) = s(bool,i(s(fun(Q4051,bool),U_0),s(Q4051,Z0)))) -> (all X all X0 exists V (((all X1 all Y (p(s(bool,i(s(fun(Q4051,bool),i(s(fun(Q4047,fun(Q4051,bool)),X0),s(Q4047,X))),s(Q4051,X1)))) & p(s(bool,i(s(fun(Q4051,bool),i(s(fun(Q4047,fun(Q4051,bool)),X0),s(Q4047,X))),s(Q4051,Y)))) -> s(Q4051,X1) = s(Q4051,Y))) & p(s(bool,i(s(fun(fun(Q4051,bool),bool),q_),s(fun(Q4051,bool),i(s(fun(Q4047,fun(Q4051,bool)),X0),s(Q4047,X)))))) <-> p(s(bool,V))) & s(Q4051,i(s(fun(fun(Q4047,fun(Q4051,bool)),Q4051),i(s(fun(Q4047,fun(fun(Q4047,fun(Q4051,bool)),Q4051)),u_match),s(Q4047,X))),s(fun(Q4047,fun(Q4051,bool)),X0))) = s(Q4051,i(s(fun(Q4051,Q4051),i(s(fun(Q4051,fun(Q4051,Q4051)),i(s(fun(bool,fun(Q4051,fun(Q4051,Q4051))),cond),s(bool,V))),s(Q4051,i(s(fun(fun(Q4051,bool),Q4051),h_),s(fun(Q4051,bool),i(s(fun(Q4047,fun(Q4051,bool)),X0),s(Q4047,X))))))),s(Q4051,i(s(fun(fun(Q4051,bool),Q4051),h_),s(fun(Q4051,bool),U_0))))))))) # label(au_MATCH) # label(axiom) # label(non_clause). [assumption]. 14.64/14.67 2261 (all F0 all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,P0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),F0))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,N0))),s(num,P0))))),s(fun(num,real),F0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,P0))))),s(fun(num,real),F0))))) # label(aSUMu_COMBINEu_L) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2262 (all A all B all U_0 ((all S0 all F0 all GENR_PVARR_7 ((exists Y exists V ((p(s(bool,V)) <-> (exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y)))) & p(s(bool,i(s(fun(B,bool),i(s(fun(bool,fun(B,bool)),i(s(fun(B,fun(bool,fun(B,bool))),setspec),s(B,GENR_PVARR_7))),s(bool,V))),s(B,Y)))))) <-> p(s(bool,i(s(fun(B,bool),i(s(fun(fun(A,B),fun(B,bool)),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,GENR_PVARR_7)))))) -> (all S0 all F0 s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),gspec),s(fun(B,bool),i(s(fun(fun(A,B),fun(B,bool)),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))))) = s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0)))))) # label(aIMAGE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2263 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))))) # label(aREALu_LTu_MULu_EQu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2264 (all N0 all X all Y (s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(real,Y) = s(real,X))) # label(aREALu_POWu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2265 (all B all A all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),countable),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0)))))))) # label(aCOUNTABLEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2266 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,Y))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))) # label(aREALu_SUBu_LNEG) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2267 (all Q18568 s(list(Q18568),i(s(fun(Q18568,list(Q18568)),i(s(fun(num,fun(Q18568,list(Q18568))),replicate),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(Q18568,x))) = s(list(Q18568),nil)) # label(aREPLICATEu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2268 (all Q44207 all U_0 ((all P0 all Y s(bool,i(s(fun(Q44207,bool),i(s(fun(fun(Q44207,bool),fun(Q44207,bool)),U_0),s(fun(Q44207,bool),P0))),s(Q44207,Y))) = s(bool,i(s(fun(Q44207,bool),P0),s(Q44207,Y)))) -> (all P0 all X s(bool,i(s(fun(fun(Q44207,bool),bool),i(s(fun(Q44207,fun(fun(Q44207,bool),bool)),in),s(Q44207,X))),s(fun(Q44207,bool),i(s(fun(fun(Q44207,bool),fun(Q44207,bool)),U_0),s(fun(Q44207,bool),P0))))) = s(bool,i(s(fun(Q44207,bool),P0),s(Q44207,X)))))) # label(aINu_ELIMu_THMu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2269 (all Q63996 all Q63990 all OP all F0 all S0 s(Q63990,i(s(fun(fun(Q63996,Q63990),Q63990),i(s(fun(fun(Q63996,bool),fun(fun(Q63996,Q63990),Q63990)),i(s(fun(fun(Q63990,fun(Q63990,Q63990)),fun(fun(Q63996,bool),fun(fun(Q63996,Q63990),Q63990))),iterate),s(fun(Q63990,fun(Q63990,Q63990)),OP))),s(fun(Q63996,bool),S0))),s(fun(Q63996,Q63990),F0))) = s(Q63990,i(s(fun(Q63990,Q63990),i(s(fun(Q63990,fun(Q63990,Q63990)),i(s(fun(bool,fun(Q63990,fun(Q63990,Q63990))),cond),s(bool,i(s(fun(fun(Q63996,bool),bool),finite),s(fun(Q63996,bool),i(s(fun(fun(Q63996,bool),fun(Q63996,bool)),i(s(fun(fun(Q63996,Q63990),fun(fun(Q63996,bool),fun(Q63996,bool))),i(s(fun(fun(Q63990,fun(Q63990,Q63990)),fun(fun(Q63996,Q63990),fun(fun(Q63996,bool),fun(Q63996,bool)))),support),s(fun(Q63990,fun(Q63990,Q63990)),OP))),s(fun(Q63996,Q63990),F0))),s(fun(Q63996,bool),S0))))))),s(Q63990,i(s(fun(fun(Q63996,Q63990),Q63990),i(s(fun(fun(Q63996,bool),fun(fun(Q63996,Q63990),Q63990)),i(s(fun(fun(Q63990,fun(Q63990,Q63990)),fun(fun(Q63996,bool),fun(fun(Q63996,Q63990),Q63990))),iterate),s(fun(Q63990,fun(Q63990,Q63990)),OP))),s(fun(Q63996,bool),i(s(fun(fun(Q63996,bool),fun(Q63996,bool)),i(s(fun(fun(Q63996,Q63990),fun(fun(Q63996,bool),fun(Q63996,bool))),i(s(fun(fun(Q63990,fun(Q63990,Q63990)),fun(fun(Q63996,Q63990),fun(fun(Q63996,bool),fun(Q63996,bool)))),support),s(fun(Q63990,fun(Q63990,Q63990)),OP))),s(fun(Q63996,Q63990),F0))),s(fun(Q63996,bool),S0))))),s(fun(Q63996,Q63990),F0))))),s(Q63990,i(s(fun(fun(Q63990,fun(Q63990,Q63990)),Q63990),neutral),s(fun(Q63990,fun(Q63990,Q63990)),OP)))))) # label(aITERATEu_EXPANDu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2270 (all X all Y all Z0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Z0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Y))),s(int,Z0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y))))),s(int,Z0)))) # label(aINTu_ADDu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2271 (all A all P0 (p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),empty)))) & (all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & s(fun(A,bool),empty) != s(fun(A,bool),S0) -> (exists X ((p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X)))))) -> p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),S0))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))))) -> (all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),S0)))))))) # label(aFINITEu_INDUCTu_DELETE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2272 (all A all S0 s(fun(A,bool),S0) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),S0)))) # label(aINTERu_IDEMPOT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2273 (all Q48121 all Q48105 all P0 all F0 all S0 ((exists T0 (p(s(bool,i(s(fun(fun(Q48121,bool),bool),P0),s(fun(Q48121,bool),T0)))) & p(s(bool,i(s(fun(fun(Q48121,bool),bool),i(s(fun(fun(Q48121,bool),fun(fun(Q48121,bool),bool)),subset),s(fun(Q48121,bool),T0))),s(fun(Q48121,bool),i(s(fun(fun(Q48105,bool),fun(Q48121,bool)),i(s(fun(fun(Q48105,Q48121),fun(fun(Q48105,bool),fun(Q48121,bool))),image),s(fun(Q48105,Q48121),F0))),s(fun(Q48105,bool),S0)))))))) <-> (exists T0 (p(s(bool,i(s(fun(fun(Q48105,bool),bool),i(s(fun(fun(Q48105,bool),fun(fun(Q48105,bool),bool)),subset),s(fun(Q48105,bool),T0))),s(fun(Q48105,bool),S0)))) & p(s(bool,i(s(fun(fun(Q48121,bool),bool),P0),s(fun(Q48121,bool),i(s(fun(fun(Q48105,bool),fun(Q48121,bool)),i(s(fun(fun(Q48105,Q48121),fun(fun(Q48105,bool),fun(Q48121,bool))),image),s(fun(Q48105,Q48121),F0))),s(fun(Q48105,bool),T0)))))))))) # label(aEXISTSu_SUBSETu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2274 (all X all K0 (-p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,X))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (exists N0 p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,K0))))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,N0))))),s(nadd,X))))))))) # label(aNADDu_ARCHu_MULT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2275 (all X p(s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(prod(hreal,hreal),prod(hreal,hreal)),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),prod(hreal,hreal))),trealu_mul),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(prod(hreal,hreal),X))))),s(prod(hreal,hreal),X))))) # label(aTREALu_MULu_LID) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2276 (all B all A all U_0 ((all F0 all R0 all N0 s(B,i(s(fun(recspace(A),B),F0),s(recspace(A),i(s(fun(num,recspace(A)),R0),s(num,N0))))) = s(B,i(s(fun(num,B),i(s(fun(fun(num,recspace(A)),fun(num,B)),i(s(fun(fun(recspace(A),B),fun(fun(num,recspace(A)),fun(num,B))),U_0),s(fun(recspace(A),B),F0))),s(fun(num,recspace(A)),R0))),s(num,N0)))) -> (all FN exists F0 all C0 all I0 all R0 s(B,i(s(fun(fun(num,B),B),i(s(fun(fun(num,recspace(A)),fun(fun(num,B),B)),i(s(fun(A,fun(fun(num,recspace(A)),fun(fun(num,B),B))),i(s(fun(num,fun(A,fun(fun(num,recspace(A)),fun(fun(num,B),B)))),FN),s(num,C0))),s(A,I0))),s(fun(num,recspace(A)),R0))),s(fun(num,B),i(s(fun(fun(num,recspace(A)),fun(num,B)),i(s(fun(fun(recspace(A),B),fun(fun(num,recspace(A)),fun(num,B))),U_0),s(fun(recspace(A),B),F0))),s(fun(num,recspace(A)),R0))))) = s(B,i(s(fun(recspace(A),B),F0),s(recspace(A),i(s(fun(fun(num,recspace(A)),recspace(A)),i(s(fun(A,fun(fun(num,recspace(A)),recspace(A))),i(s(fun(num,fun(A,fun(fun(num,recspace(A)),recspace(A)))),constr),s(num,C0))),s(A,I0))),s(fun(num,recspace(A)),R0)))))))) # label(aCONSTRu_REC) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2277 (all M0 all N0 s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))) # label(aADDu_SUBR2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2278 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(num,N0)) # label(aEXPu_1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2279 (all C all A all B all F0 all X all Y s(C,i(s(fun(prod(A,B),C),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y))))) = s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),i(s(fun(fun(prod(A,B),C),fun(A,fun(B,C))),curry),s(fun(prod(A,B),C),F0))),s(A,X))),s(B,Y)))) # label(aCURRYu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2280 (all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,num),F0))))),s(num,i(s(fun(num,num),F0),s(num,N0))))) = s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,num),F0))))) # label(aNSUMu_CLAUSESu_RIGHT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2281 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_max),s(real,X))),s(real,Y))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,i(s(fun(real,real),realu_neg),s(real,Y)))))))) # label(aREALu_MAXu_MIN) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2282 (all Q18583 s(bool,f0) = s(bool,i(s(fun(list(Q18583),bool),null),s(list(Q18583),i(s(fun(list(Q18583),list(Q18583)),i(s(fun(Q18583,fun(list(Q18583),list(Q18583))),cons),s(Q18583,h0))),s(list(Q18583),t0)))))) # label(aNULLu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2283 (all Q58464 all R0 all X all S0 (p(s(bool,i(s(fun(fun(Q58464,bool),bool),i(s(fun(fun(Q58464,fun(Q58464,bool)),fun(fun(Q58464,bool),bool)),pairwise),s(fun(Q58464,fun(Q58464,bool)),R0))),s(fun(Q58464,bool),S0)))) & (all Y (p(s(bool,i(s(fun(fun(Q58464,bool),bool),i(s(fun(Q58464,fun(fun(Q58464,bool),bool)),in),s(Q58464,Y))),s(fun(Q58464,bool),S0)))) & s(Q58464,X) != s(Q58464,Y) -> p(s(bool,i(s(fun(Q58464,bool),i(s(fun(Q58464,fun(Q58464,bool)),R0),s(Q58464,Y))),s(Q58464,X)))) & p(s(bool,i(s(fun(Q58464,bool),i(s(fun(Q58464,fun(Q58464,bool)),R0),s(Q58464,X))),s(Q58464,Y)))))) <-> p(s(bool,i(s(fun(fun(Q58464,bool),bool),i(s(fun(fun(Q58464,fun(Q58464,bool)),fun(fun(Q58464,bool),bool)),pairwise),s(fun(Q58464,fun(Q58464,bool)),R0))),s(fun(Q58464,bool),i(s(fun(fun(Q58464,bool),fun(Q58464,bool)),i(s(fun(Q58464,fun(fun(Q58464,bool),fun(Q58464,bool))),insert),s(Q58464,X))),s(fun(Q58464,bool),S0)))))))) # label(aPAIRWISEu_INSERT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2284 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) -> s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))),s(num,i(s(fun(fun(B,bool),num),card),s(fun(B,bool),T0))))))) # label(aCARDu_LEu_CARD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2285 (all N0 s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) # label(aREALu_POWu_ONE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2286 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Z0))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Z0))))),s(real,Y))))) # label(aREALu_LEu_LDIVu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2287 (all M0 all N0 (s(int,i(s(fun(num,int),intu_ofu_num),s(num,N0))) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,M0))) <-> s(num,M0) = s(num,N0))) # label(aINTu_OFu_NUMu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2288 (all P0 ((all N0 ((all M0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),P0),s(num,M0)))))) -> p(s(bool,i(s(fun(num,bool),P0),s(num,N0)))))) -> (all N0 p(s(bool,i(s(fun(num,bool),P0),s(num,N0))))))) # label(anumu_WF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2289 (all N0 all X (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0)))))))) # label(aREALu_POWu_LTu_1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2290 (all X all Y all Z0 s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X))),s(hreal,Y))))),s(hreal,Z0))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,X))),s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,Y))),s(hreal,Z0)))))) # label(aHREALu_ADDu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2291 (all X all M0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,X) & s(num,N0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) & s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,M0) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,X)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0)))))))) # label(aLTu_EXP) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2292 (all W all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,W)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,W))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,W))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0)))))))) # label(aREALu_LTu_MUL2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2293 (all M0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> s(num,M0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))))))) # label(aDIVISIONu_SIMPu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2294 (all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,X))) = s(real,i(s(fun(real,real),realu_neg),s(real,X)))) # label(aREALu_NEGu_MINUS1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2295 (all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0)))))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,P0)))) & s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,M0))) # label(aLTu_MULTu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2296 (all Q96754 all P0 all S0 (p(s(bool,i(s(fun(fun(Q96754,bool),bool),P0),s(fun(Q96754,bool),S0)))) -> s(fun(Q96754,bool),i(s(fun(fun(Q96754,bool),fun(Q96754,bool)),i(s(fun(fun(fun(Q96754,bool),bool),fun(fun(Q96754,bool),fun(Q96754,bool))),hull),s(fun(fun(Q96754,bool),bool),P0))),s(fun(Q96754,bool),S0))) = s(fun(Q96754,bool),S0))) # label(aHULLu_P) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2297 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y)))))) # label(aREALu_LTu_ADDR) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2298 (all U_0 ((all U ((exists X exists Y (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_mul),s(nadd,X))),s(nadd,Y))))),s(nadd,U)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(hreal,fun(nadd,bool)),destu_hreal),s(hreal,y))),s(nadd,Y)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(hreal,fun(nadd,bool)),destu_hreal),s(hreal,x))),s(nadd,X)))))) <-> p(s(bool,i(s(fun(nadd,bool),U_0),s(nadd,U)))))) -> s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,x))),s(hreal,y))) = s(hreal,i(s(fun(fun(nadd,bool),hreal),mku_hreal),s(fun(nadd,bool),U_0))))) # label(ahrealu_mul) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2299 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))))) # label(aCOUNTABLEu_UNIONu_IMP) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2300 (all M0 all N0 (s(num,M0) = s(num,N0) <-> s(num,i(s(fun(num,num),suc),s(num,M0))) = s(num,i(s(fun(num,num),suc),s(num,N0))))) # label(aSUCu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2301 (all A all X -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),empty))))) # label(aNOTu_INu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2302 (all Q18672 s(bool,f0) = s(bool,i(s(fun(list(Q18672),bool),i(s(fun(Q18672,fun(list(Q18672),bool)),mem),s(Q18672,x))),s(list(Q18672),nil)))) # label(aMEMu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2303 (all B all A all F0 all S0 all N0 ((all X all Y (s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,i(s(fun(A,B),F0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,Y) = s(A,X))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(B,bool),fun(num,bool)),hasu_size),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(num,N0)))))) # label(aHASu_SIZEu_IMAGEu_INJ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2304 (exists B0 p(s(bool,i(s(fun(bool,bool),p0),s(bool,B0))))) <-> p(s(bool,i(s(fun(bool,bool),p0),s(bool,t)))) | p(s(bool,i(s(fun(bool,bool),p0),s(bool,f0)))) # label(aEXISTSu_BOOLu_THM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2305 (all W all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,W))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,W)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,W))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Z0)))))))) # label(aREALu_LEu_MUL2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2306 (all A all B all S0 all T0 all F0 all G0 all H0 all K0 ((all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(B,A),K0),s(B,Y))))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),H0),s(A,i(s(fun(B,A),K0),s(B,Y))))) = s(B,Y))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,i(s(fun(B,A),K0),s(B,i(s(fun(A,B),H0),s(A,X))))) = s(A,X) & s(num,i(s(fun(A,num),F0),s(A,X))) = s(num,i(s(fun(B,num),G0),s(B,i(s(fun(A,B),H0),s(A,X))))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),H0),s(A,X))))),s(fun(B,bool),T0)))))) -> s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))) = s(num,i(s(fun(fun(B,num),num),i(s(fun(fun(B,bool),fun(fun(B,num),num)),nsum),s(fun(B,bool),T0))),s(fun(B,num),G0))))) # label(aNSUMu_EQu_GENERALu_INVERSES) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2307 (all A all P0 all Q0 ((exists X (p(s(bool,Q0)) | p(s(bool,i(s(fun(A,bool),P0),s(A,X)))))) <-> p(s(bool,Q0)) | (exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) # label(aLEFTu_ORu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2308 (all A all S0 all T0 all U s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),T0))),s(fun(A,bool),U))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),U)))))) # label(aUNIONu_OVERu_INTER) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2309 (all B all A all F0 ((all X all Y (s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) -> s(A,Y) = s(A,X))) <-> (all L all M0 (s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),M0))) = s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),L))) -> s(list(A),L) = s(list(A),M0))))) # label(aINJECTIVEu_MAP) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2310 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))) # label(aLTu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2311 (all K0 all N0 s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,K0))),s(num,N0))) = s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(fun(num,bool),fun(fun(num,bool),fun(num,bool))),inter),s(fun(num,bool),i(s(fun(num,fun(num,bool)),from),s(num,K0))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))))) # label(aFROMu_INTERu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2312 (all N0 all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0)))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))))) # label(aREALu_POWu_LE2u_REV) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2313 (all Q45668 all S0 all T0 all U (p(s(bool,i(s(fun(fun(Q45668,bool),bool),i(s(fun(fun(Q45668,bool),fun(fun(Q45668,bool),bool)),subset),s(fun(Q45668,bool),S0))),s(fun(Q45668,bool),U)))) & p(s(bool,i(s(fun(fun(Q45668,bool),bool),i(s(fun(fun(Q45668,bool),fun(fun(Q45668,bool),bool)),subset),s(fun(Q45668,bool),T0))),s(fun(Q45668,bool),U)))) <-> p(s(bool,i(s(fun(fun(Q45668,bool),bool),i(s(fun(fun(Q45668,bool),fun(fun(Q45668,bool),bool)),subset),s(fun(Q45668,bool),i(s(fun(fun(Q45668,bool),fun(Q45668,bool)),i(s(fun(fun(Q45668,bool),fun(fun(Q45668,bool),fun(Q45668,bool))),union),s(fun(Q45668,bool),S0))),s(fun(Q45668,bool),T0))))),s(fun(Q45668,bool),U)))))) # label(aUNIONu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2314 (all F0 all M0 all N0 ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,N0)))) -> s(real,i(s(fun(num,real),F0),s(num,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) -> s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aSUMu_EQu_0u_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2315 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),T0)))))) # label(aCOUNTABLEu_UNION) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2316 (all X all Y s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y)))))) # label(aintu_mulu_th) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2317 (all A all S0 all T0 (s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))) = s(fun(A,bool),empty) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aDISJOINT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2318 p(s(bool,q)) & p(s(bool,p1)) & p(s(bool,p1)) <-> p(s(bool,p1)) & p(s(bool,q)) # label(aCONJu_ACIu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2319 (all A all B all R0 ((exists A5 exists B0 s(fun(A,fun(B,bool)),R0) = s(fun(A,fun(B,bool)),i(s(fun(B,fun(A,fun(B,bool))),i(s(fun(A,fun(B,fun(A,fun(B,bool)))),mku_pair),s(A,A5))),s(B,B0)))) <-> s(fun(A,fun(B,bool)),i(s(fun(prod(A,B),fun(A,fun(B,bool))),repu_prod),s(prod(A,B),i(s(fun(fun(A,fun(B,bool)),prod(A,B)),absu_prod),s(fun(A,fun(B,bool)),R0))))) = s(fun(A,fun(B,bool)),R0))) # label(aprodu_tybiju_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2320 (all X exists B0 exists N0 all N1 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,N1)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(nadd,fun(num,num)),destu_nadd),s(nadd,X))),s(num,N1))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,B0))),s(num,N1)))))))) # label(aNADDu_UBOUND) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2321 (all A all X all Y all Z0 (s(A,Y) = s(A,Z0) & s(A,X) = s(A,Y) -> s(A,X) = s(A,Z0))) # label(aEQu_TRANS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2322 (all B all A all F0 all L1 all L2 s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),L1))),s(list(A),L2))))) = s(list(B),i(s(fun(list(B),list(B)),i(s(fun(list(B),fun(list(B),list(B))),append),s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),L1))))),s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),L2)))))) # label(aMAPu_APPEND) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2323 (all Q60001 all Q60002 all T0 all S0 s(bool,i(s(fun(fun(Q60002,bool),bool),i(s(fun(fun(Q60001,bool),fun(fun(Q60002,bool),bool)),l_u_c),s(fun(Q60001,bool),T0))),s(fun(Q60002,bool),S0))) = s(bool,i(s(fun(fun(Q60001,bool),bool),i(s(fun(fun(Q60002,bool),fun(fun(Q60001,bool),bool)),g_u_c),s(fun(Q60002,bool),S0))),s(fun(Q60001,bool),T0)))) # label(agtu_c) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2324 (all Q44190 all U_0 ((all P0 all V ((exists Y p(s(bool,i(s(fun(Q44190,bool),i(s(fun(bool,fun(Q44190,bool)),i(s(fun(Q44190,fun(bool,fun(Q44190,bool))),setspec),s(Q44190,V))),s(bool,i(s(fun(Q44190,bool),P0),s(Q44190,Y))))),s(Q44190,Y))))) <-> p(s(bool,i(s(fun(Q44190,bool),i(s(fun(fun(Q44190,bool),fun(Q44190,bool)),U_0),s(fun(Q44190,bool),P0))),s(Q44190,V)))))) -> (all P0 all X s(bool,i(s(fun(Q44190,bool),P0),s(Q44190,X))) = s(bool,i(s(fun(Q44190,bool),i(s(fun(fun(Q44190,bool),fun(Q44190,bool)),gspec),s(fun(Q44190,bool),i(s(fun(fun(Q44190,bool),fun(Q44190,bool)),U_0),s(fun(Q44190,bool),P0))))),s(Q44190,X)))))) # label(aINu_ELIMu_THMu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2325 (all Q79301 all Q79350 all Q79349 all Q79309 all U_0 ((all Y s(bool,t) = s(bool,i(s(fun(Q79309,bool),U_0),s(Q79309,Y)))) -> s(Q79309,i(s(fun(fun(Q79309,bool),Q79309),h_),s(fun(Q79309,bool),U_0))) = s(Q79309,i(s(fun(Q79349,Q79309),i(s(fun(Q79350,fun(Q79349,Q79309)),i(s(fun(list(prod(fun(Q79301,Q79349),fun(Q79350,fun(Q79301,Q79309)))),fun(Q79350,fun(Q79349,Q79309))),casewise),s(list(prod(fun(Q79301,Q79349),fun(Q79350,fun(Q79301,Q79309)))),nil))),s(Q79350,f))),s(Q79349,x))))) # label(aCASEWISEu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2326 (all U_0 ((all GENR_PVARR_264 (p(s(bool,i(s(fun(fun(real,bool),bool),U_0),s(fun(real,bool),GENR_PVARR_264)))) <-> (exists S0 p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(bool,fun(fun(real,bool),bool)),i(s(fun(fun(real,bool),fun(bool,fun(fun(real,bool),bool))),setspec),s(fun(real,bool),GENR_PVARR_264))),s(bool,i(s(fun(fun(real,bool),bool),countable),s(fun(real,bool),S0))))),s(fun(real,bool),S0))))))) -> p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(fun(fun(real,bool),bool),fun(fun(real,bool),bool)),a_u_c),s(fun(fun(real,bool),bool),i(s(fun(fun(fun(real,bool),bool),fun(fun(real,bool),bool)),gspec),s(fun(fun(real,bool),bool),U_0))))),s(fun(real,bool),univ)))))) # label(aCARDu_EQu_COUNTABLEu_SUBSETSu_REAL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2327 (all A5 (s(ind0,indu_0) = s(ind0,A5) | (exists I0 (s(ind0,A5) = s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,I0))) & p(s(bool,i(s(fun(ind0,bool),numu_rep),s(ind0,I0)))))) <-> p(s(bool,i(s(fun(ind0,bool),numu_rep),s(ind0,A5)))))) # label(aNUMu_REPu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2328 (all X all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0))))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,Z0)))))) # label(aREALu_LTu_SUBu_LADD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2329 (all N0 -(p(s(bool,i(s(fun(num,bool),even),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))))) # label(aEVENu_ANDu_ODD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2330 (all Q58537 all U_1 ((all X all Y (p(s(bool,i(s(fun(Q58537,bool),i(s(fun(Q58537,fun(Q58537,bool)),U_1),s(Q58537,X))),s(Q58537,Y)))) <-> s(Q58537,X) != s(Q58537,Y))) -> (all U_0 ((all X s(fun(Q58537,bool),i(s(fun(Q58537,fun(Q58537,bool)),U_1),s(Q58537,X))) = s(fun(Q58537,bool),i(s(fun(Q58537,fun(Q58537,bool)),U_0),s(Q58537,X)))) -> (all L s(bool,i(s(fun(num,bool),i(s(fun(fun(Q58537,bool),fun(num,bool)),hasu_size),s(fun(Q58537,bool),i(s(fun(list(Q58537),fun(Q58537,bool)),setu_ofu_list),s(list(Q58537),L))))),s(num,i(s(fun(list(Q58537),num),length),s(list(Q58537),L))))) = s(bool,i(s(fun(list(Q58537),bool),i(s(fun(fun(Q58537,fun(Q58537,bool)),fun(list(Q58537),bool)),pairwise0),s(fun(Q58537,fun(Q58537,bool)),U_0))),s(list(Q58537),L)))))))) # label(aHASu_SIZEu_SETu_OFu_LIST) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2331 (all A all Q89498 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(Q89498,bool),fun(fun(A,bool),bool)),a_u_c),s(fun(Q89498,bool),S0))),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q89498,bool),bool),finite),s(fun(Q89498,bool),S0)))))) # label(aCARDu_EQu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2332 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_LTu_conjunct8) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2333 (all Q67136 all U_1 ((all F0 all G0 all X s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(Q67136,num),F0),s(Q67136,X))))),s(num,i(s(fun(Q67136,num),G0),s(Q67136,X))))) = s(num,i(s(fun(Q67136,num),i(s(fun(fun(Q67136,num),fun(Q67136,num)),i(s(fun(fun(Q67136,num),fun(fun(Q67136,num),fun(Q67136,num))),U_1),s(fun(Q67136,num),F0))),s(fun(Q67136,num),G0))),s(Q67136,X)))) -> (all U_0 ((all S0 all F0 all GENR_PVARR_155 ((exists X exists V ((s(num,i(s(fun(Q67136,num),F0),s(Q67136,X))) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) & p(s(bool,i(s(fun(fun(Q67136,bool),bool),i(s(fun(Q67136,fun(fun(Q67136,bool),bool)),in),s(Q67136,X))),s(fun(Q67136,bool),S0)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(Q67136,bool),i(s(fun(bool,fun(Q67136,bool)),i(s(fun(Q67136,fun(bool,fun(Q67136,bool))),setspec),s(Q67136,GENR_PVARR_155))),s(bool,V))),s(Q67136,X)))))) <-> p(s(bool,i(s(fun(Q67136,bool),i(s(fun(fun(Q67136,num),fun(Q67136,bool)),i(s(fun(fun(Q67136,bool),fun(fun(Q67136,num),fun(Q67136,bool))),U_0),s(fun(Q67136,bool),S0))),s(fun(Q67136,num),F0))),s(Q67136,GENR_PVARR_155)))))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q67136,bool),bool),finite),s(fun(Q67136,bool),i(s(fun(fun(Q67136,bool),fun(Q67136,bool)),gspec),s(fun(Q67136,bool),i(s(fun(fun(Q67136,num),fun(Q67136,bool)),i(s(fun(fun(Q67136,bool),fun(fun(Q67136,num),fun(Q67136,bool))),U_0),s(fun(Q67136,bool),S0))),s(fun(Q67136,num),F0)))))))) & p(s(bool,i(s(fun(fun(Q67136,bool),bool),finite),s(fun(Q67136,bool),i(s(fun(fun(Q67136,bool),fun(Q67136,bool)),gspec),s(fun(Q67136,bool),i(s(fun(fun(Q67136,num),fun(Q67136,bool)),i(s(fun(fun(Q67136,bool),fun(fun(Q67136,num),fun(Q67136,bool))),U_0),s(fun(Q67136,bool),S0))),s(fun(Q67136,num),G0)))))))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(Q67136,num),num),i(s(fun(fun(Q67136,bool),fun(fun(Q67136,num),num)),nsum),s(fun(Q67136,bool),S0))),s(fun(Q67136,num),F0))))),s(num,i(s(fun(fun(Q67136,num),num),i(s(fun(fun(Q67136,bool),fun(fun(Q67136,num),num)),nsum),s(fun(Q67136,bool),S0))),s(fun(Q67136,num),G0))))) = s(num,i(s(fun(fun(Q67136,num),num),i(s(fun(fun(Q67136,bool),fun(fun(Q67136,num),num)),nsum),s(fun(Q67136,bool),S0))),s(fun(Q67136,num),i(s(fun(fun(Q67136,num),fun(Q67136,num)),i(s(fun(fun(Q67136,num),fun(fun(Q67136,num),fun(Q67136,num))),U_1),s(fun(Q67136,num),F0))),s(fun(Q67136,num),G0))))))))))) # label(aNSUMu_ADDu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2334 (all M0 all N0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> ((exists Q0 s(num,M0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,Q0))),s(num,N0)))) <-> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,M0))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aMODu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2335 (all X all Y all D0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y))),s(int,X))))))),s(int,D0)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,D0))))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,D0)))))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,D0)))))) # label(aINTu_ABSu_BETWEEN) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2336 (all Q20703 s(fun(list(Q20703),list(Q20703)),i1) = s(fun(list(Q20703),list(Q20703)),i(s(fun(fun(Q20703,Q20703),fun(list(Q20703),list(Q20703))),map0),s(fun(Q20703,Q20703),i1)))) # label(aMAPu_I) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2337 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),fact),s(num,N0))))))) # label(aFACTu_LE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2338 (all A5 all B0 all N0 (s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,A5))),s(num,B0))))),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,A5))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,B0))),s(num,N0))))))),s(num,N0))))) # label(aMODu_ADDu_MOD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2339 (all Q96788 all P0 all S0 ((all F0 ((all S0 (p(s(bool,i(s(fun(fun(fun(Q96788,bool),bool),bool),i(s(fun(fun(Q96788,bool),fun(fun(fun(Q96788,bool),bool),bool)),in),s(fun(Q96788,bool),S0))),s(fun(fun(Q96788,bool),bool),F0)))) -> p(s(bool,i(s(fun(fun(Q96788,bool),bool),P0),s(fun(Q96788,bool),S0)))))) -> p(s(bool,i(s(fun(fun(Q96788,bool),bool),P0),s(fun(Q96788,bool),i(s(fun(fun(fun(Q96788,bool),bool),fun(Q96788,bool)),inters),s(fun(fun(Q96788,bool),bool),F0)))))))) -> p(s(bool,i(s(fun(fun(Q96788,bool),bool),P0),s(fun(Q96788,bool),i(s(fun(fun(Q96788,bool),fun(Q96788,bool)),i(s(fun(fun(fun(Q96788,bool),bool),fun(fun(Q96788,bool),fun(Q96788,bool))),hull),s(fun(fun(Q96788,bool),bool),P0))),s(fun(Q96788,bool),S0)))))))) # label(aPu_HULL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2340 (all A5 all B0 exists D0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,D0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_divides),s(int,D0))),s(int,A5)))) & (exists X exists Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,A5))),s(int,X))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,B0))),s(int,Y))))) = s(int,D0)) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_divides),s(int,D0))),s(int,B0)))))) # label(aINTu_GCDu_EXISTSu_POS) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2341 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))) # label(aMULTu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.68 2342 (all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,i(s(fun(real,real),realu_neg),s(real,Y)))))) # label(aREALu_LTu_NEG2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2343 (all X all M0 all N0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,M0))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))))) = s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0)))))) # label(aINTu_POWu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2344 p(s(bool,q)) & p(s(bool,p1)) <-> p(s(bool,q)) & p(s(bool,p1)) # label(aCONJu_ACIu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2345 (all X all Y (s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y))) = s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))) <-> s(int,X) = s(int,Y))) # label(aintu_eq) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2346 (all A all B all A5 s(finite_sum(A,B),i(s(fun(num,finite_sum(A,B)),mku_finiteu_sum),s(num,i(s(fun(finite_sum(A,B),num),destu_finiteu_sum),s(finite_sum(A,B),A5))))) = s(finite_sum(A,B),A5)) # label(afiniteu_sumu_tybiju_conjunct0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2347 (all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aREALu_MULu_RZERO) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2348 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,Y))),s(real,X))) = s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y)))))) # label(aREALu_INVu_DIV) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2349 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))))),s(num,P0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0)))))) # label(aRIGHTu_SUBu_DISTRIB) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2350 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),intu_sgn),s(int,X))))),s(int,i(s(fun(int,int),intu_sgn),s(int,Y))))) = s(int,i(s(fun(int,int),intu_sgn),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y)))))) # label(aINTu_SGNu_MUL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2351 (all N0 all X all Y (p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0))))))) # label(aREALu_POWu_LE2u_ODDu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2352 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Z0)))) -> s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Z0))),s(int,X))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Z0))),s(int,Y))))))) # label(aINTu_LTu_LMULu_EQ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2353 (all N0 s(num,i(s(fun(num,num),bit1),s(num,N0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,u_0))),s(num,i(s(fun(num,num),bit1),s(num,N0)))))) # label(aARITHu_ADDu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2354 (all A all B all F0 all B0 ((all X all Y all S0 (s(A,Y) != s(A,X) -> s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,S0))))) = s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,S0))))))) -> (all N1 all N2 all S0 all A10 all A20 (p(s(bool,i(s(fun(num,bool),i(s(fun(B,fun(num,bool)),i(s(fun(fun(A,bool),fun(B,fun(num,bool))),i(s(fun(B,fun(fun(A,bool),fun(B,fun(num,bool)))),i(s(fun(fun(A,fun(B,B)),fun(B,fun(fun(A,bool),fun(B,fun(num,bool))))),finrec),s(fun(A,fun(B,B)),F0))),s(B,B0))),s(fun(A,bool),S0))),s(B,A10))),s(num,N1)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(B,fun(num,bool)),i(s(fun(fun(A,bool),fun(B,fun(num,bool))),i(s(fun(B,fun(fun(A,bool),fun(B,fun(num,bool)))),i(s(fun(fun(A,fun(B,B)),fun(B,fun(fun(A,bool),fun(B,fun(num,bool))))),finrec),s(fun(A,fun(B,B)),F0))),s(B,B0))),s(fun(A,bool),S0))),s(B,A20))),s(num,N2)))) -> s(B,A20) = s(B,A10) & s(num,N2) = s(num,N1))))) # label(aFINRECu_UNIQUEu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2355 (all M0 all N0 all X (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,M0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0)))))))) # label(aREALu_POWu_MONOu_LT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2356 (all U_0 ((all X all Y all N0 all I0 s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(real,fun(num,fun(num,real))),i(s(fun(real,fun(real,fun(num,fun(num,real)))),U_0),s(real,X))),s(real,Y))),s(num,N0))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0)))))))) -> (all X all Y all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(real,fun(num,fun(num,real))),i(s(fun(real,fun(real,fun(num,fun(num,real)))),U_0),s(real,X))),s(real,Y))),s(num,N0))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0))))))))) # label(aREALu_SUBu_POW) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2357 (all X s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) # label(aINTu_MULu_LZERO) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2358 (all A all B all C all U_2 ((all X all F0 ((all I0 all J0 p(s(bool,i(s(fun(C,bool),i(s(fun(C,fun(C,bool)),geq),s(C,i(s(fun(prod(A,B),C),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,I0))),s(B,J0))))))),s(C,i(s(fun(B,C),i(s(fun(A,fun(B,C)),X),s(A,I0))),s(B,J0))))))) <-> p(s(bool,i(s(fun(fun(prod(A,B),C),bool),i(s(fun(fun(A,fun(B,C)),fun(fun(prod(A,B),C),bool)),U_2),s(fun(A,fun(B,C)),X))),s(fun(prod(A,B),C),F0)))))) -> (all U_1 ((all S0 all T0 all GENR_PVARR_146 (p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(prod(A,B),GENR_PVARR_146)))) <-> (exists I0 exists J0 exists V ((p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(bool,fun(prod(A,B),bool)),i(s(fun(prod(A,B),fun(bool,fun(prod(A,B),bool))),setspec),s(prod(A,B),GENR_PVARR_146))),s(bool,V))),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,I0))),s(B,J0)))))))))) -> (all U_0 ((all OP all T0 all X all I0 s(C,i(s(fun(A,C),i(s(fun(fun(A,fun(B,C)),fun(A,C)),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(A,C))),i(s(fun(fun(C,fun(C,C)),fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(A,C)))),U_0),s(fun(C,fun(C,C)),OP))),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,C)),X))),s(A,I0))) = s(C,i(s(fun(fun(B,C),C),i(s(fun(fun(B,bool),fun(fun(B,C),C)),i(s(fun(fun(C,fun(C,C)),fun(fun(B,bool),fun(fun(B,C),C))),iterate),s(fun(C,fun(C,C)),OP))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0))))),s(fun(B,C),i(s(fun(A,fun(B,C)),X),s(A,I0)))))) -> (all OP (p(s(bool,i(s(fun(fun(C,fun(C,C)),bool),monoidal),s(fun(C,fun(C,C)),OP)))) -> (all S0 all T0 all X ((all I0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0)))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(C,i(s(fun(fun(A,C),C),i(s(fun(fun(A,bool),fun(fun(A,C),C)),i(s(fun(fun(C,fun(C,C)),fun(fun(A,bool),fun(fun(A,C),C))),iterate),s(fun(C,fun(C,C)),OP))),s(fun(A,bool),S0))),s(fun(A,C),i(s(fun(fun(A,fun(B,C)),fun(A,C)),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(A,C))),i(s(fun(fun(C,fun(C,C)),fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,C)),fun(A,C)))),U_0),s(fun(C,fun(C,C)),OP))),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,C)),X))))) = s(C,i(s(fun(fun(prod(A,B),C),C),i(s(fun(fun(prod(A,B),bool),fun(fun(prod(A,B),C),C)),i(s(fun(fun(C,fun(C,C)),fun(fun(prod(A,B),bool),fun(fun(prod(A,B),C),C))),iterate),s(fun(C,fun(C,C)),OP))),s(fun(prod(A,B),bool),i(s(fun(fun(prod(A,B),bool),fun(prod(A,B),bool)),gspec),s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))))))),s(fun(prod(A,B),C),i(s(fun(fun(fun(prod(A,B),C),bool),fun(prod(A,B),C)),gabs),s(fun(fun(prod(A,B),C),bool),i(s(fun(fun(A,fun(B,C)),fun(fun(prod(A,B),C),bool)),U_2),s(fun(A,fun(B,C)),X))))))))))))))))) # label(aITERATEu_ITERATEu_PRODUCT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2359 (all M0 all N0 (p(s(bool,i(s(fun(num,bool),even),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0)))))) <-> s(bool,i(s(fun(num,bool),even),s(num,M0))) = s(bool,i(s(fun(num,bool),even),s(num,N0))) | p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))))) # label(aEVENu_SUB) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2360 (all X all Y s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_max),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,i(s(fun(int,int),intu_neg),s(int,Y))))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y)))) # label(aINTu_MINu_MAX) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2361 (all B all A all F0 all X s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),let),s(fun(A,B),F0))),s(A,X)))) # label(aLETu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2362 (all W all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,Z0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,W))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,W))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0)))))))) # label(aREALu_LEu_ADD2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2363 (all A all P0 all Q0 ((p(s(bool,P0)) -> (exists X p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))) <-> (exists X (p(s(bool,P0)) -> p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))))) # label(aRIGHTu_IMPu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2364 (all A all B (p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))) -> (all H0 ((all F0 all G0 all X ((all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Z0))),s(A,X)))) -> s(B,i(s(fun(A,B),G0),s(A,Z0))) = s(B,i(s(fun(A,B),F0),s(A,Z0))))) -> s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),G0))),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X))))) -> (all F0 all XI_ ((all X s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X)))) & (all X s(B,i(s(fun(A,B),XI_),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),XI_))),s(A,X)))) -> s(fun(A,B),XI_) = s(fun(A,B),F0))) & (exists F0 all X s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,X)))))))) # label(aWFu_EREC) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2365 (all A all S0 all T0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aSUBSET) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2366 (all S0 all T0 (s(fun(real,bool),T0) != s(fun(real,bool),empty) & p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(fun(real,bool),fun(fun(real,bool),bool)),subset),s(fun(real,bool),T0))),s(fun(real,bool),S0)))) & (exists B0 all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,X)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),T0)))))))) # label(aREALu_LEu_INFu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2367 (all Q20755 all P0 all Q0 exists V (s(Q20755,i(s(fun(list(Q20755),Q20755),last0),s(list(Q20755),i(s(fun(list(Q20755),list(Q20755)),i(s(fun(list(Q20755),fun(list(Q20755),list(Q20755))),append),s(list(Q20755),P0))),s(list(Q20755),Q0))))) = s(Q20755,i(s(fun(Q20755,Q20755),i(s(fun(Q20755,fun(Q20755,Q20755)),i(s(fun(bool,fun(Q20755,fun(Q20755,Q20755))),cond),s(bool,V))),s(Q20755,i(s(fun(list(Q20755),Q20755),last0),s(list(Q20755),P0))))),s(Q20755,i(s(fun(list(Q20755),Q20755),last0),s(list(Q20755),Q0))))) & (p(s(bool,V)) <-> s(list(Q20755),nil) = s(list(Q20755),Q0)))) # label(aLASTu_APPEND) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2368 (all T0 (s(bool,f0) = s(bool,T0) | s(bool,T0) = s(bool,t))) # label(aBOOLu_CASESu_AX) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2369 (all A all S0 all F0 all B0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(A,real),F0),s(A,X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,B0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0)))))))))))) & s(fun(A,bool),S0) != s(fun(A,bool),empty) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),F0))))),s(real,B0)))))) # label(aSUMu_BOUNDu_GEN) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2370 (all X s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_neg),s(real,X)))))) # label(aREALu_NEGu_GE0) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2371 (all A all P0 (p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),empty)))) & (all X all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),S0)))) & -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0)))))))) -> (all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),S0)))))))) # label(aFINITEu_INDUCTu_STRONG) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2372 (all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))) # label(aLEu_ADD) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2373 (all A all R0 (s(num,i(s(fun(finite_image(A),num),destu_finiteu_image),s(finite_image(A),i(s(fun(num,finite_image(A)),finiteu_index),s(num,R0))))) = s(num,R0) <-> p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,R0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),univ)))))))))) # label(afiniteu_imageu_tybiju_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2374 (exists M0 (p(s(bool,i(s(fun(num,bool),p0),s(num,M0)))) & (s(num,n) = s(num,i(s(fun(num,num),suc),s(num,M0))) | s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,M0) & s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,n)))) <-> p(s(bool,i(s(fun(num,bool),p0),s(num,i(s(fun(num,num),pre),s(num,n)))))) # label(aPREu_ELIMu_THMi_) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2375 (all A all P0 all Q0 ((all X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) | p(s(bool,Q0)))) <-> p(s(bool,Q0)) | (all X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))))) # label(aLEFTu_FORALLu_ORu_THM) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2376 (all A all S0 all X all XI_ (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))),s(A,XI_)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0)))) | s(A,X) = s(A,XI_))) # label(aINSERTu_DEF) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2377 (all A all S0 all X s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0))) = s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X)))))) # label(aFINITEu_DELETE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2378 (all X all Y all Z0 (s(int,X) = s(int,Y) | s(int,Z0) = s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Z0))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Y))),s(int,Z0))))) # label(aINTu_EQu_MULu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2379 (all X all Y all A5 all U all V (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,U)))) & s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,U))),s(real,V))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,V)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,A5)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,A5)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,U))),s(real,X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,V))),s(real,Y))))))),s(real,A5)))))) # label(aREALu_CONVEXu_BOUNDu_LE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2380 (all X all Y all Z0 s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,Z0))),s(int,Y))))) = s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,i(s(fun(int,int),intu_neg),s(int,Y))))))),s(int,Z0)))) # label(aINTu_LTu_ADDNEG2) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2381 (all A all F1 all F2 all X all X0 s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(A,bool)),fun(num,fun(A,bool))),i(s(fun(fun(num,fun(A,bool)),fun(fun(num,fun(A,bool)),fun(num,fun(A,bool)))),injp),s(fun(num,fun(A,bool)),F1))),s(fun(num,fun(A,bool)),F2))),s(num,X))),s(A,X0))) = s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,i(s(fun(num,bool),numleft),s(num,X))))),s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),F1),s(num,i(s(fun(num,num),numright),s(num,X))))),s(A,X0))))),s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),F2),s(num,i(s(fun(num,num),numright),s(num,X))))),s(A,X0)))))) # label(aINJP) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2382 (all N0 s(num,i(s(fun(num,num),numeral),s(num,N0))) = s(num,N0)) # label(aNUMERAL) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2383 (all M0 all N0 (s(num,M0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),mod),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,M0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aMODu_MULT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2384 (all X (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> s(int,X) != s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aINTu_POSu_NZ) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2385 (all M0 all P0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,P0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,P0)))) -> s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))) = s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(fun(num,bool),fun(fun(num,bool),fun(num,bool))),union),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,P0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,P0))),s(num,N0))))))) # label(aNUMSEGu_COMBINEu_L) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2386 (all X all Y all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,X))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,Y))),s(num,N0)))))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,X))),s(num,Y)))) & s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aEXPu_MONOu_LT) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2387 (all A s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),i(s(fun(list(A),list(A)),reverse),s(list(A),l0))))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),nil))))) = s(list(A),i(s(fun(list(A),list(A)),reverse),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),l0)))))) # label(aREVERSEu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2388 (all Q46704 s(fun(Q46704,bool),i(s(fun(fun(Q46704,bool),fun(Q46704,bool)),i(s(fun(fun(Q46704,bool),fun(fun(Q46704,bool),fun(Q46704,bool))),union),s(fun(Q46704,bool),p1))),s(fun(Q46704,bool),p1))) = s(fun(Q46704,bool),p1)) # label(aUNIONu_ACIu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2389 (all A all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))))) # label(aINFINITEu_DIFFu_FINITE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2390 (all X (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(real,real),realu_sgn),s(real,X))) | s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(real,real),realu_sgn),s(real,X))) | s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),realu_sgn),s(real,X))))) # label(aREALu_SGNu_CASES) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2391 (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,X))))))) # label(aREALu_LEu_SQUARE) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2392 (all X all Y all D0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))))),s(real,D0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,D0)))))))) # label(aREALu_ABSu_BOUND) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2393 (all M0 s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_mul),s(hreal,M0))),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aHREALu_MULu_RZERO) # label(axiom) # label(non_clause). [assumption]. 14.64/14.69 2394 (all A all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),S0))),s(fun(A,bool),empty)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),disjoint),s(fun(A,bool),empty))),s(fun(A,bool),S0)))))) # label(aDISJOINTu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2395 (all B0 all A5 ((exists X s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,A5))),s(int,X))) = s(int,B0)) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_divides),s(int,A5))),s(int,B0)))))) # label(aintu_divides) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2396 (all Q92448 all B all Q92455 all S0 all T0 all U (p(s(bool,i(s(fun(fun(Q92455,bool),bool),i(s(fun(fun(B,bool),fun(fun(Q92455,bool),bool)),l_u_c),s(fun(B,bool),T0))),s(fun(Q92455,bool),U)))) & p(s(bool,i(s(fun(fun(Q92455,bool),bool),infinite),s(fun(Q92455,bool),U)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(Q92448,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(Q92448,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(Q92455,bool),bool),i(s(fun(fun(prod(Q92448,B),bool),fun(fun(Q92455,bool),bool)),l_u_c),s(fun(prod(Q92448,B),bool),i(s(fun(fun(B,bool),fun(prod(Q92448,B),bool)),i(s(fun(fun(Q92448,bool),fun(fun(B,bool),fun(prod(Q92448,B),bool))),t_u_c),s(fun(Q92448,bool),S0))),s(fun(B,bool),T0))))),s(fun(Q92455,bool),U)))))) # label(aCARDu_MULu_LTu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2397 (all Q83010 all Q83030 all Q83026 all U_6 ((all F0 all F1 (p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(Q83010,Q83026),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),U_6),s(fun(Q83010,Q83026),F0))),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F1)))) <-> (all S0 all T0 exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F1),s(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))))),c_),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))),s(bool,V)))) & ((all X s(Q83026,i(s(fun(Q83010,Q83026),F0),s(Q83010,i(s(fun(Q83030,Q83010),S0),s(Q83030,X))))) = s(Q83026,i(s(fun(Q83030,Q83026),i(s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0),s(fun(Q83010,Q83026),F0))),s(Q83030,X)))) <-> p(s(bool,V))))))) -> (all U_5 ((all S0 all T0 all F0 ((all SI_ all TI_ exists V (((all F1 all X all Y (s(Q83010,i(s(fun(Q83030,Q83010),S0),s(Q83030,X))) = s(Q83010,i(s(fun(Q83030,Q83010),SI_),s(Q83030,Y))) -> s(Q83026,i(s(fun(Q83030,Q83026),i(s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0),s(fun(Q83010,Q83026),F1))),s(Q83030,X))) = s(Q83026,i(s(fun(Q83030,Q83026),i(s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),TI_),s(fun(Q83010,Q83026),F1))),s(Q83030,Y))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0),s(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))))),c_),s(fun(Q83030,Q83010),SI_))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),TI_))))))),s(bool,V)))))) <-> p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool))),U_5),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0)))))) -> (all U_4 ((all F0 ((all S0 all T0 p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),geq),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),i(s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),F0),s(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))))),c_),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),i(s(fun(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),gabs),s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool))),U_5),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))))) <-> p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),bool),U_4),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),F0)))))) -> (all U_3 ((all F0 (p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),U_3),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0)))) <-> (all S0 all T0 exists V (((all F1 all X all Y (s(Q83010,i(s(fun(Q83030,Q83010),S0),s(Q83030,Y))) = s(Q83010,i(s(fun(Q83030,Q83010),S0),s(Q83030,X))) -> s(Q83026,i(s(fun(Q83030,Q83026),i(s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0),s(fun(Q83010,Q83026),F1))),s(Q83030,Y))) = s(Q83026,i(s(fun(Q83030,Q83026),i(s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0),s(fun(Q83010,Q83026),F1))),s(Q83030,X))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0),s(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))))),c_),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))),s(bool,V)))))))) -> (all U_2 ((all A5 s(bool,i(s(fun(Q83030,bool),U_2),s(Q83030,A5))) = s(bool,t)) -> (all U_1 ((all F0 s(fun(Q83030,bool),i(s(fun(fun(Q83010,Q83026),fun(Q83030,bool)),U_1),s(fun(Q83010,Q83026),F0))) = s(fun(Q83030,bool),U_2)) -> (all U_0 ((all L_L_ all F0 ((all S0 all T0 p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0),s(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))))),c_),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))),s(bool,i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),bool),i(s(fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),bool)),i(s(fun(fun(fun(Q83010,Q83026),fun(Q83030,bool)),fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),bool))),i(s(fun(fun(Q83010,fun(Q83010,bool)),fun(fun(fun(Q83010,Q83026),fun(Q83030,bool)),fun(fun(Q83030,Q83010),fun(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),bool)))),superadmissible),s(fun(Q83010,fun(Q83010,bool)),L_L_))),s(fun(fun(Q83010,Q83026),fun(Q83030,bool)),U_1))),s(fun(Q83030,Q83010),S0))),s(fun(fun(Q83010,Q83026),fun(Q83030,Q83026)),T0))))))) <-> p(s(bool,i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(Q83010,fun(Q83010,bool)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),U_0),s(fun(Q83010,fun(Q83010,bool)),L_L_))),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),F0)))))) -> (all CLAUSES ((exists L_L_ (p(s(bool,i(s(fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool),i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool)),all0),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),i(s(fun(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),gabs),s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(Q83010,fun(Q83010,bool)),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),U_0),s(fun(Q83010,fun(Q83010,bool)),L_L_))))))),s(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),CLAUSES)))) & p(s(bool,i(s(fun(fun(Q83010,fun(Q83010,bool)),bool),wf),s(fun(Q83010,fun(Q83010,bool)),L_L_)))))) & p(s(bool,i(s(fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool),i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool)),all0),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),i(s(fun(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),gabs),s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),U_3))))),s(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),CLAUSES)))) & p(s(bool,i(s(fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool),i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool)),pairwise0),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),i(s(fun(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),bool),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool))),gabs),s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),bool),U_4))))),s(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),CLAUSES)))) -> (exists F0 p(s(bool,i(s(fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool),i(s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),fun(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),bool)),all0),s(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),i(s(fun(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool)),gabs),s(fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool),i(s(fun(fun(Q83010,Q83026),fun(fun(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026))),bool),bool)),U_6),s(fun(Q83010,Q83026),F0))))))),s(list(prod(fun(Q83030,Q83010),fun(fun(Q83010,Q83026),fun(Q83030,Q83026)))),CLAUSES))))))))))))))))))))) # label(aRECURSIONu_SUPERADMISSIBLE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2398 (all T1 all T2 all T3 (p(s(bool,T2)) | p(s(bool,T3)) | p(s(bool,T1)) <-> p(s(bool,T2)) | p(s(bool,T3)) | p(s(bool,T1)))) # label(aDISJu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2399 (all A all B all S0 all T0 all F0 all G0 all H0 ((all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> (all X all XI_ (s(B,Y) = s(B,i(s(fun(A,B),H0),s(A,X))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),H0),s(A,XI_))) = s(B,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,X) = s(A,XI_))) & (exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),H0),s(A,X))) = s(B,Y))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(num,i(s(fun(A,num),F0),s(A,X))) = s(num,i(s(fun(B,num),G0),s(B,i(s(fun(A,B),H0),s(A,X))))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),H0),s(A,X))))),s(fun(B,bool),T0)))))) -> s(num,i(s(fun(fun(B,num),num),i(s(fun(fun(B,bool),fun(fun(B,num),num)),nsum),s(fun(B,bool),T0))),s(fun(B,num),G0))) = s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))))) # label(aNSUMu_EQu_GENERAL) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2400 (all A all P0 ((all A5 all S0 (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,A5))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,A5))),s(fun(A,bool),S0)))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),empty)))) -> (all S0 p(s(bool,i(s(fun(fun(A,bool),bool),P0),s(fun(A,bool),S0))))))) # label(aSETu_PROVEu_CASES) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2401 (all Q72493 all Q72469 all F0 all G0 all S0 ((all X all Y (p(s(bool,i(s(fun(fun(Q72493,bool),bool),i(s(fun(Q72493,fun(fun(Q72493,bool),bool)),in),s(Q72493,X))),s(fun(Q72493,bool),S0)))) & s(Q72469,i(s(fun(Q72493,Q72469),F0),s(Q72493,Y))) = s(Q72469,i(s(fun(Q72493,Q72469),F0),s(Q72493,X))) & p(s(bool,i(s(fun(fun(Q72493,bool),bool),i(s(fun(Q72493,fun(fun(Q72493,bool),bool)),in),s(Q72493,Y))),s(fun(Q72493,bool),S0)))) -> s(Q72493,Y) = s(Q72493,X))) -> s(real,i(s(fun(fun(Q72493,real),real),i(s(fun(fun(Q72493,bool),fun(fun(Q72493,real),real)),sum),s(fun(Q72493,bool),S0))),s(fun(Q72493,real),i(s(fun(fun(Q72493,Q72469),fun(Q72493,real)),i(s(fun(fun(Q72469,real),fun(fun(Q72493,Q72469),fun(Q72493,real))),o),s(fun(Q72469,real),G0))),s(fun(Q72493,Q72469),F0))))) = s(real,i(s(fun(fun(Q72469,real),real),i(s(fun(fun(Q72469,bool),fun(fun(Q72469,real),real)),sum),s(fun(Q72469,bool),i(s(fun(fun(Q72493,bool),fun(Q72469,bool)),i(s(fun(fun(Q72493,Q72469),fun(fun(Q72493,bool),fun(Q72469,bool))),image),s(fun(Q72493,Q72469),F0))),s(fun(Q72493,bool),S0))))),s(fun(Q72469,real),G0))))) # label(aSUMu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2402 (all N0 exists V ((p(s(bool,V)) <-> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,N0)) & s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(num,N0))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),i(s(fun(bool,fun(int,fun(int,int))),cond),s(bool,V))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) # label(aINTu_POWu_ZERO) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2403 (all Q59933 all Q59932 all T0 all S0 (p(s(bool,i(s(fun(fun(Q59933,bool),bool),i(s(fun(fun(Q59932,bool),fun(fun(Q59933,bool),bool)),l_u_c),s(fun(Q59932,bool),S0))),s(fun(Q59933,bool),T0)))) <-> p(s(bool,i(s(fun(fun(Q59933,bool),bool),i(s(fun(fun(Q59932,bool),fun(fun(Q59933,bool),bool)),l_a_u_c),s(fun(Q59932,bool),S0))),s(fun(Q59933,bool),T0)))) & -p(s(bool,i(s(fun(fun(Q59932,bool),bool),i(s(fun(fun(Q59933,bool),fun(fun(Q59932,bool),bool)),l_a_u_c),s(fun(Q59933,bool),T0))),s(fun(Q59932,bool),S0)))))) # label(altu_c) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2404 (all Q63608 all Q63602 all OP all F0 all S0 (p(s(bool,i(s(fun(fun(Q63602,bool),bool),finite),s(fun(Q63602,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q63602,bool),bool),finite),s(fun(Q63602,bool),i(s(fun(fun(Q63602,bool),fun(Q63602,bool)),i(s(fun(fun(Q63602,Q63608),fun(fun(Q63602,bool),fun(Q63602,bool))),i(s(fun(fun(Q63608,fun(Q63608,Q63608)),fun(fun(Q63602,Q63608),fun(fun(Q63602,bool),fun(Q63602,bool)))),support),s(fun(Q63608,fun(Q63608,Q63608)),OP))),s(fun(Q63602,Q63608),F0))),s(fun(Q63602,bool),S0)))))))) # label(aFINITEu_SUPPORT) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2405 (all M0 all N0 (p(s(bool,i(s(fun(hreal,bool),i(s(fun(hreal,fun(hreal,bool)),hrealu_le),s(hreal,M0))),s(hreal,N0)))) <-> (exists D0 s(hreal,N0) = s(hreal,i(s(fun(hreal,hreal),i(s(fun(hreal,fun(hreal,hreal)),hrealu_add),s(hreal,M0))),s(hreal,D0)))))) # label(aHREALu_LEu_EXISTSu_DEF) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2406 (all Q56534 all Q56537 all U_0 ((all T0 all S0 all GENR_PVARR_93 ((exists F0 exists V (p(s(bool,i(s(fun(fun(Q56537,Q56534),bool),i(s(fun(bool,fun(fun(Q56537,Q56534),bool)),i(s(fun(fun(Q56537,Q56534),fun(bool,fun(fun(Q56537,Q56534),bool))),setspec),s(fun(Q56537,Q56534),GENR_PVARR_93))),s(bool,V))),s(fun(Q56537,Q56534),F0)))) & ((all X (p(s(bool,i(s(fun(fun(Q56537,bool),bool),i(s(fun(Q56537,fun(fun(Q56537,bool),bool)),in),s(Q56537,X))),s(fun(Q56537,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q56534,bool),bool),i(s(fun(Q56534,fun(fun(Q56534,bool),bool)),in),s(Q56534,i(s(fun(Q56537,Q56534),F0),s(Q56537,X))))),s(fun(Q56534,bool),T0)))))) & (all X (-p(s(bool,i(s(fun(fun(Q56537,bool),bool),i(s(fun(Q56537,fun(fun(Q56537,bool),bool)),in),s(Q56537,X))),s(fun(Q56537,bool),S0)))) -> s(Q56534,d) = s(Q56534,i(s(fun(Q56537,Q56534),F0),s(Q56537,X))))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(fun(Q56537,Q56534),bool),i(s(fun(fun(Q56537,bool),fun(fun(Q56537,Q56534),bool)),i(s(fun(fun(Q56534,bool),fun(fun(Q56537,bool),fun(fun(Q56537,Q56534),bool))),U_0),s(fun(Q56534,bool),T0))),s(fun(Q56537,bool),S0))),s(fun(Q56537,Q56534),GENR_PVARR_93)))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(Q56537,bool),bool),finite),s(fun(Q56537,bool),S0)))) & p(s(bool,i(s(fun(fun(Q56534,bool),bool),finite),s(fun(Q56534,bool),T0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(fun(Q56534,bool),num),card),s(fun(Q56534,bool),T0))))),s(num,i(s(fun(fun(Q56537,bool),num),card),s(fun(Q56537,bool),S0))))) = s(num,i(s(fun(fun(fun(Q56537,Q56534),bool),num),card),s(fun(fun(Q56537,Q56534),bool),i(s(fun(fun(fun(Q56537,Q56534),bool),fun(fun(Q56537,Q56534),bool)),gspec),s(fun(fun(Q56537,Q56534),bool),i(s(fun(fun(Q56537,bool),fun(fun(Q56537,Q56534),bool)),i(s(fun(fun(Q56534,bool),fun(fun(Q56537,bool),fun(fun(Q56537,Q56534),bool))),U_0),s(fun(Q56534,bool),T0))),s(fun(Q56537,bool),S0))))))))))) # label(aCARDu_FUNSPACE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2407 (all A s(fun(A,bool),univ) != s(fun(A,bool),empty)) # label(aUNIVu_NOTu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2408 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,u_0))),s(num,i(s(fun(num,num),bit0),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,u_0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,u_0))),s(num,N0)))))) # label(aARITHu_EXPu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2409 (all M0 all N0 p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,M0))))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,N0))))))),s(nadd,i(s(fun(num,nadd),naddu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))))))) # label(aNADDu_OFu_NUMu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2410 (all A all L (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> (all X s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,X))))) = s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,X)))))) # label(aWOSETu_FLEQ) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2411 (all A all B all F0 all B0 ((all X all Y all S0 (s(A,Y) != s(A,X) -> s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,S0))))) = s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,Y))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,S0))))))) -> s(B,i(s(fun(B,B),i(s(fun(fun(A,bool),fun(B,B)),i(s(fun(fun(A,fun(B,B)),fun(fun(A,bool),fun(B,B))),itset),s(fun(A,fun(B,B)),F0))),s(fun(A,bool),empty))),s(B,B0))) = s(B,B0) & (all X all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(B,i(s(fun(B,B),i(s(fun(fun(A,bool),fun(B,B)),i(s(fun(fun(A,fun(B,B)),fun(fun(A,bool),fun(B,B))),itset),s(fun(A,fun(B,B)),F0))),s(fun(A,bool),S0))),s(B,B0))))),s(B,i(s(fun(B,B),i(s(fun(A,fun(B,B)),F0),s(A,X))),s(B,i(s(fun(B,B),i(s(fun(fun(A,bool),fun(B,B)),i(s(fun(fun(A,fun(B,B)),fun(fun(A,bool),fun(B,B))),itset),s(fun(A,fun(B,B)),F0))),s(fun(A,bool),S0))),s(B,B0))))))) = s(B,i(s(fun(B,B),i(s(fun(fun(A,bool),fun(B,B)),i(s(fun(fun(A,fun(B,B)),fun(fun(A,bool),fun(B,B))),itset),s(fun(A,fun(B,B)),F0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))))),s(B,B0))))))) # label(aFINITEu_RECURSION) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2412 (all S0 all B0 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,B0))),s(real,X)))))) & (all BI_ (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,B0))),s(real,BI_)))) -> (exists X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,BI_)))))))) -> s(real,B0) = s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))) # label(aREALu_INFu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2413 (all F0 all G0 all M0 all N0 ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,I0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),F0),s(num,I0))))),s(real,i(s(fun(num,real),G0),s(num,I0)))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),G0)))))))) # label(aSUMu_LEu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2414 (all Y all X s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_gt),s(real,X))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,X)))) # label(arealu_gt) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2415 (all A all C0 all I0 all R0 s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))),i(s(fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool)))),i(s(fun(num,fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))))),zconstr),s(num,C0))),s(A,I0))),s(fun(num,fun(num,fun(A,bool))),R0))) != s(fun(num,fun(A,bool)),zbot)) # label(aZCONSTRu_ZBOT) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2416 (all X all Y all Z0 (s(real,X) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,Z0))) <-> s(real,Y) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0))))) # label(aREALu_EQu_SUBu_LADD) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2417 (all Q47261 all S0 ((all T0 (p(s(bool,i(s(fun(fun(fun(Q47261,bool),bool),bool),i(s(fun(fun(Q47261,bool),fun(fun(fun(Q47261,bool),bool),bool)),in),s(fun(Q47261,bool),T0))),s(fun(fun(Q47261,bool),bool),S0)))) -> s(fun(Q47261,bool),T0) = s(fun(Q47261,bool),empty))) <-> s(fun(Q47261,bool),empty) = s(fun(Q47261,bool),i(s(fun(fun(fun(Q47261,bool),bool),fun(Q47261,bool)),unions),s(fun(fun(Q47261,bool),bool),S0))))) # label(aEMPTYu_UNIONS) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2418 (all Q4620 all Q4624 all Q4628 all Q4627 all Q4604 all U_0 ((all F0 all FI_ (p(s(bool,i(s(fun(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),bool),i(s(fun(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),fun(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),bool)),U_0),s(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),F0))),s(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),FI_)))) <-> (all W all X all Y all Z0 p(s(bool,i(s(fun(Q4604,bool),i(s(fun(Q4604,fun(Q4604,bool)),geq),s(Q4604,i(s(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),FI_),s(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),i(s(fun(prod(Q4624,prod(Q4628,Q4627)),prod(Q4620,prod(Q4624,prod(Q4628,Q4627)))),i(s(fun(Q4620,fun(prod(Q4624,prod(Q4628,Q4627)),prod(Q4620,prod(Q4624,prod(Q4628,Q4627))))),c_),s(Q4620,W))),s(prod(Q4624,prod(Q4628,Q4627)),i(s(fun(prod(Q4628,Q4627),prod(Q4624,prod(Q4628,Q4627))),i(s(fun(Q4624,fun(prod(Q4628,Q4627),prod(Q4624,prod(Q4628,Q4627)))),c_),s(Q4624,X))),s(prod(Q4628,Q4627),i(s(fun(Q4627,prod(Q4628,Q4627)),i(s(fun(Q4628,fun(Q4627,prod(Q4628,Q4627))),c_),s(Q4628,Y))),s(Q4627,Z0))))))))))),s(Q4604,i(s(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),F0),s(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),i(s(fun(prod(Q4624,prod(Q4628,Q4627)),prod(Q4620,prod(Q4624,prod(Q4628,Q4627)))),i(s(fun(Q4620,fun(prod(Q4624,prod(Q4628,Q4627)),prod(Q4620,prod(Q4624,prod(Q4628,Q4627))))),c_),s(Q4620,W))),s(prod(Q4624,prod(Q4628,Q4627)),i(s(fun(prod(Q4628,Q4627),prod(Q4624,prod(Q4628,Q4627))),i(s(fun(Q4624,fun(prod(Q4628,Q4627),prod(Q4624,prod(Q4628,Q4627)))),c_),s(Q4624,X))),s(prod(Q4628,Q4627),i(s(fun(Q4627,prod(Q4628,Q4627)),i(s(fun(Q4628,fun(Q4627,prod(Q4628,Q4627))),c_),s(Q4628,Y))),s(Q4627,Z0))))))))))))))) -> (all F0 s(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),F0) = s(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),i(s(fun(fun(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),bool),fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604)),gabs),s(fun(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),bool),i(s(fun(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),fun(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),bool)),U_0),s(fun(prod(Q4620,prod(Q4624,prod(Q4628,Q4627))),Q4604),F0)))))))) # label(aPAIREDu_ETAu_THMu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2419 (all X s(real,i(s(fun(real,real),realu_neg),s(real,X))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) # label(aREALu_SUBu_LZERO) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2420 (all E0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,E0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) = s(real,E0)) # label(aREALu_HALFu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2421 (all A all B (p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))) -> (all H0 ((all F0 all G0 all X ((all Z0 (p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,Z0))),s(A,X)))) -> s(B,i(s(fun(A,B),F0),s(A,Z0))) = s(B,i(s(fun(A,B),G0),s(A,Z0))))) -> s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),G0))),s(A,X))) = s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X))))) -> (all F0 all G0 ((all X s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),G0))),s(A,X))) = s(B,i(s(fun(A,B),G0),s(A,X)))) & (all X s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),H0),s(fun(A,B),F0))),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,X)))) -> s(fun(A,B),F0) = s(fun(A,B),G0))))))) # label(aWFu_UREC) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2422 (all X all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,Y))),s(real,Z0))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Z0)))))) # label(aREALu_LTu_LADD) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2423 (all A all B all C all L all M0 ((all X all Y s(C,i(s(fun(prod(A,B),C),L),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y))))) = s(C,i(s(fun(prod(A,B),C),M0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))) <-> s(fun(prod(A,B),C),M0) = s(fun(prod(A,B),C),L))) # label(aPAIREDu_EXT) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2424 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y)))))))) # label(aREALu_LTu_DIV) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2425 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_min),s(real,X))),s(real,Y))))),s(real,Z0)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,Z0)))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Z0)))))) # label(aREALu_MINu_LE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2426 (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),realu_abs),s(real,X))))))) # label(aREALu_ABSu_POS) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2427 (all Q90290 all Q90309 all Y s(bool,i(s(fun(fun(Q90309,bool),bool),i(s(fun(Q90309,fun(fun(Q90309,bool),bool)),in),s(Q90309,Y))),s(fun(Q90309,bool),t0))) = s(bool,i(s(fun(fun(sum0(Q90290,Q90309),bool),bool),i(s(fun(sum0(Q90290,Q90309),fun(fun(sum0(Q90290,Q90309),bool),bool)),in),s(sum0(Q90290,Q90309),i(s(fun(Q90309,sum0(Q90290,Q90309)),inr),s(Q90309,Y))))),s(fun(sum0(Q90290,Q90309),bool),i(s(fun(fun(Q90309,bool),fun(sum0(Q90290,Q90309),bool)),i(s(fun(fun(Q90290,bool),fun(fun(Q90309,bool),fun(sum0(Q90290,Q90309),bool))),p_u_c),s(fun(Q90290,bool),s0))),s(fun(Q90309,bool),t0)))))) # label(aINu_CARDu_ADDu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2428 (all Q47137 s(fun(Q47137,bool),i(s(fun(fun(fun(Q47137,bool),bool),fun(Q47137,bool)),unions),s(fun(fun(Q47137,bool),bool),i(s(fun(fun(fun(Q47137,bool),bool),fun(fun(Q47137,bool),bool)),i(s(fun(fun(Q47137,bool),fun(fun(fun(Q47137,bool),bool),fun(fun(Q47137,bool),bool))),insert),s(fun(Q47137,bool),s0))),s(fun(fun(Q47137,bool),bool),i(s(fun(fun(fun(Q47137,bool),bool),fun(fun(Q47137,bool),bool)),i(s(fun(fun(Q47137,bool),fun(fun(fun(Q47137,bool),bool),fun(fun(Q47137,bool),bool))),insert),s(fun(Q47137,bool),t0))),s(fun(fun(Q47137,bool),bool),empty))))))) = s(fun(Q47137,bool),i(s(fun(fun(Q47137,bool),fun(Q47137,bool)),i(s(fun(fun(Q47137,bool),fun(fun(Q47137,bool),fun(Q47137,bool))),union),s(fun(Q47137,bool),s0))),s(fun(Q47137,bool),t0)))) # label(aUNIONSu_2) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2429 (all U_0 ((all U (p(s(bool,i(s(fun(nadd,bool),U_0),s(nadd,U)))) <-> (exists X (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,i(s(fun(nadd,nadd),naddu_inv),s(nadd,X))))),s(nadd,U)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(hreal,fun(nadd,bool)),destu_hreal),s(hreal,x))),s(nadd,X)))))))) -> s(hreal,i(s(fun(hreal,hreal),hrealu_inv),s(hreal,x))) = s(hreal,i(s(fun(fun(nadd,bool),hreal),mku_hreal),s(fun(nadd,bool),U_0))))) # label(ahrealu_inv) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2430 (all N0 s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,N0))) = s(prod(hreal,hreal),i(s(fun(hreal,prod(hreal,hreal)),i(s(fun(hreal,fun(hreal,prod(hreal,hreal))),c_),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,N0))))),s(hreal,i(s(fun(num,hreal),hrealu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(atrealu_ofu_num) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2431 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,Y))),s(real,Z0))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))) # label(aREALu_LTu_DIV2u_EQ) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2432 (all A all S0 all T0 ((exists A5 (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,A5))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,A5))),s(fun(A,bool),T0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),psubset),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aPSUBSETu_ALT) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2433 (all Q71673 all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q71673,bool),bool),finite),s(fun(Q71673,bool),S0)))) & s(fun(Q71673,bool),S0) != s(fun(Q71673,bool),empty) & (all X (p(s(bool,i(s(fun(fun(Q71673,bool),bool),i(s(fun(Q71673,fun(fun(Q71673,bool),bool)),in),s(Q71673,X))),s(fun(Q71673,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(Q71673,real),F0),s(Q71673,X))))),s(real,i(s(fun(Q71673,real),G0),s(Q71673,X)))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(fun(Q71673,real),real),i(s(fun(fun(Q71673,bool),fun(fun(Q71673,real),real)),sum),s(fun(Q71673,bool),S0))),s(fun(Q71673,real),F0))))),s(real,i(s(fun(fun(Q71673,real),real),i(s(fun(fun(Q71673,bool),fun(fun(Q71673,real),real)),sum),s(fun(Q71673,bool),S0))),s(fun(Q71673,real),G0)))))))) # label(aSUMu_LTu_ALL) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2434 (all X all Y all Z0 s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Z0))),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))),s(real,Z0)))) # label(aREALu_LTu_ADDu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2435 (all S0 (p(s(bool,i(s(fun(fun(num,bool),bool),infinite),s(fun(num,bool),S0)))) -> (exists R0 ((all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),R0),s(num,M0))))),s(num,i(s(fun(num,num),R0),s(num,N0)))))))) & (all N0 p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,i(s(fun(num,num),R0),s(num,N0))))),s(fun(num,bool),S0))))))))) # label(aINFINITEu_ENUMERATE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2436 (all M0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,N0))))))),s(num,M0))))) # label(aDIVu_MULu_LE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2437 (all Q97208 all P0 all A5 all S0 (p(s(bool,i(s(fun(fun(Q97208,bool),bool),i(s(fun(Q97208,fun(fun(Q97208,bool),bool)),in),s(Q97208,A5))),s(fun(Q97208,bool),i(s(fun(fun(Q97208,bool),fun(Q97208,bool)),i(s(fun(fun(fun(Q97208,bool),bool),fun(fun(Q97208,bool),fun(Q97208,bool))),hull),s(fun(fun(Q97208,bool),bool),P0))),s(fun(Q97208,bool),S0)))))) -> s(fun(Q97208,bool),i(s(fun(fun(Q97208,bool),fun(Q97208,bool)),i(s(fun(fun(fun(Q97208,bool),bool),fun(fun(Q97208,bool),fun(Q97208,bool))),hull),s(fun(fun(Q97208,bool),bool),P0))),s(fun(Q97208,bool),S0))) = s(fun(Q97208,bool),i(s(fun(fun(Q97208,bool),fun(Q97208,bool)),i(s(fun(fun(fun(Q97208,bool),bool),fun(fun(Q97208,bool),fun(Q97208,bool))),hull),s(fun(fun(Q97208,bool),bool),P0))),s(fun(Q97208,bool),i(s(fun(fun(Q97208,bool),fun(Q97208,bool)),i(s(fun(Q97208,fun(fun(Q97208,bool),fun(Q97208,bool))),insert),s(Q97208,A5))),s(fun(Q97208,bool),S0))))))) # label(aHULLu_REDUNDANT) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2438 (all A all I0 ((exists N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))) & s(finite_image(A),i(s(fun(num,finite_image(A)),finiteu_index),s(num,N0))) = s(finite_image(A),I0) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),univ)))))))) & (all N0 all XI_ (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),univ)))))) & s(finite_image(A),i(s(fun(num,finite_image(A)),finiteu_index),s(num,N0))) = s(finite_image(A),I0) & s(finite_image(A),I0) = s(finite_image(A),i(s(fun(num,finite_image(A)),finiteu_index),s(num,XI_))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,XI_))),s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,XI_)))) -> s(num,N0) = s(num,XI_))))) # label(aFINITEu_INDEXu_WORKS) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2439 (all A all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))) = s(num,i(s(fun(list(A),num),length),s(list(A),i(s(fun(fun(A,bool),list(A)),listu_ofu_set),s(fun(A,bool),S0))))) & s(fun(A,bool),i(s(fun(list(A),fun(A,bool)),setu_ofu_list),s(list(A),i(s(fun(fun(A,bool),list(A)),listu_ofu_set),s(fun(A,bool),S0))))) = s(fun(A,bool),S0))) # label(aLISTu_OFu_SETu_PROPERTIES) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2440 (all A all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),univ))),s(fun(A,bool),S0)))) <-> s(fun(A,bool),S0) = s(fun(A,bool),univ))) # label(aUNIVu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2441 (all N0 s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),bit0),s(num,N0))))))) = s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aBIT0u_DEFu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2442 (all U_0 ((all B0 all GENR_PVARR_125 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),U_0),s(real,B0))),s(real,GENR_PVARR_125)))) <-> (exists X p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_125))),s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0))))),s(real,X))))))) -> (all B0 -p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(real,fun(real,bool)),U_0),s(real,B0))))))))))) # label(aFINITEu_REALu_INTERVALu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2443 (all M0 all N0 all P0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,P0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0)))))) # label(aLEFTu_SUBu_DISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2444 (all A all S0 all X ((exists T0 (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) & s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),T0))) = s(fun(A,bool),S0))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))) # label(aDECOMPOSITION) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2445 (all Q59041 all P0 (p(s(bool,f0)) <-> (exists X (p(s(bool,i(s(fun(fun(Q59041,bool),bool),i(s(fun(Q59041,fun(fun(Q59041,bool),bool)),in),s(Q59041,X))),s(fun(Q59041,bool),empty)))) & p(s(bool,i(s(fun(Q59041,bool),P0),s(Q59041,X)))))))) # label(aEXISTSu_INu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2446 (all A all U_0 ((all S0 all GENR_PVARR_98 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))),s(fun(A,bool),GENR_PVARR_98)))) <-> (exists T0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_98))),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0))))),s(fun(A,bool),T0))))))) -> (all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))) = s(num,i(s(fun(fun(fun(A,bool),bool),num),card),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))))))))))) # label(aCARDu_POWERSET) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2447 (all Q47974 all Q47975 all F0 all S0 ((exists Y (p(s(bool,i(s(fun(Q47974,bool),p0),s(Q47974,Y)))) & p(s(bool,i(s(fun(fun(Q47974,bool),bool),i(s(fun(Q47974,fun(fun(Q47974,bool),bool)),in),s(Q47974,Y))),s(fun(Q47974,bool),i(s(fun(fun(Q47975,bool),fun(Q47974,bool)),i(s(fun(fun(Q47975,Q47974),fun(fun(Q47975,bool),fun(Q47974,bool))),image),s(fun(Q47975,Q47974),F0))),s(fun(Q47975,bool),S0)))))))) <-> (exists X (p(s(bool,i(s(fun(Q47974,bool),p0),s(Q47974,i(s(fun(Q47975,Q47974),F0),s(Q47975,X)))))) & p(s(bool,i(s(fun(fun(Q47975,bool),bool),i(s(fun(Q47975,fun(fun(Q47975,bool),bool)),in),s(Q47975,X))),s(fun(Q47975,bool),S0)))))))) # label(aEXISTSu_INu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2448 (all A all B all OP (p(s(bool,i(s(fun(fun(B,fun(B,B)),bool),monoidal),s(fun(B,fun(B,B)),OP)))) -> (all F0 all P0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(A,i(s(fun(A,A),P0),s(A,Y))) = s(A,i(s(fun(A,A),P0),s(A,X))) -> s(A,Y) = s(A,X))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(A,A),P0),s(A,X))))),s(fun(A,bool),S0)))))) -> s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),i(s(fun(fun(A,A),fun(A,B)),i(s(fun(fun(A,B),fun(fun(A,A),fun(A,B))),o),s(fun(A,B),F0))),s(fun(A,A),P0))))) = s(B,i(s(fun(fun(A,B),B),i(s(fun(fun(A,bool),fun(fun(A,B),B)),i(s(fun(fun(B,fun(B,B)),fun(fun(A,bool),fun(fun(A,B),B))),iterate),s(fun(B,fun(B,B)),OP))),s(fun(A,bool),S0))),s(fun(A,B),F0))))))) # label(aITERATEu_INJECTION) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2449 (all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0)))))) # label(aLEu_1u_conjunct3) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2450 (all N0 all X all Y (p(s(bool,i(s(fun(num,bool),odd),s(num,N0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,Y)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,N0)))))))) # label(aINTu_POWu_LE2u_ODD) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2451 (all X all Y all H0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,H0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),realu_abs),s(real,Y))))),s(real,i(s(fun(real,real),realu_abs),s(real,X)))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,H0))))))),s(real,i(s(fun(real,real),realu_abs),s(real,Y)))))))) # label(aREALu_ABSu_CIRCLE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2452 (all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))))) # label(aLEu_1u_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.03/15.06 2453 (all X all K0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),intu_abs),s(int,X))))),s(int,K0)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,X))),s(int,K0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(int,int),intu_neg),s(int,K0))))),s(int,X)))))) # label(aINTu_BOUNDSu_LE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2454 (all N0 all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,N0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,N0)))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))))) # label(aREALu_POWu_LT2u_REV) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2455 (all A5 all B0 all C0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,A5))),s(real,B0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,B0))),s(real,C0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,A5))),s(real,C0)))) # label(aREALu_SUBu_TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2456 (all M0 all N0 all P0 all Q0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,M0))),s(num,P0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,P0))),s(num,Q0))))))))),s(num,i(s(fun(prod(num,num),num),dist),s(prod(num,num),i(s(fun(num,prod(num,num)),i(s(fun(num,fun(num,prod(num,num))),c_),s(num,N0))),s(num,Q0))))))))))) # label(aDISTu_ADD2u_REV) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2457 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_inv),s(real,Y))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_inv),s(real,X))))),s(real,Y)))))) # label(aREALu_LTu_LINV) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2458 (all Q59915 all Q59920 all T0 all S0 ((exists F0 ((all X all Y (p(s(bool,i(s(fun(fun(Q59920,bool),bool),i(s(fun(Q59920,fun(fun(Q59920,bool),bool)),in),s(Q59920,X))),s(fun(Q59920,bool),S0)))) & s(Q59915,i(s(fun(Q59920,Q59915),F0),s(Q59920,Y))) = s(Q59915,i(s(fun(Q59920,Q59915),F0),s(Q59920,X))) & p(s(bool,i(s(fun(fun(Q59920,bool),bool),i(s(fun(Q59920,fun(fun(Q59920,bool),bool)),in),s(Q59920,Y))),s(fun(Q59920,bool),S0)))) -> s(Q59920,X) = s(Q59920,Y))) & (all X (p(s(bool,i(s(fun(fun(Q59920,bool),bool),i(s(fun(Q59920,fun(fun(Q59920,bool),bool)),in),s(Q59920,X))),s(fun(Q59920,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q59915,bool),bool),i(s(fun(Q59915,fun(fun(Q59915,bool),bool)),in),s(Q59915,i(s(fun(Q59920,Q59915),F0),s(Q59920,X))))),s(fun(Q59915,bool),T0)))))))) <-> p(s(bool,i(s(fun(fun(Q59915,bool),bool),i(s(fun(fun(Q59920,bool),fun(fun(Q59915,bool),bool)),l_a_u_c),s(fun(Q59920,bool),S0))),s(fun(Q59915,bool),T0)))))) # label(aleu_c) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2459 (all Q87197 all Q87196 ((exists X p(s(bool,i(s(fun(sum0(Q87197,Q87196),bool),p0),s(sum0(Q87197,Q87196),i(s(fun(Q87197,sum0(Q87197,Q87196)),inl),s(Q87197,X))))))) | (exists X p(s(bool,i(s(fun(sum0(Q87197,Q87196),bool),p0),s(sum0(Q87197,Q87196),i(s(fun(Q87196,sum0(Q87197,Q87196)),inr),s(Q87196,X))))))) <-> (exists Z0 p(s(bool,i(s(fun(sum0(Q87197,Q87196),bool),p0),s(sum0(Q87197,Q87196),Z0))))))) # label(aEXISTSu_SUMu_THM) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2460 (all B all A all B0 all F0 all G0 all X s(B,i(s(fun(A,B),i(s(fun(fun(A,B),fun(A,B)),i(s(fun(fun(A,B),fun(fun(A,B),fun(A,B))),i(s(fun(bool,fun(fun(A,B),fun(fun(A,B),fun(A,B)))),cond),s(bool,B0))),s(fun(A,B),F0))),s(fun(A,B),G0))),s(A,X))) = s(B,i(s(fun(B,B),i(s(fun(B,fun(B,B)),i(s(fun(bool,fun(B,fun(B,B))),cond),s(bool,B0))),s(B,i(s(fun(A,B),F0),s(A,X))))),s(B,i(s(fun(A,B),G0),s(A,X)))))) # label(aCONDu_ABS) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2461 (all A all A5 all X all X0 (s(A,A5) = s(A,X0) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(num,fun(A,bool)),i(s(fun(A,fun(num,fun(A,bool))),inja),s(A,A5))),s(num,X))),s(A,X0)))))) # label(aINJA) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2462 (all A all L s(list(A),i(s(fun(list(A),list(A)),i(s(fun(list(A),fun(list(A),list(A))),append),s(list(A),nil))),s(list(A),L))) = s(list(A),L)) # label(aAPPENDu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2463 (all A all L all M0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),woset),s(fun(prod(A,A),bool),L)))) -> ((exists A5 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(prod(A,A),bool),fun(A,bool)),fl),s(fun(prod(A,A),bool),L))),s(A,A5)))) & s(fun(prod(A,A),bool),i(s(fun(A,fun(prod(A,A),bool)),i(s(fun(fun(prod(A,A),bool),fun(A,fun(prod(A,A),bool))),linseg),s(fun(prod(A,A),bool),L))),s(A,A5))) = s(fun(prod(A,A),bool),M0))) | s(fun(prod(A,A),bool),M0) = s(fun(prod(A,A),bool),L) <-> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),M0))),s(fun(prod(A,A),bool),L))))))) # label(aINSEGu_LINSEG) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2464 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y)))))))) # label(aREALu_LEu_DIV) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2465 (all Q20576 all Q20580 all F0 all L (s(list(Q20576),i(s(fun(list(Q20580),list(Q20576)),i(s(fun(fun(Q20580,Q20576),fun(list(Q20580),list(Q20576))),map0),s(fun(Q20580,Q20576),F0))),s(list(Q20580),L))) = s(list(Q20576),nil) <-> s(list(Q20580),L) = s(list(Q20580),nil))) # label(aMAPu_EQu_NIL) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2466 (all P0 ((all M0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,i(s(fun(fun(num,bool),num),minimal),s(fun(num,bool),P0)))))) -> -p(s(bool,i(s(fun(num,bool),P0),s(num,M0)))))) & p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(fun(num,bool),num),minimal),s(fun(num,bool),P0)))))) <-> (exists N0 p(s(bool,i(s(fun(num,bool),P0),s(num,N0))))))) # label(aMINIMAL) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2467 (all A all L all M0 (p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(prod(A,A),bool),fun(fun(prod(A,A),bool),bool)),inseg),s(fun(prod(A,A),bool),M0))),s(fun(prod(A,A),bool),L)))) -> (all X all Y (p(s(bool,i(s(fun(prod(A,A),bool),M0),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))) -> p(s(bool,i(s(fun(prod(A,A),bool),L),s(prod(A,A),i(s(fun(A,prod(A,A)),i(s(fun(A,fun(A,prod(A,A))),c_),s(A,X))),s(A,Y)))))))))) # label(aINSEGu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2468 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,Y))) = s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y)))))) # label(aINTu_MULu_LNEG) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2469 (all Q54262 all S0 all T0 (p(s(bool,i(s(fun(fun(Q54262,bool),bool),finite),s(fun(Q54262,bool),T0)))) & p(s(bool,i(s(fun(fun(Q54262,bool),bool),i(s(fun(fun(Q54262,bool),fun(fun(Q54262,bool),bool)),subset),s(fun(Q54262,bool),S0))),s(fun(Q54262,bool),T0)))) -> (s(fun(Q54262,bool),T0) = s(fun(Q54262,bool),S0) <-> s(num,i(s(fun(fun(Q54262,bool),num),card),s(fun(Q54262,bool),T0))) = s(num,i(s(fun(fun(Q54262,bool),num),card),s(fun(Q54262,bool),S0)))))) # label(aSUBSETu_CARDu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2470 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,Y))),s(real,X)))) <-> s(real,X) = s(real,Y))) # label(aREALu_LEu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2471 (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) # label(aREALu_LEu_POWu_2) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2472 (all A all X all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),S0))) != s(fun(A,bool),empty)) # label(aNOTu_INSERTu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2473 (all Q79352 all Q79310 all Q79350 all Q79349 all U_0 ((all Y (p(s(bool,i(s(fun(Q79352,bool),U_0),s(Q79352,Y)))) <-> s(Q79349,x) = s(Q79349,i(s(fun(Q79352,Q79349),s0),s(Q79352,Y))))) -> (exists V ((p(s(bool,V)) <-> (exists Y s(Q79349,i(s(fun(Q79352,Q79349),s0),s(Q79352,Y))) = s(Q79349,x))) & s(Q79310,i(s(fun(Q79349,Q79310),i(s(fun(Q79350,fun(Q79349,Q79310)),i(s(fun(list(prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310)))),fun(Q79350,fun(Q79349,Q79310))),casewise),s(list(prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310)))),i(s(fun(list(prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310)))),list(prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310))))),i(s(fun(prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310))),fun(list(prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310)))),list(prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310)))))),cons),s(prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310))),i(s(fun(fun(Q79350,fun(Q79352,Q79310)),prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310)))),i(s(fun(fun(Q79352,Q79349),fun(fun(Q79350,fun(Q79352,Q79310)),prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310))))),c_),s(fun(Q79352,Q79349),s0))),s(fun(Q79350,fun(Q79352,Q79310)),t0))))),s(list(prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310)))),clauses))))),s(Q79350,f))),s(Q79349,x))) = s(Q79310,i(s(fun(Q79310,Q79310),i(s(fun(Q79310,fun(Q79310,Q79310)),i(s(fun(bool,fun(Q79310,fun(Q79310,Q79310))),cond),s(bool,V))),s(Q79310,i(s(fun(Q79352,Q79310),i(s(fun(Q79350,fun(Q79352,Q79310)),t0),s(Q79350,f))),s(Q79352,i(s(fun(fun(Q79352,bool),Q79352),h_),s(fun(Q79352,bool),U_0))))))),s(Q79310,i(s(fun(Q79349,Q79310),i(s(fun(Q79350,fun(Q79349,Q79310)),i(s(fun(list(prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310)))),fun(Q79350,fun(Q79349,Q79310))),casewise),s(list(prod(fun(Q79352,Q79349),fun(Q79350,fun(Q79352,Q79310)))),clauses))),s(Q79350,f))),s(Q79349,x))))))))) # label(aCASEWISEu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2474 (all X all Y (s(int,i(s(fun(int,int),intu_neg),s(int,X))) = s(int,i(s(fun(int,int),intu_neg),s(int,Y))) <-> s(int,Y) = s(int,X))) # label(aINTu_EQu_NEG2) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2475 (all X s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(real,real),realu_neg),s(real,X))))) = s(real,X)) # label(aREALu_NEGNEG) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2476 (all M0 all N0 s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aADDu_SUC) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2477 (all A all S0 all T0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,bool),S0))))) # label(aINTERu_SUBSETu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2478 (all A p(s(bool,i(s(fun(fun(finite_image(A),bool),bool),finite),s(fun(finite_image(A),bool),univ))))) # label(aFINITEu_FINITEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2479 (all X all M0 all N0 s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))) = s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,M0))))),s(num,N0)))) # label(aINTu_POWu_POW) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2480 (all A all S0 all T0 all X s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(A,fun(fun(A,bool),fun(A,bool))),insert),s(A,X))),s(fun(A,bool),T0))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(fun(A,bool),T0)))) # label(aDIFFu_INSERT) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2481 (all A all B all T0 all S0 all F0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(fun(B,bool),bool))),surj),s(fun(A,B),F0))),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) <-> (all X (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,X))),s(fun(B,bool),T0)))) -> (exists Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,Y))) = s(B,X))))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0)))))))) # label(aSURJ) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2482 (all A all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> (exists A5 all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,A5))),s(num,i(s(fun(A,num),F0),s(A,X)))))))))) # label(aLOWERu_BOUNDu_FINITEu_SET) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2483 (all N0 s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,N0))),s(num,N0))) = s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(num,fun(fun(num,bool),fun(num,bool))),insert),s(num,N0))),s(fun(num,bool),empty)))) # label(aNUMSEGu_SING) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2484 (all S0 all A5 (s(fun(real,bool),empty) != s(fun(real,bool),S0) & p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),S0)))) -> (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))))),s(real,A5)))) <-> (exists X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,A5)))) & p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0))))))))) # label(aREALu_INFu_LEu_FINITE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2485 (all X s(int,X) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aINTu_MULu_RID) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2486 (all A all U all V all F0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),V)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),U))),s(fun(A,bool),V)))))) -> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(A,num),F0),s(A,X))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),U)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),U))),s(fun(A,num),F0))))),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),V))),s(fun(A,num),F0)))))))) # label(aNSUMu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2487 (all A all B all U_1 ((all T0 all GENR_PVARR_251 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),U_1),s(fun(B,bool),T0))),s(fun(B,bool),GENR_PVARR_251)))) <-> (exists V exists V0 ((p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),V))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),V)))) <-> p(s(bool,V0))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(bool,fun(fun(B,bool),bool)),i(s(fun(fun(B,bool),fun(bool,fun(fun(B,bool),bool))),setspec),s(fun(B,bool),GENR_PVARR_251))),s(bool,V0))),s(fun(B,bool),V)))))))) -> (all U_0 ((all S0 all GENR_PVARR_250 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))),s(fun(A,bool),GENR_PVARR_250)))) <-> (exists U exists V ((p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),U))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),U)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_250))),s(bool,V))),s(fun(A,bool),U)))))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(fun(B,bool),bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(fun(B,bool),bool),bool)),l_a_u_c),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))))))),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),gspec),s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),U_1),s(fun(B,bool),T0)))))))))))))) # label(aCARDu_LEu_FINITEu_SUBSETS) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2488 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y)))) # label(aREALu_POLYu_NEGu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2489 (all A5 all B0 all N0 (s(num,A5) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,B0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,N0)))))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,B0))),s(num,A5))))),s(num,N0)))))) # label(aLEu_LDIV) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2490 (all M0 all N0 s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,M0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0)))))) # label(aREALu_OFu_NUMu_MUL) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2491 (all X all Y all Z0 (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Z0))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y)))))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Z0))),s(int,X)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Z0))),s(int,Y)))))) # label(aINTu_LEu_MIN) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2492 (all Q48509 all Q48508 all U_1 ((all P0 all GENR_PVARR_20 ((exists A5 exists B0 p(s(bool,i(s(fun(prod(Q48509,Q48508),bool),i(s(fun(bool,fun(prod(Q48509,Q48508),bool)),i(s(fun(prod(Q48509,Q48508),fun(bool,fun(prod(Q48509,Q48508),bool))),setspec),s(prod(Q48509,Q48508),GENR_PVARR_20))),s(bool,i(s(fun(prod(Q48509,Q48508),bool),P0),s(prod(Q48509,Q48508),i(s(fun(Q48508,prod(Q48509,Q48508)),i(s(fun(Q48509,fun(Q48508,prod(Q48509,Q48508))),c_),s(Q48509,A5))),s(Q48508,B0))))))),s(prod(Q48509,Q48508),i(s(fun(Q48508,prod(Q48509,Q48508)),i(s(fun(Q48509,fun(Q48508,prod(Q48509,Q48508))),c_),s(Q48509,A5))),s(Q48508,B0))))))) <-> p(s(bool,i(s(fun(prod(Q48509,Q48508),bool),i(s(fun(fun(prod(Q48509,Q48508),bool),fun(prod(Q48509,Q48508),bool)),U_1),s(fun(prod(Q48509,Q48508),bool),P0))),s(prod(Q48509,Q48508),GENR_PVARR_20)))))) -> (all U_0 ((all P0 all GENR_PVARR_19 ((exists P1 p(s(bool,i(s(fun(prod(Q48509,Q48508),bool),i(s(fun(bool,fun(prod(Q48509,Q48508),bool)),i(s(fun(prod(Q48509,Q48508),fun(bool,fun(prod(Q48509,Q48508),bool))),setspec),s(prod(Q48509,Q48508),GENR_PVARR_19))),s(bool,i(s(fun(prod(Q48509,Q48508),bool),P0),s(prod(Q48509,Q48508),P1))))),s(prod(Q48509,Q48508),P1))))) <-> p(s(bool,i(s(fun(prod(Q48509,Q48508),bool),i(s(fun(fun(prod(Q48509,Q48508),bool),fun(prod(Q48509,Q48508),bool)),U_0),s(fun(prod(Q48509,Q48508),bool),P0))),s(prod(Q48509,Q48508),GENR_PVARR_19)))))) -> (all P0 s(fun(prod(Q48509,Q48508),bool),i(s(fun(fun(prod(Q48509,Q48508),bool),fun(prod(Q48509,Q48508),bool)),gspec),s(fun(prod(Q48509,Q48508),bool),i(s(fun(fun(prod(Q48509,Q48508),bool),fun(prod(Q48509,Q48508),bool)),U_1),s(fun(prod(Q48509,Q48508),bool),P0))))) = s(fun(prod(Q48509,Q48508),bool),i(s(fun(fun(prod(Q48509,Q48508),bool),fun(prod(Q48509,Q48508),bool)),gspec),s(fun(prod(Q48509,Q48508),bool),i(s(fun(fun(prod(Q48509,Q48508),bool),fun(prod(Q48509,Q48508),bool)),U_0),s(fun(prod(Q48509,Q48508),bool),P0)))))))))) # label(aSETu_PAIRu_THM) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2493 (all S0 all T0 ((all A5 ((all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X)))))) <-> (all X (p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),T0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X)))))))) -> s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),S0))) = s(real,i(s(fun(fun(real,bool),real),inf),s(fun(real,bool),T0))))) # label(aINFu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2494 (all A all P0 all Q0 ((exists X (p(s(bool,Q0)) & p(s(bool,i(s(fun(A,bool),P0),s(A,X)))))) <-> (exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) & p(s(bool,Q0)))) # label(aLEFTu_ANDu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2495 (all M0 all N0 all P0 all Q0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,P0))),s(num,Q0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,Q0)))))))) # label(aLTu_MULT2) # label(axiom) # label(non_clause). [assumption]. 15.03/15.07 2496 (all M0 exists V (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),f),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(num,real),f))) & (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,M0) <-> p(s(bool,V))))) # label(aSUMu_CLAUSESu_NUMSEGu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2497 (all X all Y all Z0 (s(int,Y) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Z0))) <-> s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y))),s(int,Z0))) = s(int,X))) # label(aINTu_EQu_SUBu_LADD) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2498 (all U_0 ((all C0 all X all I0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),C0),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),C0))),s(real,X))),s(num,I0)))) -> (all N0 all C0 ((all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))),s(fun(num,real),i(s(fun(real,fun(num,real)),i(s(fun(fun(num,real),fun(real,fun(num,real))),U_0),s(fun(num,real),C0))),s(real,X)))))) <-> (all I0 (p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,I0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(num,real),C0),s(num,I0))))))))) # label(aREALu_POLYFUNu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2499 (all Q50185 all Q50182 ((exists G0 all X s(Q50182,i(s(fun(Q50185,Q50182),G0),s(Q50185,i(s(fun(Q50182,Q50185),f),s(Q50182,X))))) = s(Q50182,X)) <-> (all X all Y (s(Q50185,i(s(fun(Q50182,Q50185),f),s(Q50182,Y))) = s(Q50185,i(s(fun(Q50182,Q50185),f),s(Q50182,X))) -> s(Q50182,X) = s(Q50182,Y))))) # label(aINJECTIVEu_LEFTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2500 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,u_0))) = s(num,i(s(fun(num,num),bit0),s(num,N0)))) # label(aARITHu_SUBu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2501 (all Q80137 all Q80138 all Q80169 all P all Q80194 all U_5 ((all P0 all H0 all K0 all F0 all X s(Q80194,i(s(fun(P,Q80194),i(s(fun(fun(Q80138,Q80169),fun(P,Q80194)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194)))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194))))),U_5),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(fun(Q80138,Q80169),fun(P,Q80194)),H0))),s(fun(fun(Q80138,Q80169),fun(P,Q80194)),K0))),s(fun(Q80138,Q80169),F0))),s(P,X))) = s(Q80194,i(s(fun(Q80194,Q80194),i(s(fun(Q80194,fun(Q80194,Q80194)),i(s(fun(bool,fun(Q80194,fun(Q80194,Q80194))),cond),s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80138,Q80169),fun(P,bool)),P0),s(fun(Q80138,Q80169),F0))),s(P,X))))),s(Q80194,i(s(fun(P,Q80194),i(s(fun(fun(Q80138,Q80169),fun(P,Q80194)),H0),s(fun(Q80138,Q80169),F0))),s(P,X))))),s(Q80194,i(s(fun(P,Q80194),i(s(fun(fun(Q80138,Q80169),fun(P,Q80194)),K0),s(fun(Q80138,Q80169),F0))),s(P,X)))))) -> (all U_4 ((all P0 all H0 all K0 all F0 s(fun(P,Q80194),i(s(fun(fun(Q80138,Q80169),fun(P,Q80194)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194)))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194))))),U_5),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(fun(Q80138,Q80169),fun(P,Q80194)),H0))),s(fun(fun(Q80138,Q80169),fun(P,Q80194)),K0))),s(fun(Q80138,Q80169),F0))) = s(fun(P,Q80194),i(s(fun(fun(Q80138,Q80169),fun(P,Q80194)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194)))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194))))),U_4),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(fun(Q80138,Q80169),fun(P,Q80194)),H0))),s(fun(fun(Q80138,Q80169),fun(P,Q80194)),K0))),s(fun(Q80138,Q80169),F0)))) -> (all U_3 ((all P0 all F0 all X (-p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80138,Q80169),fun(P,bool)),P0),s(fun(Q80138,Q80169),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80138,Q80169),fun(P,bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool))),U_3),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(Q80138,Q80169),F0))),s(P,X)))))) -> (all U_2 ((all P0 all F0 s(fun(P,bool),i(s(fun(fun(Q80138,Q80169),fun(P,bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool))),U_2),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(Q80138,Q80169),F0))) = s(fun(P,bool),i(s(fun(fun(Q80138,Q80169),fun(P,bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool))),U_3),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(Q80138,Q80169),F0)))) -> (all U_1 ((all P0 all P1 all F0 all X (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80138,Q80169),fun(P,bool)),P0),s(fun(Q80138,Q80169),F0))),s(P,X)))) & p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80138,Q80169),fun(P,bool)),P1),s(fun(Q80138,Q80169),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80138,Q80169),fun(P,bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool)))),U_1),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(fun(Q80138,Q80169),fun(P,bool)),P1))),s(fun(Q80138,Q80169),F0))),s(P,X)))))) -> (all U_0 ((all P0 all P1 all F0 s(fun(P,bool),i(s(fun(fun(Q80138,Q80169),fun(P,bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool)))),U_0),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(fun(Q80138,Q80169),fun(P,bool)),P1))),s(fun(Q80138,Q80169),F0))) = s(fun(P,bool),i(s(fun(fun(Q80138,Q80169),fun(P,bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool)))),U_1),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(fun(Q80138,Q80169),fun(P,bool)),P1))),s(fun(Q80138,Q80169),F0)))) -> (all L_L_ all P0 all P1 all S0 all H0 all K0 (p(s(bool,i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),bool),i(s(fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,bool)),bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,bool)),bool))),i(s(fun(fun(Q80138,fun(Q80137,bool)),fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,bool)),bool)))),admissible),s(fun(Q80138,fun(Q80137,bool)),L_L_))),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(P,Q80137),S0))),s(fun(fun(Q80138,Q80169),fun(P,bool)),P1)))) & p(s(bool,i(s(fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool),i(s(fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool))),i(s(fun(fun(Q80138,fun(Q80137,bool)),fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool)))),admissible),s(fun(Q80138,fun(Q80137,bool)),L_L_))),s(fun(fun(Q80138,Q80169),fun(P,bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool)))),U_0),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(fun(Q80138,Q80169),fun(P,bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool))),U_2),s(fun(fun(Q80138,Q80169),fun(P,bool)),P1))))))),s(fun(P,Q80137),S0))),s(fun(fun(Q80138,Q80169),fun(P,Q80194)),K0)))) & p(s(bool,i(s(fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool),i(s(fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool))),i(s(fun(fun(Q80138,fun(Q80137,bool)),fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool)))),admissible),s(fun(Q80138,fun(Q80137,bool)),L_L_))),s(fun(fun(Q80138,Q80169),fun(P,bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(Q80138,Q80169),fun(P,bool)))),U_0),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(fun(Q80138,Q80169),fun(P,bool)),P1))))),s(fun(P,Q80137),S0))),s(fun(fun(Q80138,Q80169),fun(P,Q80194)),H0)))) -> p(s(bool,i(s(fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool),i(s(fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool))),i(s(fun(fun(Q80138,fun(Q80137,bool)),fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(P,Q80137),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),bool)))),admissible),s(fun(Q80138,fun(Q80137,bool)),L_L_))),s(fun(fun(Q80138,Q80169),fun(P,bool)),P0))),s(fun(P,Q80137),S0))),s(fun(fun(Q80138,Q80169),fun(P,Q80194)),i(s(fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194)))),i(s(fun(fun(fun(Q80138,Q80169),fun(P,bool)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(fun(Q80138,Q80169),fun(P,Q80194)),fun(fun(Q80138,Q80169),fun(P,Q80194))))),U_4),s(fun(fun(Q80138,Q80169),fun(P,bool)),P1))),s(fun(fun(Q80138,Q80169),fun(P,Q80194)),H0))),s(fun(fun(Q80138,Q80169),fun(P,Q80194)),K0)))))))))))))))))))) # label(aADMISSIBLEu_COND) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2502 (all A all U_0 ((all S0 all T0 all GENR_PVARR_0 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,bool),T0))),s(A,GENR_PVARR_0)))) <-> (exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_0))),s(bool,V))),s(A,X)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) | p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0))))))))) -> (all S0 all T0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_0),s(fun(A,bool),S0))),s(fun(A,bool),T0))))) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0)))))) # label(aUNION) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2503 (all X0 all X all Y0 all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X0))),s(int,Y0)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,X0))))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y0))),s(int,X0)))))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(int,i(s(fun(int,int),intu_abs),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y))),s(int,Y0))))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,Y0))),s(int,X0)))))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))))) # label(aINTu_ABSu_BETWEEN2) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2504 (all A all S0 s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),diff),s(fun(A,bool),S0))),s(fun(A,bool),univ))) = s(fun(A,bool),empty)) # label(aDIFFu_UNIV) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2505 (all A all B all C all S0 all T0 all U (p(s(bool,i(s(fun(fun(C,bool),bool),infinite),s(fun(C,bool),U)))) & p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(B,bool),fun(fun(C,bool),bool)),l_a_u_c),s(fun(B,bool),T0))),s(fun(C,bool),U)))) & p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(A,bool),fun(fun(C,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(C,bool),U)))) -> p(s(bool,i(s(fun(fun(C,bool),bool),i(s(fun(fun(sum0(A,B),bool),fun(fun(C,bool),bool)),l_a_u_c),s(fun(sum0(A,B),bool),i(s(fun(fun(B,bool),fun(sum0(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(sum0(A,B),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0))))),s(fun(C,bool),U)))))) # label(aCARDu_ADD2u_ABSORBu_LE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2506 (all A all C0 all I0 all R0 s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(A,bool)),fun(num,fun(A,bool))),i(s(fun(fun(num,fun(A,bool)),fun(fun(num,fun(A,bool)),fun(num,fun(A,bool)))),injp),s(fun(num,fun(A,bool)),i(s(fun(num,fun(num,fun(A,bool))),injn),s(num,i(s(fun(num,num),suc),s(num,C0))))))),s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(A,bool)),fun(num,fun(A,bool))),i(s(fun(fun(num,fun(A,bool)),fun(fun(num,fun(A,bool)),fun(num,fun(A,bool)))),injp),s(fun(num,fun(A,bool)),i(s(fun(A,fun(num,fun(A,bool))),inja),s(A,I0))))),s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))),injf),s(fun(num,fun(num,fun(A,bool))),R0))))))) = s(fun(num,fun(A,bool)),i(s(fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))),i(s(fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool)))),i(s(fun(num,fun(A,fun(fun(num,fun(num,fun(A,bool))),fun(num,fun(A,bool))))),zconstr),s(num,C0))),s(A,I0))),s(fun(num,fun(num,fun(A,bool))),R0)))) # label(aZCONSTR) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2507 p(s(bool,i(s(fun(real,bool),integer),s(real,r0)))) <-> s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(real,int),intu_ofu_real),s(real,r0))))) = s(real,r0) # label(aintu_rep) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2508 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y)))))))) # label(aINTu_LEu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2509 (all Q71846 all U_0 ((all C0 all N0 s(real,i(s(fun(Q71846,real),i(s(fun(real,fun(Q71846,real)),U_0),s(real,C0))),s(Q71846,N0))) = s(real,C0)) -> (all C0 all S0 (p(s(bool,i(s(fun(fun(Q71846,bool),bool),finite),s(fun(Q71846,bool),S0)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(Q71846,bool),num),card),s(fun(Q71846,bool),S0))))))),s(real,C0))) = s(real,i(s(fun(fun(Q71846,real),real),i(s(fun(fun(Q71846,bool),fun(fun(Q71846,real),real)),sum),s(fun(Q71846,bool),S0))),s(fun(Q71846,real),i(s(fun(real,fun(Q71846,real)),U_0),s(real,C0))))))))) # label(aSUMu_CONST) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2510 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),realu_neg),s(real,X))))),s(real,i(s(fun(real,real),realu_neg),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X)))) # label(aREALu_SUBu_NEG2) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2511 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))))))),s(num,u_0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aARITHu_SUBu_conjunct8) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2512 (p(s(bool,p1)) & p(s(bool,q)) -> p(s(bool,r0))) <-> (p(s(bool,q)) -> (p(s(bool,p1)) -> p(s(bool,r0)))) # label(aIMPu_CONJu_ALT) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2513 (all A all N all I0 exists K0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & (all X s(A,i(s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),d_),s(cart(A,N),X))),s(num,I0))) = s(A,i(s(fun(num,A),i(s(fun(cart(A,N),fun(num,A)),d_),s(cart(A,N),X))),s(num,K0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0)))))) # label(aFINITEu_INDEXu_INRANGE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2514 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,Y))),s(int,X)))) # label(aINTu_MULu_SYM) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2515 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),bit0),s(num,M0))))),s(num,i(s(fun(num,num),bit1),s(num,N0))))) = s(num,i(s(fun(num,num),pre),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0)))))))) # label(aARITHu_SUBu_conjunct7) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2516 (all A all C all B all D all S0 all SI_ all T0 all TI_ (p(s(bool,i(s(fun(fun(D,bool),bool),i(s(fun(fun(C,bool),fun(fun(D,bool),bool)),a_u_c),s(fun(C,bool),T0))),s(fun(D,bool),TI_)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),SI_)))) -> p(s(bool,i(s(fun(fun(prod(B,D),bool),bool),i(s(fun(fun(prod(A,C),bool),fun(fun(prod(B,D),bool),bool)),a_u_c),s(fun(prod(A,C),bool),i(s(fun(fun(C,bool),fun(prod(A,C),bool)),i(s(fun(fun(A,bool),fun(fun(C,bool),fun(prod(A,C),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(C,bool),T0))))),s(fun(prod(B,D),bool),i(s(fun(fun(D,bool),fun(prod(B,D),bool)),i(s(fun(fun(B,bool),fun(fun(D,bool),fun(prod(B,D),bool))),t_u_c),s(fun(B,bool),SI_))),s(fun(D,bool),TI_)))))))) # label(aCARDu_MULu_CONG) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2517 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aLTu_SUCu_LE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2518 (all Q60092 all T0 s(bool,i(s(fun(fun(Q60092,bool),bool),i(s(fun(fun(num,bool),fun(fun(Q60092,bool),bool)),g_a_u_c),s(fun(num,bool),univ))),s(fun(Q60092,bool),T0))) = s(bool,i(s(fun(fun(Q60092,bool),bool),countable),s(fun(Q60092,bool),T0)))) # label(aCOUNTABLE) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2519 (all B all A all T0 all X s(B,i(s(fun(A,B),T0),s(A,X))) = s(B,i(s(fun(A,B),T0),s(A,X)))) # label(aETAu_AX) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2520 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),hasu_size),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,N0))))),s(num,N0))))) # label(aHASu_SIZEu_NUMSEGu_1) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2521 (all A all S0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),univ))))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),univ))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(num,i(s(fun(fun(A,bool),num),dimindex),s(fun(A,bool),S0)))) # label(adimindex) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2522 (all M0 s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aMULTu_0) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2523 (all A all S0 all F0 all B0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(A,num),F0),s(A,X))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,B0))),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0)))))))))) & s(fun(A,bool),S0) != s(fun(A,bool),empty) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(A,num),num),i(s(fun(fun(A,bool),fun(fun(A,num),num)),nsum),s(fun(A,bool),S0))),s(fun(A,num),F0))))),s(num,B0)))))) # label(aNSUMu_BOUNDu_GEN) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2524 (all Q47510 s(fun(Q47510,bool),s0) = s(fun(Q47510,bool),i(s(fun(fun(fun(Q47510,bool),bool),fun(Q47510,bool)),inters),s(fun(fun(Q47510,bool),bool),i(s(fun(fun(fun(Q47510,bool),bool),fun(fun(Q47510,bool),bool)),i(s(fun(fun(Q47510,bool),fun(fun(fun(Q47510,bool),bool),fun(fun(Q47510,bool),bool))),insert),s(fun(Q47510,bool),s0))),s(fun(fun(Q47510,bool),bool),empty)))))) # label(aINTERSu_1) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2525 (all X all N0 s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(num,N0))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),i(s(fun(bool,fun(int,fun(int,int))),cond),s(bool,i(s(fun(num,bool),even),s(num,N0))))),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))))),s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0)))))))) # label(aINTu_POWu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2526 (all A s(list(A),i(s(fun(list(A),list(A)),tl),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,h0))),s(list(A),t0))))) = s(list(A),t0)) # label(aTL) # label(axiom) # label(non_clause). [assumption]. 15.03/15.08 2527 (all A all C all B all D all S0 all SI_ all T0 all TI_ (p(s(bool,i(s(fun(fun(D,bool),bool),i(s(fun(fun(C,bool),fun(fun(D,bool),bool)),l_a_u_c),s(fun(C,bool),T0))),s(fun(D,bool),TI_)))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),l_a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),SI_)))) -> p(s(bool,i(s(fun(fun(sum0(B,D),bool),bool),i(s(fun(fun(sum0(A,C),bool),fun(fun(sum0(B,D),bool),bool)),l_a_u_c),s(fun(sum0(A,C),bool),i(s(fun(fun(C,bool),fun(sum0(A,C),bool)),i(s(fun(fun(A,bool),fun(fun(C,bool),fun(sum0(A,C),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(C,bool),T0))))),s(fun(sum0(B,D),bool),i(s(fun(fun(D,bool),fun(sum0(B,D),bool)),i(s(fun(fun(B,bool),fun(fun(D,bool),fun(sum0(B,D),bool))),p_u_c),s(fun(B,bool),SI_))),s(fun(D,bool),TI_)))))))) # label(aCARDu_LEu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2528 (all Q19920 all Q19919 all P0 all F0 all L s(bool,i(s(fun(list(Q19919),bool),i(s(fun(fun(Q19919,bool),fun(list(Q19919),bool)),ex0),s(fun(Q19919,bool),i(s(fun(fun(Q19919,Q19920),fun(Q19919,bool)),i(s(fun(fun(Q19920,bool),fun(fun(Q19919,Q19920),fun(Q19919,bool))),o),s(fun(Q19920,bool),P0))),s(fun(Q19919,Q19920),F0))))),s(list(Q19919),L))) = s(bool,i(s(fun(list(Q19920),bool),i(s(fun(fun(Q19920,bool),fun(list(Q19920),bool)),ex0),s(fun(Q19920,bool),P0))),s(list(Q19920),i(s(fun(list(Q19919),list(Q19920)),i(s(fun(fun(Q19919,Q19920),fun(list(Q19919),list(Q19920))),map0),s(fun(Q19919,Q19920),F0))),s(list(Q19919),L)))))) # label(aEXu_MAP) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2529 (all X all Y s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_sub),s(int,X))),s(int,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y)))))) # label(aintu_subu_th) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2530 (all A all P0 all Q0 ((p(s(bool,P0)) -> (all X p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))) <-> (all X (p(s(bool,P0)) -> p(s(bool,i(s(fun(A,bool),Q0),s(A,X)))))))) # label(aRIGHTu_IMPu_FORALLu_THM) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2531 (all X all Y all Z0 s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,Y))))),s(int,Z0))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,X))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_min),s(int,Y))),s(int,Z0)))))) # label(aINTu_MINu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2532 (all M0 all N0 all P0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,P0) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,N0))),s(num,P0)))))))) # label(aDIVu_MONO) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2533 (all Q19851 all P0 all Q0 all L (p(s(bool,i(s(fun(list(Q19851),bool),i(s(fun(fun(Q19851,bool),fun(list(Q19851),bool)),ex0),s(fun(Q19851,bool),P0))),s(list(Q19851),L)))) & (all X (p(s(bool,i(s(fun(Q19851,bool),P0),s(Q19851,X)))) & p(s(bool,i(s(fun(list(Q19851),bool),i(s(fun(Q19851,fun(list(Q19851),bool)),mem),s(Q19851,X))),s(list(Q19851),L)))) -> p(s(bool,i(s(fun(Q19851,bool),Q0),s(Q19851,X)))))) -> p(s(bool,i(s(fun(list(Q19851),bool),i(s(fun(fun(Q19851,bool),fun(list(Q19851),bool)),ex0),s(fun(Q19851,bool),Q0))),s(list(Q19851),L)))))) # label(aEXu_IMP) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2534 (all Q80312 all Q80391 all Q80313 all Q80375 all P all Q80401 all U_9 ((all C1 all C2 all F0 all X s(fun(Q80401,fun(Q80391,bool)),i(s(fun(fun(Q80401,fun(Q80391,bool)),fun(Q80401,fun(Q80391,bool))),i(s(fun(fun(Q80401,fun(Q80391,bool)),fun(fun(Q80401,fun(Q80391,bool)),fun(Q80401,fun(Q80391,bool)))),u_seqpattern),s(fun(Q80401,fun(Q80391,bool)),i(s(fun(P,fun(Q80401,fun(Q80391,bool))),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1),s(fun(Q80313,Q80375),F0))),s(P,X))))),s(fun(Q80401,fun(Q80391,bool)),i(s(fun(P,fun(Q80401,fun(Q80391,bool))),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C2),s(fun(Q80313,Q80375),F0))),s(P,X))))) = s(fun(Q80401,fun(Q80391,bool)),i(s(fun(P,fun(Q80401,fun(Q80391,bool))),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool))))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))))),U_9),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C2))),s(fun(Q80313,Q80375),F0))),s(P,X)))) -> (all U_8 ((all C1 all C2 all F0 s(fun(P,fun(Q80401,fun(Q80391,bool))),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool))))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))))),U_9),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C2))),s(fun(Q80313,Q80375),F0))) = s(fun(P,fun(Q80401,fun(Q80391,bool))),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool))))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))))),U_8),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C2))),s(fun(Q80313,Q80375),F0)))) -> (all U_7 ((all P0 all C1 all E0 all F0 all X (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))))),U_7),s(fun(fun(Q80313,Q80375),fun(P,bool)),P0))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80313,Q80375),fun(P,bool)),P0),s(fun(Q80313,Q80375),F0))),s(P,X)))) & -(exists Y p(s(bool,i(s(fun(Q80391,bool),i(s(fun(Q80401,fun(Q80391,bool)),i(s(fun(P,fun(Q80401,fun(Q80391,bool))),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1),s(fun(Q80313,Q80375),F0))),s(P,X))),s(Q80401,i(s(fun(P,Q80401),i(s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0),s(fun(Q80313,Q80375),F0))),s(P,X))))),s(Q80391,Y))))))) -> (all U_6 ((all P0 all C1 all E0 all F0 s(fun(P,bool),i(s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))))),U_6),s(fun(fun(Q80313,Q80375),fun(P,bool)),P0))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0))) = s(fun(P,bool),i(s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))))),U_7),s(fun(fun(Q80313,Q80375),fun(P,bool)),P0))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0)))) -> (all U_5 ((all C1 all E0 all F0 all X s(fun(Q80391,bool),i(s(fun(Q80401,fun(Q80391,bool)),i(s(fun(P,fun(Q80401,fun(Q80391,bool))),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1),s(fun(Q80313,Q80375),F0))),s(P,X))),s(Q80401,i(s(fun(P,Q80401),i(s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0),s(fun(Q80313,Q80375),F0))),s(P,X))))) = s(fun(Q80391,bool),i(s(fun(P,fun(Q80391,bool)),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))))),U_5),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0))),s(P,X)))) -> (all U_4 ((all C1 all E0 all F0 s(fun(P,fun(Q80391,bool)),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))))),U_4),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0))) = s(fun(P,fun(Q80391,bool)),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))))),U_5),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0)))) -> (all U_3 ((all P0 all C1 all E0 all F0 all X (p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))))),U_3),s(fun(fun(Q80313,Q80375),fun(P,bool)),P0))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0))),s(P,X)))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80313,Q80375),fun(P,bool)),P0),s(fun(Q80313,Q80375),F0))),s(P,X)))) & (exists Y p(s(bool,i(s(fun(Q80391,bool),i(s(fun(Q80401,fun(Q80391,bool)),i(s(fun(P,fun(Q80401,fun(Q80391,bool))),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1),s(fun(Q80313,Q80375),F0))),s(P,X))),s(Q80401,i(s(fun(P,Q80401),i(s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0),s(fun(Q80313,Q80375),F0))),s(P,X))))),s(Q80391,Y))))))) -> (all U_2 ((all P0 all C1 all E0 all F0 s(fun(P,bool),i(s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))))),U_3),s(fun(fun(Q80313,Q80375),fun(P,bool)),P0))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0))) = s(fun(P,bool),i(s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))))),U_2),s(fun(fun(Q80313,Q80375),fun(P,bool)),P0))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0)))) -> (all U_1 ((all C1 all E0 all F0 all X ((exists Y p(s(bool,i(s(fun(Q80391,bool),i(s(fun(Q80401,fun(Q80391,bool)),i(s(fun(P,fun(Q80401,fun(Q80391,bool))),i(s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1),s(fun(Q80313,Q80375),F0))),s(P,X))),s(Q80401,i(s(fun(P,Q80401),i(s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0),s(fun(Q80313,Q80375),F0))),s(P,X))))),s(Q80391,Y))))) <-> p(s(bool,i(s(fun(P,bool),i(s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),U_1),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0))),s(P,X)))))) -> (all U_0 ((all C1 all E0 all F0 s(fun(P,bool),i(s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),U_1),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0))) = s(fun(P,bool),i(s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),U_0),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))),s(fun(Q80313,Q80375),F0)))) -> (all L_L_ all P0 all S0 all C1 all C2 all E0 (p(s(bool,i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),bool),i(s(fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,bool)),bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,bool)),bool))),i(s(fun(fun(Q80313,fun(Q80312,bool)),fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,bool)),bool)))),admissible),s(fun(Q80313,fun(Q80312,bool)),L_L_))),s(fun(fun(Q80313,Q80375),fun(P,bool)),P0))),s(fun(P,Q80312),S0))),s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),U_0),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0)))))) & p(s(bool,i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool),i(s(fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool))),i(s(fun(fun(Q80313,fun(Q80312,bool)),fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool)))),admissible),s(fun(Q80313,fun(Q80312,bool)),L_L_))),s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))))),U_6),s(fun(fun(Q80313,Q80375),fun(P,bool)),P0))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))))),s(fun(P,Q80312),S0))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))))),U_4),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C2))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0)))))) & p(s(bool,i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool),i(s(fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool))),i(s(fun(fun(Q80313,fun(Q80312,bool)),fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool)))),admissible),s(fun(Q80313,fun(Q80312,bool)),L_L_))),s(fun(fun(Q80313,Q80375),fun(P,bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,bool))))),U_2),s(fun(fun(Q80313,Q80375),fun(P,bool)),P0))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0))))),s(fun(P,Q80312),S0))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))))),U_4),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0)))))) -> p(s(bool,i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool),i(s(fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool)),i(s(fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool))),i(s(fun(fun(Q80313,fun(Q80312,bool)),fun(fun(fun(Q80313,Q80375),fun(P,bool)),fun(fun(P,Q80312),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),bool)))),admissible),s(fun(Q80313,fun(Q80312,bool)),L_L_))),s(fun(fun(Q80313,Q80375),fun(P,bool)),P0))),s(fun(P,Q80312),S0))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,Q80401)),fun(fun(Q80313,Q80375),fun(P,fun(Q80391,bool))))),U_4),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool))))),i(s(fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))))),U_8),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C1))),s(fun(fun(Q80313,Q80375),fun(P,fun(Q80401,fun(Q80391,bool)))),C2))))),s(fun(fun(Q80313,Q80375),fun(P,Q80401)),E0)))))))))))))))))))))))))))) # label(aADMISSIBLEu_SEQPATTERN) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2535 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))))),s(real,i(s(fun(real,real),realu_abs),s(real,Y)))))) -> s(real,X) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aREALu_ABSu_STILLNZ) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2536 (all A s(list(A),i(s(fun(list(A),list(A)),reverse),s(list(A),nil))) = s(list(A),nil)) # label(aREVERSEu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2537 (all A all B all A5 all AI_ (s(B,A5) = s(B,AI_) <-> s(sum0(A,B),i(s(fun(B,sum0(A,B)),inr),s(B,A5))) = s(sum0(A,B),i(s(fun(B,sum0(A,B)),inr),s(B,AI_))))) # label(asumu_INJECTIVEu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2538 (all A all B all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(A,bool),fun(fun(B,bool),bool)),a_u_c),s(fun(A,bool),S0))),s(fun(B,bool),T0)))) -> s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),S0))) = s(bool,i(s(fun(fun(B,bool),bool),infinite),s(fun(B,bool),T0))))) # label(aCARDu_INFINITEu_CONG) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2539 (all A all P0 all Q0 ((all X (p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) -> p(s(bool,Q0)))) <-> ((exists X p(s(bool,i(s(fun(A,bool),P0),s(A,X))))) -> p(s(bool,Q0))))) # label(aLEFTu_IMPu_EXISTSu_THM) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2540 (all N0 s(num,i(s(fun(num,num),bit1),s(num,N0))) = s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),bit0),s(num,N0)))))) # label(aBIT1u_DEF) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2541 (all N0 (p(s(bool,f0)) <-> s(num,i(s(fun(num,num),bit1),s(num,N0))) = s(num,u_0))) # label(aARITHu_EQu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2542 (all A all N (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),univ)))) -> s(num,i(s(fun(fun(cart(A,N),bool),num),card),s(fun(cart(A,N),bool),univ))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),univ))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))) # label(aCARDu_CARTu_UNIV) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2543 (all A5 s(real,A5) = s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),i(s(fun(real,fun(fun(real,bool),fun(real,bool))),insert),s(real,A5))),s(fun(real,bool),empty)))))) # label(aSUPu_SING) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2544 (all M0 all N0 (s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(int,N0) -> s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),div0),s(int,M0))),s(int,N0))))),s(int,N0))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),rem),s(int,M0))),s(int,N0))))) = s(int,M0) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),rem),s(int,M0))),s(int,N0))))),s(int,i(s(fun(int,int),intu_abs),s(int,N0)))))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),rem),s(int,M0))),s(int,N0)))))))) # label(aINTu_DIVISION) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2545 (all X all Y (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y)))) -> (exists D0 p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_eq),s(nadd,Y))),s(nadd,i(s(fun(nadd,nadd),i(s(fun(nadd,fun(nadd,nadd)),naddu_add),s(nadd,X))),s(nadd,D0))))))))) # label(aNADDu_LEu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2546 (all Q18985 all Q18984 all Q18983 s(Q18983,b0) = s(Q18983,i(s(fun(Q18983,Q18983),i(s(fun(list(Q18984),fun(Q18983,Q18983)),i(s(fun(list(Q18985),fun(list(Q18984),fun(Q18983,Q18983))),i(s(fun(fun(Q18985,fun(Q18984,fun(Q18983,Q18983))),fun(list(Q18985),fun(list(Q18984),fun(Q18983,Q18983)))),itlist2),s(fun(Q18985,fun(Q18984,fun(Q18983,Q18983))),f))),s(list(Q18985),nil))),s(list(Q18984),nil))),s(Q18983,b0)))) # label(aITLIST2u_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2547 (all Q19690 all Q19689 all U_1 ((all P0 all Q0 all X all Y (p(s(bool,i(s(fun(Q19689,bool),i(s(fun(Q19690,fun(Q19689,bool)),i(s(fun(fun(Q19690,fun(Q19689,bool)),fun(Q19690,fun(Q19689,bool))),i(s(fun(fun(Q19690,bool),fun(fun(Q19690,fun(Q19689,bool)),fun(Q19690,fun(Q19689,bool)))),U_1),s(fun(Q19690,bool),P0))),s(fun(Q19690,fun(Q19689,bool)),Q0))),s(Q19690,X))),s(Q19689,Y)))) <-> p(s(bool,i(s(fun(Q19690,bool),P0),s(Q19690,X)))) & p(s(bool,i(s(fun(Q19689,bool),i(s(fun(Q19690,fun(Q19689,bool)),Q0),s(Q19690,X))),s(Q19689,Y)))))) -> (all U_0 ((all P0 all Q0 all X s(fun(Q19689,bool),i(s(fun(Q19690,fun(Q19689,bool)),i(s(fun(fun(Q19690,fun(Q19689,bool)),fun(Q19690,fun(Q19689,bool))),i(s(fun(fun(Q19690,bool),fun(fun(Q19690,fun(Q19689,bool)),fun(Q19690,fun(Q19689,bool)))),U_1),s(fun(Q19690,bool),P0))),s(fun(Q19690,fun(Q19689,bool)),Q0))),s(Q19690,X))) = s(fun(Q19689,bool),i(s(fun(Q19690,fun(Q19689,bool)),i(s(fun(fun(Q19690,fun(Q19689,bool)),fun(Q19690,fun(Q19689,bool))),i(s(fun(fun(Q19690,bool),fun(fun(Q19690,fun(Q19689,bool)),fun(Q19690,fun(Q19689,bool)))),U_0),s(fun(Q19690,bool),P0))),s(fun(Q19690,fun(Q19689,bool)),Q0))),s(Q19690,X)))) -> (all L all M0 all P0 all Q0 (p(s(bool,i(s(fun(list(Q19689),bool),i(s(fun(list(Q19690),fun(list(Q19689),bool)),i(s(fun(fun(Q19690,fun(Q19689,bool)),fun(list(Q19690),fun(list(Q19689),bool))),all2),s(fun(Q19690,fun(Q19689,bool)),i(s(fun(fun(Q19690,fun(Q19689,bool)),fun(Q19690,fun(Q19689,bool))),i(s(fun(fun(Q19690,bool),fun(fun(Q19690,fun(Q19689,bool)),fun(Q19690,fun(Q19689,bool)))),U_0),s(fun(Q19690,bool),P0))),s(fun(Q19690,fun(Q19689,bool)),Q0))))),s(list(Q19690),L))),s(list(Q19689),M0)))) <-> p(s(bool,i(s(fun(list(Q19690),bool),i(s(fun(fun(Q19690,bool),fun(list(Q19690),bool)),all0),s(fun(Q19690,bool),P0))),s(list(Q19690),L)))) & p(s(bool,i(s(fun(list(Q19689),bool),i(s(fun(list(Q19690),fun(list(Q19689),bool)),i(s(fun(fun(Q19690,fun(Q19689,bool)),fun(list(Q19690),fun(list(Q19689),bool))),all2),s(fun(Q19690,fun(Q19689,bool)),Q0))),s(list(Q19690),L))),s(list(Q19689),M0)))))))))) # label(aALL2u_ANDu_RIGHT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2548 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,y1)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,y2)))) -> (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x2))),s(real,y1))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,x1))),s(real,y2))) <-> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,x2))),s(real,y2))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,x1))),s(real,y1)))) # label(aRATu_LEMMA5) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2549 (all Q49786 all Q49791 all P0 all F0 ((all X all Y (s(Q49786,i(s(fun(Q49791,Q49786),F0),s(Q49791,X))) = s(Q49786,i(s(fun(Q49791,Q49786),F0),s(Q49791,Y))) & p(s(bool,i(s(fun(Q49791,bool),P0),s(Q49791,Y)))) & p(s(bool,i(s(fun(Q49791,bool),P0),s(Q49791,X)))) -> s(Q49791,Y) = s(Q49791,X))) <-> (all X all Y (p(s(bool,i(s(fun(Q49791,bool),P0),s(Q49791,X)))) & p(s(bool,i(s(fun(Q49791,bool),P0),s(Q49791,Y)))) -> (s(Q49786,i(s(fun(Q49791,Q49786),F0),s(Q49791,Y))) = s(Q49786,i(s(fun(Q49791,Q49786),F0),s(Q49791,X))) <-> s(Q49791,X) = s(Q49791,Y)))))) # label(aINJECTIVEu_ONu_ALT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2550 (all F0 all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,P0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,real),F0))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,P0))))),s(fun(num,real),F0))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,P0))))),s(fun(num,real),F0))))) # label(aSUMu_COMBINEu_R) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2551 (all X all Y s(real,i(s(fun(real,real),realu_sgn),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_sgn),s(real,X))))),s(real,i(s(fun(real,real),realu_sgn),s(real,Y)))))) # label(aREALu_SGNu_MUL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2552 (all Q93175 all S0 (p(s(bool,i(s(fun(fun(Q93175,bool),bool),countable),s(fun(Q93175,bool),S0)))) -> (exists F0 p(s(bool,i(s(fun(fun(Q93175,bool),bool),i(s(fun(fun(Q93175,bool),fun(fun(Q93175,bool),bool)),subset),s(fun(Q93175,bool),S0))),s(fun(Q93175,bool),i(s(fun(fun(num,bool),fun(Q93175,bool)),i(s(fun(fun(num,Q93175),fun(fun(num,bool),fun(Q93175,bool))),image),s(fun(num,Q93175),F0))),s(fun(num,bool),univ))))))))) # label(aCOUNTABLEu_ASu_IMAGEu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2553 (all X all Y all Z0 (p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Y)))) & p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,Y))),s(nadd,Z0)))) -> p(s(bool,i(s(fun(nadd,bool),i(s(fun(nadd,fun(nadd,bool)),naddu_le),s(nadd,X))),s(nadd,Z0)))))) # label(aNADDu_LEu_TRANS) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2554 (all A all S0 ((exists K0 exists F0 ((all I0 all J0 (p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,I0))),s(fun(num,bool),K0)))) & p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,J0))),s(fun(num,bool),K0)))) & s(A,i(s(fun(num,A),F0),s(num,I0))) = s(A,i(s(fun(num,A),F0),s(num,J0))) -> s(num,J0) = s(num,I0))) & p(s(bool,i(s(fun(fun(num,bool),bool),finite),s(fun(num,bool),K0)))) & s(fun(A,bool),i(s(fun(fun(num,bool),fun(A,bool)),i(s(fun(fun(num,A),fun(fun(num,bool),fun(A,bool))),image),s(fun(num,A),F0))),s(fun(num,bool),K0))) = s(fun(A,bool),S0))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))))) # label(aFINITEu_INDEXu_NUMBERS) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2555 (all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,X)) # label(aREALu_DIVu_1) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2556 (all P0 ((exists B0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),P0),s(num,N0))))),s(num,B0))))) <-> (exists A5 exists B0 all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,i(s(fun(num,num),P0),s(num,N0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,A5))),s(num,N0))))),s(num,B0))))))))) # label(aBOUNDSu_DIVIDED) # label(axiom) # label(non_clause). [assumption]. 15.12/15.09 2557 (all M0 exists V (s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(fun(num,bool),fun(fun(num,bool),fun(num,bool))),i(s(fun(bool,fun(fun(num,bool),fun(fun(num,bool),fun(num,bool)))),cond),s(bool,V))),s(fun(num,bool),i(s(fun(fun(num,bool),fun(num,bool)),i(s(fun(num,fun(fun(num,bool),fun(num,bool))),insert),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(fun(num,bool),empty))))),s(fun(num,bool),empty))) & (s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) <-> p(s(bool,V))))) # label(aNUMSEGu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2558 (all Q48848 all Q48851 all Q48850 all Q48849 all U_0 ((all P0 all F0 all GENR_PVARR_26 (p(s(bool,i(s(fun(Q48848,bool),i(s(fun(fun(Q48851,fun(Q48850,fun(Q48849,Q48848))),fun(Q48848,bool)),i(s(fun(fun(Q48851,fun(Q48850,fun(Q48849,bool))),fun(fun(Q48851,fun(Q48850,fun(Q48849,Q48848))),fun(Q48848,bool))),U_0),s(fun(Q48851,fun(Q48850,fun(Q48849,bool))),P0))),s(fun(Q48851,fun(Q48850,fun(Q48849,Q48848))),F0))),s(Q48848,GENR_PVARR_26)))) <-> (exists W exists X exists Y p(s(bool,i(s(fun(Q48848,bool),i(s(fun(bool,fun(Q48848,bool)),i(s(fun(Q48848,fun(bool,fun(Q48848,bool))),setspec),s(Q48848,GENR_PVARR_26))),s(bool,i(s(fun(Q48849,bool),i(s(fun(Q48850,fun(Q48849,bool)),i(s(fun(Q48851,fun(Q48850,fun(Q48849,bool))),P0),s(Q48851,W))),s(Q48850,X))),s(Q48849,Y))))),s(Q48848,i(s(fun(Q48849,Q48848),i(s(fun(Q48850,fun(Q48849,Q48848)),i(s(fun(Q48851,fun(Q48850,fun(Q48849,Q48848))),F0),s(Q48851,W))),s(Q48850,X))),s(Q48849,Y))))))))) -> (all P0 all F0 ((exists W exists X exists Y (p(s(bool,i(s(fun(Q48848,bool),q0),s(Q48848,i(s(fun(Q48849,Q48848),i(s(fun(Q48850,fun(Q48849,Q48848)),i(s(fun(Q48851,fun(Q48850,fun(Q48849,Q48848))),F0),s(Q48851,W))),s(Q48850,X))),s(Q48849,Y)))))) & p(s(bool,i(s(fun(Q48849,bool),i(s(fun(Q48850,fun(Q48849,bool)),i(s(fun(Q48851,fun(Q48850,fun(Q48849,bool))),P0),s(Q48851,W))),s(Q48850,X))),s(Q48849,Y)))))) <-> (exists Z0 (p(s(bool,i(s(fun(fun(Q48848,bool),bool),i(s(fun(Q48848,fun(fun(Q48848,bool),bool)),in),s(Q48848,Z0))),s(fun(Q48848,bool),i(s(fun(fun(Q48848,bool),fun(Q48848,bool)),gspec),s(fun(Q48848,bool),i(s(fun(fun(Q48851,fun(Q48850,fun(Q48849,Q48848))),fun(Q48848,bool)),i(s(fun(fun(Q48851,fun(Q48850,fun(Q48849,bool))),fun(fun(Q48851,fun(Q48850,fun(Q48849,Q48848))),fun(Q48848,bool))),U_0),s(fun(Q48851,fun(Q48850,fun(Q48849,bool))),P0))),s(fun(Q48851,fun(Q48850,fun(Q48849,Q48848))),F0)))))))) & p(s(bool,i(s(fun(Q48848,bool),q0),s(Q48848,Z0)))))))))) # label(aEXISTSu_INu_GSPECu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2559 (all A all B all U_1 ((all S0 all F0 all T0 all GENR_PVARR_61 ((exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_61))),s(bool,V))),s(A,X)))) & (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(B,bool),fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(B,bool),T0))),s(A,GENR_PVARR_61)))))) -> (all U_0 ((all S0 all F0 all Y all GENR_PVARR_60 (p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))),s(A,GENR_PVARR_60)))) <-> (exists X exists V ((p(s(bool,V)) <-> s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_60))),s(bool,V))),s(A,X)))))))) -> (all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),T0)))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y)))))))))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(B,bool),fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(B,bool),T0)))))))))))))) # label(aFINITEu_FINITEu_PREIMAGEu_GENERAL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2560 (all X (s(real,X) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_inv),s(real,X))))),s(real,X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) # label(aREALu_MULu_LINV) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2561 (all M0 all N0 s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_a_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,i(s(fun(num,num),bit1),s(num,M0))))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,N0))),s(num,M0)))) # label(aARITHu_GEu_conjunct8) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2562 (all Q4069 all Q4073 all U_0 ((all Z0 s(bool,i(s(fun(Q4073,bool),U_0),s(Q4073,Z0))) = s(bool,f0)) -> (all X all X0 exists V (s(Q4073,i(s(fun(Q4073,Q4073),i(s(fun(Q4073,fun(Q4073,Q4073)),i(s(fun(bool,fun(Q4073,fun(Q4073,Q4073))),cond),s(bool,V))),s(Q4073,i(s(fun(fun(Q4073,bool),Q4073),h_),s(fun(Q4073,bool),i(s(fun(Q4069,fun(Q4073,bool)),X),s(Q4069,X0))))))),s(Q4073,i(s(fun(fun(Q4073,bool),Q4073),h_),s(fun(Q4073,bool),U_0))))) = s(Q4073,i(s(fun(Q4069,Q4073),i(s(fun(fun(Q4069,fun(Q4073,bool)),fun(Q4069,Q4073)),u_function),s(fun(Q4069,fun(Q4073,bool)),X))),s(Q4069,X0))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(Q4073,bool),bool),q_),s(fun(Q4073,bool),i(s(fun(Q4069,fun(Q4073,bool)),X),s(Q4069,X0)))))) & (all X1 all Y (p(s(bool,i(s(fun(Q4073,bool),i(s(fun(Q4069,fun(Q4073,bool)),X),s(Q4069,X0))),s(Q4073,Y)))) & p(s(bool,i(s(fun(Q4073,bool),i(s(fun(Q4069,fun(Q4073,bool)),X),s(Q4069,X0))),s(Q4073,X1)))) -> s(Q4073,X1) = s(Q4073,Y)))))))) # label(au_FUNCTION) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2563 (all A all B all U_0 ((all S0 all T0 all GENR_PVARR_87 (p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),U_0),s(fun(A,bool),S0))),s(fun(B,bool),T0))),s(prod(A,B),GENR_PVARR_87)))) <-> (exists X exists Y exists V (p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(bool,fun(prod(A,B),bool)),i(s(fun(prod(A,B),fun(bool,fun(prod(A,B),bool))),setspec),s(prod(A,B),GENR_PVARR_87))),s(bool,V))),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,X))),s(B,Y)))))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))))))) -> (all S0 all M0 all T0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(B,bool),fun(num,bool)),hasu_size),s(fun(B,bool),T0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,M0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(prod(A,B),bool),fun(num,bool)),hasu_size),s(fun(prod(A,B),bool),i(s(fun(fun(prod(A,B),bool),fun(prod(A,B),bool)),gspec),s(fun(prod(A,B),bool),i(s(fun(fun(B,bool),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(B,bool),fun(prod(A,B),bool))),U_0),s(fun(A,bool),S0))),s(fun(B,bool),T0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))))))) # label(aHASu_SIZEu_PRODUCT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2564 (all M0 all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),bit1),s(num,M0))))),s(num,i(s(fun(num,num),bit0),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),bit0),s(num,N0))))),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0)))))))))) # label(aARITHu_MULTu_conjunct8) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2565 (all A (p(s(bool,i(s(fun(fun(A,fun(A,bool)),bool),wf),s(fun(A,fun(A,bool)),l_l_)))) <-> -(exists S0 all N0 p(s(bool,i(s(fun(A,bool),i(s(fun(A,fun(A,bool)),l_l_),s(A,i(s(fun(num,A),S0),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(A,i(s(fun(num,A),S0),s(num,N0))))))))) # label(aWFu_DCHAIN) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2566 (all X all Y s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,i(s(fun(int,int),intu_neg),s(int,X))))),s(int,Y))) = s(int,i(s(fun(int,int),intu_neg),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y)))))) # label(aINTu_NEGu_LMUL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2567 (all Q12515 all M0 all X all XI_ s(bool,i(s(fun(Q12515,bool),i(s(fun(Q12515,fun(Q12515,bool)),i(s(fun(fun(Q12515,num),fun(Q12515,fun(Q12515,bool))),measure0),s(fun(Q12515,num),M0))),s(Q12515,X))),s(Q12515,XI_))) = s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(Q12515,num),M0),s(Q12515,X))))),s(num,i(s(fun(Q12515,num),M0),s(Q12515,XI_)))))) # label(aMEASURE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2568 (all B all A all T1 all T2 s(A,T1) = s(A,T1)) # label(aABSu_SIMP) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2569 (all X all Y (p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_mul),s(int,X))),s(int,Y)))))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) | p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,Y))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) # label(aINTu_MULu_POSu_LT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2570 (all M0 exists V ((p(s(bool,V)) <-> s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))) & s(num,i(s(fun(fun(num,num),num),i(s(fun(fun(num,bool),fun(fun(num,num),num)),nsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(num,num),f))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,V))),s(num,i(s(fun(num,num),f),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aNSUMu_CLAUSESu_NUMSEGu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2571 (all A all E0 all F0 ((all FN all XI_ (s(A,E0) = s(A,i(s(fun(num,A),XI_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & (all N0 s(A,i(s(fun(num,A),i(s(fun(A,fun(num,A)),F0),s(A,i(s(fun(num,A),XI_),s(num,N0))))),s(num,N0))) = s(A,i(s(fun(num,A),XI_),s(num,i(s(fun(num,num),suc),s(num,N0)))))) & (all N0 s(A,i(s(fun(num,A),i(s(fun(A,fun(num,A)),F0),s(A,i(s(fun(num,A),FN),s(num,N0))))),s(num,N0))) = s(A,i(s(fun(num,A),FN),s(num,i(s(fun(num,num),suc),s(num,N0)))))) & s(A,E0) = s(A,i(s(fun(num,A),FN),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(fun(num,A),XI_) = s(fun(num,A),FN))) & (exists FN ((all N0 s(A,i(s(fun(num,A),FN),s(num,i(s(fun(num,num),suc),s(num,N0))))) = s(A,i(s(fun(num,A),i(s(fun(A,fun(num,A)),F0),s(A,i(s(fun(num,A),FN),s(num,N0))))),s(num,N0)))) & s(A,i(s(fun(num,A),FN),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(A,E0))))) # label(anumu_Axiom) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2572 (all X all Y s(real,i(s(fun(real,real),realu_neg),s(real,Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))),s(real,X)))) # label(aREALu_SUBu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2573 (all N0 all X all Y (s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,N0) & s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,Y))),s(num,N0))) = s(int,i(s(fun(num,int),i(s(fun(int,fun(num,int)),intu_pow),s(int,X))),s(num,N0))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,Y)))) & p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(int,X)))) -> s(int,X) = s(int,Y))) # label(aINTu_POWu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2574 (all Z all F0 exists FN all A01 all A10 all A20 all A30 all A40 all A5 all A6 all A7 s(Z,i(s(fun(char,Z),FN),s(char,i(s(fun(bool,char),i(s(fun(bool,fun(bool,char)),i(s(fun(bool,fun(bool,fun(bool,char))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,char)))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,char))))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,char)))))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,char))))))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,char)))))))),ascii),s(bool,A01))),s(bool,A10))),s(bool,A20))),s(bool,A30))),s(bool,A40))),s(bool,A5))),s(bool,A6))),s(bool,A7))))) = s(Z,i(s(fun(bool,Z),i(s(fun(bool,fun(bool,Z)),i(s(fun(bool,fun(bool,fun(bool,Z))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,Z)))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,Z))))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,Z)))))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,Z))))))),i(s(fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,fun(bool,Z)))))))),F0),s(bool,A01))),s(bool,A10))),s(bool,A20))),s(bool,A30))),s(bool,A40))),s(bool,A5))),s(bool,A6))),s(bool,A7)))) # label(acharu_RECURSION) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2575 (all R0 (s(bool,R0) = s(bool,i(s(fun(n10,bool),oneu_rep),s(n10,i(s(fun(bool,n10),oneu_abs),s(bool,R0))))) <-> p(s(bool,R0)))) # label(aoneu_tydefu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2576 p(s(bool,f0)) <-> -p(s(bool,t)) # label(aNOTu_CLAUSESu_WEAKu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2577 (all X all Y s(int,i(s(fun(real,int),intu_ofu_real),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(int,real),realu_ofu_int),s(int,X))))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,Y))))))) = s(int,i(s(fun(int,int),i(s(fun(int,fun(int,int)),intu_add),s(int,X))),s(int,Y)))) # label(aintu_add) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2578 (all A (s(fun(A,bool),univ) = s(fun(A,bool),s0) <-> (all X p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),s0))))))) # label(aEQu_UNIV) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2579 (all B all A all R0 (s(fun(finite_image(B),A),R0) = s(fun(finite_image(B),A),i(s(fun(cart(A,B),fun(finite_image(B),A)),destu_cart),s(cart(A,B),i(s(fun(fun(finite_image(B),A),cart(A,B)),mku_cart),s(fun(finite_image(B),A),R0))))) <-> p(s(bool,t)))) # label(acartu_tybiju_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2580 (all Q58242 all X all L s(bool,i(s(fun(list(Q58242),bool),i(s(fun(Q58242,fun(list(Q58242),bool)),mem),s(Q58242,X))),s(list(Q58242),L))) = s(bool,i(s(fun(fun(Q58242,bool),bool),i(s(fun(Q58242,fun(fun(Q58242,bool),bool)),in),s(Q58242,X))),s(fun(Q58242,bool),i(s(fun(list(Q58242),fun(Q58242,bool)),setu_ofu_list),s(list(Q58242),L)))))) # label(aINu_SETu_OFu_LIST) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2581 (all Q18890 s(list(Q18890),i(s(fun(list(Q18890),list(Q18890)),i(s(fun(fun(Q18890,bool),fun(list(Q18890),list(Q18890))),filter0),s(fun(Q18890,bool),p0))),s(list(Q18890),nil))) = s(list(Q18890),nil)) # label(aFILTERu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2582 (all A all B all U_0 ((all S0 all F0 all A5 all GENR_PVARR_227 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(B,bool),fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(B,bool),A5))),s(A,GENR_PVARR_227)))) <-> (exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_227))),s(bool,V))),s(A,X)))) & (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),F0),s(A,X))))),s(fun(B,bool),A5)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) <-> p(s(bool,V))))))) -> (all F0 all A5 all S0 (p(s(bool,i(s(fun(fun(B,bool),bool),countable),s(fun(B,bool),A5)))) & (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,i(s(fun(A,B),F0),s(A,Y))) -> s(A,Y) = s(A,X))) -> p(s(bool,i(s(fun(fun(A,bool),bool),countable),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(B,bool),fun(A,bool)),i(s(fun(fun(A,B),fun(fun(B,bool),fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(B,bool),fun(A,bool)))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(B,bool),A5)))))))))))) # label(aCOUNTABLEu_IMAGEu_INJu_GENERAL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2583 (all A exists V ((p(s(bool,V)) <-> s(list(A),nil) = s(list(A),t0)) & s(A,i(s(fun(list(A),A),last0),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,h0))),s(list(A),t0))))) = s(A,i(s(fun(A,A),i(s(fun(A,fun(A,A)),i(s(fun(bool,fun(A,fun(A,A))),cond),s(bool,V))),s(A,h0))),s(A,i(s(fun(list(A),A),last0),s(list(A),t0))))))) # label(aLAST) # label(axiom) # label(non_clause). [assumption]. 15.12/15.10 2584 (all Q66750 all U_0 ((all OP all F0 all I0 s(Q66750,i(s(fun(Q66750,Q66750),i(s(fun(Q66750,fun(Q66750,Q66750)),OP),s(Q66750,i(s(fun(num,Q66750),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))))),s(Q66750,i(s(fun(num,Q66750),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(Q66750,i(s(fun(num,Q66750),i(s(fun(fun(num,Q66750),fun(num,Q66750)),i(s(fun(fun(Q66750,fun(Q66750,Q66750)),fun(fun(num,Q66750),fun(num,Q66750))),U_0),s(fun(Q66750,fun(Q66750,Q66750)),OP))),s(fun(num,Q66750),F0))),s(num,I0)))) -> (all OP (p(s(bool,i(s(fun(fun(Q66750,fun(Q66750,Q66750)),bool),monoidal),s(fun(Q66750,fun(Q66750,Q66750)),OP)))) -> (all F0 all M0 all N0 s(Q66750,i(s(fun(fun(num,Q66750),Q66750),i(s(fun(fun(num,bool),fun(fun(num,Q66750),Q66750)),i(s(fun(fun(Q66750,fun(Q66750,Q66750)),fun(fun(num,bool),fun(fun(num,Q66750),Q66750))),iterate),s(fun(Q66750,fun(Q66750,Q66750)),OP))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,Q66750),F0))) = s(Q66750,i(s(fun(fun(num,Q66750),Q66750),i(s(fun(fun(num,bool),fun(fun(num,Q66750),Q66750)),i(s(fun(fun(Q66750,fun(Q66750,Q66750)),fun(fun(num,bool),fun(fun(num,Q66750),Q66750))),iterate),s(fun(Q66750,fun(Q66750,Q66750)),OP))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,Q66750),i(s(fun(fun(num,Q66750),fun(num,Q66750)),i(s(fun(fun(Q66750,fun(Q66750,Q66750)),fun(fun(num,Q66750),fun(num,Q66750))),U_0),s(fun(Q66750,fun(Q66750,Q66750)),OP))),s(fun(num,Q66750),F0)))))))))) # label(aITERATEu_PAIR) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2585 (all N0 (s(num,u_0) = s(num,i(s(fun(num,num),bit0),s(num,N0))) <-> s(num,N0) = s(num,u_0))) # label(aARITHu_EQu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2586 (all M0 all N0 (s(num,M0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) -> s(num,N0) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,N0))))),s(num,M0))))) # label(aDIVu_MULT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2587 (all X all Y all Z0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Z0)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Z0))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,Y))),s(real,Z0))))))) # label(aREALu_LEu_DIV2u_EQ) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2588 (all A all U_0 ((all S0 all GENR_PVARR_97 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))),s(fun(A,bool),GENR_PVARR_97)))) <-> (exists T0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_97))),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0))))),s(fun(A,bool),T0))))))) -> (all S0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(A,bool),fun(num,bool)),hasu_size),s(fun(A,bool),S0))),s(num,N0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(fun(A,bool),bool),fun(num,bool)),hasu_size),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),U_0),s(fun(A,bool),S0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0)))))))))) # label(aHASu_SIZEu_POWERSET) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2589 (all X all Y (-p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_lt),s(int,X))),s(int,Y)))) <-> p(s(bool,i(s(fun(int,bool),i(s(fun(int,fun(int,bool)),intu_le),s(int,Y))),s(int,X)))))) # label(aINTu_NOTu_LT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2590 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))),s(real,Y))) = s(real,X)) # label(aREALu_SUBu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2591 (all T1 all T2 (-(p(s(bool,T1)) -> p(s(bool,T2))) <-> p(s(bool,T1)) & -p(s(bool,T2)))) # label(aNOTu_IMP) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2592 (all A all P0 s(fun(A,bool),P0) = s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),P0)))) # label(aGSPEC) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2593 (all M0 all N0 all P0 (s(num,M0) = s(num,N0) | s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,P0) <-> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,N0))),s(num,P0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,M0))),s(num,P0))))) # label(aEQu_MULTu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2594 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(real,real),realu_inv),s(real,X)))))))) # label(aREALu_INVu_1u_LE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2595 (all U_0 ((all U s(bool,i(s(fun(prod(hreal,hreal),bool),i(s(fun(prod(hreal,hreal),fun(prod(hreal,hreal),bool)),trealu_eq),s(prod(hreal,hreal),i(s(fun(num,prod(hreal,hreal)),trealu_ofu_num),s(num,m))))),s(prod(hreal,hreal),U))) = s(bool,i(s(fun(prod(hreal,hreal),bool),U_0),s(prod(hreal,hreal),U)))) -> s(real,i(s(fun(fun(prod(hreal,hreal),bool),real),mku_real),s(fun(prod(hreal,hreal),bool),U_0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,m))))) # label(arealu_ofu_num) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2596 (all N0 s(num,i(s(fun(num,num),suc),s(num,N0))) != s(num,i(s(fun(num,num),numeral),s(num,u_0)))) # label(aNOTu_SUC) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2597 (all M0 all N0 s(num,i(s(fun(num,num),pre),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,N0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0)))))) # label(aSUBu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2598 (all M0 all N0 (s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),exp0),s(num,M0))),s(num,N0))) <-> s(num,N0) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) & s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aEXPu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2599 (all A all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),infinite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(prod(A,A),bool),bool),i(s(fun(fun(sum0(A,A),bool),fun(fun(prod(A,A),bool),bool)),l_a_u_c),s(fun(sum0(A,A),bool),i(s(fun(fun(A,bool),fun(sum0(A,A),bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(sum0(A,A),bool))),p_u_c),s(fun(A,bool),S0))),s(fun(A,bool),S0))))),s(fun(prod(A,A),bool),i(s(fun(fun(A,bool),fun(prod(A,A),bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(prod(A,A),bool))),t_u_c),s(fun(A,bool),S0))),s(fun(A,bool),S0)))))))) # label(aCARDu_ADDu_LEu_MULu_INFINITE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2600 (all N0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),suc),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(num,N0)) # label(aSUCu_SUB1) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2601 (all N0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,i(s(fun(num,num),bit1),s(num,N0))))),s(num,u_0))))) # label(aARITHu_GTu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2602 (all U_0 ((all X s(bool,t) = s(bool,i(s(fun(n10,bool),U_0),s(n10,X)))) -> s(n10,one) = s(n10,i(s(fun(fun(n10,bool),n10),h_),s(fun(n10,bool),U_0))))) # label(aoneu_DEF) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2603 (all Q106444 all Q106450 all U_0 ((all S0 all F0 all X s(cart(real,Q106450),i(s(fun(Q106444,cart(real,Q106450)),i(s(fun(fun(Q106444,cart(real,Q106450)),fun(Q106444,cart(real,Q106450))),i(s(fun(fun(Q106444,bool),fun(fun(Q106444,cart(real,Q106450)),fun(Q106444,cart(real,Q106450)))),U_0),s(fun(Q106444,bool),S0))),s(fun(Q106444,cart(real,Q106450)),F0))),s(Q106444,X))) = s(cart(real,Q106450),i(s(fun(cart(real,Q106450),cart(real,Q106450)),i(s(fun(cart(real,Q106450),fun(cart(real,Q106450),cart(real,Q106450))),i(s(fun(bool,fun(cart(real,Q106450),fun(cart(real,Q106450),cart(real,Q106450)))),cond),s(bool,i(s(fun(fun(Q106444,bool),bool),i(s(fun(Q106444,fun(fun(Q106444,bool),bool)),in),s(Q106444,X))),s(fun(Q106444,bool),S0))))),s(cart(real,Q106450),i(s(fun(Q106444,cart(real,Q106450)),F0),s(Q106444,X))))),s(cart(real,Q106450),i(s(fun(num,cart(real,Q106450)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (all F0 all S0 (p(s(bool,i(s(fun(fun(Q106444,bool),bool),finite),s(fun(Q106444,bool),S0)))) -> s(cart(real,Q106450),i(s(fun(fun(Q106444,cart(real,Q106450)),cart(real,Q106450)),i(s(fun(fun(Q106444,bool),fun(fun(Q106444,cart(real,Q106450)),cart(real,Q106450))),vsum),s(fun(Q106444,bool),S0))),s(fun(Q106444,cart(real,Q106450)),i(s(fun(fun(Q106444,cart(real,Q106450)),fun(Q106444,cart(real,Q106450))),i(s(fun(fun(Q106444,bool),fun(fun(Q106444,cart(real,Q106450)),fun(Q106444,cart(real,Q106450)))),U_0),s(fun(Q106444,bool),S0))),s(fun(Q106444,cart(real,Q106450)),F0))))) = s(cart(real,Q106450),i(s(fun(fun(Q106444,cart(real,Q106450)),cart(real,Q106450)),i(s(fun(fun(Q106444,bool),fun(fun(Q106444,cart(real,Q106450)),cart(real,Q106450))),vsum),s(fun(Q106444,bool),S0))),s(fun(Q106444,cart(real,Q106450)),F0))))))) # label(aVSUMu_RESTRICT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2604 (all U_0 ((all X all I0 s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),U_0),s(cart(real,n10),X))),s(num,I0)))) -> (all X s(cart(real,n10),i(s(fun(fun(num,real),cart(real,n10)),lambda),s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),U_0),s(cart(real,n10),X))))) = s(cart(real,n10),X)))) # label(aVECTORu_ONE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2605 (all N all I0 all J0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> (exists V (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0))))) & (s(num,J0) = s(num,I0) <-> p(s(bool,V))))))) # label(aDOTu_BASISu_BASIS) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2606 (all N all X all Y s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),Y))),s(cart(real,N),X)))) # label(aVECTORu_NEGu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2607 (all M all N all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))) <-> (all X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) # label(aONORMu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2608 (all Q106968 all U_0 ((all C0 all F0 all X s(cart(real,Q106968),i(s(fun(num,cart(real,Q106968)),i(s(fun(fun(num,cart(real,Q106968)),fun(num,cart(real,Q106968))),i(s(fun(real,fun(fun(num,cart(real,Q106968)),fun(num,cart(real,Q106968)))),U_0),s(real,C0))),s(fun(num,cart(real,Q106968)),F0))),s(num,X))) = s(cart(real,Q106968),i(s(fun(cart(real,Q106968),cart(real,Q106968)),i(s(fun(real,fun(cart(real,Q106968),cart(real,Q106968))),r_),s(real,C0))),s(cart(real,Q106968),i(s(fun(num,cart(real,Q106968)),F0),s(num,X)))))) -> (all F0 all C0 all M0 all N0 s(cart(real,Q106968),i(s(fun(cart(real,Q106968),cart(real,Q106968)),i(s(fun(real,fun(cart(real,Q106968),cart(real,Q106968))),r_),s(real,C0))),s(cart(real,Q106968),i(s(fun(fun(num,cart(real,Q106968)),cart(real,Q106968)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106968)),cart(real,Q106968))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q106968)),F0))))) = s(cart(real,Q106968),i(s(fun(fun(num,cart(real,Q106968)),cart(real,Q106968)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106968)),cart(real,Q106968))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q106968)),i(s(fun(fun(num,cart(real,Q106968)),fun(num,cart(real,Q106968))),i(s(fun(real,fun(fun(num,cart(real,Q106968)),fun(num,cart(real,Q106968)))),U_0),s(real,C0))),s(fun(num,cart(real,Q106968)),F0)))))))) # label(aVSUMu_CMULu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2609 (all N s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),x))),s(cart(real,N),y))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),x))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),y)))))) # label(aVECTORu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2610 (all N all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),psubset),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))) -> (exists X ((all Y (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) -> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),X))),s(cart(real,N),Y)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))) & s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(real,N),X))))) # label(aORTHOGONALu_TOu_SUBSPACEu_EXISTSu_GEN) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2611 (all N all A5 all X s(real,i(s(fun(cart(real,N),real),infnorm),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,A5))),s(cart(real,N),X))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_abs),s(real,A5))))),s(real,i(s(fun(cart(real,N),real),infnorm),s(cart(real,N),X)))))) # label(aINFNORMu_MUL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2612 (all N all S0 (s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))) <-> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))) = s(fun(cart(real,N),bool),univ))) # label(aDIMu_EQu_FULL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2613 (all Q99591 all X s(cart(real,Q99591),i(s(fun(cart(real,Q99591),cart(real,Q99591)),i(s(fun(cart(real,Q99591),fun(cart(real,Q99591),cart(real,Q99591))),vectoru_sub),s(cart(real,Q99591),X))),s(cart(real,Q99591),X))) = s(cart(real,Q99591),i(s(fun(num,cart(real,Q99591)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aVECTORu_SUBu_REFL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2614 (all N all A5 all B0 all C0 (s(cart(real,N),C0) != s(cart(real,N),A5) -> (s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),B0))),s(cart(real,N),C0))))) = s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),B0))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),C0))),s(fun(cart(real,N),bool),empty)))))))))) <-> s(cart(real,N),i(s(fun(prod(cart(real,N),cart(real,N)),cart(real,N)),midpoint),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),C0))))) = s(cart(real,N),B0)))) # label(aMIDPOINTu_COLLINEAR) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2615 (all Q118562 all Q118573 all U_0 ((all F0 all G0 all X s(cart(real,Q118573),i(s(fun(cart(real,Q118573),cart(real,Q118573)),i(s(fun(cart(real,Q118573),fun(cart(real,Q118573),cart(real,Q118573))),vectoru_add),s(cart(real,Q118573),i(s(fun(cart(real,Q118562),cart(real,Q118573)),F0),s(cart(real,Q118562),X))))),s(cart(real,Q118573),i(s(fun(cart(real,Q118562),cart(real,Q118573)),G0),s(cart(real,Q118562),X))))) = s(cart(real,Q118573),i(s(fun(cart(real,Q118562),cart(real,Q118573)),i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(cart(real,Q118562),cart(real,Q118573))),i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(cart(real,Q118562),cart(real,Q118573)))),U_0),s(fun(cart(real,Q118562),cart(real,Q118573)),F0))),s(fun(cart(real,Q118562),cart(real,Q118573)),G0))),s(cart(real,Q118562),X)))) -> (all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),bool),linear),s(fun(cart(real,Q118562),cart(real,Q118573)),G0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),real),onorm),s(fun(cart(real,Q118562),cart(real,Q118573)),F0))))),s(real,i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),real),onorm),s(fun(cart(real,Q118562),cart(real,Q118573)),G0))))))),s(real,e0)))) & p(s(bool,i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),bool),linear),s(fun(cart(real,Q118562),cart(real,Q118573)),F0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),real),onorm),s(fun(cart(real,Q118562),cart(real,Q118573)),i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(cart(real,Q118562),cart(real,Q118573))),i(s(fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(fun(cart(real,Q118562),cart(real,Q118573)),fun(cart(real,Q118562),cart(real,Q118573)))),U_0),s(fun(cart(real,Q118562),cart(real,Q118573)),F0))),s(fun(cart(real,Q118562),cart(real,Q118573)),G0))))))),s(real,e0)))))))) # label(aONORMu_TRIANGLEu_LE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2616 (all M all N all A5 all V s(cart(cart(real,n10),M),i(s(fun(cart(real,M),cart(cart(real,n10),M)),columnvector),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),V))))) = s(cart(cart(real,n10),M),i(s(fun(cart(cart(real,n10),N),cart(cart(real,n10),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,n10),N),cart(cart(real,n10),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,n10),N),i(s(fun(cart(real,N),cart(cart(real,n10),N)),columnvector),s(cart(real,N),V)))))) # label(aDOTu_ROWVECTORu_COLUMNVECTOR) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2617 (all Q122169 p(s(bool,i(s(fun(fun(cart(real,Q122169),bool),bool),independent),s(fun(cart(real,Q122169),bool),empty))))) # label(aINDEPENDENTu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2618 (all Q128666 all Q128687 all U_0 ((all F0 all GENR_PVARR_321 ((exists X exists V ((s(cart(real,Q128687),i(s(fun(num,cart(real,Q128687)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q128687),i(s(fun(cart(real,Q128666),cart(real,Q128687)),F0),s(cart(real,Q128666),X))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(cart(real,Q128666),bool),i(s(fun(bool,fun(cart(real,Q128666),bool)),i(s(fun(cart(real,Q128666),fun(bool,fun(cart(real,Q128666),bool))),setspec),s(cart(real,Q128666),GENR_PVARR_321))),s(bool,V))),s(cart(real,Q128666),X)))))) <-> p(s(bool,i(s(fun(cart(real,Q128666),bool),i(s(fun(fun(cart(real,Q128666),cart(real,Q128687)),fun(cart(real,Q128666),bool)),U_0),s(fun(cart(real,Q128666),cart(real,Q128687)),F0))),s(cart(real,Q128666),GENR_PVARR_321)))))) -> (all F0 (p(s(bool,i(s(fun(fun(cart(real,Q128666),cart(real,Q128687)),bool),linear),s(fun(cart(real,Q128666),cart(real,Q128687)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q128666),bool),bool),subspace),s(fun(cart(real,Q128666),bool),i(s(fun(fun(cart(real,Q128666),bool),fun(cart(real,Q128666),bool)),gspec),s(fun(cart(real,Q128666),bool),i(s(fun(fun(cart(real,Q128666),cart(real,Q128687)),fun(cart(real,Q128666),bool)),U_0),s(fun(cart(real,Q128666),cart(real,Q128687)),F0)))))))))))) # label(aSUBSPACEu_KERNEL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2619 (all N all U_0 ((all X all I0 s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X))),s(num,I0)))) -> (all X s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),X)))))) # label(avectoru_neg) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2620 (all Q103415 all X s(real,i(s(fun(cart(real,Q103415),real),i(s(fun(cart(real,Q103415),fun(cart(real,Q103415),real)),dot),s(cart(real,Q103415),X))),s(cart(real,Q103415),X))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q103415),real),vectoru_norm),s(cart(real,Q103415),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aDOTu_SQUAREu_NORM) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2621 (all M all N all A5 ((all Y exists X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),Y)) <-> s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))) # label(aFULLu_RANKu_SURJECTIVE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2622 (all M all N all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> ((exists B0 s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))),s(cart(cart(real,N),M),B0))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) <-> (exists G0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0)))) & s(fun(cart(real,N),cart(real,N)),i1) = s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,M)),G0)))))))) # label(aMATRIXu_RIGHTu_INVERTIBLE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2623 (all M all N all U_0 ((all F0 all FI_ ((all X all Y s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),Y))) = s(real,i(s(fun(cart(real,M),real),i(s(fun(cart(real,M),fun(cart(real,M),real)),dot),s(cart(real,M),X))),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),FI_),s(cart(real,N),Y)))))) <-> p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,N),cart(real,M)),bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,M)),FI_)))))) -> (all F0 s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(fun(cart(real,N),cart(real,M)),bool),fun(cart(real,N),cart(real,M))),h_),s(fun(fun(cart(real,N),cart(real,M)),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,N),cart(real,M)),bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))))) = s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0)))))) # label(aadjoint) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2624 (all M all N all X1 all Y1 all X2 all Y2 s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_sub),s(cart(real,M),X1))),s(cart(real,M),X2))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),Y1))),s(cart(real,N),Y2))))) = s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_sub),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X1))),s(cart(real,N),Y1))))),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X2))),s(cart(real,N),Y2)))))) # label(aPASTECARTu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2625 (all N all X all E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) -> (exists Y s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),X))),s(cart(real,N),Y))))) = s(real,E0)))) # label(aVECTORu_CHOOSEu_DIST) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2626 (all Q112837 all Q112835 all Q112836 all H0 (p(s(bool,i(s(fun(fun(cart(real,Q112835),fun(cart(real,Q112836),cart(real,Q112837))),bool),bilinear),s(fun(cart(real,Q112835),fun(cart(real,Q112836),cart(real,Q112837))),H0)))) -> (exists B0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,B0)))) & (all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q112837),real),vectoru_norm),s(cart(real,Q112837),i(s(fun(cart(real,Q112836),cart(real,Q112837)),i(s(fun(cart(real,Q112835),fun(cart(real,Q112836),cart(real,Q112837))),H0),s(cart(real,Q112835),X))),s(cart(real,Q112836),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,Q112835),real),vectoru_norm),s(cart(real,Q112835),X))))),s(real,i(s(fun(cart(real,Q112836),real),vectoru_norm),s(cart(real,Q112836),Y))))))))))))))) # label(aBILINEARu_BOUNDEDu_POS) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2627 (all N all M all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> ((all Y exists X s(cart(real,M),Y) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,N),X)))) <-> (all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) -> s(cart(real,M),X) = s(cart(real,M),Y)))))) # label(aADJOINTu_SURJECTIVE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2628 (all Q132023 all U_0 ((all S0 all GENR_PVARR_328 (p(s(bool,i(s(fun(cart(real,Q132023),bool),i(s(fun(fun(cart(real,Q132023),bool),fun(cart(real,Q132023),bool)),U_0),s(fun(cart(real,Q132023),bool),S0))),s(cart(real,Q132023),GENR_PVARR_328)))) <-> (exists Y exists V ((p(s(bool,V)) <-> (all X (p(s(bool,i(s(fun(fun(cart(real,Q132023),bool),bool),i(s(fun(cart(real,Q132023),fun(fun(cart(real,Q132023),bool),bool)),in),s(cart(real,Q132023),X))),s(fun(cart(real,Q132023),bool),S0)))) -> p(s(bool,i(s(fun(cart(real,Q132023),bool),i(s(fun(cart(real,Q132023),fun(cart(real,Q132023),bool)),orthogonal),s(cart(real,Q132023),X))),s(cart(real,Q132023),Y))))))) & p(s(bool,i(s(fun(cart(real,Q132023),bool),i(s(fun(bool,fun(cart(real,Q132023),bool)),i(s(fun(cart(real,Q132023),fun(bool,fun(cart(real,Q132023),bool))),setspec),s(cart(real,Q132023),GENR_PVARR_328))),s(bool,V))),s(cart(real,Q132023),Y)))))))) -> (all S0 p(s(bool,i(s(fun(fun(cart(real,Q132023),bool),bool),subspace),s(fun(cart(real,Q132023),bool),i(s(fun(fun(cart(real,Q132023),bool),fun(cart(real,Q132023),bool)),gspec),s(fun(cart(real,Q132023),bool),i(s(fun(fun(cart(real,Q132023),bool),fun(cart(real,Q132023),bool)),U_0),s(fun(cart(real,Q132023),bool),S0))))))))))) # label(aSUBSPACEu_ORTHOGONALu_TOu_VECTORS) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2629 (all X all Y s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))) = s(real,i(s(fun(prod(cart(real,n10),cart(real,n10)),real),distance),s(prod(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),prod(cart(real,n10),cart(real,n10))),i(s(fun(cart(real,n10),fun(cart(real,n10),prod(cart(real,n10),cart(real,n10)))),c_),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,Y)))))))) # label(aDISTu_LIFT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2630 (all Q110949 all A5 p(s(bool,i(s(fun(cart(real,Q110949),bool),i(s(fun(cart(real,Q110949),fun(cart(real,Q110949),bool)),orthogonal),s(cart(real,Q110949),i(s(fun(num,cart(real,Q110949)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q110949),A5))))) # label(aORTHOGONALu_CLAUSESu_conjunct5) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2631 (all Q108573 all Q108564 all U_0 ((all X all F0 all Y s(real,i(s(fun(cart(real,Q108564),real),i(s(fun(cart(real,Q108564),fun(cart(real,Q108564),real)),dot),s(cart(real,Q108564),X))),s(cart(real,Q108564),i(s(fun(Q108573,cart(real,Q108564)),F0),s(Q108573,Y))))) = s(real,i(s(fun(Q108573,real),i(s(fun(fun(Q108573,cart(real,Q108564)),fun(Q108573,real)),i(s(fun(cart(real,Q108564),fun(fun(Q108573,cart(real,Q108564)),fun(Q108573,real))),U_0),s(cart(real,Q108564),X))),s(fun(Q108573,cart(real,Q108564)),F0))),s(Q108573,Y)))) -> (all S0 all F0 all X (p(s(bool,i(s(fun(fun(Q108573,bool),bool),finite),s(fun(Q108573,bool),S0)))) -> s(real,i(s(fun(fun(Q108573,real),real),i(s(fun(fun(Q108573,bool),fun(fun(Q108573,real),real)),sum),s(fun(Q108573,bool),S0))),s(fun(Q108573,real),i(s(fun(fun(Q108573,cart(real,Q108564)),fun(Q108573,real)),i(s(fun(cart(real,Q108564),fun(fun(Q108573,cart(real,Q108564)),fun(Q108573,real))),U_0),s(cart(real,Q108564),X))),s(fun(Q108573,cart(real,Q108564)),F0))))) = s(real,i(s(fun(cart(real,Q108564),real),i(s(fun(cart(real,Q108564),fun(cart(real,Q108564),real)),dot),s(cart(real,Q108564),X))),s(cart(real,Q108564),i(s(fun(fun(Q108573,cart(real,Q108564)),cart(real,Q108564)),i(s(fun(fun(Q108573,bool),fun(fun(Q108573,cart(real,Q108564)),cart(real,Q108564))),vsum),s(fun(Q108573,bool),S0))),s(fun(Q108573,cart(real,Q108564)),F0))))))))) # label(aDOTu_RSUM) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2632 (all Q102710 all X s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,Q102710),real),vectoru_norm),s(cart(real,Q102710),X))))) = s(real,i(s(fun(cart(real,Q102710),real),vectoru_norm),s(cart(real,Q102710),X)))) # label(aREALu_ABSu_NORM) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2633 (all N all X all C0 all S0 (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(real,C0) -> s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))))) # label(aSPANu_MULu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2634 (all X p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))))) <-> (all X p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),X))))) # label(aFORALLu_LIFT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2635 (all X all Y s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,X))),s(real,Y))))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),fun(cart(real,n10),cart(real,n10))),vectoru_sub),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,Y)))))) # label(aLIFTu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2636 (all N all U_0 ((all F0 all I0 s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),U_0),s(fun(num,cart(real,N)),F0))),s(num,I0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(num,cart(real,N)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) -> (all F0 all N0 s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),U_0),s(fun(num,cart(real,N)),F0))))) = s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,N)),F0)))))) # label(aVSUMu_PAIRu_0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2637 (all N all M all U_0 ((all X all A5 all I0 s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,M),N),fun(num,cart(real,M))),d_),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(num,I0))))) = s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(cart(real,N),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(cart(real,N),X))),s(cart(cart(real,N),M),A5))),s(num,I0)))) -> (all A5 all X s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(fun(num,cart(real,M)),cart(real,M)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,M)),cart(real,M))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(cart(real,N),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(cart(real,N),X))),s(cart(cart(real,N),M),A5)))))))) # label(aMATRIXu_VECTORu_COLUMN) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2638 (all Q99877 s(cart(real,Q99877),i(s(fun(cart(real,Q99877),cart(real,Q99877)),i(s(fun(real,fun(cart(real,Q99877),cart(real,Q99877))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,a0))),s(real,b0))))),s(cart(real,Q99877),x))) = s(cart(real,Q99877),i(s(fun(cart(real,Q99877),cart(real,Q99877)),i(s(fun(cart(real,Q99877),fun(cart(real,Q99877),cart(real,Q99877))),vectoru_sub),s(cart(real,Q99877),i(s(fun(cart(real,Q99877),cart(real,Q99877)),i(s(fun(real,fun(cart(real,Q99877),cart(real,Q99877))),r_),s(real,a0))),s(cart(real,Q99877),x))))),s(cart(real,Q99877),i(s(fun(cart(real,Q99877),cart(real,Q99877)),i(s(fun(real,fun(cart(real,Q99877),cart(real,Q99877))),r_),s(real,b0))),s(cart(real,Q99877),x)))))) # label(aVECTORu_SUBu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2639 (all M all N all A5 ((exists B0 s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),B0))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) <-> (all X all Y (s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),Y))) -> s(cart(real,N),Y) = s(cart(real,N),X))))) # label(aMATRIXu_LEFTu_INVERTIBLEu_INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2640 (all N all X (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))) <-> s(cart(real,N),X) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aDOTu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2641 (all N all M all A5 s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),matrixu_neg),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5)))))) # label(aTRANSPu_MATRIXu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.12/15.11 2642 (all M all N all P all U_1 ((all H0 all F0 all G0 all K0 s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_1),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_sub),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,K0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0)))))) -> (all U_0 ((all H0 all F0 all G0 all K0 s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,K0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) -> (all F0 all G0 all H0 all M0 all N0 (p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0)))) -> s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),i(s(fun(bool,fun(cart(real,P),fun(cart(real,P),cart(real,P)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),vectoru_sub),s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),vectoru_sub),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,N0))))))),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,M0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))))),s(cart(real,P),i(s(fun(fun(num,cart(real,P)),cart(real,P)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,P)),cart(real,P))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_1),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))))))))),s(cart(real,P),i(s(fun(num,cart(real,P)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,P),i(s(fun(fun(num,cart(real,P)),cart(real,P)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,P)),cart(real,P))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))))))))))) # label(aBILINEARu_VSUMu_PARTIALu_PRE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2643 (all A all Q106306 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),T0))),s(fun(A,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) -> s(cart(real,Q106306),i(s(fun(A,cart(real,Q106306)),F0),s(A,X))) = s(cart(real,Q106306),i(s(fun(A,cart(real,Q106306)),g),s(A,X))))) & (all X (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(cart(real,Q106306),i(s(fun(A,cart(real,Q106306)),F0),s(A,X))) = s(cart(real,Q106306),i(s(fun(num,cart(real,Q106306)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) -> s(cart(real,Q106306),i(s(fun(fun(A,cart(real,Q106306)),cart(real,Q106306)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q106306)),cart(real,Q106306))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q106306)),F0))) = s(cart(real,Q106306),i(s(fun(fun(A,cart(real,Q106306)),cart(real,Q106306)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q106306)),cart(real,Q106306))),vsum),s(fun(A,bool),T0))),s(fun(A,cart(real,Q106306)),g))))) # label(aVSUMu_EQu_SUPERSET) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2644 (all N all U_0 ((all C0 all V s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),C0))),s(cart(real,N),V))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),C0),s(cart(real,N),V))))),s(cart(real,N),V)))) -> (all B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0)))) & (all C0 (s(cart(real,N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(real,N)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),cart(real,N)),cart(real,N))),vsum),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),C0))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> (all V (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),V))),s(fun(cart(real,N),bool),B0)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(cart(real,N),real),C0),s(cart(real,N),V))))))) <-> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))))))) # label(aINDEPENDENTu_EXPLICIT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2645 (all U_0 ((all X all I0 s(real,i(s(fun(num,real),X),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),U_0),s(fun(num,real),X))),s(num,I0)))) -> (all X s(real,i(s(fun(num,real),X),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(fun(num,real),cart(real,n10)),lambda),s(fun(num,real),i(s(fun(fun(num,real),fun(num,real)),U_0),s(fun(num,real),X)))))))))) # label(aDROPu_LAMBDA) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2646 (all S0 s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),i(s(fun(fun(real,real),fun(fun(real,bool),fun(real,bool))),image),s(fun(real,real),i(s(fun(fun(real,cart(real,n10)),fun(real,real)),i(s(fun(fun(cart(real,n10),real),fun(fun(real,cart(real,n10)),fun(real,real))),o),s(fun(cart(real,n10),real),drop))),s(fun(real,cart(real,n10)),lift))))),s(fun(real,bool),S0))) = s(fun(real,bool),S0)) # label(aIMAGEu_LIFTu_DROPu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2647 (all N all U_1 ((all F0 all G0 all K0 s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),F0),s(num,K0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_1),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0)))) -> (all U_0 ((all F0 all G0 all K0 s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_0),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,K0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0)))))))) -> (all F0 all G0 all M0 all N0 s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),i(s(fun(bool,fun(cart(real,N),fun(cart(real,N),cart(real,N)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,M0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,M0))))))))),s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_1),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_0),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0)))))))))) # label(aVSUMu_PARTIALu_SUC) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2648 (all N all X all Y (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),Y))),s(fun(cart(real,N),bool),empty)))))))))) <-> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),Y))),s(cart(real,N),Y))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) # label(aDOTu_CAUCHYu_SCHWARZu_EQUAL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2649 (all M all N all U_0 ((all F0 all G0 all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),X))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N)))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),cart(real,N)),G0))),s(cart(real,M),X)))) -> (all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),G0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N)))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),cart(real,N)),G0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))))),s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),G0)))))))))))) # label(aONORMu_TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2650 (all Q104879 all X all Y (s(cart(real,Q104879),Y) != s(cart(real,Q104879),X) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(prod(cart(real,Q104879),cart(real,Q104879)),real),distance),s(prod(cart(real,Q104879),cart(real,Q104879)),i(s(fun(cart(real,Q104879),prod(cart(real,Q104879),cart(real,Q104879))),i(s(fun(cart(real,Q104879),fun(cart(real,Q104879),prod(cart(real,Q104879),cart(real,Q104879)))),c_),s(cart(real,Q104879),X))),s(cart(real,Q104879),Y)))))))))) # label(aDISTu_NZ) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2651 (all Q122268 all B0 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q122268),bool),bool),subspace),s(fun(cart(real,Q122268),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q122268),bool),bool),i(s(fun(fun(cart(real,Q122268),bool),fun(fun(cart(real,Q122268),bool),bool)),subset),s(fun(cart(real,Q122268),bool),S0))),s(fun(cart(real,Q122268),bool),i(s(fun(fun(cart(real,Q122268),bool),fun(cart(real,Q122268),bool)),span),s(fun(cart(real,Q122268),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q122268),bool),bool),i(s(fun(fun(cart(real,Q122268),bool),fun(fun(cart(real,Q122268),bool),bool)),subset),s(fun(cart(real,Q122268),bool),B0))),s(fun(cart(real,Q122268),bool),S0)))) -> s(fun(cart(real,Q122268),bool),S0) = s(fun(cart(real,Q122268),bool),i(s(fun(fun(cart(real,Q122268),bool),fun(cart(real,Q122268),bool)),span),s(fun(cart(real,Q122268),bool),B0))))) # label(aSPANu_SUBSPACE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2652 (all Q109341 all Q109340 all Q109337 all U_2 ((all F0 all J0 all I0 s(cart(real,Q109337),i(s(fun(Q109340,cart(real,Q109337)),i(s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0),s(Q109341,I0))),s(Q109340,J0))) = s(cart(real,Q109337),i(s(fun(Q109341,cart(real,Q109337)),i(s(fun(Q109340,fun(Q109341,cart(real,Q109337))),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,fun(Q109341,cart(real,Q109337)))),U_2),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))),s(Q109340,J0))),s(Q109341,I0)))) -> (all U_1 ((all S0 all F0 all J0 s(cart(real,Q109337),i(s(fun(fun(Q109341,cart(real,Q109337)),cart(real,Q109337)),i(s(fun(fun(Q109341,bool),fun(fun(Q109341,cart(real,Q109337)),cart(real,Q109337))),vsum),s(fun(Q109341,bool),S0))),s(fun(Q109341,cart(real,Q109337)),i(s(fun(Q109340,fun(Q109341,cart(real,Q109337))),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,fun(Q109341,cart(real,Q109337)))),U_2),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))),s(Q109340,J0))))) = s(cart(real,Q109337),i(s(fun(Q109340,cart(real,Q109337)),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,cart(real,Q109337))),i(s(fun(fun(Q109341,bool),fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,cart(real,Q109337)))),U_1),s(fun(Q109341,bool),S0))),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))),s(Q109340,J0)))) -> (all U_0 ((all T0 all F0 all I0 s(cart(real,Q109337),i(s(fun(fun(Q109340,cart(real,Q109337)),cart(real,Q109337)),i(s(fun(fun(Q109340,bool),fun(fun(Q109340,cart(real,Q109337)),cart(real,Q109337))),vsum),s(fun(Q109340,bool),T0))),s(fun(Q109340,cart(real,Q109337)),i(s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0),s(Q109341,I0))))) = s(cart(real,Q109337),i(s(fun(Q109341,cart(real,Q109337)),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109341,cart(real,Q109337))),i(s(fun(fun(Q109340,bool),fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109341,cart(real,Q109337)))),U_0),s(fun(Q109340,bool),T0))),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))),s(Q109341,I0)))) -> (all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q109340,bool),bool),finite),s(fun(Q109340,bool),T0)))) & p(s(bool,i(s(fun(fun(Q109341,bool),bool),finite),s(fun(Q109341,bool),S0)))) -> s(cart(real,Q109337),i(s(fun(fun(Q109340,cart(real,Q109337)),cart(real,Q109337)),i(s(fun(fun(Q109340,bool),fun(fun(Q109340,cart(real,Q109337)),cart(real,Q109337))),vsum),s(fun(Q109340,bool),T0))),s(fun(Q109340,cart(real,Q109337)),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,cart(real,Q109337))),i(s(fun(fun(Q109341,bool),fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109340,cart(real,Q109337)))),U_1),s(fun(Q109341,bool),S0))),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))))) = s(cart(real,Q109337),i(s(fun(fun(Q109341,cart(real,Q109337)),cart(real,Q109337)),i(s(fun(fun(Q109341,bool),fun(fun(Q109341,cart(real,Q109337)),cart(real,Q109337))),vsum),s(fun(Q109341,bool),S0))),s(fun(Q109341,cart(real,Q109337)),i(s(fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109341,cart(real,Q109337))),i(s(fun(fun(Q109340,bool),fun(fun(Q109341,fun(Q109340,cart(real,Q109337))),fun(Q109341,cart(real,Q109337)))),U_0),s(fun(Q109340,bool),T0))),s(fun(Q109341,fun(Q109340,cart(real,Q109337))),F0))))))))))))) # label(aVSUMu_SWAP) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2653 (all Q100586 all X ((all Y s(real,i(s(fun(cart(real,Q100586),real),i(s(fun(cart(real,Q100586),fun(cart(real,Q100586),real)),dot),s(cart(real,Q100586),X))),s(cart(real,Q100586),Y))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) <-> s(cart(real,Q100586),X) = s(cart(real,Q100586),i(s(fun(num,cart(real,Q100586)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aFORALLu_DOTu_EQu_0u_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2654 (all N all M all A5 all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),Y))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5)))))))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5)))))))) -> s(cart(real,M),X) = s(cart(real,M),Y))) # label(aMATRIXu_VECTORu_MULu_INJECTIVEu_ONu_ROWSPACE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2655 (all Q102180 all X s(real,i(s(fun(cart(real,Q102180),real),vectoru_norm),s(cart(real,Q102180),X))) = s(real,i(s(fun(cart(real,Q102180),real),vectoru_norm),s(cart(real,Q102180),i(s(fun(cart(real,Q102180),cart(real,Q102180)),vectoru_neg),s(cart(real,Q102180),X)))))) # label(aNORMu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2656 (all N all M all N0 all I0 all J0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> (exists V (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,N0))))),s(num,I0))))),s(num,J0))) & (s(num,J0) = s(num,I0) <-> p(s(bool,V))))))) # label(aMATu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2657 (all N s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),n))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),m))),s(cart(real,N),p1))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),m))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),n))),s(cart(real,N),p1)))))) # label(aVECTORu_ADDu_ACu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2658 (all N all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,a0)))) & s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))) <-> s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))) = s(real,a0))) # label(aNORMu_EQu_SQUARE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2659 (all N all X all Y all I0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),Y))))),s(num,I0)))) # label(aVECTORu_SUBu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2660 (all N all X all Y ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0)))))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y)))))))) # label(aNORMu_LEu_COMPONENTWISE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2661 (all N s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(fun(cart(real,N),cart(real,N)),real),onorm),s(fun(cart(real,N),cart(real,N)),i1)))) # label(aONORMu_I) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2662 (all N all U_0 ((all F0 all I0 s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(num,cart(real,N)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,I0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),U_0),s(fun(num,cart(real,N)),F0))),s(num,I0)))) -> (all F0 all M0 all N0 s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),U_0),s(fun(num,cart(real,N)),F0))))) = s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),t_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,N)),F0)))))) # label(aVSUMu_PAIR) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2663 (all N all M all A5 all B0 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),B0)))))) # label(aMATRIXu_NEGu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2664 (all Q104610 all X all Y s(real,i(s(fun(cart(real,Q104610),real),i(s(fun(cart(real,Q104610),fun(cart(real,Q104610),real)),dot),s(cart(real,Q104610),X))),s(cart(real,Q104610),Y))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104610),real),vectoru_norm),s(cart(real,Q104610),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104610),real),vectoru_norm),s(cart(real,Q104610),Y))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104610),real),vectoru_norm),s(cart(real,Q104610),i(s(fun(cart(real,Q104610),cart(real,Q104610)),i(s(fun(cart(real,Q104610),fun(cart(real,Q104610),cart(real,Q104610))),vectoru_sub),s(cart(real,Q104610),X))),s(cart(real,Q104610),Y))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aDOTu_NORMu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2665 (all N all M all A5 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(cart(real,N),M),A5)) # label(aMATRIXu_SUBu_RZERO) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2666 (all B all A all Q107150 all U_1 ((all S0 all F0 all Y all GENR_PVARR_282 ((exists X exists V (p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_282))),s(bool,V))),s(A,X)))) & (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),F0),s(A,X))) = s(B,Y) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))),s(A,GENR_PVARR_282)))))) -> (all U_0 ((all S0 all F0 all G0 all Y s(cart(real,Q107150),i(s(fun(B,cart(real,Q107150)),i(s(fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150))),i(s(fun(fun(A,B),fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150)))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150))))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,cart(real,Q107150)),G0))),s(B,Y))) = s(cart(real,Q107150),i(s(fun(fun(A,cart(real,Q107150)),cart(real,Q107150)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107150)),cart(real,Q107150))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))))))),s(fun(A,cart(real,Q107150)),G0)))) -> (all F0 all G0 all S0 all T0 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(B,bool),fun(fun(B,bool),bool)),subset),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,bool),T0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(cart(real,Q107150),i(s(fun(fun(A,cart(real,Q107150)),cart(real,Q107150)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107150)),cart(real,Q107150))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q107150)),G0))) = s(cart(real,Q107150),i(s(fun(fun(B,cart(real,Q107150)),cart(real,Q107150)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,Q107150)),cart(real,Q107150))),vsum),s(fun(B,bool),T0))),s(fun(B,cart(real,Q107150)),i(s(fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150))),i(s(fun(fun(A,B),fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150)))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,cart(real,Q107150)),fun(B,cart(real,Q107150))))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,cart(real,Q107150)),G0))))))))))) # label(aVSUMu_GROUP) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2667 (all X s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),vectoru_neg),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(real,real),realu_neg),s(real,X)))))) # label(aLIFTu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2668 (all N all I0 (s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))) <-> -p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,I0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))))))) # label(aBASISu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2669 (all N all A5 (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),A5))) -> (exists S0 ((all X (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0)))) -> s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))) & s(fun(cart(real,N),bool),univ) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),S0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0)))))))) # label(aVECTORu_INu_ORTHONORMALu_BASIS) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2670 (all Q99705 all X all Y (s(cart(real,Q99705),i(s(fun(cart(real,Q99705),cart(real,Q99705)),i(s(fun(cart(real,Q99705),fun(cart(real,Q99705),cart(real,Q99705))),vectoru_sub),s(cart(real,Q99705),X))),s(cart(real,Q99705),Y))) = s(cart(real,Q99705),i(s(fun(num,cart(real,Q99705)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(cart(real,Q99705),X) = s(cart(real,Q99705),Y))) # label(aVECTORu_SUBu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2671 (all Q122015 all S0 p(s(bool,i(s(fun(fun(cart(real,Q122015),bool),bool),subspace),s(fun(cart(real,Q122015),bool),i(s(fun(fun(cart(real,Q122015),bool),fun(cart(real,Q122015),bool)),span),s(fun(cart(real,Q122015),bool),S0))))))) # label(aSUBSPACEu_SPAN) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2672 (all N all M all U_0 ((all A5 all X s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X)))) -> (all A5 p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5))))))))) # label(aMATRIXu_VECTORu_MULu_LINEAR) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2673 (all N all X all Y (s(cart(real,N),X) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) | s(cart(real,N),Y) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) | (exists C0 s(cart(real,N),Y) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X)))) <-> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),Y))),s(fun(cart(real,N),bool),empty)))))))))))) # label(aCOLLINEARu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2674 (all Q104559 all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104559),real),vectoru_norm),s(cart(real,Q104559),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104559),real),vectoru_norm),s(cart(real,Q104559),Y))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104559),real),vectoru_norm),s(cart(real,Q104559),i(s(fun(cart(real,Q104559),cart(real,Q104559)),i(s(fun(cart(real,Q104559),fun(cart(real,Q104559),cart(real,Q104559))),vectoru_sub),s(cart(real,Q104559),X))),s(cart(real,Q104559),Y))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(cart(real,Q104559),real),i(s(fun(cart(real,Q104559),fun(cart(real,Q104559),real)),dot),s(cart(real,Q104559),X))),s(cart(real,Q104559),Y)))) # label(aDOTu_NORMu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2675 (all Q106132 all Q106140 all U_0 ((all F0 all X s(cart(real,Q106140),i(s(fun(Q106132,cart(real,Q106140)),i(s(fun(fun(Q106132,cart(real,Q106140)),fun(Q106132,cart(real,Q106140))),U_0),s(fun(Q106132,cart(real,Q106140)),F0))),s(Q106132,X))) = s(cart(real,Q106140),i(s(fun(cart(real,Q106140),cart(real,Q106140)),vectoru_neg),s(cart(real,Q106140),i(s(fun(Q106132,cart(real,Q106140)),F0),s(Q106132,X)))))) -> (all F0 all S0 s(cart(real,Q106140),i(s(fun(fun(Q106132,cart(real,Q106140)),cart(real,Q106140)),i(s(fun(fun(Q106132,bool),fun(fun(Q106132,cart(real,Q106140)),cart(real,Q106140))),vsum),s(fun(Q106132,bool),S0))),s(fun(Q106132,cart(real,Q106140)),i(s(fun(fun(Q106132,cart(real,Q106140)),fun(Q106132,cart(real,Q106140))),U_0),s(fun(Q106132,cart(real,Q106140)),F0))))) = s(cart(real,Q106140),i(s(fun(cart(real,Q106140),cart(real,Q106140)),vectoru_neg),s(cart(real,Q106140),i(s(fun(fun(Q106132,cart(real,Q106140)),cart(real,Q106140)),i(s(fun(fun(Q106132,bool),fun(fun(Q106132,cart(real,Q106140)),cart(real,Q106140))),vsum),s(fun(Q106132,bool),S0))),s(fun(Q106132,cart(real,Q106140)),F0)))))))) # label(aVSUMu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2676 (all N all A all S0 all F0 all G0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))))))),s(real,i(s(fun(A,real),G0),s(A,X)))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))))),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),G0)))))))) # label(aVSUMu_NORMu_LE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2677 (all N all U_1 ((all V all J0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_1),s(cart(real,N),V))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),V))),s(num,J0)))) -> (all U_0 ((all V all I0 s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_1),s(cart(real,N),V))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(real,N),fun(num,cart(real,N))),U_0),s(cart(real,N),V))),s(num,I0)))) -> (all V s(cart(cart(real,N),n10),i(s(fun(cart(real,N),cart(cart(real,N),n10)),rowvector),s(cart(real,N),V))) = s(cart(cart(real,N),n10),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),n10)),lambda),s(fun(num,cart(real,N)),i(s(fun(cart(real,N),fun(num,cart(real,N))),U_0),s(cart(real,N),V)))))))))) # label(arowvector) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2678 (all N all U_0 ((all GENR_PVARR_376 (p(s(bool,i(s(fun(real,bool),U_0),s(real,GENR_PVARR_376)))) <-> (exists I0 exists V (p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_376))),s(bool,V))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),x))),s(num,I0)))))))) & (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) <-> p(s(bool,V))))))) -> p(s(bool,i(s(fun(fun(real,bool),bool),finite),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),U_0)))))))) # label(aINFNORMu_SETu_LEMMAu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2679 (all N all X all Y p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),Y))),s(fun(cart(real,N),bool),empty))))))))) # label(aCOLLINEARu_2) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2680 (all Q112067 all Q112072 all F0 (p(s(bool,i(s(fun(fun(cart(real,Q112072),cart(real,Q112067)),bool),linear),s(fun(cart(real,Q112072),cart(real,Q112067)),F0)))) -> ((all X all Y (s(cart(real,Q112067),i(s(fun(cart(real,Q112072),cart(real,Q112067)),F0),s(cart(real,Q112072),X))) = s(cart(real,Q112067),i(s(fun(cart(real,Q112072),cart(real,Q112067)),F0),s(cart(real,Q112072),Y))) -> s(cart(real,Q112072),Y) = s(cart(real,Q112072),X))) <-> (all X (s(cart(real,Q112067),i(s(fun(cart(real,Q112072),cart(real,Q112067)),F0),s(cart(real,Q112072),X))) = s(cart(real,Q112067),i(s(fun(num,cart(real,Q112067)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(cart(real,Q112072),i(s(fun(num,cart(real,Q112072)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q112072),X)))))) # label(aLINEARu_INJECTIVEu_0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2681 (all X all S0 s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(cart(real,n10),fun(fun(cart(real,n10),bool),bool)),in),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(fun(cart(real,n10),bool),S0))) = s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),S0)))))) # label(aINu_IMAGEu_LIFTu_DROPu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.12/15.12 2682 (all N all M all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & (all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) -> s(cart(real,M),Y) = s(cart(real,M),X))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),independent),s(fun(cart(real,M),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0)))))))) # label(aINDEPENDENTu_INJECTIVEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2683 (all Q100306 all X all Y all Z0 s(real,i(s(fun(cart(real,Q100306),real),i(s(fun(cart(real,Q100306),fun(cart(real,Q100306),real)),dot),s(cart(real,Q100306),i(s(fun(cart(real,Q100306),cart(real,Q100306)),i(s(fun(cart(real,Q100306),fun(cart(real,Q100306),cart(real,Q100306))),vectoru_sub),s(cart(real,Q100306),X))),s(cart(real,Q100306),Y))))),s(cart(real,Q100306),Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(cart(real,Q100306),real),i(s(fun(cart(real,Q100306),fun(cart(real,Q100306),real)),dot),s(cart(real,Q100306),X))),s(cart(real,Q100306),Z0))))),s(real,i(s(fun(cart(real,Q100306),real),i(s(fun(cart(real,Q100306),fun(cart(real,Q100306),real)),dot),s(cart(real,Q100306),Y))),s(cart(real,Q100306),Z0)))))) # label(aDOTu_LSUB) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2684 (all Q105761 all Q105774 all U_0 ((all F0 all G0 all X s(cart(real,Q105774),i(s(fun(cart(real,Q105774),cart(real,Q105774)),i(s(fun(cart(real,Q105774),fun(cart(real,Q105774),cart(real,Q105774))),vectoru_sub),s(cart(real,Q105774),i(s(fun(Q105761,cart(real,Q105774)),F0),s(Q105761,X))))),s(cart(real,Q105774),i(s(fun(Q105761,cart(real,Q105774)),G0),s(Q105761,X))))) = s(cart(real,Q105774),i(s(fun(Q105761,cart(real,Q105774)),i(s(fun(fun(Q105761,cart(real,Q105774)),fun(Q105761,cart(real,Q105774))),i(s(fun(fun(Q105761,cart(real,Q105774)),fun(fun(Q105761,cart(real,Q105774)),fun(Q105761,cart(real,Q105774)))),U_0),s(fun(Q105761,cart(real,Q105774)),F0))),s(fun(Q105761,cart(real,Q105774)),G0))),s(Q105761,X)))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q105761,bool),bool),finite),s(fun(Q105761,bool),S0)))) -> s(cart(real,Q105774),i(s(fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774)),i(s(fun(fun(Q105761,bool),fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774))),vsum),s(fun(Q105761,bool),S0))),s(fun(Q105761,cart(real,Q105774)),i(s(fun(fun(Q105761,cart(real,Q105774)),fun(Q105761,cart(real,Q105774))),i(s(fun(fun(Q105761,cart(real,Q105774)),fun(fun(Q105761,cart(real,Q105774)),fun(Q105761,cart(real,Q105774)))),U_0),s(fun(Q105761,cart(real,Q105774)),F0))),s(fun(Q105761,cart(real,Q105774)),G0))))) = s(cart(real,Q105774),i(s(fun(cart(real,Q105774),cart(real,Q105774)),i(s(fun(cart(real,Q105774),fun(cart(real,Q105774),cart(real,Q105774))),vectoru_sub),s(cart(real,Q105774),i(s(fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774)),i(s(fun(fun(Q105761,bool),fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774))),vsum),s(fun(Q105761,bool),S0))),s(fun(Q105761,cart(real,Q105774)),F0))))),s(cart(real,Q105774),i(s(fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774)),i(s(fun(fun(Q105761,bool),fun(fun(Q105761,cart(real,Q105774)),cart(real,Q105774))),vsum),s(fun(Q105761,bool),S0))),s(fun(Q105761,cart(real,Q105774)),G0))))))))) # label(aVSUMu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2685 (all N all U_0 ((all GENR_PVARR_377 (p(s(bool,i(s(fun(real,bool),U_0),s(real,GENR_PVARR_377)))) <-> (exists I0 exists V (p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_377))),s(bool,V))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),x))),s(num,I0)))))))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))))))) -> s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),U_0))) != s(fun(real,bool),empty))) # label(aINFNORMu_SETu_LEMMAu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2686 (all Q133117 all Q133118 s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(cart(cart(real,Q133117),Q133118),num),rank),s(cart(cart(real,Q133117),Q133118),i(s(fun(num,cart(cart(real,Q133117),Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aRANKu_0) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2687 (all N all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0)))) -> (exists B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),S0)))) & s(fun(cart(real,N),bool),S0) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),B0))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))))))) # label(aBASISu_SUBSPACEu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2688 (all Q99962 s(cart(real,Q99962),i(s(fun(cart(real,Q99962),cart(real,Q99962)),vectoru_neg),s(cart(real,Q99962),x))) = s(cart(real,Q99962),i(s(fun(cart(real,Q99962),cart(real,Q99962)),i(s(fun(real,fun(cart(real,Q99962),cart(real,Q99962))),r_),s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,Q99962),x)))) # label(aVECTORu_NEGu_MINUS1) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2689 (all N all X all XI_ all Y all YI_ (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),X))),s(cart(real,N),XI_))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),Y))),s(cart(real,N),YI_))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),XI_))),s(cart(real,N),YI_))))))))),s(real,e0)))))) # label(aDISTu_TRIANGLEu_ADDu_HALF) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2690 (all Q121648 all Q121655 all S0 all F0 all T0 (p(s(bool,i(s(fun(fun(cart(real,Q121655),bool),bool),subspace),s(fun(cart(real,Q121655),bool),S0)))) & p(s(bool,i(s(fun(fun(Q121648,bool),bool),finite),s(fun(Q121648,bool),T0)))) & (all X (p(s(bool,i(s(fun(fun(Q121648,bool),bool),i(s(fun(Q121648,fun(fun(Q121648,bool),bool)),in),s(Q121648,X))),s(fun(Q121648,bool),T0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121655),bool),bool),i(s(fun(cart(real,Q121655),fun(fun(cart(real,Q121655),bool),bool)),in),s(cart(real,Q121655),i(s(fun(Q121648,cart(real,Q121655)),F0),s(Q121648,X))))),s(fun(cart(real,Q121655),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,Q121655),bool),bool),i(s(fun(cart(real,Q121655),fun(fun(cart(real,Q121655),bool),bool)),in),s(cart(real,Q121655),i(s(fun(fun(Q121648,cart(real,Q121655)),cart(real,Q121655)),i(s(fun(fun(Q121648,bool),fun(fun(Q121648,cart(real,Q121655)),cart(real,Q121655))),vsum),s(fun(Q121648,bool),T0))),s(fun(Q121648,cart(real,Q121655)),F0))))),s(fun(cart(real,Q121655),bool),S0)))))) # label(aSUBSPACEu_VSUM) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2691 (all A all N all F0 all U all V ((all X (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V)))) -> s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),U)))) -> s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),U))),s(fun(A,bool),V))))),s(fun(A,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),U))),s(fun(A,cart(real,N)),F0))))) # label(aVSUMu_UNIONu_RZERO) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2692 (all Q109650 all T0 s(cart(real,Q109650),i(s(fun(fun(num,cart(real,Q109650)),cart(real,Q109650)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109650)),cart(real,Q109650))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,Q109650)),T0))) = s(cart(real,Q109650),i(s(fun(cart(real,Q109650),cart(real,Q109650)),i(s(fun(cart(real,Q109650),fun(cart(real,Q109650),cart(real,Q109650))),vectoru_add),s(cart(real,Q109650),i(s(fun(num,cart(real,Q109650)),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(real,Q109650),i(s(fun(cart(real,Q109650),cart(real,Q109650)),i(s(fun(cart(real,Q109650),fun(cart(real,Q109650),cart(real,Q109650))),vectoru_add),s(cart(real,Q109650),i(s(fun(num,cart(real,Q109650)),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,Q109650),i(s(fun(num,cart(real,Q109650)),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) # label(aVSUMu_3) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2693 (all Q114643 all Q114644 all A5 s(cart(cart(real,Q114643),Q114644),i(s(fun(cart(cart(real,Q114643),Q114644),cart(cart(real,Q114643),Q114644)),i(s(fun(cart(cart(real,Q114643),Q114644),fun(cart(cart(real,Q114643),Q114644),cart(cart(real,Q114643),Q114644))),matrixu_add),s(cart(cart(real,Q114643),Q114644),i(s(fun(cart(cart(real,Q114643),Q114644),cart(cart(real,Q114643),Q114644)),matrixu_neg),s(cart(cart(real,Q114643),Q114644),A5))))),s(cart(cart(real,Q114643),Q114644),A5))) = s(cart(cart(real,Q114643),Q114644),i(s(fun(num,cart(cart(real,Q114643),Q114644)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aMATRIXu_ADDu_LNEG) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2694 (all N all B0 all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),B0))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),B0))),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),B0))),s(cart(real,N),B0))))))),s(cart(real,N),B0)))))))) # label(aVECTORu_SUBu_PROJECTu_ORTHOGONAL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2695 (all N all M all A5 all I0 all J0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))))),s(num,I0))))),s(num,J0))) = s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0)))))) # label(aMATRIXu_NEGu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2696 (all Q126529 all V all B0 (p(s(bool,i(s(fun(fun(cart(real,Q126529),bool),bool),i(s(fun(fun(cart(real,Q126529),bool),fun(fun(cart(real,Q126529),bool),bool)),subset),s(fun(cart(real,Q126529),bool),V))),s(fun(cart(real,Q126529),bool),i(s(fun(fun(cart(real,Q126529),bool),fun(cart(real,Q126529),bool)),span),s(fun(cart(real,Q126529),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q126529),bool),bool),independent),s(fun(cart(real,Q126529),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,Q126529),bool),bool),i(s(fun(fun(cart(real,Q126529),bool),fun(fun(cart(real,Q126529),bool),bool)),subset),s(fun(cart(real,Q126529),bool),B0))),s(fun(cart(real,Q126529),bool),V)))) -> s(num,i(s(fun(fun(cart(real,Q126529),bool),num),card),s(fun(cart(real,Q126529),bool),B0))) = s(num,i(s(fun(fun(cart(real,Q126529),bool),num),dim),s(fun(cart(real,Q126529),bool),V))) & p(s(bool,i(s(fun(fun(cart(real,Q126529),bool),bool),finite),s(fun(cart(real,Q126529),bool),B0)))))) # label(aBASISu_CARDu_EQu_DIM) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2697 (all Q126589 all V all B0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126589),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126589),bool),B0))),s(num,n)))) & p(s(bool,i(s(fun(fun(cart(real,Q126589),bool),bool),independent),s(fun(cart(real,Q126589),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,Q126589),bool),bool),i(s(fun(fun(cart(real,Q126589),bool),fun(fun(cart(real,Q126589),bool),bool)),subset),s(fun(cart(real,Q126589),bool),V))),s(fun(cart(real,Q126589),bool),i(s(fun(fun(cart(real,Q126589),bool),fun(cart(real,Q126589),bool)),span),s(fun(cart(real,Q126589),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q126589),bool),bool),i(s(fun(fun(cart(real,Q126589),bool),fun(fun(cart(real,Q126589),bool),bool)),subset),s(fun(cart(real,Q126589),bool),B0))),s(fun(cart(real,Q126589),bool),V)))) -> s(num,i(s(fun(fun(cart(real,Q126589),bool),num),dim),s(fun(cart(real,Q126589),bool),V))) = s(num,n))) # label(aDIMu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2698 (all Q100159 all M0 all N0 (s(cart(real,Q100159),i(s(fun(num,cart(real,Q100159)),vec),s(num,M0))) = s(cart(real,Q100159),i(s(fun(num,cart(real,Q100159)),vec),s(num,N0))) <-> s(num,N0) = s(num,M0))) # label(aVECu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2699 (all Q104658 all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(prod(cart(real,Q104658),cart(real,Q104658)),real),distance),s(prod(cart(real,Q104658),cart(real,Q104658)),i(s(fun(cart(real,Q104658),prod(cart(real,Q104658),cart(real,Q104658))),i(s(fun(cart(real,Q104658),fun(cart(real,Q104658),prod(cart(real,Q104658),cart(real,Q104658)))),c_),s(cart(real,Q104658),X))),s(cart(real,Q104658),X)))))) # label(aDISTu_REFL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2700 (all Q102424 all A5 all X all Y (s(real,A5) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) | s(cart(real,Q102424),X) = s(cart(real,Q102424),Y) <-> s(cart(real,Q102424),i(s(fun(cart(real,Q102424),cart(real,Q102424)),i(s(fun(real,fun(cart(real,Q102424),cart(real,Q102424))),r_),s(real,A5))),s(cart(real,Q102424),Y))) = s(cart(real,Q102424),i(s(fun(cart(real,Q102424),cart(real,Q102424)),i(s(fun(real,fun(cart(real,Q102424),cart(real,Q102424))),r_),s(real,A5))),s(cart(real,Q102424),X))))) # label(aVECTORu_MULu_LCANCEL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2701 (all Q127771 all S0 all X (p(s(bool,i(s(fun(fun(cart(real,Q127771),bool),bool),i(s(fun(cart(real,Q127771),fun(fun(cart(real,Q127771),bool),bool)),in),s(cart(real,Q127771),X))),s(fun(cart(real,Q127771),bool),i(s(fun(fun(cart(real,Q127771),bool),fun(cart(real,Q127771),bool)),span),s(fun(cart(real,Q127771),bool),S0)))))) <-> s(fun(cart(real,Q127771),bool),i(s(fun(fun(cart(real,Q127771),bool),fun(cart(real,Q127771),bool)),span),s(fun(cart(real,Q127771),bool),i(s(fun(fun(cart(real,Q127771),bool),fun(cart(real,Q127771),bool)),i(s(fun(cart(real,Q127771),fun(fun(cart(real,Q127771),bool),fun(cart(real,Q127771),bool))),insert),s(cart(real,Q127771),X))),s(fun(cart(real,Q127771),bool),S0))))) = s(fun(cart(real,Q127771),bool),i(s(fun(fun(cart(real,Q127771),bool),fun(cart(real,Q127771),bool)),span),s(fun(cart(real,Q127771),bool),S0))))) # label(aSPANu_EQu_INSERT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2702 (all Q112532 all Q112524 all Q112534 all H0 all X (p(s(bool,i(s(fun(fun(cart(real,Q112532),fun(cart(real,Q112524),cart(real,Q112534))),bool),bilinear),s(fun(cart(real,Q112532),fun(cart(real,Q112524),cart(real,Q112534))),H0)))) -> s(cart(real,Q112534),i(s(fun(cart(real,Q112524),cart(real,Q112534)),i(s(fun(cart(real,Q112532),fun(cart(real,Q112524),cart(real,Q112534))),H0),s(cart(real,Q112532),i(s(fun(num,cart(real,Q112532)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q112524),X))) = s(cart(real,Q112534),i(s(fun(num,cart(real,Q112534)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aBILINEARu_LZERO) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2703 (all M all N all U_1 ((all A5 all I0 all X all J0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(num,fun(cart(real,N),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(real,N),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(real,N),X))),s(num,J0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,J0)))))) -> (all U_0 ((all A5 all X all I0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(num,fun(cart(real,N),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(real,N),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(real,N),X))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))),s(num,I0)))) -> (all A5 all X s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(fun(num,real),cart(real,M)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X)))))))))) # label(amatrixu_vectoru_mul) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2704 (all N all F0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) & (all X all Y (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y))) -> s(cart(real,N),X) = s(cart(real,N),Y))) -> (exists FI_ ((all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),FI_),s(cart(real,N),X))))) = s(cart(real,N),X)) & (all X s(cart(real,N),X) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),FI_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X)))))) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),FI_)))))))) # label(aLINEARu_INJECTIVEu_ISOMORPHISM) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2705 (all M all N all U_1 ((all F0 all I0 all J0 s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real))),U_1),s(fun(cart(real,M),cart(real,N)),F0))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,J0))))))),s(num,I0)))) -> (all U_0 ((all F0 all I0 s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,cart(real,M))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(num,I0))) = s(cart(real,M),i(s(fun(fun(num,real),cart(real,M)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real))),U_1),s(fun(cart(real,M),cart(real,N)),F0))),s(num,I0)))))) -> (all F0 s(cart(cart(real,M),N),i(s(fun(fun(num,cart(real,M)),cart(cart(real,M),N)),lambda),s(fun(num,cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,cart(real,M))),U_0),s(fun(cart(real,M),cart(real,N)),F0))))) = s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0)))))))) # label(amatrix) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2706 (all Q139038 all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q139038),real),infnorm),s(cart(real,Q139038),i(s(fun(cart(real,Q139038),cart(real,Q139038)),i(s(fun(cart(real,Q139038),fun(cart(real,Q139038),cart(real,Q139038))),vectoru_add),s(cart(real,Q139038),X))),s(cart(real,Q139038),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q139038),real),infnorm),s(cart(real,Q139038),X))))),s(real,i(s(fun(cart(real,Q139038),real),infnorm),s(cart(real,Q139038),Y))))))))) # label(aINFNORMu_TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2707 (all N all B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))) & s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0))) = s(fun(cart(real,N),bool),univ) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),B0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))))) # label(aBASISu_HASu_SIZEu_UNIV) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2708 (all M all N all A5 ((exists B0 s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),B0))),s(cart(cart(real,N),M),A5)))) <-> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),rows),s(cart(cart(real,N),M),A5))))) = s(fun(cart(real,N),bool),univ))) # label(aMATRIXu_LEFTu_INVERTIBLEu_SPANu_ROWS) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2709 (all Q107021 all F0 all G0 all M0 all N0 ((all X (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,X)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,X))),s(num,N0)))) -> s(cart(real,Q107021),i(s(fun(num,cart(real,Q107021)),G0),s(num,X))) = s(cart(real,Q107021),i(s(fun(num,cart(real,Q107021)),F0),s(num,X))))) -> s(cart(real,Q107021),i(s(fun(fun(num,cart(real,Q107021)),cart(real,Q107021)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107021)),cart(real,Q107021))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107021)),G0))) = s(cart(real,Q107021),i(s(fun(fun(num,cart(real,Q107021)),cart(real,Q107021)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107021)),cart(real,Q107021))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107021)),F0))))) # label(aVSUMu_EQu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2710 (all N all U_0 ((all X all I0 s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(real,N),fun(num,cart(real,N))),U_0),s(cart(real,N),X))),s(num,I0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))) -> (all X s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,cart(real,N)),i(s(fun(cart(real,N),fun(num,cart(real,N))),U_0),s(cart(real,N),X))))) = s(cart(real,N),X)))) # label(aBASISu_EXPANSION) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2711 (all Q119643 all Q119649 all U_0 ((all F0 all V all X s(cart(real,Q119649),i(s(fun(cart(real,Q119643),cart(real,Q119649)),i(s(fun(cart(real,Q119649),fun(cart(real,Q119643),cart(real,Q119649))),i(s(fun(fun(cart(real,Q119643),cart(real,n10)),fun(cart(real,Q119649),fun(cart(real,Q119643),cart(real,Q119649)))),U_0),s(fun(cart(real,Q119643),cart(real,n10)),F0))),s(cart(real,Q119649),V))),s(cart(real,Q119643),X))) = s(cart(real,Q119649),i(s(fun(cart(real,Q119649),cart(real,Q119649)),i(s(fun(real,fun(cart(real,Q119649),cart(real,Q119649))),r_),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(cart(real,Q119643),cart(real,n10)),F0),s(cart(real,Q119643),X))))))),s(cart(real,Q119649),V)))) -> (all F0 all V (p(s(bool,i(s(fun(fun(cart(real,Q119643),cart(real,n10)),bool),linear),s(fun(cart(real,Q119643),cart(real,n10)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q119643),cart(real,Q119649)),bool),linear),s(fun(cart(real,Q119643),cart(real,Q119649)),i(s(fun(cart(real,Q119649),fun(cart(real,Q119643),cart(real,Q119649))),i(s(fun(fun(cart(real,Q119643),cart(real,n10)),fun(cart(real,Q119649),fun(cart(real,Q119643),cart(real,Q119649)))),U_0),s(fun(cart(real,Q119643),cart(real,n10)),F0))),s(cart(real,Q119649),V)))))))))) # label(aLINEARu_VMULu_DROP) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2712 (all Q120489 all Q120491 all N0 s(cart(real,finite_sum(Q120489,Q120491)),i(s(fun(cart(real,Q120491),cart(real,finite_sum(Q120489,Q120491))),i(s(fun(cart(real,Q120489),fun(cart(real,Q120491),cart(real,finite_sum(Q120489,Q120491)))),pastecart),s(cart(real,Q120489),i(s(fun(num,cart(real,Q120489)),vec),s(num,N0))))),s(cart(real,Q120491),i(s(fun(num,cart(real,Q120491)),vec),s(num,N0))))) = s(cart(real,finite_sum(Q120489,Q120491)),i(s(fun(num,cart(real,finite_sum(Q120489,Q120491))),vec),s(num,N0)))) # label(aPASTECARTu_VEC) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2713 (all Q142719 all A5 all B0 p(s(bool,i(s(fun(fun(cart(real,Q142719),bool),bool),collinear),s(fun(cart(real,Q142719),bool),i(s(fun(fun(cart(real,Q142719),bool),fun(cart(real,Q142719),bool)),i(s(fun(cart(real,Q142719),fun(fun(cart(real,Q142719),bool),fun(cart(real,Q142719),bool))),insert),s(cart(real,Q142719),A5))),s(fun(cart(real,Q142719),bool),i(s(fun(fun(cart(real,Q142719),bool),fun(cart(real,Q142719),bool)),i(s(fun(cart(real,Q142719),fun(fun(cart(real,Q142719),bool),fun(cart(real,Q142719),bool))),insert),s(cart(real,Q142719),i(s(fun(prod(cart(real,Q142719),cart(real,Q142719)),cart(real,Q142719)),midpoint),s(prod(cart(real,Q142719),cart(real,Q142719)),i(s(fun(cart(real,Q142719),prod(cart(real,Q142719),cart(real,Q142719))),i(s(fun(cart(real,Q142719),fun(cart(real,Q142719),prod(cart(real,Q142719),cart(real,Q142719)))),c_),s(cart(real,Q142719),A5))),s(cart(real,Q142719),B0))))))),s(fun(cart(real,Q142719),bool),i(s(fun(fun(cart(real,Q142719),bool),fun(cart(real,Q142719),bool)),i(s(fun(cart(real,Q142719),fun(fun(cart(real,Q142719),bool),fun(cart(real,Q142719),bool))),insert),s(cart(real,Q142719),B0))),s(fun(cart(real,Q142719),bool),empty))))))))))) # label(aCOLLINEARu_MIDPOINT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2714 (all N s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(fun(cart(real,N),fun(cart(real,N),cart(real,N))),cart(real,N)),neutral),s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add)))) # label(aNEUTRALu_VECTORu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2715 (all Q111054 all A5 all X all Y (p(s(bool,i(s(fun(cart(real,Q111054),bool),i(s(fun(cart(real,Q111054),fun(cart(real,Q111054),bool)),orthogonal),s(cart(real,Q111054),A5))),s(cart(real,Q111054),X)))) & p(s(bool,i(s(fun(cart(real,Q111054),bool),i(s(fun(cart(real,Q111054),fun(cart(real,Q111054),bool)),orthogonal),s(cart(real,Q111054),A5))),s(cart(real,Q111054),Y)))) -> p(s(bool,i(s(fun(cart(real,Q111054),bool),i(s(fun(cart(real,Q111054),fun(cart(real,Q111054),bool)),orthogonal),s(cart(real,Q111054),A5))),s(cart(real,Q111054),i(s(fun(cart(real,Q111054),cart(real,Q111054)),i(s(fun(cart(real,Q111054),fun(cart(real,Q111054),cart(real,Q111054))),vectoru_add),s(cart(real,Q111054),X))),s(cart(real,Q111054),Y)))))))) # label(aORTHOGONALu_CLAUSESu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2716 (all N all M all U_1 ((all A5 all I0 all J0 s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,J0))))),s(num,I0)))) -> (all U_0 ((all A5 all I0 s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),U_0),s(cart(cart(real,N),M),A5))),s(num,I0))) = s(cart(real,M),i(s(fun(fun(num,real),cart(real,M)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0)))))) -> (all A5 s(cart(cart(real,M),N),i(s(fun(fun(num,cart(real,M)),cart(cart(real,M),N)),lambda),s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),U_0),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5)))))))) # label(atransp) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2717 (all Q122006 all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,Q122006),bool),bool),i(s(fun(fun(cart(real,Q122006),bool),fun(fun(cart(real,Q122006),bool),bool)),subset),s(fun(cart(real,Q122006),bool),S0))),s(fun(cart(real,Q122006),bool),T0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q122006),bool),bool),i(s(fun(fun(cart(real,Q122006),bool),fun(fun(cart(real,Q122006),bool),bool)),subset),s(fun(cart(real,Q122006),bool),i(s(fun(fun(cart(real,Q122006),bool),fun(cart(real,Q122006),bool)),span),s(fun(cart(real,Q122006),bool),S0))))),s(fun(cart(real,Q122006),bool),i(s(fun(fun(cart(real,Q122006),bool),fun(cart(real,Q122006),bool)),span),s(fun(cart(real,Q122006),bool),T0)))))))) # label(aSPANu_MONO) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2718 (all Q111897 all Q111896 all F0 all X all Y (p(s(bool,i(s(fun(fun(cart(real,Q111896),cart(real,Q111897)),bool),linear),s(fun(cart(real,Q111896),cart(real,Q111897)),F0)))) -> s(cart(real,Q111897),i(s(fun(cart(real,Q111896),cart(real,Q111897)),F0),s(cart(real,Q111896),i(s(fun(cart(real,Q111896),cart(real,Q111896)),i(s(fun(cart(real,Q111896),fun(cart(real,Q111896),cart(real,Q111896))),vectoru_add),s(cart(real,Q111896),X))),s(cart(real,Q111896),Y))))) = s(cart(real,Q111897),i(s(fun(cart(real,Q111897),cart(real,Q111897)),i(s(fun(cart(real,Q111897),fun(cart(real,Q111897),cart(real,Q111897))),vectoru_add),s(cart(real,Q111897),i(s(fun(cart(real,Q111896),cart(real,Q111897)),F0),s(cart(real,Q111896),X))))),s(cart(real,Q111897),i(s(fun(cart(real,Q111896),cart(real,Q111897)),F0),s(cart(real,Q111896),Y))))))) # label(aLINEARu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2719 (all M all N all A5 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5))))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,N),bool)),columns),s(cart(cart(real,M),N),A5))))))))) # label(aDIMu_ROWSu_LEu_DIMu_COLUMNS) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2720 (all Q119533 all K0 all X (p(s(bool,i(s(fun(fun(Q119533,bool),bool),finite),s(fun(Q119533,bool),K0)))) -> s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(fun(Q119533,cart(real,n10)),cart(real,n10)),i(s(fun(fun(Q119533,bool),fun(fun(Q119533,cart(real,n10)),cart(real,n10))),vsum),s(fun(Q119533,bool),K0))),s(fun(Q119533,cart(real,n10)),X))))) = s(real,i(s(fun(fun(Q119533,real),real),i(s(fun(fun(Q119533,bool),fun(fun(Q119533,real),real)),sum),s(fun(Q119533,bool),K0))),s(fun(Q119533,real),i(s(fun(fun(Q119533,cart(real,n10)),fun(Q119533,real)),i(s(fun(fun(cart(real,n10),real),fun(fun(Q119533,cart(real,n10)),fun(Q119533,real))),o),s(fun(cart(real,n10),real),drop))),s(fun(Q119533,cart(real,n10)),X))))))) # label(aDROPu_VSUM) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2721 (all Q102254 all X (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(cart(real,Q102254),real),vectoru_norm),s(cart(real,Q102254),X))) <-> s(real,i(s(fun(cart(real,Q102254),real),i(s(fun(cart(real,Q102254),fun(cart(real,Q102254),real)),dot),s(cart(real,Q102254),X))),s(cart(real,Q102254),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aNORMu_EQu_0u_DOT) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2722 (all Q111057 all A5 all X all Y (p(s(bool,i(s(fun(cart(real,Q111057),bool),i(s(fun(cart(real,Q111057),fun(cart(real,Q111057),bool)),orthogonal),s(cart(real,Q111057),X))),s(cart(real,Q111057),A5)))) & p(s(bool,i(s(fun(cart(real,Q111057),bool),i(s(fun(cart(real,Q111057),fun(cart(real,Q111057),bool)),orthogonal),s(cart(real,Q111057),Y))),s(cart(real,Q111057),A5)))) -> p(s(bool,i(s(fun(cart(real,Q111057),bool),i(s(fun(cart(real,Q111057),fun(cart(real,Q111057),bool)),orthogonal),s(cart(real,Q111057),i(s(fun(cart(real,Q111057),cart(real,Q111057)),i(s(fun(cart(real,Q111057),fun(cart(real,Q111057),cart(real,Q111057))),vectoru_add),s(cart(real,Q111057),X))),s(cart(real,Q111057),Y))))),s(cart(real,Q111057),A5)))))) # label(aORTHOGONALu_CLAUSESu_conjunct8) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2723 (all N all A all B all D0 all I0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(A,X) != s(A,Y) & s(B,i(s(fun(A,B),I0),s(A,X))) = s(B,i(s(fun(A,B),I0),s(A,Y))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) -> s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(B,cart(real,N)),D0),s(B,i(s(fun(A,B),I0),s(A,X))))))) -> s(cart(real,N),i(s(fun(fun(B,cart(real,N)),cart(real,N)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,N)),cart(real,N))),vsum),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),I0))),s(fun(A,bool),S0))))),s(fun(B,cart(real,N)),D0))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),i(s(fun(fun(A,B),fun(A,cart(real,N))),i(s(fun(fun(B,cart(real,N)),fun(fun(A,B),fun(A,cart(real,N)))),o),s(fun(B,cart(real,N)),D0))),s(fun(A,B),I0))))))) # label(aVSUMu_IMAGEu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2724 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),Y)))))) -> p(s(bool,i(s(fun(cart(real,n10),bool),i(s(fun(cart(real,n10),fun(cart(real,n10),bool)),p0),s(cart(real,n10),X))),s(cart(real,n10),Y)))))) & (all X all Y s(bool,i(s(fun(cart(real,n10),bool),i(s(fun(cart(real,n10),fun(cart(real,n10),bool)),p0),s(cart(real,n10),Y))),s(cart(real,n10),X))) = s(bool,i(s(fun(cart(real,n10),bool),i(s(fun(cart(real,n10),fun(cart(real,n10),bool)),p0),s(cart(real,n10),X))),s(cart(real,n10),Y)))) -> (all X all Y p(s(bool,i(s(fun(cart(real,n10),bool),i(s(fun(cart(real,n10),fun(cart(real,n10),bool)),p0),s(cart(real,n10),X))),s(cart(real,n10),Y))))) # label(aDROPu_WLOGu_LE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2725 (all N all U_1 ((all X all J0 all I0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))),s(num,J0))))) = s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(real,N),fun(num,fun(num,real))),U_1),s(cart(real,N),X))),s(num,J0))),s(num,I0)))) -> (all U_0 ((all X all J0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(real,N),fun(num,fun(num,real))),U_1),s(cart(real,N),X))),s(num,J0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X))),s(num,J0)))) -> (all X s(cart(real,N),X) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X)))))))))) # label(aVECTORu_COMPONENTWISE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2726 (all Q123656 all U_0 ((all A5 all GENR_PVARR_301 (p(s(bool,i(s(fun(cart(real,Q123656),bool),i(s(fun(cart(real,Q123656),fun(cart(real,Q123656),bool)),U_0),s(cart(real,Q123656),A5))),s(cart(real,Q123656),GENR_PVARR_301)))) <-> (exists U p(s(bool,i(s(fun(cart(real,Q123656),bool),i(s(fun(bool,fun(cart(real,Q123656),bool)),i(s(fun(cart(real,Q123656),fun(bool,fun(cart(real,Q123656),bool))),setspec),s(cart(real,Q123656),GENR_PVARR_301))),s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,U))),s(fun(real,bool),univ))))),s(cart(real,Q123656),i(s(fun(cart(real,Q123656),cart(real,Q123656)),i(s(fun(real,fun(cart(real,Q123656),cart(real,Q123656))),r_),s(real,U))),s(cart(real,Q123656),A5))))))))) -> (all A5 s(fun(cart(real,Q123656),bool),i(s(fun(fun(cart(real,Q123656),bool),fun(cart(real,Q123656),bool)),span),s(fun(cart(real,Q123656),bool),i(s(fun(fun(cart(real,Q123656),bool),fun(cart(real,Q123656),bool)),i(s(fun(cart(real,Q123656),fun(fun(cart(real,Q123656),bool),fun(cart(real,Q123656),bool))),insert),s(cart(real,Q123656),A5))),s(fun(cart(real,Q123656),bool),empty))))) = s(fun(cart(real,Q123656),bool),i(s(fun(fun(cart(real,Q123656),bool),fun(cart(real,Q123656),bool)),gspec),s(fun(cart(real,Q123656),bool),i(s(fun(cart(real,Q123656),fun(cart(real,Q123656),bool)),U_0),s(cart(real,Q123656),A5)))))))) # label(aSPANu_SING) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2727 (all Q140117 all S0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,Q140117),bool),num),card),s(fun(cart(real,Q140117),bool),S0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(fun(cart(real,Q140117),bool),bool),finite),s(fun(cart(real,Q140117),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q140117),bool),bool),collinear),s(fun(cart(real,Q140117),bool),S0)))))) # label(aCOLLINEARu_SMALL) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2728 (all Q122633 all X all Y all S0 (p(s(bool,i(s(fun(fun(cart(real,Q122633),bool),bool),i(s(fun(cart(real,Q122633),fun(fun(cart(real,Q122633),bool),bool)),in),s(cart(real,Q122633),X))),s(fun(cart(real,Q122633),bool),i(s(fun(fun(cart(real,Q122633),bool),fun(cart(real,Q122633),bool)),span),s(fun(cart(real,Q122633),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q122633),bool),bool),i(s(fun(cart(real,Q122633),fun(fun(cart(real,Q122633),bool),bool)),in),s(cart(real,Q122633),Y))),s(fun(cart(real,Q122633),bool),i(s(fun(fun(cart(real,Q122633),bool),fun(cart(real,Q122633),bool)),span),s(fun(cart(real,Q122633),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,Q122633),bool),bool),i(s(fun(cart(real,Q122633),fun(fun(cart(real,Q122633),bool),bool)),in),s(cart(real,Q122633),i(s(fun(cart(real,Q122633),cart(real,Q122633)),i(s(fun(cart(real,Q122633),fun(cart(real,Q122633),cart(real,Q122633))),vectoru_sub),s(cart(real,Q122633),X))),s(cart(real,Q122633),Y))))),s(fun(cart(real,Q122633),bool),i(s(fun(fun(cart(real,Q122633),bool),fun(cart(real,Q122633),bool)),span),s(fun(cart(real,Q122633),bool),S0)))))))) # label(aSPANu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2729 (all Q100046 s(cart(real,Q100046),i(s(fun(cart(real,Q100046),cart(real,Q100046)),vectoru_neg),s(cart(real,Q100046),i(s(fun(cart(real,Q100046),cart(real,Q100046)),i(s(fun(real,fun(cart(real,Q100046),cart(real,Q100046))),r_),s(real,c))),s(cart(real,Q100046),x))))) = s(cart(real,Q100046),i(s(fun(cart(real,Q100046),cart(real,Q100046)),i(s(fun(real,fun(cart(real,Q100046),cart(real,Q100046))),r_),s(real,c))),s(cart(real,Q100046),i(s(fun(cart(real,Q100046),cart(real,Q100046)),vectoru_neg),s(cart(real,Q100046),x)))))) # label(aVECTORu_MULu_RNEG) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2730 (all Q127058 all Q127043 all F0 all B0 all V (p(s(bool,i(s(fun(fun(cart(real,Q127043),cart(real,Q127058)),bool),linear),s(fun(cart(real,Q127043),cart(real,Q127058)),F0)))) & p(s(bool,i(s(fun(fun(cart(real,Q127043),bool),bool),i(s(fun(fun(cart(real,Q127043),bool),fun(fun(cart(real,Q127043),bool),bool)),subset),s(fun(cart(real,Q127043),bool),V))),s(fun(cart(real,Q127043),bool),i(s(fun(fun(cart(real,Q127043),bool),fun(cart(real,Q127043),bool)),span),s(fun(cart(real,Q127043),bool),B0)))))) -> p(s(bool,i(s(fun(fun(cart(real,Q127058),bool),bool),i(s(fun(fun(cart(real,Q127058),bool),fun(fun(cart(real,Q127058),bool),bool)),subset),s(fun(cart(real,Q127058),bool),i(s(fun(fun(cart(real,Q127043),bool),fun(cart(real,Q127058),bool)),i(s(fun(fun(cart(real,Q127043),cart(real,Q127058)),fun(fun(cart(real,Q127043),bool),fun(cart(real,Q127058),bool))),image),s(fun(cart(real,Q127043),cart(real,Q127058)),F0))),s(fun(cart(real,Q127043),bool),V))))),s(fun(cart(real,Q127058),bool),i(s(fun(fun(cart(real,Q127058),bool),fun(cart(real,Q127058),bool)),span),s(fun(cart(real,Q127058),bool),i(s(fun(fun(cart(real,Q127043),bool),fun(cart(real,Q127058),bool)),i(s(fun(fun(cart(real,Q127043),cart(real,Q127058)),fun(fun(cart(real,Q127043),bool),fun(cart(real,Q127058),bool))),image),s(fun(cart(real,Q127043),cart(real,Q127058)),F0))),s(fun(cart(real,Q127043),bool),B0)))))))))) # label(aSPANSu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2731 (all P0 ((exists S0 p(s(bool,i(s(fun(fun(real,bool),bool),P0),s(fun(real,bool),S0))))) <-> (exists S0 p(s(bool,i(s(fun(fun(real,bool),bool),P0),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),S0))))))))) # label(aEXISTSu_DROPu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2732 (all N all X all Y (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))) <-> s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(cart(real,N),Y))))) # label(aNORMu_CAUCHYu_SCHWARZu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2733 (all N all M all A5 all B0 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),B0))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0)))) # label(aMATRIXu_ADDu_SYM) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2734 (all N all M all A5 ((exists X (s(cart(real,M),X) != s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) <-> s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))) != s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))))) # label(aMATRIXu_NONFULLu_LINEARu_EQUATIONSu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.12/15.13 2735 (all Q122994 all U_0 ((all S0 all T0 all GENR_PVARR_298 (p(s(bool,i(s(fun(cart(real,Q122994),bool),i(s(fun(fun(cart(real,Q122994),bool),fun(cart(real,Q122994),bool)),i(s(fun(fun(cart(real,Q122994),bool),fun(fun(cart(real,Q122994),bool),fun(cart(real,Q122994),bool))),U_0),s(fun(cart(real,Q122994),bool),S0))),s(fun(cart(real,Q122994),bool),T0))),s(cart(real,Q122994),GENR_PVARR_298)))) <-> (exists X exists Y exists V (p(s(bool,i(s(fun(cart(real,Q122994),bool),i(s(fun(bool,fun(cart(real,Q122994),bool)),i(s(fun(cart(real,Q122994),fun(bool,fun(cart(real,Q122994),bool))),setspec),s(cart(real,Q122994),GENR_PVARR_298))),s(bool,V))),s(cart(real,Q122994),i(s(fun(cart(real,Q122994),cart(real,Q122994)),i(s(fun(cart(real,Q122994),fun(cart(real,Q122994),cart(real,Q122994))),vectoru_add),s(cart(real,Q122994),X))),s(cart(real,Q122994),Y)))))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(cart(real,Q122994),bool),bool),i(s(fun(cart(real,Q122994),fun(fun(cart(real,Q122994),bool),bool)),in),s(cart(real,Q122994),Y))),s(fun(cart(real,Q122994),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,Q122994),bool),bool),i(s(fun(cart(real,Q122994),fun(fun(cart(real,Q122994),bool),bool)),in),s(cart(real,Q122994),X))),s(fun(cart(real,Q122994),bool),S0))))))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,Q122994),bool),bool),subspace),s(fun(cart(real,Q122994),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,Q122994),bool),bool),subspace),s(fun(cart(real,Q122994),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q122994),bool),bool),subspace),s(fun(cart(real,Q122994),bool),i(s(fun(fun(cart(real,Q122994),bool),fun(cart(real,Q122994),bool)),gspec),s(fun(cart(real,Q122994),bool),i(s(fun(fun(cart(real,Q122994),bool),fun(cart(real,Q122994),bool)),i(s(fun(fun(cart(real,Q122994),bool),fun(fun(cart(real,Q122994),bool),fun(cart(real,Q122994),bool))),U_0),s(fun(cart(real,Q122994),bool),S0))),s(fun(cart(real,Q122994),bool),T0)))))))))))) # label(aSUBSPACEu_SUMS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2736 (all T0 s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),T0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) # label(aSUMu_3) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2737 (all Q143377 all Q143405 all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q143405),cart(real,Q143377)),bool),linear),s(fun(cart(real,Q143405),cart(real,Q143377)),F0)))) & (all X all Y (s(cart(real,Q143377),i(s(fun(cart(real,Q143405),cart(real,Q143377)),F0),s(cart(real,Q143405),X))) = s(cart(real,Q143377),i(s(fun(cart(real,Q143405),cart(real,Q143377)),F0),s(cart(real,Q143405),Y))) -> s(cart(real,Q143405),X) = s(cart(real,Q143405),Y))) -> s(bool,i(s(fun(fun(cart(real,Q143377),bool),bool),subspace),s(fun(cart(real,Q143377),bool),i(s(fun(fun(cart(real,Q143405),bool),fun(cart(real,Q143377),bool)),i(s(fun(fun(cart(real,Q143405),cart(real,Q143377)),fun(fun(cart(real,Q143405),bool),fun(cart(real,Q143377),bool))),image),s(fun(cart(real,Q143405),cart(real,Q143377)),F0))),s(fun(cart(real,Q143405),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,Q143405),bool),bool),subspace),s(fun(cart(real,Q143405),bool),S0))))) # label(aSUBSPACEu_LINEARu_IMAGEu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2738 (all N all X all Y s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),i(s(fun(num,cart(real,n10)),i(s(fun(cart(cart(real,n10),n10),fun(num,cart(real,n10))),d_),s(cart(cart(real,n10),n10),i(s(fun(cart(cart(real,n10),N),cart(cart(real,n10),n10)),i(s(fun(cart(cart(real,N),n10),fun(cart(cart(real,n10),N),cart(cart(real,n10),n10))),matrixu_mul),s(cart(cart(real,N),n10),i(s(fun(cart(real,N),cart(cart(real,N),n10)),rowvector),s(cart(real,N),X))))),s(cart(cart(real,n10),N),i(s(fun(cart(real,N),cart(cart(real,n10),N)),columnvector),s(cart(real,N),Y))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y)))) # label(aDOTu_MATRIXu_PRODUCT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2739 (all N all M all F0 ((all X s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))) = s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X)))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) -> s(cart(real,M),X) = s(cart(real,M),Y))))) # label(aPRESERVESu_NORMu_INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2740 (all A all B all U_5 ((all R0 all F0 all GENR_PVARR_386 (p(s(bool,i(s(fun(list(A),bool),i(s(fun(fun(A,B),fun(list(A),bool)),i(s(fun(fun(list(B),bool),fun(fun(A,B),fun(list(A),bool))),U_5),s(fun(list(B),bool),R0))),s(fun(A,B),F0))),s(list(A),GENR_PVARR_386)))) <-> (exists L p(s(bool,i(s(fun(list(A),bool),i(s(fun(bool,fun(list(A),bool)),i(s(fun(list(A),fun(bool,fun(list(A),bool))),setspec),s(list(A),GENR_PVARR_386))),s(bool,i(s(fun(list(B),bool),R0),s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),L))))))),s(list(A),L))))))) -> (all U_4 ((all R0 all GENR_PVARR_385 ((exists L p(s(bool,i(s(fun(list(B),bool),i(s(fun(bool,fun(list(B),bool)),i(s(fun(list(B),fun(bool,fun(list(B),bool))),setspec),s(list(B),GENR_PVARR_385))),s(bool,i(s(fun(list(B),bool),R0),s(list(B),L))))),s(list(B),L))))) <-> p(s(bool,i(s(fun(list(B),bool),i(s(fun(fun(list(B),bool),fun(list(B),bool)),U_4),s(fun(list(B),bool),R0))),s(list(B),GENR_PVARR_385)))))) -> (all U_3 ((all Q0 all F0 all GENR_PVARR_384 ((exists S0 p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(bool,fun(fun(A,bool),bool)),i(s(fun(fun(A,bool),fun(bool,fun(fun(A,bool),bool))),setspec),s(fun(A,bool),GENR_PVARR_384))),s(bool,i(s(fun(fun(B,bool),bool),Q0),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))))),s(fun(A,bool),S0))))) <-> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,B),fun(fun(A,bool),bool)),i(s(fun(fun(fun(B,bool),bool),fun(fun(A,B),fun(fun(A,bool),bool))),U_3),s(fun(fun(B,bool),bool),Q0))),s(fun(A,B),F0))),s(fun(A,bool),GENR_PVARR_384)))))) -> (all U_2 ((all Q0 all GENR_PVARR_383 (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),U_2),s(fun(fun(B,bool),bool),Q0))),s(fun(B,bool),GENR_PVARR_383)))) <-> (exists S0 p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(bool,fun(fun(B,bool),bool)),i(s(fun(fun(B,bool),fun(bool,fun(fun(B,bool),bool))),setspec),s(fun(B,bool),GENR_PVARR_383))),s(bool,i(s(fun(fun(B,bool),bool),Q0),s(fun(B,bool),S0))))),s(fun(B,bool),S0))))))) -> (all U_1 ((all P0 all F0 all GENR_PVARR_382 (p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),i(s(fun(fun(B,bool),fun(fun(A,B),fun(A,bool))),U_1),s(fun(B,bool),P0))),s(fun(A,B),F0))),s(A,GENR_PVARR_382)))) <-> (exists X p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_382))),s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(A,B),F0),s(A,X))))))),s(A,X))))))) -> (all U_0 ((all P0 all GENR_PVARR_381 ((exists X p(s(bool,i(s(fun(B,bool),i(s(fun(bool,fun(B,bool)),i(s(fun(B,fun(bool,fun(B,bool))),setspec),s(B,GENR_PVARR_381))),s(bool,i(s(fun(B,bool),P0),s(B,X))))),s(B,X))))) <-> p(s(bool,i(s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),U_0),s(fun(B,bool),P0))),s(B,GENR_PVARR_381)))))) -> (all F0 ((all Y exists X s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X)))) -> (all Q0 ((all S0 p(s(bool,i(s(fun(fun(B,bool),bool),Q0),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))))) <-> (all S0 p(s(bool,i(s(fun(fun(B,bool),bool),Q0),s(fun(B,bool),S0))))))) & (all P0 ((all G0 p(s(bool,i(s(fun(fun(cart(real,n10),B),bool),P0),s(fun(cart(real,n10),B),i(s(fun(fun(cart(real,n10),A),fun(cart(real,n10),B)),i(s(fun(fun(A,B),fun(fun(cart(real,n10),A),fun(cart(real,n10),B))),o),s(fun(A,B),F0))),s(fun(cart(real,n10),A),G0))))))) <-> (all G0 p(s(bool,i(s(fun(fun(cart(real,n10),B),bool),P0),s(fun(cart(real,n10),B),G0))))))) & (all P0 ((all G0 p(s(bool,i(s(fun(fun(num,B),bool),P0),s(fun(num,B),G0))))) <-> (all G0 p(s(bool,i(s(fun(fun(num,B),bool),P0),s(fun(num,B),i(s(fun(fun(num,A),fun(num,B)),i(s(fun(fun(A,B),fun(fun(num,A),fun(num,B))),o),s(fun(A,B),F0))),s(fun(num,A),G0))))))))) & (all P0 ((exists G0 p(s(bool,i(s(fun(fun(num,B),bool),P0),s(fun(num,B),G0))))) <-> (exists G0 p(s(bool,i(s(fun(fun(num,B),bool),P0),s(fun(num,B),i(s(fun(fun(num,A),fun(num,B)),i(s(fun(fun(A,B),fun(fun(num,A),fun(num,B))),o),s(fun(A,B),F0))),s(fun(num,A),G0))))))))) & (all Q0 ((exists L p(s(bool,i(s(fun(list(B),bool),Q0),s(list(B),L))))) <-> (exists L p(s(bool,i(s(fun(list(B),bool),Q0),s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),L))))))))) & (all Q0 s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),gspec),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(B,bool),bool),fun(fun(B,bool),bool)),U_2),s(fun(fun(B,bool),bool),Q0))))) = s(fun(fun(B,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(B,bool),bool)),i(s(fun(fun(fun(A,bool),fun(B,bool)),fun(fun(fun(A,bool),bool),fun(fun(B,bool),bool))),image),s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))))),s(fun(fun(A,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(A,bool),bool)),gspec),s(fun(fun(A,bool),bool),i(s(fun(fun(A,B),fun(fun(A,bool),bool)),i(s(fun(fun(fun(B,bool),bool),fun(fun(A,B),fun(fun(A,bool),bool))),U_3),s(fun(fun(B,bool),bool),Q0))),s(fun(A,B),F0)))))))) & (all R0 s(fun(list(B),bool),i(s(fun(fun(list(A),bool),fun(list(B),bool)),i(s(fun(fun(list(A),list(B)),fun(fun(list(A),bool),fun(list(B),bool))),image),s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))))),s(fun(list(A),bool),i(s(fun(fun(list(A),bool),fun(list(A),bool)),gspec),s(fun(list(A),bool),i(s(fun(fun(A,B),fun(list(A),bool)),i(s(fun(fun(list(B),bool),fun(fun(A,B),fun(list(A),bool))),U_5),s(fun(list(B),bool),R0))),s(fun(A,B),F0))))))) = s(fun(list(B),bool),i(s(fun(fun(list(B),bool),fun(list(B),bool)),gspec),s(fun(list(B),bool),i(s(fun(fun(list(B),bool),fun(list(B),bool)),U_4),s(fun(list(B),bool),R0)))))) & (all P0 s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),gspec),s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),U_0),s(fun(B,bool),P0))))) = s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),i(s(fun(fun(B,bool),fun(fun(A,B),fun(A,bool))),U_1),s(fun(B,bool),P0))),s(fun(A,B),F0)))))))) & (all Q0 ((all L p(s(bool,i(s(fun(list(B),bool),Q0),s(list(B),i(s(fun(list(A),list(B)),i(s(fun(fun(A,B),fun(list(A),list(B))),map0),s(fun(A,B),F0))),s(list(A),L))))))) <-> (all L p(s(bool,i(s(fun(list(B),bool),Q0),s(list(B),L))))))) & (all P0 ((exists G0 p(s(bool,i(s(fun(fun(cart(real,n10),B),bool),P0),s(fun(cart(real,n10),B),i(s(fun(fun(cart(real,n10),A),fun(cart(real,n10),B)),i(s(fun(fun(A,B),fun(fun(cart(real,n10),A),fun(cart(real,n10),B))),o),s(fun(A,B),F0))),s(fun(cart(real,n10),A),G0))))))) <-> (exists G0 p(s(bool,i(s(fun(fun(cart(real,n10),B),bool),P0),s(fun(cart(real,n10),B),G0))))))) & (all Q0 ((exists S0 p(s(bool,i(s(fun(fun(fun(B,bool),bool),bool),Q0),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(B,bool),bool)),i(s(fun(fun(fun(A,bool),fun(B,bool)),fun(fun(fun(A,bool),bool),fun(fun(B,bool),bool))),image),s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))))),s(fun(fun(A,bool),bool),S0))))))) <-> (exists S0 p(s(bool,i(s(fun(fun(fun(B,bool),bool),bool),Q0),s(fun(fun(B,bool),bool),S0))))))) & (all Q0 ((all S0 p(s(bool,i(s(fun(fun(fun(B,bool),bool),bool),Q0),s(fun(fun(B,bool),bool),S0))))) <-> (all S0 p(s(bool,i(s(fun(fun(fun(B,bool),bool),bool),Q0),s(fun(fun(B,bool),bool),i(s(fun(fun(fun(A,bool),bool),fun(fun(B,bool),bool)),i(s(fun(fun(fun(A,bool),fun(B,bool)),fun(fun(fun(A,bool),bool),fun(fun(B,bool),bool))),image),s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))))),s(fun(fun(A,bool),bool),S0))))))))) & (all Q0 ((exists S0 p(s(bool,i(s(fun(fun(B,bool),bool),Q0),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))))) <-> (exists S0 p(s(bool,i(s(fun(fun(B,bool),bool),Q0),s(fun(B,bool),S0))))))) & (all P0 ((exists X p(s(bool,i(s(fun(B,bool),P0),s(B,X))))) <-> (exists X p(s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(A,B),F0),s(A,X))))))))) & (all P0 ((all X p(s(bool,i(s(fun(B,bool),P0),s(B,X))))) <-> (all X p(s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(A,B),F0),s(A,X))))))))))))))))))))))) # label(aQUANTIFYu_SURJECTIONu_HIGHERu_THM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2741 (all Q111694 all Q111699 all U_0 ((all X s(cart(real,Q111699),i(s(fun(num,cart(real,Q111699)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q111699),i(s(fun(cart(real,Q111694),cart(real,Q111699)),U_0),s(cart(real,Q111694),X)))) -> p(s(bool,i(s(fun(fun(cart(real,Q111694),cart(real,Q111699)),bool),linear),s(fun(cart(real,Q111694),cart(real,Q111699)),U_0)))))) # label(aLINEARu_ZERO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2742 (all N all C0 ((all X all Y (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),Y))) -> s(cart(real,N),Y) = s(cart(real,N),X))) <-> s(real,C0) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aINJECTIVEu_SCALING) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2743 (all Q109481 all Q109494 all U_1 ((all F0 all G0 all X s(cart(real,Q109494),i(s(fun(Q109481,cart(real,Q109494)),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,cart(real,Q109494))),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,cart(real,Q109494)))),U_1),s(fun(Q109481,cart(real,Q109494)),F0))),s(fun(Q109481,cart(real,Q109494)),G0))),s(Q109481,X))) = s(cart(real,Q109494),i(s(fun(cart(real,Q109494),cart(real,Q109494)),i(s(fun(cart(real,Q109494),fun(cart(real,Q109494),cart(real,Q109494))),vectoru_add),s(cart(real,Q109494),i(s(fun(Q109481,cart(real,Q109494)),F0),s(Q109481,X))))),s(cart(real,Q109494),i(s(fun(Q109481,cart(real,Q109494)),G0),s(Q109481,X)))))) -> (all U_0 ((all S0 all F0 all GENR_PVARR_286 ((exists X exists V (p(s(bool,i(s(fun(Q109481,bool),i(s(fun(bool,fun(Q109481,bool)),i(s(fun(Q109481,fun(bool,fun(Q109481,bool))),setspec),s(Q109481,GENR_PVARR_286))),s(bool,V))),s(Q109481,X)))) & (p(s(bool,V)) <-> s(cart(real,Q109494),i(s(fun(Q109481,cart(real,Q109494)),F0),s(Q109481,X))) != s(cart(real,Q109494),i(s(fun(num,cart(real,Q109494)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & p(s(bool,i(s(fun(fun(Q109481,bool),bool),i(s(fun(Q109481,fun(fun(Q109481,bool),bool)),in),s(Q109481,X))),s(fun(Q109481,bool),S0))))))) <-> p(s(bool,i(s(fun(Q109481,bool),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool))),U_0),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),F0))),s(Q109481,GENR_PVARR_286)))))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q109481,bool),bool),finite),s(fun(Q109481,bool),i(s(fun(fun(Q109481,bool),fun(Q109481,bool)),gspec),s(fun(Q109481,bool),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool))),U_0),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),G0)))))))) & p(s(bool,i(s(fun(fun(Q109481,bool),bool),finite),s(fun(Q109481,bool),i(s(fun(fun(Q109481,bool),fun(Q109481,bool)),gspec),s(fun(Q109481,bool),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,bool))),U_0),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),F0)))))))) -> s(cart(real,Q109494),i(s(fun(cart(real,Q109494),cart(real,Q109494)),i(s(fun(cart(real,Q109494),fun(cart(real,Q109494),cart(real,Q109494))),vectoru_add),s(cart(real,Q109494),i(s(fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494))),vsum),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),F0))))),s(cart(real,Q109494),i(s(fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494))),vsum),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),G0))))) = s(cart(real,Q109494),i(s(fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494)),i(s(fun(fun(Q109481,bool),fun(fun(Q109481,cart(real,Q109494)),cart(real,Q109494))),vsum),s(fun(Q109481,bool),S0))),s(fun(Q109481,cart(real,Q109494)),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,cart(real,Q109494))),i(s(fun(fun(Q109481,cart(real,Q109494)),fun(fun(Q109481,cart(real,Q109494)),fun(Q109481,cart(real,Q109494)))),U_1),s(fun(Q109481,cart(real,Q109494)),F0))),s(fun(Q109481,cart(real,Q109494)),G0))))))))))) # label(aVSUMu_ADDu_GEN) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2744 (all N all U_0 ((all S0 all T0 all GENR_PVARR_357 ((exists X exists Y exists V (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_357))),s(bool,V))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y)))))) & (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0)))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),U_0),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))),s(cart(real,N),GENR_PVARR_357)))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),U_0),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),inter),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))))))))) # label(aDIMu_SUMSu_INTER) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2745 (all N all M all U_0 ((all C0 all A5 all I0 s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),C0),s(num,I0))))),s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),A5))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(fun(num,real),C0))),s(cart(cart(real,N),M),A5))),s(num,I0)))) -> (all A5 ((all C0 (s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))))),s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(fun(num,real),C0))),s(cart(cart(real,N),M),A5))))) -> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(num,real),C0),s(num,I0))))))) <-> (exists B0 s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),B0))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aMATRIXu_RIGHTu_INVERTIBLEu_INDEPENDENTu_ROWS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2746 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X)))))) -> s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))) = s(real,i(s(fun(cart(real,n10),real),vectoru_norm),s(cart(real,n10),X))))) # label(aNORMu_1u_POS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2747 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> (s(real,Y) = s(real,X) <-> s(real,i(s(fun(real,real),sqrt),s(real,Y))) = s(real,i(s(fun(real,real),sqrt),s(real,X)))))) # label(aSQRTu_INJ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2748 (all N all M all A5 all I0 all J0 s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),d_),s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,M),N),fun(num,cart(real,M))),d_),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(num,I0))))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,J0))))),s(num,I0)))) # label(aTRANSPu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2749 (all M all N all X s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(real,fun(cart(cart(real,M),N),cart(cart(real,M),N))),r_r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(cart(real,M),N),X))) = s(cart(cart(real,M),N),X)) # label(aMATRIXu_CMULu_LID) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2750 (all Q109147 all F0 all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,P0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(cart(real,Q109147),i(s(fun(cart(real,Q109147),cart(real,Q109147)),i(s(fun(cart(real,Q109147),fun(cart(real,Q109147),cart(real,Q109147))),vectoru_add),s(cart(real,Q109147),i(s(fun(fun(num,cart(real,Q109147)),cart(real,Q109147)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109147)),cart(real,Q109147))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,Q109147)),F0))))),s(cart(real,Q109147),i(s(fun(fun(num,cart(real,Q109147)),cart(real,Q109147)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109147)),cart(real,Q109147))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,N0))),s(num,P0))))),s(fun(num,cart(real,Q109147)),F0))))) = s(cart(real,Q109147),i(s(fun(fun(num,cart(real,Q109147)),cart(real,Q109147)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109147)),cart(real,Q109147))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,P0))))),s(fun(num,cart(real,Q109147)),F0))))) # label(aVSUMu_COMBINEu_L) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2751 (all Q106500 all Q106502 all U_1 ((all P0 all F0 all X s(cart(real,Q106502),i(s(fun(Q106500,cart(real,Q106502)),i(s(fun(fun(Q106500,cart(real,Q106502)),fun(Q106500,cart(real,Q106502))),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,cart(real,Q106502)),fun(Q106500,cart(real,Q106502)))),U_1),s(fun(Q106500,bool),P0))),s(fun(Q106500,cart(real,Q106502)),F0))),s(Q106500,X))) = s(cart(real,Q106502),i(s(fun(cart(real,Q106502),cart(real,Q106502)),i(s(fun(cart(real,Q106502),fun(cart(real,Q106502),cart(real,Q106502))),i(s(fun(bool,fun(cart(real,Q106502),fun(cart(real,Q106502),cart(real,Q106502)))),cond),s(bool,i(s(fun(Q106500,bool),P0),s(Q106500,X))))),s(cart(real,Q106502),i(s(fun(Q106500,cart(real,Q106502)),F0),s(Q106500,X))))),s(cart(real,Q106502),i(s(fun(num,cart(real,Q106502)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (all U_0 ((all S0 all P0 all GENR_PVARR_278 ((exists X exists V (p(s(bool,i(s(fun(Q106500,bool),i(s(fun(bool,fun(Q106500,bool)),i(s(fun(Q106500,fun(bool,fun(Q106500,bool))),setspec),s(Q106500,GENR_PVARR_278))),s(bool,V))),s(Q106500,X)))) & (p(s(bool,i(s(fun(Q106500,bool),P0),s(Q106500,X)))) & p(s(bool,i(s(fun(fun(Q106500,bool),bool),i(s(fun(Q106500,fun(fun(Q106500,bool),bool)),in),s(Q106500,X))),s(fun(Q106500,bool),S0)))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(Q106500,bool),i(s(fun(fun(Q106500,bool),fun(Q106500,bool)),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,bool),fun(Q106500,bool))),U_0),s(fun(Q106500,bool),S0))),s(fun(Q106500,bool),P0))),s(Q106500,GENR_PVARR_278)))))) -> (all P0 all S0 all F0 s(cart(real,Q106502),i(s(fun(fun(Q106500,cart(real,Q106502)),cart(real,Q106502)),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,cart(real,Q106502)),cart(real,Q106502))),vsum),s(fun(Q106500,bool),i(s(fun(fun(Q106500,bool),fun(Q106500,bool)),gspec),s(fun(Q106500,bool),i(s(fun(fun(Q106500,bool),fun(Q106500,bool)),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,bool),fun(Q106500,bool))),U_0),s(fun(Q106500,bool),S0))),s(fun(Q106500,bool),P0))))))),s(fun(Q106500,cart(real,Q106502)),F0))) = s(cart(real,Q106502),i(s(fun(fun(Q106500,cart(real,Q106502)),cart(real,Q106502)),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,cart(real,Q106502)),cart(real,Q106502))),vsum),s(fun(Q106500,bool),S0))),s(fun(Q106500,cart(real,Q106502)),i(s(fun(fun(Q106500,cart(real,Q106502)),fun(Q106500,cart(real,Q106502))),i(s(fun(fun(Q106500,bool),fun(fun(Q106500,cart(real,Q106502)),fun(Q106500,cart(real,Q106502)))),U_1),s(fun(Q106500,bool),P0))),s(fun(Q106500,cart(real,Q106502)),F0)))))))))) # label(aVSUMu_RESTRICTu_SET) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2752 (all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),Y))))) = s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),fun(cart(real,n10),cart(real,n10))),vectoru_sub),s(cart(real,n10),X))),s(cart(real,n10),Y)))))) # label(aDROPu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2753 (all N s(cart(real,N),x) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),x)))))) # label(aVECTORu_NEGu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2754 (all Q104710 all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(prod(cart(real,Q104710),cart(real,Q104710)),real),distance),s(prod(cart(real,Q104710),cart(real,Q104710)),i(s(fun(cart(real,Q104710),prod(cart(real,Q104710),cart(real,Q104710))),i(s(fun(cart(real,Q104710),fun(cart(real,Q104710),prod(cart(real,Q104710),cart(real,Q104710)))),c_),s(cart(real,Q104710),X))),s(cart(real,Q104710),Y))))))))) # label(aDISTu_POSu_LE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2755 (all P0 (p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) & p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) <-> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) -> p(s(bool,i(s(fun(num,bool),P0),s(num,I0)))))))) # label(aFORALLu_2) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2756 (all Q100390 all C0 all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(cart(real,Q100390),real),i(s(fun(cart(real,Q100390),fun(cart(real,Q100390),real)),dot),s(cart(real,Q100390),X))),s(cart(real,Q100390),Y))))) = s(real,i(s(fun(cart(real,Q100390),real),i(s(fun(cart(real,Q100390),fun(cart(real,Q100390),real)),dot),s(cart(real,Q100390),X))),s(cart(real,Q100390),i(s(fun(cart(real,Q100390),cart(real,Q100390)),i(s(fun(real,fun(cart(real,Q100390),cart(real,Q100390))),r_),s(real,C0))),s(cart(real,Q100390),Y)))))) # label(aDOTu_RMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2757 (all Q99907 (s(cart(real,Q99907),i(s(fun(num,cart(real,Q99907)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q99907),y) <-> s(cart(real,Q99907),x) = s(cart(real,Q99907),i(s(fun(cart(real,Q99907),cart(real,Q99907)),i(s(fun(cart(real,Q99907),fun(cart(real,Q99907),cart(real,Q99907))),vectoru_add),s(cart(real,Q99907),x))),s(cart(real,Q99907),y))))) # label(aVECTORu_EQu_ADDR) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2758 (all A ((exists V p(s(bool,i(s(fun(cart(A,n10),bool),p0),s(cart(A,n10),V))))) <-> (exists X p(s(bool,i(s(fun(cart(A,n10),bool),p0),s(cart(A,n10),i(s(fun(list(A),cart(A,n10)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),nil))))))))))) # label(aEXISTSu_VECTORu_1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2759 (all N all U_0 ((all A5 all GENR_PVARR_332 (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),U_0),s(cart(real,N),A5))),s(cart(real,N),GENR_PVARR_332)))) <-> (exists X exists V (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_332))),s(bool,V))),s(cart(real,N),X)))) & (s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),A5))),s(cart(real,N),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> p(s(bool,V))))))) -> (all F0 (-(all X all Y (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y))) -> s(cart(real,N),Y) = s(cart(real,N),X))) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> (exists A5 (s(cart(real,N),A5) != s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & (all S0 p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,N),cart(real,N)),F0))),s(fun(cart(real,N),bool),S0))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),U_0),s(cart(real,N),A5))))))))))))))) # label(aLINEARu_SINGULARu_IMAGEu_HYPERPLANE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2760 (all Q117887 all Q117888 all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,Q117887),cart(real,Q117888)),bool),linear),s(fun(cart(real,Q117887),cart(real,Q117888)),F0)))) & s(cart(cart(real,Q117887),Q117888),i(s(fun(fun(cart(real,Q117887),cart(real,Q117888)),cart(cart(real,Q117887),Q117888)),matrix),s(fun(cart(real,Q117887),cart(real,Q117888)),F0))) = s(cart(cart(real,Q117887),Q117888),i(s(fun(fun(cart(real,Q117887),cart(real,Q117888)),cart(cart(real,Q117887),Q117888)),matrix),s(fun(cart(real,Q117887),cart(real,Q117888)),G0))) & p(s(bool,i(s(fun(fun(cart(real,Q117887),cart(real,Q117888)),bool),linear),s(fun(cart(real,Q117887),cart(real,Q117888)),G0)))) -> s(fun(cart(real,Q117887),cart(real,Q117888)),F0) = s(fun(cart(real,Q117887),cart(real,Q117888)),G0))) # label(aLINEARu_EQu_MATRIX) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2761 (all N all S0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))) # label(aDIMu_SUBSETu_UNIV) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2762 (all Q110833 all A5 p(s(bool,i(s(fun(cart(real,Q110833),bool),i(s(fun(cart(real,Q110833),fun(cart(real,Q110833),bool)),orthogonal),s(cart(real,Q110833),A5))),s(cart(real,Q110833),i(s(fun(num,cart(real,Q110833)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) # label(aORTHOGONALu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2763 (all Q132744 all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,Q132744),bool),bool),i(s(fun(fun(cart(real,Q132744),bool),fun(fun(cart(real,Q132744),bool),bool)),psubset),s(fun(cart(real,Q132744),bool),i(s(fun(fun(cart(real,Q132744),bool),fun(cart(real,Q132744),bool)),span),s(fun(cart(real,Q132744),bool),S0))))),s(fun(cart(real,Q132744),bool),i(s(fun(fun(cart(real,Q132744),bool),fun(cart(real,Q132744),bool)),span),s(fun(cart(real,Q132744),bool),T0)))))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(cart(real,Q132744),bool),num),dim),s(fun(cart(real,Q132744),bool),S0))))),s(num,i(s(fun(fun(cart(real,Q132744),bool),num),dim),s(fun(cart(real,Q132744),bool),T0)))))))) # label(aDIMu_PSUBSET) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2764 (all M all N all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),F0)))) & s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,M),cart(real,N)),G0))),s(fun(cart(real,N),cart(real,M)),F0))) = s(fun(cart(real,N),cart(real,N)),i1) & s(fun(cart(real,M),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M))),i(s(fun(fun(cart(real,N),cart(real,M)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M)))),o),s(fun(cart(real,N),cart(real,M)),F0))),s(fun(cart(real,M),cart(real,N)),G0))) = s(fun(cart(real,M),cart(real,M)),i1) -> p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),G0)))))) # label(aLEFTu_RIGHTu_INVERSEu_LINEAR) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2765 (all P all N all M all A5 all B0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(cart(cart(real,P),M),num),rank),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))))),s(num,i(s(fun(cart(cart(real,N),M),num),rank),s(cart(cart(real,N),M),A5))))))) # label(aRANKu_MULu_LEu_LEFT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2766 (all M all N all U_0 ((all F0 all GENR_PVARR_319 ((exists X p(s(bool,i(s(fun(cart(real,finite_sum(M,N)),bool),i(s(fun(bool,fun(cart(real,finite_sum(M,N)),bool)),i(s(fun(cart(real,finite_sum(M,N)),fun(bool,fun(cart(real,finite_sum(M,N)),bool))),setspec),s(cart(real,finite_sum(M,N)),GENR_PVARR_319))),s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),univ))))),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))))) <-> p(s(bool,i(s(fun(cart(real,finite_sum(M,N)),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,finite_sum(M,N)),bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,finite_sum(M,N)),GENR_PVARR_319)))))) -> (all F0 s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0))) = s(bool,i(s(fun(fun(cart(real,finite_sum(M,N)),bool),bool),subspace),s(fun(cart(real,finite_sum(M,N)),bool),i(s(fun(fun(cart(real,finite_sum(M,N)),bool),fun(cart(real,finite_sum(M,N)),bool)),gspec),s(fun(cart(real,finite_sum(M,N)),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,finite_sum(M,N)),bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0)))))))))) # label(aLINEARu_SUBSPACEu_GRAPH) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2767 p(s(bool,i(s(fun(num,bool),p0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) <-> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) -> p(s(bool,i(s(fun(num,bool),p0),s(num,I0)))))) # label(aFORALLu_1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.79 2768 (all Q143197 all Q143187 all P0 all Q0 all F0 all S0 ((all G0 all T0 (p(s(bool,i(s(fun(fun(cart(real,Q143197),bool),bool),Q0),s(fun(cart(real,Q143197),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,Q143197),cart(real,Q143187)),bool),linear),s(fun(cart(real,Q143197),cart(real,Q143187)),G0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q143187),bool),bool),P0),s(fun(cart(real,Q143187),bool),i(s(fun(fun(cart(real,Q143197),bool),fun(cart(real,Q143187),bool)),i(s(fun(fun(cart(real,Q143197),cart(real,Q143187)),fun(fun(cart(real,Q143197),bool),fun(cart(real,Q143187),bool))),image),s(fun(cart(real,Q143197),cart(real,Q143187)),G0))),s(fun(cart(real,Q143197),bool),T0)))))))) & p(s(bool,i(s(fun(fun(cart(real,Q143187),cart(real,Q143197)),bool),linear),s(fun(cart(real,Q143187),cart(real,Q143197)),F0)))) & (all X all Y (s(cart(real,Q143197),i(s(fun(cart(real,Q143187),cart(real,Q143197)),F0),s(cart(real,Q143187),Y))) = s(cart(real,Q143197),i(s(fun(cart(real,Q143187),cart(real,Q143197)),F0),s(cart(real,Q143187),X))) -> s(cart(real,Q143187),X) = s(cart(real,Q143187),Y))) & (all H0 all U (p(s(bool,i(s(fun(fun(cart(real,Q143187),bool),bool),P0),s(fun(cart(real,Q143187),bool),U)))) & p(s(bool,i(s(fun(fun(cart(real,Q143187),cart(real,Q143197)),bool),linear),s(fun(cart(real,Q143187),cart(real,Q143197)),H0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q143197),bool),bool),Q0),s(fun(cart(real,Q143197),bool),i(s(fun(fun(cart(real,Q143187),bool),fun(cart(real,Q143197),bool)),i(s(fun(fun(cart(real,Q143187),cart(real,Q143197)),fun(fun(cart(real,Q143187),bool),fun(cart(real,Q143197),bool))),image),s(fun(cart(real,Q143187),cart(real,Q143197)),H0))),s(fun(cart(real,Q143187),bool),U)))))))) -> s(bool,i(s(fun(fun(cart(real,Q143197),bool),bool),Q0),s(fun(cart(real,Q143197),bool),i(s(fun(fun(cart(real,Q143187),bool),fun(cart(real,Q143197),bool)),i(s(fun(fun(cart(real,Q143187),cart(real,Q143197)),fun(fun(cart(real,Q143187),bool),fun(cart(real,Q143197),bool))),image),s(fun(cart(real,Q143187),cart(real,Q143197)),F0))),s(fun(cart(real,Q143187),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,Q143187),bool),bool),P0),s(fun(cart(real,Q143187),bool),S0))))) # label(aWLOGu_LINEARu_INJECTIVEu_IMAGEu_2u_ALT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2769 (all N all U_0 ((all GENR_PVARR_311 ((exists I0 exists V (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_311))),s(bool,V))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))))) <-> p(s(bool,i(s(fun(cart(real,N),bool),U_0),s(cart(real,N),GENR_PVARR_311)))))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),U_0))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))))) # label(aHASu_SIZEu_STDBASIS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2770 (all N all X all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))))),s(real,i(s(fun(cart(real,N),real),infnorm),s(cart(real,N),X)))))))) # label(aCOMPONENTu_LEu_INFNORM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2771 (all X all S0 s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(cart(real,n10),fun(fun(cart(real,n10),bool),bool)),in),s(cart(real,n10),X))),s(fun(cart(real,n10),bool),S0))) = s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),S0)))))) # label(aDROPu_INu_IMAGEu_DROP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2772 (all Q105914 all Q105918 all Q105892 all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q105918,bool),bool),finite),s(fun(Q105918,bool),S0)))) & (all X all Y (p(s(bool,i(s(fun(fun(Q105918,bool),bool),i(s(fun(Q105918,fun(fun(Q105918,bool),bool)),in),s(Q105918,Y))),s(fun(Q105918,bool),S0)))) & s(Q105892,i(s(fun(Q105918,Q105892),F0),s(Q105918,X))) = s(Q105892,i(s(fun(Q105918,Q105892),F0),s(Q105918,Y))) & p(s(bool,i(s(fun(fun(Q105918,bool),bool),i(s(fun(Q105918,fun(fun(Q105918,bool),bool)),in),s(Q105918,X))),s(fun(Q105918,bool),S0)))) -> s(Q105918,X) = s(Q105918,Y))) -> s(cart(real,Q105914),i(s(fun(fun(Q105892,cart(real,Q105914)),cart(real,Q105914)),i(s(fun(fun(Q105892,bool),fun(fun(Q105892,cart(real,Q105914)),cart(real,Q105914))),vsum),s(fun(Q105892,bool),i(s(fun(fun(Q105918,bool),fun(Q105892,bool)),i(s(fun(fun(Q105918,Q105892),fun(fun(Q105918,bool),fun(Q105892,bool))),image),s(fun(Q105918,Q105892),F0))),s(fun(Q105918,bool),S0))))),s(fun(Q105892,cart(real,Q105914)),G0))) = s(cart(real,Q105914),i(s(fun(fun(Q105918,cart(real,Q105914)),cart(real,Q105914)),i(s(fun(fun(Q105918,bool),fun(fun(Q105918,cart(real,Q105914)),cart(real,Q105914))),vsum),s(fun(Q105918,bool),S0))),s(fun(Q105918,cart(real,Q105914)),i(s(fun(fun(Q105918,Q105892),fun(Q105918,cart(real,Q105914))),i(s(fun(fun(Q105892,cart(real,Q105914)),fun(fun(Q105918,Q105892),fun(Q105918,cart(real,Q105914)))),o),s(fun(Q105892,cart(real,Q105914)),G0))),s(fun(Q105918,Q105892),F0))))))) # label(aVSUMu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2773 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y))))))) # label(aSQRTu_MONOu_LEu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2774 (all Q111672 all Q111668 all Q111669 all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,Q111668),cart(real,Q111669)),bool),linear),s(fun(cart(real,Q111668),cart(real,Q111669)),F0)))) & p(s(bool,i(s(fun(fun(cart(real,Q111669),cart(real,Q111672)),bool),linear),s(fun(cart(real,Q111669),cart(real,Q111672)),G0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q111668),cart(real,Q111672)),bool),linear),s(fun(cart(real,Q111668),cart(real,Q111672)),i(s(fun(fun(cart(real,Q111668),cart(real,Q111669)),fun(cart(real,Q111668),cart(real,Q111672))),i(s(fun(fun(cart(real,Q111669),cart(real,Q111672)),fun(fun(cart(real,Q111668),cart(real,Q111669)),fun(cart(real,Q111668),cart(real,Q111672)))),o),s(fun(cart(real,Q111669),cart(real,Q111672)),G0))),s(fun(cart(real,Q111668),cart(real,Q111669)),F0)))))))) # label(aLINEARu_COMPOSE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2775 (all Q108605 all U_0 ((all F0 all P0 all I0 s(cart(real,Q108605),i(s(fun(num,cart(real,Q108605)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,I0))),s(num,P0))))) = s(cart(real,Q108605),i(s(fun(num,cart(real,Q108605)),i(s(fun(num,fun(num,cart(real,Q108605))),i(s(fun(fun(num,cart(real,Q108605)),fun(num,fun(num,cart(real,Q108605)))),U_0),s(fun(num,cart(real,Q108605)),F0))),s(num,P0))),s(num,I0)))) -> (all F0 all M0 all P0 s(cart(real,Q108605),i(s(fun(fun(num,cart(real,Q108605)),cart(real,Q108605)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108605)),cart(real,Q108605))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,P0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,n))),s(num,P0))))))),s(fun(num,cart(real,Q108605)),F0))) = s(cart(real,Q108605),i(s(fun(fun(num,cart(real,Q108605)),cart(real,Q108605)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108605)),cart(real,Q108605))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,n))))),s(fun(num,cart(real,Q108605)),i(s(fun(num,fun(num,cart(real,Q108605))),i(s(fun(fun(num,cart(real,Q108605)),fun(num,fun(num,cart(real,Q108605)))),U_0),s(fun(num,cart(real,Q108605)),F0))),s(num,P0)))))))) # label(aVSUMu_OFFSET) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2776 (all N all S0 all T0 ((all X (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),S0)))) -> (exists U (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),disjoint),s(fun(cart(real,N),bool),U))),s(fun(cart(real,N),bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),U)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))) & s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),U))))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),U)))))))))) # label(aORTHONORMALu_EXTENSION) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2777 (all N all M all A5 ((all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),Y))) -> s(cart(real,M),Y) = s(cart(real,M),X))) <-> s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))) = s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))))) # label(aFULLu_RANKu_INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2778 (all N all A5 all B0 exists V ((exists VI_ ((s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),A5) <-> p(s(bool,VI_))) & (exists VI_I_ (s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),empty))))))) = s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,VI_I_))),s(bool,VI_))),s(bool,V))) & (s(cart(real,N),B0) = s(cart(real,N),A5) <-> p(s(bool,VI_I_))))))) & (p(s(bool,V)) <-> (exists X exists Y (-(s(real,Y) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) & s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,X))),s(cart(real,N),A5))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Y))),s(cart(real,N),B0)))))))))) # label(aDEPENDENTu_2) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2779 (all Q127174 all X exists V (s(num,i(s(fun(fun(cart(real,Q127174),bool),num),dim),s(fun(cart(real,Q127174),bool),i(s(fun(fun(cart(real,Q127174),bool),fun(cart(real,Q127174),bool)),i(s(fun(cart(real,Q127174),fun(fun(cart(real,Q127174),bool),fun(cart(real,Q127174),bool))),insert),s(cart(real,Q127174),X))),s(fun(cart(real,Q127174),bool),empty))))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,V))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) & (s(cart(real,Q127174),i(s(fun(num,cart(real,Q127174)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q127174),X) <-> p(s(bool,V))))) # label(aDIMu_SING) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2780 (all N all M all A5 all B0 all C0 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,B0))),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,B0))),s(real,C0))))),s(cart(cart(real,N),M),A5)))) # label(aMATRIXu_CMULu_ADDu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2781 (all N all V exists B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),B0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),B0))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),V)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),V)))))))) # label(aORTHOGONALu_BASISu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2782 (all N all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),S0)))) -> (exists U (s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),U))))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),U)))))))))) # label(aORTHOGONALu_EXTENSION) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2783 (all N all U_0 ((all A5 all B0 s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),B0))),s(cart(real,N),A5))))),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),B0))),s(cart(real,N),B0))))))),s(cart(real,N),B0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),U_0),s(cart(real,N),A5))),s(cart(real,N),B0)))) -> (all S0 all A5 all X (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),S0)))) -> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),X))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),A5))),s(cart(real,N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(real,N)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),cart(real,N)),cart(real,N))),vsum),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),U_0),s(cart(real,N),A5)))))))))))))) # label(aGRAMu_SCHMIDTu_STEP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2784 (all N all X all Y all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0)))))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))))) # label(aSPANu_TRANS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2785 (all Q102285 all X (s(real,i(s(fun(cart(real,Q102285),real),vectoru_norm),s(cart(real,Q102285),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(cart(real,Q102285),i(s(fun(num,cart(real,Q102285)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q102285),X))) # label(aNORMu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2786 (all Q123623 all S0 s(fun(cart(real,Q123623),bool),i(s(fun(fun(cart(real,Q123623),bool),fun(cart(real,Q123623),bool)),span),s(fun(cart(real,Q123623),bool),S0))) = s(fun(cart(real,Q123623),bool),i(s(fun(fun(cart(real,Q123623),bool),fun(cart(real,Q123623),bool)),span),s(fun(cart(real,Q123623),bool),i(s(fun(fun(cart(real,Q123623),bool),fun(cart(real,Q123623),bool)),i(s(fun(cart(real,Q123623),fun(fun(cart(real,Q123623),bool),fun(cart(real,Q123623),bool))),insert),s(cart(real,Q123623),i(s(fun(num,cart(real,Q123623)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q123623),bool),S0)))))) # label(aSPANu_INSERTu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2787 (all N all C0 ((all Y exists X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X))) = s(cart(real,N),Y)) <-> s(real,C0) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aSURJECTIVEu_SCALING) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2788 (all Q130465 all Q130466 all F0 all G0 (s(fun(Q130465,Q130465),i1) = s(fun(Q130465,Q130465),i(s(fun(fun(Q130465,Q130466),fun(Q130465,Q130465)),i(s(fun(fun(Q130466,Q130465),fun(fun(Q130465,Q130466),fun(Q130465,Q130465))),o),s(fun(Q130466,Q130465),F0))),s(fun(Q130465,Q130466),G0))) & s(fun(Q130466,Q130466),i1) = s(fun(Q130466,Q130466),i(s(fun(fun(Q130466,Q130465),fun(Q130466,Q130466)),i(s(fun(fun(Q130465,Q130466),fun(fun(Q130466,Q130465),fun(Q130466,Q130466))),o),s(fun(Q130465,Q130466),G0))),s(fun(Q130466,Q130465),F0))) <-> (all X s(Q130466,X) = s(Q130466,i(s(fun(Q130465,Q130466),G0),s(Q130465,i(s(fun(Q130466,Q130465),F0),s(Q130466,X)))))) & (all X s(Q130465,i(s(fun(Q130466,Q130465),F0),s(Q130466,i(s(fun(Q130465,Q130466),G0),s(Q130465,X))))) = s(Q130465,X)))) # label(aISOMORPHISMu_EXPAND) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2789 (all N all M s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),b))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),a))),s(cart(cart(real,N),M),c0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),a))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),b))),s(cart(cart(real,N),M),c0)))))) # label(aMATRIXu_ADDu_ACu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2790 (all Q139869 all X all Y all Z0 (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,Q139869),cart(real,Q139869)),real),distance),s(prod(cart(real,Q139869),cart(real,Q139869)),i(s(fun(cart(real,Q139869),prod(cart(real,Q139869),cart(real,Q139869))),i(s(fun(cart(real,Q139869),fun(cart(real,Q139869),prod(cart(real,Q139869),cart(real,Q139869)))),c_),s(cart(real,Q139869),X))),s(cart(real,Q139869),Y))))))),s(real,i(s(fun(prod(cart(real,Q139869),cart(real,Q139869)),real),distance),s(prod(cart(real,Q139869),cart(real,Q139869)),i(s(fun(cart(real,Q139869),prod(cart(real,Q139869),cart(real,Q139869))),i(s(fun(cart(real,Q139869),fun(cart(real,Q139869),prod(cart(real,Q139869),cart(real,Q139869)))),c_),s(cart(real,Q139869),Y))),s(cart(real,Q139869),Z0))))))) = s(real,i(s(fun(prod(cart(real,Q139869),cart(real,Q139869)),real),distance),s(prod(cart(real,Q139869),cart(real,Q139869)),i(s(fun(cart(real,Q139869),prod(cart(real,Q139869),cart(real,Q139869))),i(s(fun(cart(real,Q139869),fun(cart(real,Q139869),prod(cart(real,Q139869),cart(real,Q139869)))),c_),s(cart(real,Q139869),X))),s(cart(real,Q139869),Z0))))) <-> s(cart(real,Q139869),i(s(fun(cart(real,Q139869),cart(real,Q139869)),i(s(fun(real,fun(cart(real,Q139869),cart(real,Q139869))),r_),s(real,i(s(fun(cart(real,Q139869),real),vectoru_norm),s(cart(real,Q139869),i(s(fun(cart(real,Q139869),cart(real,Q139869)),i(s(fun(cart(real,Q139869),fun(cart(real,Q139869),cart(real,Q139869))),vectoru_sub),s(cart(real,Q139869),Y))),s(cart(real,Q139869),Z0))))))),s(cart(real,Q139869),i(s(fun(cart(real,Q139869),cart(real,Q139869)),i(s(fun(cart(real,Q139869),fun(cart(real,Q139869),cart(real,Q139869))),vectoru_sub),s(cart(real,Q139869),X))),s(cart(real,Q139869),Y))))) = s(cart(real,Q139869),i(s(fun(cart(real,Q139869),cart(real,Q139869)),i(s(fun(real,fun(cart(real,Q139869),cart(real,Q139869))),r_),s(real,i(s(fun(cart(real,Q139869),real),vectoru_norm),s(cart(real,Q139869),i(s(fun(cart(real,Q139869),cart(real,Q139869)),i(s(fun(cart(real,Q139869),fun(cart(real,Q139869),cart(real,Q139869))),vectoru_sub),s(cart(real,Q139869),X))),s(cart(real,Q139869),Y))))))),s(cart(real,Q139869),i(s(fun(cart(real,Q139869),cart(real,Q139869)),i(s(fun(cart(real,Q139869),fun(cart(real,Q139869),cart(real,Q139869))),vectoru_sub),s(cart(real,Q139869),Y))),s(cart(real,Q139869),Z0))))))) # label(aDISTu_TRIANGLEu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2791 (all N all M all U_1 ((all A5 all I0 all J0 s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))) = s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(num,J0)))) -> (all U_0 ((all A5 all I0 s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),U_0),s(cart(cart(real,N),M),A5))),s(num,I0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0)))))) -> (all A5 s(cart(cart(real,N),M),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),M)),lambda),s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),U_0),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5)))))))) # label(amatrixu_neg) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2792 (all N all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,a0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_gt),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_gt),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,a0)))))) # label(aNORMu_GTu_SQUARE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2793 (all Q107795 all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(cart(real,Q107795),i(s(fun(cart(real,Q107795),cart(real,Q107795)),i(s(fun(cart(real,Q107795),fun(cart(real,Q107795),cart(real,Q107795))),vectoru_add),s(cart(real,Q107795),i(s(fun(num,cart(real,Q107795)),F0),s(num,M0))))),s(cart(real,Q107795),i(s(fun(fun(num,cart(real,Q107795)),cart(real,Q107795)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107795)),cart(real,Q107795))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,N0))))),s(fun(num,cart(real,Q107795)),F0))))) = s(cart(real,Q107795),i(s(fun(fun(num,cart(real,Q107795)),cart(real,Q107795)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107795)),cart(real,Q107795))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107795)),F0))))) # label(aVSUMu_CLAUSESu_LEFT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2794 (all Q114719 all Q114720 all A5 s(cart(cart(real,Q114719),Q114720),i(s(fun(cart(cart(real,Q114719),Q114720),cart(cart(real,Q114719),Q114720)),i(s(fun(cart(cart(real,Q114719),Q114720),fun(cart(cart(real,Q114719),Q114720),cart(cart(real,Q114719),Q114720))),matrixu_sub),s(cart(cart(real,Q114719),Q114720),A5))),s(cart(cart(real,Q114719),Q114720),A5))) = s(cart(cart(real,Q114719),Q114720),i(s(fun(num,cart(cart(real,Q114719),Q114720)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aMATRIXu_SUBu_REFL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2795 (all Q112424 all Q112411 all Q112421 all H0 all C0 all X all Y (p(s(bool,i(s(fun(fun(cart(real,Q112411),fun(cart(real,Q112421),cart(real,Q112424))),bool),bilinear),s(fun(cart(real,Q112411),fun(cart(real,Q112421),cart(real,Q112424))),H0)))) -> s(cart(real,Q112424),i(s(fun(cart(real,Q112421),cart(real,Q112424)),i(s(fun(cart(real,Q112411),fun(cart(real,Q112421),cart(real,Q112424))),H0),s(cart(real,Q112411),X))),s(cart(real,Q112421),i(s(fun(cart(real,Q112421),cart(real,Q112421)),i(s(fun(real,fun(cart(real,Q112421),cart(real,Q112421))),r_),s(real,C0))),s(cart(real,Q112421),Y))))) = s(cart(real,Q112424),i(s(fun(cart(real,Q112424),cart(real,Q112424)),i(s(fun(real,fun(cart(real,Q112424),cart(real,Q112424))),r_),s(real,C0))),s(cart(real,Q112424),i(s(fun(cart(real,Q112421),cart(real,Q112424)),i(s(fun(cart(real,Q112411),fun(cart(real,Q112421),cart(real,Q112424))),H0),s(cart(real,Q112411),X))),s(cart(real,Q112421),Y))))))) # label(aBILINEARu_RMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2796 (all N all M all U_0 ((all A5 all AI_ (p(s(bool,i(s(fun(cart(cart(real,M),N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),bool)),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),AI_)))) <-> s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),AI_))) & s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),AI_))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) -> (all A5 s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),matrixu_inv),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,M),N),i(s(fun(fun(cart(cart(real,M),N),bool),cart(cart(real,M),N)),h_),s(fun(cart(cart(real,M),N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),bool)),U_0),s(cart(cart(real,N),M),A5)))))))) # label(amatrixu_inv) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2797 (all N all M all U_1 ((all A5 all B0 all I0 all J0 s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),B0))),s(num,I0))))),s(num,J0)))))) -> (all U_0 ((all A5 all B0 all I0 s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0)))))) -> (all A5 all B0 s(cart(cart(real,N),M),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),M)),lambda),s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0)))))))) # label(amatrixu_sub) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2798 (all Q122152 all S0 all H0 ((all X (p(s(bool,i(s(fun(fun(cart(real,Q122152),bool),bool),i(s(fun(cart(real,Q122152),fun(fun(cart(real,Q122152),bool),bool)),in),s(cart(real,Q122152),X))),s(fun(cart(real,Q122152),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q122152),bool),bool),i(s(fun(cart(real,Q122152),fun(fun(cart(real,Q122152),bool),bool)),in),s(cart(real,Q122152),X))),s(fun(cart(real,Q122152),bool),H0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q122152),bool),bool),subspace),s(fun(cart(real,Q122152),bool),H0)))) -> (all X (p(s(bool,i(s(fun(fun(cart(real,Q122152),bool),bool),i(s(fun(cart(real,Q122152),fun(fun(cart(real,Q122152),bool),bool)),in),s(cart(real,Q122152),X))),s(fun(cart(real,Q122152),bool),i(s(fun(fun(cart(real,Q122152),bool),fun(cart(real,Q122152),bool)),span),s(fun(cart(real,Q122152),bool),S0)))))) -> p(s(bool,i(s(fun(cart(real,Q122152),bool),H0),s(cart(real,Q122152),X)))))))) # label(aSPANu_INDUCT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2799 (all X s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))) = s(real,i(s(fun(cart(real,n10),real),vectoru_norm),s(cart(real,n10),X)))) # label(aABSu_DROP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2800 (all M all P all N all A5 all B0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(cart(cart(real,P),M),num),rank),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))))),s(num,i(s(fun(cart(cart(real,P),N),num),rank),s(cart(cart(real,P),N),B0))))))) # label(aRANKu_MULu_LEu_RIGHT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2801 (all N all U_0 ((all S0 all T0 all GENR_PVARR_299 ((exists X exists Y exists V (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_299))),s(bool,V))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y)))))) & (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),U_0),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))),s(cart(real,N),GENR_PVARR_299)))))) -> (all S0 all T0 s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),U_0),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0)))))))) # label(aSPANu_UNION) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2802 (all M all N all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))),s(real,i(s(fun(cart(real,finite_sum(M,N)),real),vectoru_norm),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X))),s(cart(real,N),Y)))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))),s(real,i(s(fun(cart(real,finite_sum(M,N)),real),vectoru_norm),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X))),s(cart(real,N),Y)))))))))) # label(aNORMu_LEu_PASTECART) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2803 (all N all V exists B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),V)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))))) # label(aMAXIMALu_INDEPENDENTu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2804 (all N all U_0 ((all K0 all GENR_PVARR_342 ((exists X exists V ((p(s(bool,V)) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,K0)))) & p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_342))),s(bool,V))),s(cart(real,N),X)))))) <-> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(num,fun(cart(real,N),bool)),U_0),s(num,K0))),s(cart(real,N),GENR_PVARR_342)))))) -> (all K0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(num,fun(cart(real,N),bool)),U_0),s(num,K0))))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(num,bool),fun(cart(real,N),bool)),i(s(fun(fun(num,cart(real,N)),fun(fun(num,bool),fun(cart(real,N),bool))),image),s(fun(num,cart(real,N)),basis))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(fun(num,bool),fun(num,fun(num,bool))),delete),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(num,K0))))))))))) # label(aSPECIALu_HYPERPLANEu_SPAN) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2805 (all N all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0)))) -> (exists B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),B0)))) & s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0))) = s(fun(cart(real,N),bool),S0) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),B0))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),S0)))) & -p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,N),bool),B0)))))))) # label(aORTHOGONALu_BASISu_SUBSPACE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2806 (all M all N all A5 all B0 (s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))) -> (exists X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),B0)))) # label(aMATRIXu_FULLu_LINEARu_EQUATIONS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2807 (all N all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0)))))))) # label(aDIMu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2808 (all Q112563 all Q112572 all Q112574 all H0 all X (p(s(bool,i(s(fun(fun(cart(real,Q112563),fun(cart(real,Q112572),cart(real,Q112574))),bool),bilinear),s(fun(cart(real,Q112563),fun(cart(real,Q112572),cart(real,Q112574))),H0)))) -> s(cart(real,Q112574),i(s(fun(num,cart(real,Q112574)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q112574),i(s(fun(cart(real,Q112572),cart(real,Q112574)),i(s(fun(cart(real,Q112563),fun(cart(real,Q112572),cart(real,Q112574))),H0),s(cart(real,Q112563),X))),s(cart(real,Q112572),i(s(fun(num,cart(real,Q112572)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) # label(aBILINEARu_RZERO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2809 (all M all P all N all A5 all B0 all C0 s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),N)),i(s(fun(cart(cart(real,P),N),fun(cart(cart(real,P),N),cart(cart(real,P),N))),matrixu_sub),s(cart(cart(real,P),N),B0))),s(cart(cart(real,P),N),C0))))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(cart(cart(real,P),M),fun(cart(cart(real,P),M),cart(cart(real,P),M))),matrixu_sub),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),C0)))))) # label(aMATRIXu_SUBu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2810 (all M all N all A5 s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5))))) = s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5)))) # label(aRANKu_ROW) # label(axiom) # label(non_clause). [assumption]. 15.81/15.80 2811 (all M all N all F0 ((all Y exists X s(cart(real,N),Y) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (exists G0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0)))) & s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,N),cart(real,M)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,M)),G0))) = s(fun(cart(real,N),cart(real,N)),i1))))) # label(aLINEARu_SURJECTIVEu_RIGHTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2812 (all N all M all A5 all X all Y s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_add),s(cart(real,M),X))),s(cart(real,M),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),Y)))))) # label(aMATRIXu_VECTORu_MULu_ADDu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2813 (all M all N all A5 ((exists B0 s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),B0))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) <-> (exists B0 s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),B0)))))) # label(aRIGHTu_INVERTIBLEu_TRANSP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2814 (all N all A5 all B0 all C0 (s(cart(real,N),A5) != s(cart(real,N),C0) & s(cart(real,N),B0) != s(cart(real,N),C0) & s(cart(real,N),B0) != s(cart(real,N),A5) -> ((exists X exists Y exists Z0 (-(s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,X) & s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,Y) & s(real,Z0) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) & s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,X))),s(cart(real,N),A5))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Y))),s(cart(real,N),B0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Z0))),s(cart(real,N),C0))))))))) <-> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),C0))),s(fun(cart(real,N),bool),empty))))))))))))) # label(aDEPENDENTu_3) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2815 (all M all N all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0)))))))) # label(aADJOINTu_LINEAR) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2816 (all N all S0 all X all Y (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),Y))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) -> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0))))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),Y))),s(fun(cart(real,N),bool),S0))))))) # label(aEQu_SPANu_INSERTu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2817 (all Q120883 all Q120881 all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q120883),cart(real,Q120883)),real),distance),s(prod(cart(real,Q120883),cart(real,Q120883)),i(s(fun(cart(real,Q120883),prod(cart(real,Q120883),cart(real,Q120883))),i(s(fun(cart(real,Q120883),fun(cart(real,Q120883),prod(cart(real,Q120883),cart(real,Q120883)))),c_),s(cart(real,Q120883),i(s(fun(cart(real,finite_sum(Q120883,Q120881)),cart(real,Q120883)),fstcart),s(cart(real,finite_sum(Q120883,Q120881)),X))))),s(cart(real,Q120883),i(s(fun(cart(real,finite_sum(Q120883,Q120881)),cart(real,Q120883)),fstcart),s(cart(real,finite_sum(Q120883,Q120881)),Y))))))))),s(real,i(s(fun(prod(cart(real,finite_sum(Q120883,Q120881)),cart(real,finite_sum(Q120883,Q120881))),real),distance),s(prod(cart(real,finite_sum(Q120883,Q120881)),cart(real,finite_sum(Q120883,Q120881))),i(s(fun(cart(real,finite_sum(Q120883,Q120881)),prod(cart(real,finite_sum(Q120883,Q120881)),cart(real,finite_sum(Q120883,Q120881)))),i(s(fun(cart(real,finite_sum(Q120883,Q120881)),fun(cart(real,finite_sum(Q120883,Q120881)),prod(cart(real,finite_sum(Q120883,Q120881)),cart(real,finite_sum(Q120883,Q120881))))),c_),s(cart(real,finite_sum(Q120883,Q120881)),X))),s(cart(real,finite_sum(Q120883,Q120881)),Y))))))))) # label(aDISTu_FSTCART) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2818 (all N all U_1 ((all U all V s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_1),s(fun(cart(real,N),real),U))),s(cart(real,N),V))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V))))),s(cart(real,N),V)))) -> (all U_0 ((all P0 all GENR_PVARR_304 ((exists Y exists V ((p(s(bool,V)) <-> (exists S0 exists U (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))) & s(cart(real,N),Y) = s(cart(real,N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(real,N)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),cart(real,N)),cart(real,N))),vsum),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_1),s(fun(cart(real,N),real),U))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),P0))))))) & p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_304))),s(bool,V))),s(cart(real,N),Y)))))) <-> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),U_0),s(fun(cart(real,N),bool),P0))),s(cart(real,N),GENR_PVARR_304)))))) -> (all P0 s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),P0))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),U_0),s(fun(cart(real,N),bool),P0)))))))))) # label(aSPANu_EXPLICIT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2819 (all M all P all N all A5 all B0 all C0 s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),N)),i(s(fun(cart(cart(real,P),N),fun(cart(cart(real,P),N),cart(cart(real,P),N))),matrixu_add),s(cart(cart(real,P),N),B0))),s(cart(cart(real,P),N),C0))))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(cart(cart(real,P),M),fun(cart(cart(real,P),M),cart(cart(real,P),M))),matrixu_add),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),C0)))))) # label(aMATRIXu_ADDu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2820 (all Q99762 all X s(cart(real,Q99762),i(s(fun(cart(real,Q99762),cart(real,Q99762)),i(s(fun(real,fun(cart(real,Q99762),cart(real,Q99762))),r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q99762),X))) = s(cart(real,Q99762),i(s(fun(num,cart(real,Q99762)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aVECTORu_MULu_LZERO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2821 (all N all M (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> (exists F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & (all X s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))))))) # label(aISOMETRYu_UNIVu_UNIV) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2822 (all Q107186 all Q107185 all U_0 ((all F0 all V all X s(cart(real,Q107185),i(s(fun(cart(real,Q107185),cart(real,Q107185)),i(s(fun(real,fun(cart(real,Q107185),cart(real,Q107185))),r_),s(real,i(s(fun(Q107186,real),F0),s(Q107186,X))))),s(cart(real,Q107185),V))) = s(cart(real,Q107185),i(s(fun(Q107186,cart(real,Q107185)),i(s(fun(cart(real,Q107185),fun(Q107186,cart(real,Q107185))),i(s(fun(fun(Q107186,real),fun(cart(real,Q107185),fun(Q107186,cart(real,Q107185)))),U_0),s(fun(Q107186,real),F0))),s(cart(real,Q107185),V))),s(Q107186,X)))) -> (all F0 all V all S0 (p(s(bool,i(s(fun(fun(Q107186,bool),bool),finite),s(fun(Q107186,bool),S0)))) -> s(cart(real,Q107185),i(s(fun(cart(real,Q107185),cart(real,Q107185)),i(s(fun(real,fun(cart(real,Q107185),cart(real,Q107185))),r_),s(real,i(s(fun(fun(Q107186,real),real),i(s(fun(fun(Q107186,bool),fun(fun(Q107186,real),real)),sum),s(fun(Q107186,bool),S0))),s(fun(Q107186,real),F0))))),s(cart(real,Q107185),V))) = s(cart(real,Q107185),i(s(fun(fun(Q107186,cart(real,Q107185)),cart(real,Q107185)),i(s(fun(fun(Q107186,bool),fun(fun(Q107186,cart(real,Q107185)),cart(real,Q107185))),vsum),s(fun(Q107186,bool),S0))),s(fun(Q107186,cart(real,Q107185)),i(s(fun(cart(real,Q107185),fun(Q107186,cart(real,Q107185))),i(s(fun(fun(Q107186,real),fun(cart(real,Q107185),fun(Q107186,cart(real,Q107185)))),U_0),s(fun(Q107186,real),F0))),s(cart(real,Q107185),V))))))))) # label(aVSUMu_VMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2823 (all Q125698 all X (s(cart(real,Q125698),i(s(fun(num,cart(real,Q125698)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q125698),X) <-> p(s(bool,i(s(fun(fun(cart(real,Q125698),bool),bool),dependent),s(fun(cart(real,Q125698),bool),i(s(fun(fun(cart(real,Q125698),bool),fun(cart(real,Q125698),bool)),i(s(fun(cart(real,Q125698),fun(fun(cart(real,Q125698),bool),fun(cart(real,Q125698),bool))),insert),s(cart(real,Q125698),X))),s(fun(cart(real,Q125698),bool),empty)))))))) # label(aDEPENDENTu_SING) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2824 (all Q118409 all Q118421 all U_0 ((all F0 all X s(cart(real,Q118421),i(s(fun(cart(real,Q118421),cart(real,Q118421)),vectoru_neg),s(cart(real,Q118421),i(s(fun(cart(real,Q118409),cart(real,Q118421)),F0),s(cart(real,Q118409),X))))) = s(cart(real,Q118421),i(s(fun(cart(real,Q118409),cart(real,Q118421)),i(s(fun(fun(cart(real,Q118409),cart(real,Q118421)),fun(cart(real,Q118409),cart(real,Q118421))),U_0),s(fun(cart(real,Q118409),cart(real,Q118421)),F0))),s(cart(real,Q118409),X)))) -> (all F0 (p(s(bool,i(s(fun(fun(cart(real,Q118409),cart(real,Q118421)),bool),linear),s(fun(cart(real,Q118409),cart(real,Q118421)),F0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(cart(real,Q118409),cart(real,Q118421)),real),onorm),s(fun(cart(real,Q118409),cart(real,Q118421)),i(s(fun(fun(cart(real,Q118409),cart(real,Q118421)),fun(cart(real,Q118409),cart(real,Q118421))),U_0),s(fun(cart(real,Q118409),cart(real,Q118421)),F0))))))),s(real,i(s(fun(fun(cart(real,Q118409),cart(real,Q118421)),real),onorm),s(fun(cart(real,Q118409),cart(real,Q118421)),F0)))))))))) # label(aONORMu_NEGu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2825 (all Q123742 all U_0 ((all A5 all B0 all GENR_PVARR_302 (p(s(bool,i(s(fun(cart(real,Q123742),bool),i(s(fun(cart(real,Q123742),fun(cart(real,Q123742),bool)),i(s(fun(cart(real,Q123742),fun(cart(real,Q123742),fun(cart(real,Q123742),bool))),U_0),s(cart(real,Q123742),A5))),s(cart(real,Q123742),B0))),s(cart(real,Q123742),GENR_PVARR_302)))) <-> (exists U exists V exists V0 ((p(s(bool,V0)) <-> p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,V))),s(fun(real,bool),univ)))) & p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,U))),s(fun(real,bool),univ))))) & p(s(bool,i(s(fun(cart(real,Q123742),bool),i(s(fun(bool,fun(cart(real,Q123742),bool)),i(s(fun(cart(real,Q123742),fun(bool,fun(cart(real,Q123742),bool))),setspec),s(cart(real,Q123742),GENR_PVARR_302))),s(bool,V0))),s(cart(real,Q123742),i(s(fun(cart(real,Q123742),cart(real,Q123742)),i(s(fun(cart(real,Q123742),fun(cart(real,Q123742),cart(real,Q123742))),vectoru_add),s(cart(real,Q123742),i(s(fun(cart(real,Q123742),cart(real,Q123742)),i(s(fun(real,fun(cart(real,Q123742),cart(real,Q123742))),r_),s(real,U))),s(cart(real,Q123742),A5))))),s(cart(real,Q123742),i(s(fun(cart(real,Q123742),cart(real,Q123742)),i(s(fun(real,fun(cart(real,Q123742),cart(real,Q123742))),r_),s(real,V))),s(cart(real,Q123742),B0)))))))))))) -> (all A5 all B0 s(fun(cart(real,Q123742),bool),i(s(fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool)),span),s(fun(cart(real,Q123742),bool),i(s(fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool)),i(s(fun(cart(real,Q123742),fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool))),insert),s(cart(real,Q123742),A5))),s(fun(cart(real,Q123742),bool),i(s(fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool)),i(s(fun(cart(real,Q123742),fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool))),insert),s(cart(real,Q123742),B0))),s(fun(cart(real,Q123742),bool),empty))))))) = s(fun(cart(real,Q123742),bool),i(s(fun(fun(cart(real,Q123742),bool),fun(cart(real,Q123742),bool)),gspec),s(fun(cart(real,Q123742),bool),i(s(fun(cart(real,Q123742),fun(cart(real,Q123742),bool)),i(s(fun(cart(real,Q123742),fun(cart(real,Q123742),fun(cart(real,Q123742),bool))),U_0),s(cart(real,Q123742),A5))),s(cart(real,Q123742),B0)))))))) # label(aSPANu_2) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2826 (all N all M all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & s(fun(cart(real,M),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M))),i(s(fun(fun(cart(real,N),cart(real,M)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M)))),o),s(fun(cart(real,N),cart(real,M)),G0))),s(fun(cart(real,M),cart(real,N)),F0))) = s(fun(cart(real,M),cart(real,M)),i1) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0)))) -> (exists B0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,B0)))) & (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))))))))) # label(aLINEARu_INVERTIBLEu_BOUNDEDu_BELOWu_POS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2827 (all N all X all Y s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),Y)))) # label(aVECTORu_SUBu_RADD) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2828 (all X s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,X))),s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aLIFTu_EQu_CMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2829 (all N all A5 all B0 all X (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),A5))))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),B0))),s(cart(real,N),X))))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),A5))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),B0))),s(cart(real,N),X))))) <-> p(s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(cart(real,N),fun(prod(cart(real,N),cart(real,N)),bool)),between),s(cart(real,N),X))),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),B0)))))))) # label(aBETWEENu_DOT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.81 2830 (all N all M all A5 all B0 (s(cart(cart(real,N),M),B0) = s(cart(cart(real,N),M),A5) <-> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),A5))) = s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),B0))))))) # label(aMATRIXu_EQUALu_ROWS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2831 (all Q99561 all X s(cart(real,Q99561),i(s(fun(cart(real,Q99561),cart(real,Q99561)),i(s(fun(cart(real,Q99561),fun(cart(real,Q99561),cart(real,Q99561))),vectoru_add),s(cart(real,Q99561),i(s(fun(num,cart(real,Q99561)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q99561),X))) = s(cart(real,Q99561),X)) # label(aVECTORu_ADDu_LID) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2832 (all N all M all A5 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5)))) # label(aMATRIXu_SUBu_LZERO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2833 (all M all N all P all U_2 ((all G0 all GENR_PVARR_366 ((exists Y exists V (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_366))),s(bool,V))),s(cart(real,N),Y)))) & (p(s(bool,V)) <-> s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),G0),s(cart(real,N),Y))) = s(cart(real,P),i(s(fun(num,cart(real,P)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) <-> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),cart(real,P)),fun(cart(real,N),bool)),U_2),s(fun(cart(real,N),cart(real,P)),G0))),s(cart(real,N),GENR_PVARR_366)))))) -> (all U_1 ((all F0 all GENR_PVARR_365 (p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool)),U_1),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,M),GENR_PVARR_365)))) <-> (exists X exists V ((p(s(bool,V)) <-> s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))) & p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(bool,fun(cart(real,M),bool)),i(s(fun(cart(real,M),fun(bool,fun(cart(real,M),bool))),setspec),s(cart(real,M),GENR_PVARR_365))),s(bool,V))),s(cart(real,M),X)))))))) -> (all U_0 ((all G0 all F0 all GENR_PVARR_364 (p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool)),i(s(fun(fun(cart(real,N),cart(real,P)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool))),U_0),s(fun(cart(real,N),cart(real,P)),G0))),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,M),GENR_PVARR_364)))) <-> (exists X exists V ((s(cart(real,P),i(s(fun(num,cart(real,P)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,P),i(s(fun(cart(real,M),cart(real,P)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,P))),i(s(fun(fun(cart(real,N),cart(real,P)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,P)))),o),s(fun(cart(real,N),cart(real,P)),G0))),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,M),X))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(bool,fun(cart(real,M),bool)),i(s(fun(cart(real,M),fun(bool,fun(cart(real,M),bool))),setspec),s(cart(real,M),GENR_PVARR_364))),s(bool,V))),s(cart(real,M),X)))))))) -> (all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,P)),bool),linear),s(fun(cart(real,N),cart(real,P)),G0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),gspec),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool)),i(s(fun(fun(cart(real,N),cart(real,P)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool))),U_0),s(fun(cart(real,N),cart(real,P)),G0))),s(fun(cart(real,M),cart(real,N)),F0))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),gspec),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool)),U_1),s(fun(cart(real,M),cart(real,N)),F0))))))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),cart(real,P)),fun(cart(real,N),bool)),U_2),s(fun(cart(real,N),cart(real,P)),G0)))))))))))))))))))) # label(aDIMu_KERNELu_COMPOSE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2834 (all N all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))))) # label(aINDEPENDENTu_BOUND) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2835 (all Q141347 all A5 all X (s(cart(real,Q141347),X) = s(cart(real,Q141347),A5) <-> p(s(bool,i(s(fun(prod(cart(real,Q141347),cart(real,Q141347)),bool),i(s(fun(cart(real,Q141347),fun(prod(cart(real,Q141347),cart(real,Q141347)),bool)),between),s(cart(real,Q141347),X))),s(prod(cart(real,Q141347),cart(real,Q141347)),i(s(fun(cart(real,Q141347),prod(cart(real,Q141347),cart(real,Q141347))),i(s(fun(cart(real,Q141347),fun(cart(real,Q141347),prod(cart(real,Q141347),cart(real,Q141347)))),c_),s(cart(real,Q141347),A5))),s(cart(real,Q141347),A5)))))))) # label(aBETWEENu_REFLu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2836 (all N s(cart(real,N),x) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),x))),s(cart(real,N),y))))),s(cart(real,N),y)))) # label(aVECTORu_SUBu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2837 (all Q106171 all Q106182 all F0 all G0 all S0 ((all X (p(s(bool,i(s(fun(fun(Q106171,bool),bool),i(s(fun(Q106171,fun(fun(Q106171,bool),bool)),in),s(Q106171,X))),s(fun(Q106171,bool),S0)))) -> s(cart(real,Q106182),i(s(fun(Q106171,cart(real,Q106182)),G0),s(Q106171,X))) = s(cart(real,Q106182),i(s(fun(Q106171,cart(real,Q106182)),F0),s(Q106171,X))))) -> s(cart(real,Q106182),i(s(fun(fun(Q106171,cart(real,Q106182)),cart(real,Q106182)),i(s(fun(fun(Q106171,bool),fun(fun(Q106171,cart(real,Q106182)),cart(real,Q106182))),vsum),s(fun(Q106171,bool),S0))),s(fun(Q106171,cart(real,Q106182)),F0))) = s(cart(real,Q106182),i(s(fun(fun(Q106171,cart(real,Q106182)),cart(real,Q106182)),i(s(fun(fun(Q106171,bool),fun(fun(Q106171,cart(real,Q106182)),cart(real,Q106182))),vsum),s(fun(Q106171,bool),S0))),s(fun(Q106171,cart(real,Q106182)),G0))))) # label(aVSUMu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2838 (all Q105190 all X all Y all C0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_abs),s(real,C0))))),s(real,i(s(fun(prod(cart(real,Q105190),cart(real,Q105190)),real),distance),s(prod(cart(real,Q105190),cart(real,Q105190)),i(s(fun(cart(real,Q105190),prod(cart(real,Q105190),cart(real,Q105190))),i(s(fun(cart(real,Q105190),fun(cart(real,Q105190),prod(cart(real,Q105190),cart(real,Q105190)))),c_),s(cart(real,Q105190),X))),s(cart(real,Q105190),Y))))))) = s(real,i(s(fun(prod(cart(real,Q105190),cart(real,Q105190)),real),distance),s(prod(cart(real,Q105190),cart(real,Q105190)),i(s(fun(cart(real,Q105190),prod(cart(real,Q105190),cart(real,Q105190))),i(s(fun(cart(real,Q105190),fun(cart(real,Q105190),prod(cart(real,Q105190),cart(real,Q105190)))),c_),s(cart(real,Q105190),i(s(fun(cart(real,Q105190),cart(real,Q105190)),i(s(fun(real,fun(cart(real,Q105190),cart(real,Q105190))),r_),s(real,C0))),s(cart(real,Q105190),X))))),s(cart(real,Q105190),i(s(fun(cart(real,Q105190),cart(real,Q105190)),i(s(fun(real,fun(cart(real,Q105190),cart(real,Q105190))),r_),s(real,C0))),s(cart(real,Q105190),Y)))))))) # label(aDISTu_MUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2839 (all M all N all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),G0)))) & (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) -> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0))))))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> s(fun(cart(real,M),cart(real,N)),G0) = s(fun(cart(real,M),cart(real,N)),F0))) # label(aLINEARu_EQu_STDBASIS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2840 (all Q102822 all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q102822),real),vectoru_norm),s(cart(real,Q102822),i(s(fun(cart(real,Q102822),cart(real,Q102822)),i(s(fun(cart(real,Q102822),fun(cart(real,Q102822),cart(real,Q102822))),vectoru_add),s(cart(real,Q102822),X))),s(cart(real,Q102822),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q102822),real),vectoru_norm),s(cart(real,Q102822),X))))),s(real,i(s(fun(cart(real,Q102822),real),vectoru_norm),s(cart(real,Q102822),Y))))))))) # label(aNORMu_TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2841 (all N all M all F0 all B0 (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),finite),s(fun(cart(real,M),bool),B0)))) -> (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),independent),s(fun(cart(real,M),bool),B0)))) -> (exists G0 ((all X all C0 (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0)))))) -> s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),X))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,C0))),s(cart(real,M),X))))))) & (all X (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),B0)))) -> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),X))))) & (all X all Y (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0)))))) -> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_add),s(cart(real,M),X))),s(cart(real,M),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),Y)))))))))))) # label(aLINEARu_INDEPENDENTu_EXTENDu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2842 (all Q100698 all X all Y s(real,i(s(fun(prod(cart(real,Q100698),cart(real,Q100698)),real),distance),s(prod(cart(real,Q100698),cart(real,Q100698)),i(s(fun(cart(real,Q100698),prod(cart(real,Q100698),cart(real,Q100698))),i(s(fun(cart(real,Q100698),fun(cart(real,Q100698),prod(cart(real,Q100698),cart(real,Q100698)))),c_),s(cart(real,Q100698),X))),s(cart(real,Q100698),Y))))) = s(real,i(s(fun(cart(real,Q100698),real),vectoru_norm),s(cart(real,Q100698),i(s(fun(cart(real,Q100698),cart(real,Q100698)),i(s(fun(cart(real,Q100698),fun(cart(real,Q100698),cart(real,Q100698))),vectoru_sub),s(cart(real,Q100698),X))),s(cart(real,Q100698),Y)))))) # label(adist) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2843 (all M all N all A5 all X s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(cart(real,M),fun(cart(cart(real,N),M),cart(real,N))),vectoru_matrixu_mul),s(cart(real,M),X))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),A5))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X)))) # label(aMATRIXu_VECTORu_MULu_TRANSP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2844 (all Q121443 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q121443),bool),bool),subspace),s(fun(cart(real,Q121443),bool),S0)))) -> s(fun(cart(real,Q121443),bool),S0) != s(fun(cart(real,Q121443),bool),empty))) # label(aSUBSPACEu_IMPu_NONEMPTY) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2845 (all N all X all Y all I0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y))))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0)))))) # label(aVECTORu_ADDu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2846 (all Q140026 p(s(bool,i(s(fun(fun(cart(real,Q140026),bool),bool),collinear),s(fun(cart(real,Q140026),bool),empty))))) # label(aCOLLINEARu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2847 (all A s(A,i(s(fun(num,A),i(s(fun(cart(A,n3),fun(num,A)),d_),s(cart(A,n3),i(s(fun(list(A),cart(A,n3)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,y))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,z))),s(list(A),nil))))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(A,y)) # label(aVECTORu_3u_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2848 (all N all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,a0)))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,a0)))))) # label(aNORMu_LTu_SQUAREu_ALT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2849 (all Q121741 all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,Q121741),bool),bool),subspace),s(fun(cart(real,Q121741),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,Q121741),bool),bool),subspace),s(fun(cart(real,Q121741),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121741),bool),bool),subspace),s(fun(cart(real,Q121741),bool),i(s(fun(fun(cart(real,Q121741),bool),fun(cart(real,Q121741),bool)),i(s(fun(fun(cart(real,Q121741),bool),fun(fun(cart(real,Q121741),bool),fun(cart(real,Q121741),bool))),inter),s(fun(cart(real,Q121741),bool),S0))),s(fun(cart(real,Q121741),bool),T0)))))))) # label(aSUBSPACEu_INTER) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2850 (all Q121142 all Q121143 all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,finite_sum(Q121142,Q121143)),real),vectoru_norm),s(cart(real,finite_sum(Q121142,Q121143)),i(s(fun(cart(real,Q121143),cart(real,finite_sum(Q121142,Q121143))),i(s(fun(cart(real,Q121142),fun(cart(real,Q121143),cart(real,finite_sum(Q121142,Q121143)))),pastecart),s(cart(real,Q121142),X))),s(cart(real,Q121143),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q121142),real),vectoru_norm),s(cart(real,Q121142),X))))),s(real,i(s(fun(cart(real,Q121143),real),vectoru_norm),s(cart(real,Q121143),Y))))))))) # label(aNORMu_PASTECARTu_LE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2851 (all M all N all X all Y s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_sub),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),X))))),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),Y))))) = s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_sub),s(cart(real,finite_sum(M,N)),X))),s(cart(real,finite_sum(M,N)),Y)))))) # label(aFSTCARTu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2852 (all Q121671 all Q121673 all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q121673),cart(real,Q121671)),bool),linear),s(fun(cart(real,Q121673),cart(real,Q121671)),F0)))) & p(s(bool,i(s(fun(fun(cart(real,Q121673),bool),bool),subspace),s(fun(cart(real,Q121673),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121671),bool),bool),subspace),s(fun(cart(real,Q121671),bool),i(s(fun(fun(cart(real,Q121673),bool),fun(cart(real,Q121671),bool)),i(s(fun(fun(cart(real,Q121673),cart(real,Q121671)),fun(fun(cart(real,Q121673),bool),fun(cart(real,Q121671),bool))),image),s(fun(cart(real,Q121673),cart(real,Q121671)),F0))),s(fun(cart(real,Q121673),bool),S0)))))))) # label(aSUBSPACEu_LINEARu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2853 (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,X))))))))) # label(aSQUAREu_BOUNDu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2854 (all A all N all F0 all U all V ((all X (-p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V)))) -> s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),U))),s(fun(A,bool),V)))) -> s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),U))),s(fun(A,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),V))),s(fun(A,cart(real,N)),F0))))) # label(aVSUMu_SUPERSET) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2855 (all Q121723 p(s(bool,i(s(fun(fun(cart(real,Q121723),bool),bool),subspace),s(fun(cart(real,Q121723),bool),i(s(fun(fun(cart(real,Q121723),bool),fun(cart(real,Q121723),bool)),i(s(fun(cart(real,Q121723),fun(fun(cart(real,Q121723),bool),fun(cart(real,Q121723),bool))),insert),s(cart(real,Q121723),i(s(fun(num,cart(real,Q121723)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121723),bool),empty))))))) # label(aSUBSPACEu_TRIVIAL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2856 (all Q104964 all X all Y all Z0 all E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,Q104964),cart(real,Q104964)),real),distance),s(prod(cart(real,Q104964),cart(real,Q104964)),i(s(fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964))),i(s(fun(cart(real,Q104964),fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964)))),c_),s(cart(real,Q104964),X))),s(cart(real,Q104964),Z0))))))),s(real,i(s(fun(prod(cart(real,Q104964),cart(real,Q104964)),real),distance),s(prod(cart(real,Q104964),cart(real,Q104964)),i(s(fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964))),i(s(fun(cart(real,Q104964),fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964)))),c_),s(cart(real,Q104964),Y))),s(cart(real,Q104964),Z0))))))))),s(real,E0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q104964),cart(real,Q104964)),real),distance),s(prod(cart(real,Q104964),cart(real,Q104964)),i(s(fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964))),i(s(fun(cart(real,Q104964),fun(cart(real,Q104964),prod(cart(real,Q104964),cart(real,Q104964)))),c_),s(cart(real,Q104964),X))),s(cart(real,Q104964),Y))))))),s(real,E0)))))) # label(aDISTu_TRIANGLEu_LT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2857 (all P0 ((exists S0 p(s(bool,i(s(fun(fun(cart(real,n10),bool),bool),P0),s(fun(cart(real,n10),bool),S0))))) <-> (exists S0 p(s(bool,i(s(fun(fun(cart(real,n10),bool),bool),P0),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),S0))))))))) # label(aEXISTSu_LIFTu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2858 (all N all X all Y (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))))) <-> s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(cart(real,N),Y))) | s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(cart(real,N),Y))))) # label(aNORMu_CAUCHYu_SCHWARZu_ABSu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2859 (all Q127017 all S0 all T0 (s(fun(cart(real,Q127017),bool),i(s(fun(fun(cart(real,Q127017),bool),fun(cart(real,Q127017),bool)),span),s(fun(cart(real,Q127017),bool),T0))) = s(fun(cart(real,Q127017),bool),i(s(fun(fun(cart(real,Q127017),bool),fun(cart(real,Q127017),bool)),span),s(fun(cart(real,Q127017),bool),S0))) -> s(num,i(s(fun(fun(cart(real,Q127017),bool),num),dim),s(fun(cart(real,Q127017),bool),T0))) = s(num,i(s(fun(fun(cart(real,Q127017),bool),num),dim),s(fun(cart(real,Q127017),bool),S0))))) # label(aSPANu_EQu_DIM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2860 (all N all A5 all B0 all C0 (s(cart(real,N),A5) = s(cart(real,N),C0) | (exists U s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,U))),s(cart(real,N),A5))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,U))))),s(cart(real,N),C0))))) = s(cart(real,N),B0)) <-> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),C0))),s(fun(cart(real,N),bool),empty)))))))))))) # label(aCOLLINEARu_3u_EXPAND) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2861 (all Q119844 all F0 all S0 (p(s(bool,i(s(fun(fun(Q119844,bool),bool),finite),s(fun(Q119844,bool),S0)))) -> s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(fun(Q119844,cart(real,n10)),cart(real,n10)),i(s(fun(fun(Q119844,bool),fun(fun(Q119844,cart(real,n10)),cart(real,n10))),vsum),s(fun(Q119844,bool),S0))),s(fun(Q119844,cart(real,n10)),i(s(fun(fun(Q119844,real),fun(Q119844,cart(real,n10))),i(s(fun(fun(real,cart(real,n10)),fun(fun(Q119844,real),fun(Q119844,cart(real,n10)))),o),s(fun(real,cart(real,n10)),lift))),s(fun(Q119844,real),F0))))))) = s(real,i(s(fun(fun(Q119844,real),real),i(s(fun(fun(Q119844,bool),fun(fun(Q119844,real),real)),sum),s(fun(Q119844,bool),S0))),s(fun(Q119844,real),F0))))) # label(aSUMu_VSUM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2862 (all A all P0 ((exists F0 p(s(bool,i(s(fun(fun(A,real),bool),P0),s(fun(A,real),i(s(fun(fun(A,cart(real,n10)),fun(A,real)),i(s(fun(fun(cart(real,n10),real),fun(fun(A,cart(real,n10)),fun(A,real))),o),s(fun(cart(real,n10),real),drop))),s(fun(A,cart(real,n10)),F0))))))) <-> (exists F0 p(s(bool,i(s(fun(fun(A,real),bool),P0),s(fun(A,real),F0))))))) # label(aEXISTSu_DROPu_FUN) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2863 (all Q100362 all C0 all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(cart(real,Q100362),real),i(s(fun(cart(real,Q100362),fun(cart(real,Q100362),real)),dot),s(cart(real,Q100362),X))),s(cart(real,Q100362),Y))))) = s(real,i(s(fun(cart(real,Q100362),real),i(s(fun(cart(real,Q100362),fun(cart(real,Q100362),real)),dot),s(cart(real,Q100362),i(s(fun(cart(real,Q100362),cart(real,Q100362)),i(s(fun(real,fun(cart(real,Q100362),cart(real,Q100362))),r_),s(real,C0))),s(cart(real,Q100362),X))))),s(cart(real,Q100362),Y)))) # label(aDOTu_LMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2864 (all N all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),S0)))) -> (exists U (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),disjoint),s(fun(cart(real,N),bool),U))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),U)))))) & s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),U))))))))) # label(aORTHOGONALu_EXTENSIONu_STRONG) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2865 (all A ((all X all Y p(s(bool,i(s(fun(cart(A,n20),bool),p0),s(cart(A,n20),i(s(fun(list(A),cart(A,n20)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Y))),s(list(A),nil))))))))))) <-> (all V p(s(bool,i(s(fun(cart(A,n20),bool),p0),s(cart(A,n20),V))))))) # label(aFORALLu_VECTORu_2) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2866 (all Q102400 all A5 all X (s(cart(real,Q102400),i(s(fun(num,cart(real,Q102400)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q102400),i(s(fun(cart(real,Q102400),cart(real,Q102400)),i(s(fun(real,fun(cart(real,Q102400),cart(real,Q102400))),r_),s(real,A5))),s(cart(real,Q102400),X))) <-> s(cart(real,Q102400),i(s(fun(num,cart(real,Q102400)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q102400),X) | s(real,A5) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aVECTORu_MULu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2867 (all Q104851 all X all Y (s(cart(real,Q104851),X) != s(cart(real,Q104851),Y) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(prod(cart(real,Q104851),cart(real,Q104851)),real),distance),s(prod(cart(real,Q104851),cart(real,Q104851)),i(s(fun(cart(real,Q104851),prod(cart(real,Q104851),cart(real,Q104851))),i(s(fun(cart(real,Q104851),fun(cart(real,Q104851),prod(cart(real,Q104851),cart(real,Q104851)))),c_),s(cart(real,Q104851),X))),s(cart(real,Q104851),Y)))))))))) # label(aDISTu_POSu_LT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2868 (all Q99609 all X s(cart(real,Q99609),i(s(fun(num,cart(real,Q99609)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q99609),i(s(fun(cart(real,Q99609),cart(real,Q99609)),i(s(fun(cart(real,Q99609),fun(cart(real,Q99609),cart(real,Q99609))),vectoru_add),s(cart(real,Q99609),i(s(fun(cart(real,Q99609),cart(real,Q99609)),vectoru_neg),s(cart(real,Q99609),X))))),s(cart(real,Q99609),X)))) # label(aVECTORu_ADDu_LINV) # label(axiom) # label(non_clause). [assumption]. 15.81/15.82 2869 (all N all M all A5 all B0 all C0 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0)))))) # label(aMATRIXu_CMULu_ADDu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2870 (all Q100339 all X all Y all Z0 s(real,i(s(fun(cart(real,Q100339),real),i(s(fun(cart(real,Q100339),fun(cart(real,Q100339),real)),dot),s(cart(real,Q100339),X))),s(cart(real,Q100339),i(s(fun(cart(real,Q100339),cart(real,Q100339)),i(s(fun(cart(real,Q100339),fun(cart(real,Q100339),cart(real,Q100339))),vectoru_sub),s(cart(real,Q100339),Y))),s(cart(real,Q100339),Z0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(cart(real,Q100339),real),i(s(fun(cart(real,Q100339),fun(cart(real,Q100339),real)),dot),s(cart(real,Q100339),X))),s(cart(real,Q100339),Y))))),s(real,i(s(fun(cart(real,Q100339),real),i(s(fun(cart(real,Q100339),fun(cart(real,Q100339),real)),dot),s(cart(real,Q100339),X))),s(cart(real,Q100339),Z0)))))) # label(aDOTu_RSUB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2871 (all N all A5 (p(s(bool,i(s(fun(cart(cart(real,N),N),bool),invertible),s(cart(cart(real,N),N),A5)))) <-> (exists B0 s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),A5))),s(cart(cart(real,N),N),B0))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aINVERTIBLEu_RIGHTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2872 (all Q110725 all X all Y s(bool,i(s(fun(cart(real,Q110725),bool),i(s(fun(cart(real,Q110725),fun(cart(real,Q110725),bool)),orthogonal),s(cart(real,Q110725),X))),s(cart(real,Q110725),Y))) = s(bool,i(s(fun(cart(real,Q110725),bool),i(s(fun(cart(real,Q110725),fun(cart(real,Q110725),bool)),orthogonal),s(cart(real,Q110725),X))),s(cart(real,Q110725),i(s(fun(cart(real,Q110725),cart(real,Q110725)),vectoru_neg),s(cart(real,Q110725),Y)))))) # label(aORTHOGONALu_RNEG) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2873 (all Q124006 all A5 all B0 all S0 (-p(s(bool,i(s(fun(fun(cart(real,Q124006),bool),bool),i(s(fun(cart(real,Q124006),fun(fun(cart(real,Q124006),bool),bool)),in),s(cart(real,Q124006),A5))),s(fun(cart(real,Q124006),bool),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),bool)),span),s(fun(cart(real,Q124006),bool),i(s(fun(cart(real,Q124006),fun(cart(real,Q124006),bool)),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),fun(cart(real,Q124006),bool))),delete),s(fun(cart(real,Q124006),bool),S0))),s(cart(real,Q124006),B0)))))))) & p(s(bool,i(s(fun(fun(cart(real,Q124006),bool),bool),i(s(fun(cart(real,Q124006),fun(fun(cart(real,Q124006),bool),bool)),in),s(cart(real,Q124006),A5))),s(fun(cart(real,Q124006),bool),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),bool)),span),s(fun(cart(real,Q124006),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,Q124006),bool),bool),i(s(fun(cart(real,Q124006),fun(fun(cart(real,Q124006),bool),bool)),in),s(cart(real,Q124006),B0))),s(fun(cart(real,Q124006),bool),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),bool)),span),s(fun(cart(real,Q124006),bool),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),bool)),i(s(fun(cart(real,Q124006),fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),bool))),insert),s(cart(real,Q124006),A5))),s(fun(cart(real,Q124006),bool),i(s(fun(cart(real,Q124006),fun(cart(real,Q124006),bool)),i(s(fun(fun(cart(real,Q124006),bool),fun(cart(real,Q124006),fun(cart(real,Q124006),bool))),delete),s(fun(cart(real,Q124006),bool),S0))),s(cart(real,Q124006),B0)))))))))))) # label(aINu_SPANu_DELETE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2874 (all N all F0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> (-(all X all Y (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) -> s(cart(real,N),X) = s(cart(real,N),Y))) <-> (exists A5 ((all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),A5))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X)))))) & s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(real,N),A5)))))) # label(aLINEARu_SINGULARu_INTOu_HYPERPLANE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2875 (all Q104680 all X all Y s(real,i(s(fun(prod(cart(real,Q104680),cart(real,Q104680)),real),distance),s(prod(cart(real,Q104680),cart(real,Q104680)),i(s(fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680))),i(s(fun(cart(real,Q104680),fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680)))),c_),s(cart(real,Q104680),Y))),s(cart(real,Q104680),X))))) = s(real,i(s(fun(prod(cart(real,Q104680),cart(real,Q104680)),real),distance),s(prod(cart(real,Q104680),cart(real,Q104680)),i(s(fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680))),i(s(fun(cart(real,Q104680),fun(cart(real,Q104680),prod(cart(real,Q104680),cart(real,Q104680)))),c_),s(cart(real,Q104680),X))),s(cart(real,Q104680),Y)))))) # label(aDISTu_SYM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2876 (all N all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_ge),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) | p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,a0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_ge),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,a0)))))) # label(aNORMu_GEu_SQUARE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2877 (all N all U_0 ((all X all I0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X))),s(num,I0))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0)))))) -> (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),U_0),s(cart(real,N),X))))))))))) # label(aNORMu_LEu_L1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2878 (all Q111837 all Q111834 all F0 all C0 all X (p(s(bool,i(s(fun(fun(cart(real,Q111834),cart(real,Q111837)),bool),linear),s(fun(cart(real,Q111834),cart(real,Q111837)),F0)))) -> s(cart(real,Q111837),i(s(fun(cart(real,Q111834),cart(real,Q111837)),F0),s(cart(real,Q111834),i(s(fun(cart(real,Q111834),cart(real,Q111834)),i(s(fun(real,fun(cart(real,Q111834),cart(real,Q111834))),r_),s(real,C0))),s(cart(real,Q111834),X))))) = s(cart(real,Q111837),i(s(fun(cart(real,Q111837),cart(real,Q111837)),i(s(fun(real,fun(cart(real,Q111837),cart(real,Q111837))),r_),s(real,C0))),s(cart(real,Q111837),i(s(fun(cart(real,Q111834),cart(real,Q111837)),F0),s(cart(real,Q111834),X))))))) # label(aLINEARu_CMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2879 (all Q109392 all U_2 ((all F0 all J0 all I0 s(cart(real,Q109392),i(s(fun(num,cart(real,Q109392)),i(s(fun(num,fun(num,cart(real,Q109392))),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,fun(num,cart(real,Q109392)))),U_2),s(fun(num,fun(num,cart(real,Q109392))),F0))),s(num,J0))),s(num,I0))) = s(cart(real,Q109392),i(s(fun(num,cart(real,Q109392)),i(s(fun(num,fun(num,cart(real,Q109392))),F0),s(num,I0))),s(num,J0)))) -> (all U_1 ((all F0 all J0 s(fun(num,cart(real,Q109392)),i(s(fun(num,fun(num,cart(real,Q109392))),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,fun(num,cart(real,Q109392)))),U_2),s(fun(num,fun(num,cart(real,Q109392))),F0))),s(num,J0))) = s(fun(num,cart(real,Q109392)),i(s(fun(num,fun(num,cart(real,Q109392))),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,fun(num,cart(real,Q109392)))),U_1),s(fun(num,fun(num,cart(real,Q109392))),F0))),s(num,J0)))) -> (all U_0 ((all C0 all D0 all F0 all I0 s(cart(real,Q109392),i(s(fun(fun(num,cart(real,Q109392)),cart(real,Q109392)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109392)),cart(real,Q109392))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,C0))),s(num,D0))))),s(fun(num,cart(real,Q109392)),i(s(fun(num,fun(num,cart(real,Q109392))),F0),s(num,I0))))) = s(cart(real,Q109392),i(s(fun(num,cart(real,Q109392)),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))),i(s(fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392)))),i(s(fun(num,fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))))),U_0),s(num,C0))),s(num,D0))),s(fun(num,fun(num,cart(real,Q109392))),F0))),s(num,I0)))) -> (all A5 all B0 all C0 all D0 all F0 s(cart(real,Q109392),i(s(fun(fun(num,cart(real,Q109392)),cart(real,Q109392)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109392)),cart(real,Q109392))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,C0))),s(num,D0))))),s(fun(num,cart(real,Q109392)),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))),i(s(fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392)))),i(s(fun(num,fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))))),U_0),s(num,A5))),s(num,B0))),s(fun(num,fun(num,cart(real,Q109392))),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,fun(num,cart(real,Q109392)))),U_1),s(fun(num,fun(num,cart(real,Q109392))),F0))))))) = s(cart(real,Q109392),i(s(fun(fun(num,cart(real,Q109392)),cart(real,Q109392)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109392)),cart(real,Q109392))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,A5))),s(num,B0))))),s(fun(num,cart(real,Q109392)),i(s(fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))),i(s(fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392)))),i(s(fun(num,fun(num,fun(fun(num,fun(num,cart(real,Q109392))),fun(num,cart(real,Q109392))))),U_0),s(num,C0))),s(num,D0))),s(fun(num,fun(num,cart(real,Q109392))),F0)))))))))))) # label(aVSUMu_SWAPu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2880 (all N all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),T0)))))) # label(aDEPENDENTu_MONO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2881 (all M all P all N all A5 all B0 all C0 s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(real,fun(cart(cart(real,P),M),cart(cart(real,P),M))),r_r_),s(real,C0))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),N)),i(s(fun(real,fun(cart(cart(real,P),N),cart(cart(real,P),N))),r_r_),s(real,C0))),s(cart(cart(real,P),N),B0)))))) # label(aMATRIXu_MULu_RMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2882 (all N all U_0 ((all F0 all I0 s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,real),fun(num,cart(real,N))),U_0),s(fun(num,real),F0))),s(num,I0)))) -> (all F0 all X ((all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> s(real,i(s(fun(num,real),F0),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))) <-> s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,real),fun(num,cart(real,N))),U_0),s(fun(num,real),F0))))) = s(cart(real,N),X))))) # label(aBASISu_EXPANSIONu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2883 (all Q102468 all A5 all B0 all X (s(cart(real,Q102468),X) = s(cart(real,Q102468),i(s(fun(num,cart(real,Q102468)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) | s(real,A5) = s(real,B0) <-> s(cart(real,Q102468),i(s(fun(cart(real,Q102468),cart(real,Q102468)),i(s(fun(real,fun(cart(real,Q102468),cart(real,Q102468))),r_),s(real,A5))),s(cart(real,Q102468),X))) = s(cart(real,Q102468),i(s(fun(cart(real,Q102468),cart(real,Q102468)),i(s(fun(real,fun(cart(real,Q102468),cart(real,Q102468))),r_),s(real,B0))),s(cart(real,Q102468),X))))) # label(aVECTORu_MULu_RCANCEL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2884 (all N all M all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),S0))))))) # label(aSPANu_LINEARu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2885 (all S0 all T0 s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(fun(real,bool),fun(fun(real,bool),bool)),subset),s(fun(real,bool),S0))),s(fun(real,bool),T0))) = s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(fun(cart(real,n10),bool),fun(fun(cart(real,n10),bool),bool)),subset),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),S0))))),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),T0)))))) # label(aSUBSETu_LIFTu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2886 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y)))))))) # label(aSQRTu_MONOu_LE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2887 (all A all B all U_1 ((all P0 all F0 all GENR_PVARR_380 ((exists X p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_380))),s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(A,B),F0),s(A,X))))))),s(A,X))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),i(s(fun(fun(B,bool),fun(fun(A,B),fun(A,bool))),U_1),s(fun(B,bool),P0))),s(fun(A,B),F0))),s(A,GENR_PVARR_380)))))) -> (all U_0 ((all P0 all GENR_PVARR_379 (p(s(bool,i(s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),U_0),s(fun(B,bool),P0))),s(B,GENR_PVARR_379)))) <-> (exists X p(s(bool,i(s(fun(B,bool),i(s(fun(bool,fun(B,bool)),i(s(fun(B,fun(bool,fun(B,bool))),setspec),s(B,GENR_PVARR_379))),s(bool,i(s(fun(B,bool),P0),s(B,X))))),s(B,X))))))) -> (all F0 ((all Y exists X s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X)))) -> (all P0 ((exists X p(s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(A,B),F0),s(A,X))))))) <-> (exists X p(s(bool,i(s(fun(B,bool),P0),s(B,X))))))) & (all Q0 ((all S0 p(s(bool,i(s(fun(fun(B,bool),bool),Q0),s(fun(B,bool),S0))))) <-> (all S0 p(s(bool,i(s(fun(fun(B,bool),bool),Q0),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))))))) & (all Q0 ((exists S0 p(s(bool,i(s(fun(fun(B,bool),bool),Q0),s(fun(B,bool),S0))))) <-> (exists S0 p(s(bool,i(s(fun(fun(B,bool),bool),Q0),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))))))) & (all P0 s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),gspec),s(fun(B,bool),i(s(fun(fun(B,bool),fun(B,bool)),U_0),s(fun(B,bool),P0))))) = s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,B),fun(A,bool)),i(s(fun(fun(B,bool),fun(fun(A,B),fun(A,bool))),U_1),s(fun(B,bool),P0))),s(fun(A,B),F0)))))))) & (all P0 ((all X p(s(bool,i(s(fun(B,bool),P0),s(B,i(s(fun(A,B),F0),s(A,X))))))) <-> (all X p(s(bool,i(s(fun(B,bool),P0),s(B,X))))))))))))) # label(aQUANTIFYu_SURJECTIONu_THM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2888 (all Q112265 all Q112255 all Q112254 all U_1 ((all F0 all Y all X s(cart(real,Q112255),i(s(fun(cart(real,Q112254),cart(real,Q112255)),i(s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0),s(cart(real,Q112265),X))),s(cart(real,Q112254),Y))) = s(cart(real,Q112255),i(s(fun(cart(real,Q112265),cart(real,Q112255)),i(s(fun(cart(real,Q112254),fun(cart(real,Q112265),cart(real,Q112255))),i(s(fun(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),fun(cart(real,Q112254),fun(cart(real,Q112265),cart(real,Q112255)))),U_1),s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0))),s(cart(real,Q112254),Y))),s(cart(real,Q112265),X)))) -> (all U_0 ((all F0 all X all Y s(cart(real,Q112255),i(s(fun(cart(real,Q112254),cart(real,Q112255)),i(s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),i(s(fun(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255)))),U_0),s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0))),s(cart(real,Q112265),X))),s(cart(real,Q112254),Y))) = s(cart(real,Q112255),i(s(fun(cart(real,Q112254),cart(real,Q112255)),i(s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0),s(cart(real,Q112265),X))),s(cart(real,Q112254),Y)))) -> (all F0 (p(s(bool,i(s(fun(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),bool),bilinear),s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0)))) <-> (all X p(s(bool,i(s(fun(fun(cart(real,Q112254),cart(real,Q112255)),bool),linear),s(fun(cart(real,Q112254),cart(real,Q112255)),i(s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),i(s(fun(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255)))),U_0),s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0))),s(cart(real,Q112265),X))))))) & (all Y p(s(bool,i(s(fun(fun(cart(real,Q112265),cart(real,Q112255)),bool),linear),s(fun(cart(real,Q112265),cart(real,Q112255)),i(s(fun(cart(real,Q112254),fun(cart(real,Q112265),cart(real,Q112255))),i(s(fun(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),fun(cart(real,Q112254),fun(cart(real,Q112265),cart(real,Q112255)))),U_1),s(fun(cart(real,Q112265),fun(cart(real,Q112254),cart(real,Q112255))),F0))),s(cart(real,Q112254),Y))))))))))))) # label(abilinear) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2889 (all N all S0 all A5 all B0 (s(cart(real,N),A5) != s(cart(real,N),B0) -> (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),S0)))))))) <-> (all X (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),empty))))))))))))))) # label(aCOLLINEARu_TRIPLES) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2890 (all Q120272 all Q120278 all N0 s(cart(real,Q120278),i(s(fun(cart(real,finite_sum(Q120272,Q120278)),cart(real,Q120278)),sndcart),s(cart(real,finite_sum(Q120272,Q120278)),i(s(fun(num,cart(real,finite_sum(Q120272,Q120278))),vec),s(num,N0))))) = s(cart(real,Q120278),i(s(fun(num,cart(real,Q120278)),vec),s(num,N0)))) # label(aSNDCARTu_VEC) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2891 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> (s(real,X) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(real,real),sqrt),s(real,X)))))) # label(aSQRTu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2892 (all M all P all N all A5 all B0 all C0 s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(real,fun(cart(cart(real,P),M),cart(cart(real,P),M))),r_r_),s(real,C0))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,P),N),B0)))) # label(aMATRIXu_MULu_LMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2893 (all X all Y (s(real,Y) = s(real,X) <-> s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,Y))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))) # label(aLIFTu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2894 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),sqrt),s(real,Y)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,Y)))))) # label(aREALu_RSQRTu_LE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2895 (all Q102322 all X s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q102322),real),vectoru_norm),s(cart(real,Q102322),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(cart(real,Q102322),real),i(s(fun(cart(real,Q102322),fun(cart(real,Q102322),real)),dot),s(cart(real,Q102322),X))),s(cart(real,Q102322),X)))) # label(aNORMu_POWu_2) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2896 (all N all F0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,n10)),bool),linear),s(fun(cart(real,N),cart(real,n10)),F0)))) -> (all X s(cart(real,n10),i(s(fun(cart(real,N),cart(real,n10)),F0),s(cart(real,N),X))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(cart(real,N),n10),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),n10),cart(real,N))),row),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(cart(cart(real,N),n10),i(s(fun(fun(cart(real,N),cart(real,n10)),cart(cart(real,N),n10)),matrix),s(fun(cart(real,N),cart(real,n10)),F0))))))),s(cart(real,N),X)))))))) # label(aLINEARu_TOu_REALS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2897 (all A all Q107975 all X all F0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(cart(real,Q107975),i(s(fun(fun(A,cart(real,Q107975)),cart(real,Q107975)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107975)),cart(real,Q107975))),vsum),s(fun(A,bool),i(s(fun(A,fun(A,bool)),i(s(fun(fun(A,bool),fun(A,fun(A,bool))),delete),s(fun(A,bool),S0))),s(A,X))))),s(fun(A,cart(real,Q107975)),F0))) = s(cart(real,Q107975),i(s(fun(cart(real,Q107975),cart(real,Q107975)),i(s(fun(cart(real,Q107975),fun(cart(real,Q107975),cart(real,Q107975))),i(s(fun(bool,fun(cart(real,Q107975),fun(cart(real,Q107975),cart(real,Q107975)))),cond),s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0))))),s(cart(real,Q107975),i(s(fun(cart(real,Q107975),cart(real,Q107975)),i(s(fun(cart(real,Q107975),fun(cart(real,Q107975),cart(real,Q107975))),vectoru_sub),s(cart(real,Q107975),i(s(fun(fun(A,cart(real,Q107975)),cart(real,Q107975)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107975)),cart(real,Q107975))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q107975)),F0))))),s(cart(real,Q107975),i(s(fun(A,cart(real,Q107975)),F0),s(A,X))))))),s(cart(real,Q107975),i(s(fun(fun(A,cart(real,Q107975)),cart(real,Q107975)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107975)),cart(real,Q107975))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q107975)),F0))))))) # label(aVSUMu_DELETEu_CASES) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2898 (all N all U_0 ((all X all Y all I0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y))),s(num,I0)))) -> (all X all Y s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),Y)))))) # label(avectoru_sub) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2899 (all Q120217 all Q120216 all Q120214 all U_0 ((all X all I0 s(cart(real,Q120216),i(s(fun(cart(real,finite_sum(Q120216,Q120214)),cart(real,Q120216)),fstcart),s(cart(real,finite_sum(Q120216,Q120214)),i(s(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),X),s(Q120217,I0))))) = s(cart(real,Q120216),i(s(fun(Q120217,cart(real,Q120216)),i(s(fun(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),fun(Q120217,cart(real,Q120216))),U_0),s(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),X))),s(Q120217,I0)))) -> (all K0 all X (p(s(bool,i(s(fun(fun(Q120217,bool),bool),finite),s(fun(Q120217,bool),K0)))) -> s(cart(real,Q120216),i(s(fun(cart(real,finite_sum(Q120216,Q120214)),cart(real,Q120216)),fstcart),s(cart(real,finite_sum(Q120216,Q120214)),i(s(fun(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),cart(real,finite_sum(Q120216,Q120214))),i(s(fun(fun(Q120217,bool),fun(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),cart(real,finite_sum(Q120216,Q120214)))),vsum),s(fun(Q120217,bool),K0))),s(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),X))))) = s(cart(real,Q120216),i(s(fun(fun(Q120217,cart(real,Q120216)),cart(real,Q120216)),i(s(fun(fun(Q120217,bool),fun(fun(Q120217,cart(real,Q120216)),cart(real,Q120216))),vsum),s(fun(Q120217,bool),K0))),s(fun(Q120217,cart(real,Q120216)),i(s(fun(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),fun(Q120217,cart(real,Q120216))),U_0),s(fun(Q120217,cart(real,finite_sum(Q120216,Q120214))),X))))))))) # label(aFSTCARTu_VSUM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2900 (all Q119933 all Q119935 p(s(bool,i(s(fun(fun(cart(real,finite_sum(Q119935,Q119933)),cart(real,Q119935)),bool),linear),s(fun(cart(real,finite_sum(Q119935,Q119933)),cart(real,Q119935)),fstcart))))) # label(aLINEARu_FSTCART) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2901 (all N all S0 all T0 ((all X all Y (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),T0)))) -> s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0))))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0))))))) # label(aDIMu_ORTHOGONALu_SUM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2902 (all Q121609 all X all Y all S0 (p(s(bool,i(s(fun(fun(cart(real,Q121609),bool),bool),i(s(fun(cart(real,Q121609),fun(fun(cart(real,Q121609),bool),bool)),in),s(cart(real,Q121609),X))),s(fun(cart(real,Q121609),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q121609),bool),bool),i(s(fun(cart(real,Q121609),fun(fun(cart(real,Q121609),bool),bool)),in),s(cart(real,Q121609),Y))),s(fun(cart(real,Q121609),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q121609),bool),bool),subspace),s(fun(cart(real,Q121609),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121609),bool),bool),i(s(fun(cart(real,Q121609),fun(fun(cart(real,Q121609),bool),bool)),in),s(cart(real,Q121609),i(s(fun(cart(real,Q121609),cart(real,Q121609)),i(s(fun(cart(real,Q121609),fun(cart(real,Q121609),cart(real,Q121609))),vectoru_sub),s(cart(real,Q121609),X))),s(cart(real,Q121609),Y))))),s(fun(cart(real,Q121609),bool),S0)))))) # label(aSUBSPACEu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2903 (all N all X all I0 s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),X))))),s(num,I0)))) # label(aVECTORu_NEGu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2904 (all Q99576 all X s(cart(real,Q99576),X) = s(cart(real,Q99576),i(s(fun(cart(real,Q99576),cart(real,Q99576)),i(s(fun(cart(real,Q99576),fun(cart(real,Q99576),cart(real,Q99576))),vectoru_add),s(cart(real,Q99576),X))),s(cart(real,Q99576),i(s(fun(num,cart(real,Q99576)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aVECTORu_ADDu_RID) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2905 (all N all S0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> (exists X (s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(real,N),X) & (all Y (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),S0)))) -> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),X))),s(cart(real,N),Y)))))))))) # label(aORTHOGONALu_TOu_SUBSPACEu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2906 (all N all S0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> (exists T0 (s(num,N0) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))))))) # label(aLOWDIMu_EXPANDu_DIMENSION) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2907 (all Q122045 p(s(bool,i(s(fun(fun(cart(real,Q122045),bool),bool),i(s(fun(cart(real,Q122045),fun(fun(cart(real,Q122045),bool),bool)),in),s(cart(real,Q122045),i(s(fun(num,cart(real,Q122045)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q122045),bool),i(s(fun(fun(cart(real,Q122045),bool),fun(cart(real,Q122045),bool)),span),s(fun(cart(real,Q122045),bool),s0))))))) # label(aSPANu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2908 (all N all A5 all B0 all X all Y s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),i(s(fun(num,cart(real,n10)),i(s(fun(cart(cart(real,n10),n10),fun(num,cart(real,n10))),d_),s(cart(cart(real,n10),n10),i(s(fun(cart(cart(real,n10),N),cart(cart(real,n10),n10)),i(s(fun(cart(cart(real,N),n10),fun(cart(cart(real,n10),N),cart(cart(real,n10),n10))),matrixu_mul),s(cart(cart(real,N),n10),i(s(fun(cart(real,N),cart(cart(real,N),n10)),rowvector),s(cart(real,N),X))))),s(cart(cart(real,n10),N),i(s(fun(cart(cart(real,n10),N),cart(cart(real,n10),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,n10),N),cart(cart(real,n10),N))),matrixu_mul),s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),transp),s(cart(cart(real,N),N),A5))))),s(cart(cart(real,N),N),B0))))),s(cart(cart(real,n10),N),i(s(fun(cart(real,N),cart(cart(real,n10),N)),columnvector),s(cart(real,N),Y))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(cart(real,N),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,N),N),A5))),s(cart(real,N),X))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(cart(real,N),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,N),N),B0))),s(cart(real,N),Y)))))) # label(aDOTu_MATRIXu_VECTORu_MUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2909 (all A all N all F0 all S0 all X ((all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),X))),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,Y)))))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),X))),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0)))))))) # label(aORTHOGONALu_RVSUM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2910 (all Q142377 all A5 all B0 s(cart(real,Q142377),i(s(fun(cart(real,Q142377),cart(real,Q142377)),i(s(fun(real,fun(cart(real,Q142377),cart(real,Q142377))),r_),s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(cart(real,Q142377),i(s(fun(cart(real,Q142377),cart(real,Q142377)),i(s(fun(cart(real,Q142377),fun(cart(real,Q142377),cart(real,Q142377))),vectoru_add),s(cart(real,Q142377),A5))),s(cart(real,Q142377),B0))))) = s(cart(real,Q142377),i(s(fun(prod(cart(real,Q142377),cart(real,Q142377)),cart(real,Q142377)),midpoint),s(prod(cart(real,Q142377),cart(real,Q142377)),i(s(fun(cart(real,Q142377),prod(cart(real,Q142377),cart(real,Q142377))),i(s(fun(cart(real,Q142377),fun(cart(real,Q142377),prod(cart(real,Q142377),cart(real,Q142377)))),c_),s(cart(real,Q142377),A5))),s(cart(real,Q142377),B0)))))) # label(amidpoint) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2911 (all N s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),m))),s(cart(real,N),n))))),s(cart(real,N),p1))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),m))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),n))),s(cart(real,N),p1)))))) # label(aVECTORu_ADDu_ACu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2912 (all N all X all Y (s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))) <-> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),Y))),s(fun(cart(real,N),bool),empty)))))))))))) # label(aNORMu_CAUCHYu_SCHWARZu_EQUAL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2913 (all F0 ((exists C0 all X s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,C0))),s(cart(real,n10),X))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),F0),s(cart(real,n10),X)))) <-> p(s(bool,i(s(fun(fun(cart(real,n10),cart(real,n10)),bool),linear),s(fun(cart(real,n10),cart(real,n10)),F0)))))) # label(aLINEARu_1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.83 2914 (all Q112722 all Q112723 all M all N all P all U_0 ((all H0 all F0 (p(s(bool,i(s(fun(fun(prod(Q112722,Q112723),cart(real,P)),bool),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(prod(Q112722,Q112723),cart(real,P)),bool)),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(prod(Q112722,Q112723),cart(real,P)),F0)))) <-> (all I0 all J0 p(s(bool,i(s(fun(cart(real,P),bool),i(s(fun(cart(real,P),fun(cart(real,P),bool)),geq),s(cart(real,P),i(s(fun(prod(Q112722,Q112723),cart(real,P)),F0),s(prod(Q112722,Q112723),i(s(fun(Q112723,prod(Q112722,Q112723)),i(s(fun(Q112722,fun(Q112723,prod(Q112722,Q112723))),c_),s(Q112722,I0))),s(Q112723,J0))))))),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(Q112722,cart(real,M)),f),s(Q112722,I0))))),s(cart(real,N),i(s(fun(Q112723,cart(real,N)),g),s(Q112723,J0))))))))))) -> (all H0 (p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0)))) & p(s(bool,i(s(fun(fun(Q112722,bool),bool),finite),s(fun(Q112722,bool),s0)))) & p(s(bool,i(s(fun(fun(Q112723,bool),bool),finite),s(fun(Q112723,bool),t0)))) -> s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(fun(Q112722,cart(real,M)),cart(real,M)),i(s(fun(fun(Q112722,bool),fun(fun(Q112722,cart(real,M)),cart(real,M))),vsum),s(fun(Q112722,bool),s0))),s(fun(Q112722,cart(real,M)),f))))),s(cart(real,N),i(s(fun(fun(Q112723,cart(real,N)),cart(real,N)),i(s(fun(fun(Q112723,bool),fun(fun(Q112723,cart(real,N)),cart(real,N))),vsum),s(fun(Q112723,bool),t0))),s(fun(Q112723,cart(real,N)),g))))) = s(cart(real,P),i(s(fun(fun(prod(Q112722,Q112723),cart(real,P)),cart(real,P)),i(s(fun(fun(prod(Q112722,Q112723),bool),fun(fun(prod(Q112722,Q112723),cart(real,P)),cart(real,P))),vsum),s(fun(prod(Q112722,Q112723),bool),i(s(fun(fun(Q112723,bool),fun(prod(Q112722,Q112723),bool)),i(s(fun(fun(Q112722,bool),fun(fun(Q112723,bool),fun(prod(Q112722,Q112723),bool))),cross0),s(fun(Q112722,bool),s0))),s(fun(Q112723,bool),t0))))),s(fun(prod(Q112722,Q112723),cart(real,P)),i(s(fun(fun(fun(prod(Q112722,Q112723),cart(real,P)),bool),fun(prod(Q112722,Q112723),cart(real,P))),gabs),s(fun(fun(prod(Q112722,Q112723),cart(real,P)),bool),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(prod(Q112722,Q112723),cart(real,P)),bool)),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))))))))))) # label(aBILINEARu_VSUM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2915 (all N all M all A5 ((exists B0 s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),B0)))) <-> (all Y exists X s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),Y)))) # label(aMATRIXu_RIGHTu_INVERTIBLEu_SURJECTIVE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2916 (all Q105493 all Q105495 all F0 s(cart(real,Q105495),i(s(fun(fun(Q105493,cart(real,Q105495)),cart(real,Q105495)),i(s(fun(fun(Q105493,bool),fun(fun(Q105493,cart(real,Q105495)),cart(real,Q105495))),vsum),s(fun(Q105493,bool),empty))),s(fun(Q105493,cart(real,Q105495)),F0))) = s(cart(real,Q105495),i(s(fun(num,cart(real,Q105495)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aVSUMu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2917 (all N all M all A5 all B0 all I0 all J0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),B0))),s(num,I0))))),s(num,J0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))),s(num,I0))))),s(num,J0)))) # label(aMATRIXu_SUBu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2918 (all Q102146 s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(cart(real,Q102146),real),vectoru_norm),s(cart(real,Q102146),i(s(fun(num,cart(real,Q102146)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aNORMu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2919 (all Q107272 all U_0 ((all F0 all G0 all I0 s(cart(real,Q107272),i(s(fun(cart(real,Q107272),cart(real,Q107272)),i(s(fun(cart(real,Q107272),fun(cart(real,Q107272),cart(real,Q107272))),vectoru_add),s(cart(real,Q107272),i(s(fun(num,cart(real,Q107272)),F0),s(num,I0))))),s(cart(real,Q107272),i(s(fun(num,cart(real,Q107272)),G0),s(num,I0))))) = s(cart(real,Q107272),i(s(fun(num,cart(real,Q107272)),i(s(fun(fun(num,cart(real,Q107272)),fun(num,cart(real,Q107272))),i(s(fun(fun(num,cart(real,Q107272)),fun(fun(num,cart(real,Q107272)),fun(num,cart(real,Q107272)))),U_0),s(fun(num,cart(real,Q107272)),F0))),s(fun(num,cart(real,Q107272)),G0))),s(num,I0)))) -> (all F0 all G0 all M0 all N0 s(cart(real,Q107272),i(s(fun(fun(num,cart(real,Q107272)),cart(real,Q107272)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107272)),cart(real,Q107272))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107272)),i(s(fun(fun(num,cart(real,Q107272)),fun(num,cart(real,Q107272))),i(s(fun(fun(num,cart(real,Q107272)),fun(fun(num,cart(real,Q107272)),fun(num,cart(real,Q107272)))),U_0),s(fun(num,cart(real,Q107272)),F0))),s(fun(num,cart(real,Q107272)),G0))))) = s(cart(real,Q107272),i(s(fun(cart(real,Q107272),cart(real,Q107272)),i(s(fun(cart(real,Q107272),fun(cart(real,Q107272),cart(real,Q107272))),vectoru_add),s(cart(real,Q107272),i(s(fun(fun(num,cart(real,Q107272)),cart(real,Q107272)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107272)),cart(real,Q107272))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107272)),F0))))),s(cart(real,Q107272),i(s(fun(fun(num,cart(real,Q107272)),cart(real,Q107272)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107272)),cart(real,Q107272))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107272)),G0)))))))) # label(aVSUMu_ADDu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2920 (all M all N all F0 all B0 ((all X (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),B0)))) -> s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (all X (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0)))))) -> s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))) # label(aLINEARu_EQu_0u_SPAN) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2921 (all Q119852 all U_0 ((all A5 all X s(cart(real,n10),i(s(fun(cart(real,Q119852),cart(real,n10)),i(s(fun(cart(real,Q119852),fun(cart(real,Q119852),cart(real,n10))),U_0),s(cart(real,Q119852),A5))),s(cart(real,Q119852),X))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(cart(real,Q119852),real),i(s(fun(cart(real,Q119852),fun(cart(real,Q119852),real)),dot),s(cart(real,Q119852),A5))),s(cart(real,Q119852),X)))))) -> (all A5 p(s(bool,i(s(fun(fun(cart(real,Q119852),cart(real,n10)),bool),linear),s(fun(cart(real,Q119852),cart(real,n10)),i(s(fun(cart(real,Q119852),fun(cart(real,Q119852),cart(real,n10))),U_0),s(cart(real,Q119852),A5))))))))) # label(aLINEARu_LIFTu_DOT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2922 (all Q126884 all V all B0 (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126884),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126884),bool),B0))),s(num,i(s(fun(fun(cart(real,Q126884),bool),num),dim),s(fun(cart(real,Q126884),bool),V)))))) & p(s(bool,i(s(fun(fun(cart(real,Q126884),bool),bool),i(s(fun(fun(cart(real,Q126884),bool),fun(fun(cart(real,Q126884),bool),bool)),subset),s(fun(cart(real,Q126884),bool),B0))),s(fun(cart(real,Q126884),bool),V)))) -> s(bool,i(s(fun(fun(cart(real,Q126884),bool),bool),i(s(fun(fun(cart(real,Q126884),bool),fun(fun(cart(real,Q126884),bool),bool)),subset),s(fun(cart(real,Q126884),bool),V))),s(fun(cart(real,Q126884),bool),i(s(fun(fun(cart(real,Q126884),bool),fun(cart(real,Q126884),bool)),span),s(fun(cart(real,Q126884),bool),B0))))) = s(bool,i(s(fun(fun(cart(real,Q126884),bool),bool),independent),s(fun(cart(real,Q126884),bool),B0))))) # label(aCARDu_EQu_DIM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2923 (all M all N all A5 all B0 (s(cart(cart(real,M),N),B0) = s(cart(cart(real,M),N),A5) <-> s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),B0))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),A5))))) # label(aTRANSPu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2924 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,X) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),sqrt),s(real,X)))))))) # label(aSQRTu_WORKS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2925 (all Q106792 all A all S0 all F0 all B0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q106792),real),vectoru_norm),s(cart(real,Q106792),i(s(fun(A,cart(real,Q106792)),F0),s(A,X))))))),s(real,B0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q106792),real),vectoru_norm),s(cart(real,Q106792),i(s(fun(fun(A,cart(real,Q106792)),cart(real,Q106792)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q106792)),cart(real,Q106792))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q106792)),F0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(A,bool),num),card),s(fun(A,bool),S0))))))),s(real,B0)))))))) # label(aVSUMu_NORMu_BOUND) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2926 (all Q105069 all X1 all X2 all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105069),cart(real,Q105069)),real),distance),s(prod(cart(real,Q105069),cart(real,Q105069)),i(s(fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069))),i(s(fun(cart(real,Q105069),fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069)))),c_),s(cart(real,Q105069),Y))),s(cart(real,Q105069),X2))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105069),cart(real,Q105069)),real),distance),s(prod(cart(real,Q105069),cart(real,Q105069)),i(s(fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069))),i(s(fun(cart(real,Q105069),fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069)))),c_),s(cart(real,Q105069),Y))),s(cart(real,Q105069),X1))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105069),cart(real,Q105069)),real),distance),s(prod(cart(real,Q105069),cart(real,Q105069)),i(s(fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069))),i(s(fun(cart(real,Q105069),fun(cart(real,Q105069),prod(cart(real,Q105069),cart(real,Q105069)))),c_),s(cart(real,Q105069),X1))),s(cart(real,Q105069),X2))))))),s(real,e0)))))) # label(aDISTu_TRIANGLEu_HALFu_R) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2927 (all N all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,N0)))) -> s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,N)),F0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),F0),s(num,N0))))) = s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),F0))))) # label(aVSUMu_CLAUSESu_RIGHT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2928 (all M all N all A5 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) -> (exists X (s(cart(real,M),X) != s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))))) # label(aMATRIXu_TRIVIALu_LINEARu_EQUATIONS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2929 (all N all U_0 ((all K0 all GENR_PVARR_344 (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(num,fun(cart(real,N),bool)),U_0),s(num,K0))),s(cart(real,N),GENR_PVARR_344)))) <-> (exists X exists V (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_344))),s(bool,V))),s(cart(real,N),X)))) & (p(s(bool,V)) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,K0)))))))) -> (all K0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(num,fun(cart(real,N),bool)),U_0),s(num,K0))))))))))) # label(aDIMu_SPECIALu_HYPERPLANE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2930 (all N all M all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0)))) & s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))) = s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))) -> (exists F0 (s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),univ))) = s(fun(cart(real,N),bool),S0) & (all X s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))) = s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X)))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))))))) # label(aISOMETRYu_UNIVu_SUBSPACE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2931 (all Q102893 all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q102893),real),vectoru_norm),s(cart(real,Q102893),X))))),s(real,i(s(fun(cart(real,Q102893),real),vectoru_norm),s(cart(real,Q102893),Y))))))),s(real,e0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q102893),real),vectoru_norm),s(cart(real,Q102893),i(s(fun(cart(real,Q102893),cart(real,Q102893)),i(s(fun(cart(real,Q102893),fun(cart(real,Q102893),cart(real,Q102893))),vectoru_add),s(cart(real,Q102893),X))),s(cart(real,Q102893),Y))))))),s(real,e0)))))) # label(aNORMu_TRIANGLEu_LE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2932 (all N all A5 all B0 all C0 (p(s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(cart(real,N),fun(prod(cart(real,N),cart(real,N)),bool)),between),s(cart(real,N),B0))),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),C0))),s(cart(real,N),A5)))))) | p(s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(cart(real,N),fun(prod(cart(real,N),cart(real,N)),bool)),between),s(cart(real,N),C0))),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),B0)))))) | p(s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(cart(real,N),fun(prod(cart(real,N),cart(real,N)),bool)),between),s(cart(real,N),A5))),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),B0))),s(cart(real,N),C0)))))) <-> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),C0))),s(fun(cart(real,N),bool),empty)))))))))))) # label(aCOLLINEARu_BETWEENu_CASES) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2933 (all Q109287 all Q109292 all F0 all P0 all S0 (p(s(bool,i(s(fun(fun(Q109287,bool),bool),finite),s(fun(Q109287,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(Q109287,bool),bool),i(s(fun(Q109287,fun(fun(Q109287,bool),bool)),in),s(Q109287,X))),s(fun(Q109287,bool),S0)))) -> p(s(bool,i(s(fun(fun(Q109287,bool),bool),i(s(fun(Q109287,fun(fun(Q109287,bool),bool)),in),s(Q109287,i(s(fun(Q109287,Q109287),P0),s(Q109287,X))))),s(fun(Q109287,bool),S0)))))) & (all X all Y (p(s(bool,i(s(fun(fun(Q109287,bool),bool),i(s(fun(Q109287,fun(fun(Q109287,bool),bool)),in),s(Q109287,Y))),s(fun(Q109287,bool),S0)))) & s(Q109287,i(s(fun(Q109287,Q109287),P0),s(Q109287,X))) = s(Q109287,i(s(fun(Q109287,Q109287),P0),s(Q109287,Y))) & p(s(bool,i(s(fun(fun(Q109287,bool),bool),i(s(fun(Q109287,fun(fun(Q109287,bool),bool)),in),s(Q109287,X))),s(fun(Q109287,bool),S0)))) -> s(Q109287,Y) = s(Q109287,X))) -> s(cart(real,Q109292),i(s(fun(fun(Q109287,cart(real,Q109292)),cart(real,Q109292)),i(s(fun(fun(Q109287,bool),fun(fun(Q109287,cart(real,Q109292)),cart(real,Q109292))),vsum),s(fun(Q109287,bool),S0))),s(fun(Q109287,cart(real,Q109292)),F0))) = s(cart(real,Q109292),i(s(fun(fun(Q109287,cart(real,Q109292)),cart(real,Q109292)),i(s(fun(fun(Q109287,bool),fun(fun(Q109287,cart(real,Q109292)),cart(real,Q109292))),vsum),s(fun(Q109287,bool),S0))),s(fun(Q109287,cart(real,Q109292)),i(s(fun(fun(Q109287,Q109287),fun(Q109287,cart(real,Q109292))),i(s(fun(fun(Q109287,cart(real,Q109292)),fun(fun(Q109287,Q109287),fun(Q109287,cart(real,Q109292)))),o),s(fun(Q109287,cart(real,Q109292)),F0))),s(fun(Q109287,Q109287),P0))))))) # label(aVSUMu_INJECTION) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2934 (all Q106879 all M0 all N0 s(cart(real,Q106879),i(s(fun(fun(num,cart(real,Q106879)),cart(real,Q106879)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106879)),cart(real,Q106879))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(fun(num,cart(real,Q106879)),f))) = s(cart(real,Q106879),i(s(fun(cart(real,Q106879),cart(real,Q106879)),i(s(fun(cart(real,Q106879),fun(cart(real,Q106879),cart(real,Q106879))),i(s(fun(bool,fun(cart(real,Q106879),fun(cart(real,Q106879),cart(real,Q106879)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),suc),s(num,N0))))))),s(cart(real,Q106879),i(s(fun(cart(real,Q106879),cart(real,Q106879)),i(s(fun(cart(real,Q106879),fun(cart(real,Q106879),cart(real,Q106879))),vectoru_add),s(cart(real,Q106879),i(s(fun(fun(num,cart(real,Q106879)),cart(real,Q106879)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106879)),cart(real,Q106879))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q106879)),f))))),s(cart(real,Q106879),i(s(fun(num,cart(real,Q106879)),f),s(num,i(s(fun(num,num),suc),s(num,N0))))))))),s(cart(real,Q106879),i(s(fun(fun(num,cart(real,Q106879)),cart(real,Q106879)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106879)),cart(real,Q106879))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q106879)),f)))))) # label(aVSUMu_CLAUSESu_NUMSEGu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2935 (all X all Y s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),fun(cart(real,n10),cart(real,n10))),vectoru_add),s(cart(real,n10),X))),s(cart(real,n10),Y))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),Y)))))) # label(aDROPu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2936 (all Q111055 all A5 all X all Y (p(s(bool,i(s(fun(cart(real,Q111055),bool),i(s(fun(cart(real,Q111055),fun(cart(real,Q111055),bool)),orthogonal),s(cart(real,Q111055),A5))),s(cart(real,Q111055),X)))) & p(s(bool,i(s(fun(cart(real,Q111055),bool),i(s(fun(cart(real,Q111055),fun(cart(real,Q111055),bool)),orthogonal),s(cart(real,Q111055),A5))),s(cart(real,Q111055),Y)))) -> p(s(bool,i(s(fun(cart(real,Q111055),bool),i(s(fun(cart(real,Q111055),fun(cart(real,Q111055),bool)),orthogonal),s(cart(real,Q111055),A5))),s(cart(real,Q111055),i(s(fun(cart(real,Q111055),cart(real,Q111055)),i(s(fun(cart(real,Q111055),fun(cart(real,Q111055),cart(real,Q111055))),vectoru_sub),s(cart(real,Q111055),X))),s(cart(real,Q111055),Y)))))))) # label(aORTHOGONALu_CLAUSESu_conjunct4) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2937 (all Q100472 all X s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(cart(real,Q100472),real),i(s(fun(cart(real,Q100472),fun(cart(real,Q100472),real)),dot),s(cart(real,Q100472),X))),s(cart(real,Q100472),i(s(fun(num,cart(real,Q100472)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aDOTu_RZERO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2938 (all N all X all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))),s(cart(real,N),X))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))) & s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))) # label(aDOTu_BASIS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2939 (all A all Q105605 all F0 all S0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(cart(real,Q105605),i(s(fun(A,cart(real,Q105605)),F0),s(A,X))) = s(cart(real,Q105605),i(s(fun(num,cart(real,Q105605)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) -> s(cart(real,Q105605),i(s(fun(fun(A,cart(real,Q105605)),cart(real,Q105605)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q105605)),cart(real,Q105605))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q105605)),F0))) = s(cart(real,Q105605),i(s(fun(num,cart(real,Q105605)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aVSUMu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2940 (all Q121453 (p(s(bool,i(s(fun(fun(cart(real,Q121453),bool),bool),subspace),s(fun(cart(real,Q121453),bool),s0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121453),bool),bool),i(s(fun(cart(real,Q121453),fun(fun(cart(real,Q121453),bool),bool)),in),s(cart(real,Q121453),i(s(fun(num,cart(real,Q121453)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121453),bool),s0)))))) # label(aSUBSPACEu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2941 (all N all A5 all B0 all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),X))),s(cart(real,N),B0))))))),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),B0)))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),X))),s(cart(real,N),A5))))))),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),B0)))))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),empty)))))))))) <-> p(s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(cart(real,N),fun(prod(cart(real,N),cart(real,N)),bool)),between),s(cart(real,N),X))),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),B0)))))))) # label(aBETWEENu_COLLINEARu_DISTu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2942 (all M all N all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,M)),fun(cart(real,M),cart(real,N))),adjoint),s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))))) = s(fun(cart(real,M),cart(real,N)),F0))) # label(aADJOINTu_ADJOINT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2943 (all Q110968 all A5 all X all C0 (p(s(bool,i(s(fun(cart(real,Q110968),bool),i(s(fun(cart(real,Q110968),fun(cart(real,Q110968),bool)),orthogonal),s(cart(real,Q110968),X))),s(cart(real,Q110968),A5)))) -> p(s(bool,i(s(fun(cart(real,Q110968),bool),i(s(fun(cart(real,Q110968),fun(cart(real,Q110968),bool)),orthogonal),s(cart(real,Q110968),i(s(fun(cart(real,Q110968),cart(real,Q110968)),i(s(fun(real,fun(cart(real,Q110968),cart(real,Q110968))),r_),s(real,C0))),s(cart(real,Q110968),X))))),s(cart(real,Q110968),A5)))))) # label(aORTHOGONALu_CLAUSESu_conjunct6) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2944 (all N all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),T0)))) -> (exists TI_ (p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),TI_))),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),T0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),TI_)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),TI_))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),TI_)))))))) # label(aEXCHANGEu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2945 (all M all N all U_0 ((all C0 all A5 all I0 s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,i(s(fun(num,real),C0),s(num,I0))))),s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),A5))))) = s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(fun(num,real),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(fun(num,real),C0))),s(cart(cart(real,N),M),A5))),s(num,I0)))) -> (all A5 ((all C0 (s(cart(real,M),i(s(fun(fun(num,cart(real,M)),cart(real,M)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,M)),cart(real,M))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(fun(num,real),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(fun(num,real),C0))),s(cart(cart(real,N),M),A5))))) = s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> s(real,i(s(fun(num,real),C0),s(num,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) <-> (exists B0 s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),B0))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aMATRIXu_LEFTu_INVERTIBLEu_INDEPENDENTu_COLUMNS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2946 (all Q108537 all Q108528 all U_0 ((all F0 all Y all X s(real,i(s(fun(Q108537,real),i(s(fun(cart(real,Q108528),fun(Q108537,real)),i(s(fun(fun(Q108537,cart(real,Q108528)),fun(cart(real,Q108528),fun(Q108537,real))),U_0),s(fun(Q108537,cart(real,Q108528)),F0))),s(cart(real,Q108528),Y))),s(Q108537,X))) = s(real,i(s(fun(cart(real,Q108528),real),i(s(fun(cart(real,Q108528),fun(cart(real,Q108528),real)),dot),s(cart(real,Q108528),i(s(fun(Q108537,cart(real,Q108528)),F0),s(Q108537,X))))),s(cart(real,Q108528),Y)))) -> (all S0 all F0 all Y (p(s(bool,i(s(fun(fun(Q108537,bool),bool),finite),s(fun(Q108537,bool),S0)))) -> s(real,i(s(fun(fun(Q108537,real),real),i(s(fun(fun(Q108537,bool),fun(fun(Q108537,real),real)),sum),s(fun(Q108537,bool),S0))),s(fun(Q108537,real),i(s(fun(cart(real,Q108528),fun(Q108537,real)),i(s(fun(fun(Q108537,cart(real,Q108528)),fun(cart(real,Q108528),fun(Q108537,real))),U_0),s(fun(Q108537,cart(real,Q108528)),F0))),s(cart(real,Q108528),Y))))) = s(real,i(s(fun(cart(real,Q108528),real),i(s(fun(cart(real,Q108528),fun(cart(real,Q108528),real)),dot),s(cart(real,Q108528),i(s(fun(fun(Q108537,cart(real,Q108528)),cart(real,Q108528)),i(s(fun(fun(Q108537,bool),fun(fun(Q108537,cart(real,Q108528)),cart(real,Q108528))),vsum),s(fun(Q108537,bool),S0))),s(fun(Q108537,cart(real,Q108528)),F0))))),s(cart(real,Q108528),Y))))))) # label(aDOTu_LSUM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2947 (all Q117867 s(cart(cart(real,Q117867),Q117867),i(s(fun(fun(cart(real,Q117867),cart(real,Q117867)),cart(cart(real,Q117867),Q117867)),matrix),s(fun(cart(real,Q117867),cart(real,Q117867)),i1))) = s(cart(cart(real,Q117867),Q117867),i(s(fun(num,cart(cart(real,Q117867),Q117867)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) # label(aMATRIXu_I) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2948 (all Q114603 all Q114604 all A5 s(cart(cart(real,Q114603),Q114604),i(s(fun(cart(cart(real,Q114603),Q114604),cart(cart(real,Q114603),Q114604)),i(s(fun(cart(cart(real,Q114603),Q114604),fun(cart(cart(real,Q114603),Q114604),cart(cart(real,Q114603),Q114604))),matrixu_add),s(cart(cart(real,Q114603),Q114604),i(s(fun(num,cart(cart(real,Q114603),Q114604)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,Q114603),Q114604),A5))) = s(cart(cart(real,Q114603),Q114604),A5)) # label(aMATRIXu_ADDu_LID) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2949 (all Q112458 all Q112457 all Q112444 all H0 all X all Y (p(s(bool,i(s(fun(fun(cart(real,Q112457),fun(cart(real,Q112444),cart(real,Q112458))),bool),bilinear),s(fun(cart(real,Q112457),fun(cart(real,Q112444),cart(real,Q112458))),H0)))) -> s(cart(real,Q112458),i(s(fun(cart(real,Q112458),cart(real,Q112458)),vectoru_neg),s(cart(real,Q112458),i(s(fun(cart(real,Q112444),cart(real,Q112458)),i(s(fun(cart(real,Q112457),fun(cart(real,Q112444),cart(real,Q112458))),H0),s(cart(real,Q112457),X))),s(cart(real,Q112444),Y))))) = s(cart(real,Q112458),i(s(fun(cart(real,Q112444),cart(real,Q112458)),i(s(fun(cart(real,Q112457),fun(cart(real,Q112444),cart(real,Q112458))),H0),s(cart(real,Q112457),i(s(fun(cart(real,Q112457),cart(real,Q112457)),vectoru_neg),s(cart(real,Q112457),X))))),s(cart(real,Q112444),Y))))) # label(aBILINEARu_LNEG) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2950 (all N all M all A5 ((exists B0 s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),B0))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) <-> (exists B0 s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),B0)))))) # label(aLEFTu_INVERTIBLEu_TRANSP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2951 (all Q139102 all X s(real,i(s(fun(cart(real,Q139102),real),infnorm),s(cart(real,Q139102),X))) = s(real,i(s(fun(cart(real,Q139102),real),infnorm),s(cart(real,Q139102),i(s(fun(cart(real,Q139102),cart(real,Q139102)),vectoru_neg),s(cart(real,Q139102),X)))))) # label(aINFNORMu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2952 (all Q119749 all F0 all S0 (p(s(bool,i(s(fun(fun(Q119749,bool),bool),finite),s(fun(Q119749,bool),S0)))) -> s(cart(real,n10),i(s(fun(fun(Q119749,cart(real,n10)),cart(real,n10)),i(s(fun(fun(Q119749,bool),fun(fun(Q119749,cart(real,n10)),cart(real,n10))),vsum),s(fun(Q119749,bool),S0))),s(fun(Q119749,cart(real,n10)),F0))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(fun(Q119749,real),real),i(s(fun(fun(Q119749,bool),fun(fun(Q119749,real),real)),sum),s(fun(Q119749,bool),S0))),s(fun(Q119749,real),i(s(fun(fun(Q119749,cart(real,n10)),fun(Q119749,real)),i(s(fun(fun(cart(real,n10),real),fun(fun(Q119749,cart(real,n10)),fun(Q119749,real))),o),s(fun(cart(real,n10),real),drop))),s(fun(Q119749,cart(real,n10)),F0))))))))) # label(aVSUMu_REAL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2953 (all Q100457 all X s(real,i(s(fun(cart(real,Q100457),real),i(s(fun(cart(real,Q100457),fun(cart(real,Q100457),real)),dot),s(cart(real,Q100457),i(s(fun(num,cart(real,Q100457)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q100457),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aDOTu_LZERO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2954 (all N p(s(bool,i(s(fun(fun(cart(real,N),fun(cart(real,N),cart(real,N))),bool),monoidal),s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add))))) # label(aMONOIDALu_VECTORu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2955 (all Q110616 all X all Y (s(cart(real,Q110616),X) = s(cart(real,Q110616),Y) <-> (all Z0 s(real,i(s(fun(cart(real,Q110616),real),i(s(fun(cart(real,Q110616),fun(cart(real,Q110616),real)),dot),s(cart(real,Q110616),Y))),s(cart(real,Q110616),Z0))) = s(real,i(s(fun(cart(real,Q110616),real),i(s(fun(cart(real,Q110616),fun(cart(real,Q110616),real)),dot),s(cart(real,Q110616),X))),s(cart(real,Q110616),Z0)))))) # label(aVECTORu_EQu_RDOT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2956 (all N all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))))))) # label(aNORMu_CAUCHYu_SCHWARZ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2957 (all A s(A,i(s(fun(num,A),i(s(fun(cart(A,n20),fun(num,A)),d_),s(cart(A,n20),i(s(fun(list(A),cart(A,n20)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,y))),s(list(A),nil))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(A,x)) # label(aVECTORu_2u_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2958 (all N all X all E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,E0)))) -> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))))),s(real,E0)))))))) # label(aNORMu_BOUNDu_COMPONENTu_LE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2959 (all Q122111 all X all Y all S0 (p(s(bool,i(s(fun(fun(cart(real,Q122111),bool),bool),i(s(fun(cart(real,Q122111),fun(fun(cart(real,Q122111),bool),bool)),in),s(cart(real,Q122111),X))),s(fun(cart(real,Q122111),bool),i(s(fun(fun(cart(real,Q122111),bool),fun(cart(real,Q122111),bool)),span),s(fun(cart(real,Q122111),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q122111),bool),bool),i(s(fun(cart(real,Q122111),fun(fun(cart(real,Q122111),bool),bool)),in),s(cart(real,Q122111),Y))),s(fun(cart(real,Q122111),bool),i(s(fun(fun(cart(real,Q122111),bool),fun(cart(real,Q122111),bool)),span),s(fun(cart(real,Q122111),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,Q122111),bool),bool),i(s(fun(cart(real,Q122111),fun(fun(cart(real,Q122111),bool),bool)),in),s(cart(real,Q122111),i(s(fun(cart(real,Q122111),cart(real,Q122111)),i(s(fun(cart(real,Q122111),fun(cart(real,Q122111),cart(real,Q122111))),vectoru_add),s(cart(real,Q122111),X))),s(cart(real,Q122111),Y))))),s(fun(cart(real,Q122111),bool),i(s(fun(fun(cart(real,Q122111),bool),fun(cart(real,Q122111),bool)),span),s(fun(cart(real,Q122111),bool),S0)))))))) # label(aSPANu_CLAUSESu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2960 (all M all N all A5 all X all K0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) -> s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,K0))))),s(cart(real,N),X))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),d_),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))))),s(num,K0))))) # label(aMATRIXu_VECTORu_MULu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2961 (all M all N all U_1 ((all I0 all K0 all J0 exists V ((s(num,I0) = s(num,J0) <-> p(s(bool,V))) & s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(num,fun(num,fun(num,real))),U_1),s(num,I0))),s(num,K0))),s(num,J0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,K0))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) -> (all U_0 ((all K0 all I0 s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(num,fun(num,fun(num,real))),U_1),s(num,I0))),s(num,K0))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(num,fun(num,cart(real,N))),U_0),s(num,K0))),s(num,I0)))) -> (all K0 s(cart(cart(real,N),M),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),M)),lambda),s(fun(num,cart(real,N)),i(s(fun(num,fun(num,cart(real,N))),U_0),s(num,K0))))) = s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,K0)))))))) # label(amat) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2962 (all N all B0 all S0 all A5 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),B0))),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) -> (exists K0 p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),A5))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,K0))),s(cart(real,N),B0))))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),fun(cart(real,N),bool))),delete),s(fun(cart(real,N),bool),S0))),s(cart(real,N),B0))))))))))) # label(aSPANu_BREAKDOWN) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2963 (all Q100487 all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q100487),real),i(s(fun(cart(real,Q100487),fun(cart(real,Q100487),real)),dot),s(cart(real,Q100487),X))),s(cart(real,Q100487),X))))))) # label(aDOTu_POSu_LE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2964 (all N s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),n))),s(cart(real,N),m))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),m))),s(cart(real,N),n)))) # label(aVECTORu_ADDu_ACu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2965 (all Q110060 s(real,i(s(fun(cart(real,Q110060),real),vectoru_norm),s(cart(real,Q110060),i(s(fun(num,cart(real,Q110060)),basis),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) # label(aNORMu_BASISu_1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2966 (all N all K0 all I0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,K0))))),s(num,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,K0)))) # label(aVECu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2967 (all N all M s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),a))),s(cart(cart(real,N),M),b))))),s(cart(cart(real,N),M),c0))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),a))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),b))),s(cart(cart(real,N),M),c0)))))) # label(aMATRIXu_ADDu_ACu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2968 (all M all N all X1 all Y1 all X2 all Y2 s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_add),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X1))),s(cart(real,N),Y1))))),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X2))),s(cart(real,N),Y2))))) = s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_add),s(cart(real,M),X1))),s(cart(real,M),X2))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),Y1))),s(cart(real,N),Y2)))))) # label(aPASTECARTu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2969 (all N all U_0 ((all U all V s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V))))),s(cart(real,N),V))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),U))),s(cart(real,N),V)))) -> (all P0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),P0)))) <-> (exists S0 exists U (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),P0)))) & (exists V (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),V))),s(fun(cart(real,N),bool),S0)))) & s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V))))) & s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(real,N)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),cart(real,N)),cart(real,N))),vsum),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),U))))))))))) # label(aDEPENDENTu_EXPLICIT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2970 (all N all U_0 ((all GENR_PVARR_308 (p(s(bool,i(s(fun(cart(real,N),bool),U_0),s(cart(real,N),GENR_PVARR_308)))) <-> (exists I0 exists V ((p(s(bool,V)) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))) & p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_308))),s(bool,V))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))))))) -> s(fun(cart(real,N),bool),univ) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),U_0))))))) # label(aSPANu_STDBASIS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2971 (all Q111056 all A5 all X (p(s(bool,i(s(fun(cart(real,Q111056),bool),i(s(fun(cart(real,Q111056),fun(cart(real,Q111056),bool)),orthogonal),s(cart(real,Q111056),X))),s(cart(real,Q111056),A5)))) -> p(s(bool,i(s(fun(cart(real,Q111056),bool),i(s(fun(cart(real,Q111056),fun(cart(real,Q111056),bool)),orthogonal),s(cart(real,Q111056),i(s(fun(cart(real,Q111056),cart(real,Q111056)),vectoru_neg),s(cart(real,Q111056),X))))),s(cart(real,Q111056),A5)))))) # label(aORTHOGONALu_CLAUSESu_conjunct7) # label(axiom) # label(non_clause). [assumption]. 15.81/15.84 2972 (all N all M all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) -> (exists F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & (all X s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))) = s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),univ)))))))))) # label(aISOMETRYu_UNIVu_SUPERSETu_SUBSPACE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2973 (all Q118333 all Q118355 all F0 (p(s(bool,i(s(fun(fun(cart(real,Q118333),cart(real,Q118355)),bool),linear),s(fun(cart(real,Q118333),cart(real,Q118355)),F0)))) -> (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(fun(cart(real,Q118333),cart(real,Q118355)),real),onorm),s(fun(cart(real,Q118333),cart(real,Q118355)),F0)))))) <-> -(all X s(cart(real,Q118355),i(s(fun(cart(real,Q118333),cart(real,Q118355)),F0),s(cart(real,Q118333),X))) = s(cart(real,Q118355),i(s(fun(num,cart(real,Q118355)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) # label(aONORMu_POSu_LT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2974 (all X all E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) -> (exists D0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D0)))) & (all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X))))))),s(real,D0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,Y))),s(real,Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,X))))))))),s(real,E0)))))))))) # label(aSQUAREu_CONTINUOUS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2975 (all N all X all S0 ((all I0 (-p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,I0))),s(fun(num,bool),S0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))) <-> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(num,bool),fun(cart(real,N),bool)),i(s(fun(fun(num,cart(real,N)),fun(fun(num,bool),fun(cart(real,N),bool))),image),s(fun(num,cart(real,N)),basis))),s(fun(num,bool),S0)))))))))) # label(aINu_SPANu_IMAGEu_BASIS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2976 (all Q121420 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q121420),bool),bool),dependent),s(fun(cart(real,Q121420),bool),S0)))) <-> (exists A5 (p(s(bool,i(s(fun(fun(cart(real,Q121420),bool),bool),i(s(fun(cart(real,Q121420),fun(fun(cart(real,Q121420),bool),bool)),in),s(cart(real,Q121420),A5))),s(fun(cart(real,Q121420),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q121420),bool),bool),i(s(fun(cart(real,Q121420),fun(fun(cart(real,Q121420),bool),bool)),in),s(cart(real,Q121420),A5))),s(fun(cart(real,Q121420),bool),i(s(fun(fun(cart(real,Q121420),bool),fun(cart(real,Q121420),bool)),span),s(fun(cart(real,Q121420),bool),i(s(fun(cart(real,Q121420),fun(cart(real,Q121420),bool)),i(s(fun(fun(cart(real,Q121420),bool),fun(cart(real,Q121420),fun(cart(real,Q121420),bool))),delete),s(fun(cart(real,Q121420),bool),S0))),s(cart(real,Q121420),A5)))))))))))) # label(adependent) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2977 (all N s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),univ))) = s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))) # label(aDIMu_UNIV) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2978 (all N all M all U_1 ((all GENR_PVARR_331 (p(s(bool,i(s(fun(cart(real,M),bool),U_1),s(cart(real,M),GENR_PVARR_331)))) <-> (exists I0 exists V (p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(bool,fun(cart(real,M),bool)),i(s(fun(cart(real,M),fun(bool,fun(cart(real,M),bool))),setspec),s(cart(real,M),GENR_PVARR_331))),s(bool,V))),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0)))))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))))))) -> (all U_0 ((all A5 all X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),U_0),s(cart(cart(real,M),N),A5))),s(cart(real,M),X)))) -> (all A5 s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),U_0),s(cart(cart(real,M),N),A5))))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),gspec),s(fun(cart(real,M),bool),U_1))))) = s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,N),bool)),columns),s(cart(cart(real,M),N),A5)))))))) # label(aCOLUMNSu_IMAGEu_BASIS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2979 (all N all B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0)))) -> (exists C0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),C0)))) & s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),C0))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),C0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),C0)))))))) # label(aBASISu_ORTHOGONAL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2980 (all Q104912 all X all Y all Z0 all E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,Q104912),cart(real,Q104912)),real),distance),s(prod(cart(real,Q104912),cart(real,Q104912)),i(s(fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912))),i(s(fun(cart(real,Q104912),fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912)))),c_),s(cart(real,Q104912),X))),s(cart(real,Q104912),Z0))))))),s(real,i(s(fun(prod(cart(real,Q104912),cart(real,Q104912)),real),distance),s(prod(cart(real,Q104912),cart(real,Q104912)),i(s(fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912))),i(s(fun(cart(real,Q104912),fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912)))),c_),s(cart(real,Q104912),Y))),s(cart(real,Q104912),Z0))))))))),s(real,E0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q104912),cart(real,Q104912)),real),distance),s(prod(cart(real,Q104912),cart(real,Q104912)),i(s(fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912))),i(s(fun(cart(real,Q104912),fun(cart(real,Q104912),prod(cart(real,Q104912),cart(real,Q104912)))),c_),s(cart(real,Q104912),X))),s(cart(real,Q104912),Y))))))),s(real,E0)))))) # label(aDISTu_TRIANGLEu_LE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2981 (all A ((all X p(s(bool,i(s(fun(cart(A,n10),bool),p0),s(cart(A,n10),i(s(fun(list(A),cart(A,n10)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),nil))))))))) <-> (all V p(s(bool,i(s(fun(cart(A,n10),bool),p0),s(cart(A,n10),V))))))) # label(aFORALLu_VECTORu_1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2982 (all Q110633 all X all Y (p(s(bool,i(s(fun(cart(real,Q110633),bool),i(s(fun(cart(real,Q110633),fun(cart(real,Q110633),bool)),orthogonal),s(cart(real,Q110633),X))),s(cart(real,Q110633),Y)))) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(cart(real,Q110633),real),i(s(fun(cart(real,Q110633),fun(cart(real,Q110633),real)),dot),s(cart(real,Q110633),X))),s(cart(real,Q110633),Y))))) # label(aorthogonal) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2983 (all N all A5 all B0 all C0 (s(cart(real,N),i(s(fun(prod(cart(real,N),cart(real,N)),cart(real,N)),midpoint),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),C0))))) = s(cart(real,N),B0) <-> p(s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(cart(real,N),fun(prod(cart(real,N),cart(real,N)),bool)),between),s(cart(real,N),B0))),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),C0)))))) & s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),B0))),s(cart(real,N),C0))))) = s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),B0))))))) # label(aMIDPOINTu_BETWEEN) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2984 (all N all M all A5 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,N),M),A5)) # label(aTRANSPu_TRANSP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2985 (all Q120474 all Q120471 all Q120473 all U_0 ((all X all I0 s(cart(real,Q120473),i(s(fun(cart(real,finite_sum(Q120471,Q120473)),cart(real,Q120473)),sndcart),s(cart(real,finite_sum(Q120471,Q120473)),i(s(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),X),s(Q120474,I0))))) = s(cart(real,Q120473),i(s(fun(Q120474,cart(real,Q120473)),i(s(fun(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),fun(Q120474,cart(real,Q120473))),U_0),s(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),X))),s(Q120474,I0)))) -> (all K0 all X (p(s(bool,i(s(fun(fun(Q120474,bool),bool),finite),s(fun(Q120474,bool),K0)))) -> s(cart(real,Q120473),i(s(fun(cart(real,finite_sum(Q120471,Q120473)),cart(real,Q120473)),sndcart),s(cart(real,finite_sum(Q120471,Q120473)),i(s(fun(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),cart(real,finite_sum(Q120471,Q120473))),i(s(fun(fun(Q120474,bool),fun(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),cart(real,finite_sum(Q120471,Q120473)))),vsum),s(fun(Q120474,bool),K0))),s(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),X))))) = s(cart(real,Q120473),i(s(fun(fun(Q120474,cart(real,Q120473)),cart(real,Q120473)),i(s(fun(fun(Q120474,bool),fun(fun(Q120474,cart(real,Q120473)),cart(real,Q120473))),vsum),s(fun(Q120474,bool),K0))),s(fun(Q120474,cart(real,Q120473)),i(s(fun(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),fun(Q120474,cart(real,Q120473))),U_0),s(fun(Q120474,cart(real,finite_sum(Q120471,Q120473))),X))))))))) # label(aSNDCARTu_VSUM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2986 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y))))) # label(aSQRTu_MONOu_LTu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2987 (all N all Q116015 all X s(cart(real,Q116015),i(s(fun(num,cart(real,Q116015)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q116015),i(s(fun(cart(real,N),cart(real,Q116015)),i(s(fun(cart(cart(real,N),Q116015),fun(cart(real,N),cart(real,Q116015))),matrixu_vectoru_mul),s(cart(cart(real,N),Q116015),i(s(fun(num,cart(cart(real,N),Q116015)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,N),X)))) # label(aMATRIXu_VECTORu_MULu_LZERO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2988 (all M all P all N all U_2 ((all A5 all I0 all B0 all J0 all K0 s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,P),N),fun(num,fun(num,real))),i(s(fun(num,fun(cart(cart(real,P),N),fun(num,fun(num,real)))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(cart(real,P),N),fun(num,fun(num,real))))),U_2),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(cart(real,P),N),B0))),s(num,J0))),s(num,K0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,K0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,P),fun(num,real)),d_),s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(cart(cart(real,P),N),fun(num,cart(real,P))),d_),s(cart(cart(real,P),N),B0))),s(num,K0))))),s(num,J0)))))) -> (all U_1 ((all A5 all I0 all B0 all J0 s(real,i(s(fun(num,real),i(s(fun(cart(cart(real,P),N),fun(num,real)),i(s(fun(num,fun(cart(cart(real,P),N),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(cart(real,P),N),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(cart(real,P),N),B0))),s(num,J0))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,P),N),fun(num,fun(num,real))),i(s(fun(num,fun(cart(cart(real,P),N),fun(num,fun(num,real)))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(cart(real,P),N),fun(num,fun(num,real))))),U_2),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(cart(real,P),N),B0))),s(num,J0)))))) -> (all U_0 ((all A5 all B0 all I0 s(cart(real,P),i(s(fun(fun(num,real),cart(real,P)),lambda),s(fun(num,real),i(s(fun(cart(cart(real,P),N),fun(num,real)),i(s(fun(num,fun(cart(cart(real,P),N),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(cart(real,P),N),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,I0))),s(cart(cart(real,P),N),B0))))) = s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(cart(cart(real,P),N),fun(num,cart(real,P))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),fun(num,cart(real,P)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))),s(num,I0)))) -> (all A5 all B0 s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))) = s(cart(cart(real,P),M),i(s(fun(fun(num,cart(real,P)),cart(cart(real,P),M)),lambda),s(fun(num,cart(real,P)),i(s(fun(cart(cart(real,P),N),fun(num,cart(real,P))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),fun(num,cart(real,P)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0)))))))))))) # label(amatrixu_mul) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2989 (all M all N all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (all X all Y s(real,i(s(fun(cart(real,M),real),i(s(fun(cart(real,M),fun(cart(real,M),real)),dot),s(cart(real,M),X))),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,N),Y))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),Y)))))) # label(aADJOINTu_WORKS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2990 (all Q141313 all A5 all B0 (p(s(bool,i(s(fun(prod(cart(real,Q141313),cart(real,Q141313)),bool),i(s(fun(cart(real,Q141313),fun(prod(cart(real,Q141313),cart(real,Q141313)),bool)),between),s(cart(real,Q141313),A5))),s(prod(cart(real,Q141313),cart(real,Q141313)),i(s(fun(cart(real,Q141313),prod(cart(real,Q141313),cart(real,Q141313))),i(s(fun(cart(real,Q141313),fun(cart(real,Q141313),prod(cart(real,Q141313),cart(real,Q141313)))),c_),s(cart(real,Q141313),A5))),s(cart(real,Q141313),B0)))))) & p(s(bool,i(s(fun(prod(cart(real,Q141313),cart(real,Q141313)),bool),i(s(fun(cart(real,Q141313),fun(prod(cart(real,Q141313),cart(real,Q141313)),bool)),between),s(cart(real,Q141313),B0))),s(prod(cart(real,Q141313),cart(real,Q141313)),i(s(fun(cart(real,Q141313),prod(cart(real,Q141313),cart(real,Q141313))),i(s(fun(cart(real,Q141313),fun(cart(real,Q141313),prod(cart(real,Q141313),cart(real,Q141313)))),c_),s(cart(real,Q141313),A5))),s(cart(real,Q141313),B0)))))) & p(s(bool,i(s(fun(prod(cart(real,Q141313),cart(real,Q141313)),bool),i(s(fun(cart(real,Q141313),fun(prod(cart(real,Q141313),cart(real,Q141313)),bool)),between),s(cart(real,Q141313),A5))),s(prod(cart(real,Q141313),cart(real,Q141313)),i(s(fun(cart(real,Q141313),prod(cart(real,Q141313),cart(real,Q141313))),i(s(fun(cart(real,Q141313),fun(cart(real,Q141313),prod(cart(real,Q141313),cart(real,Q141313)))),c_),s(cart(real,Q141313),A5))),s(cart(real,Q141313),A5)))))))) # label(aBETWEENu_REFL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2991 (all A all B all N all S0 all T0 all F0 all G0 all H0 all K0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))) = s(cart(real,N),i(s(fun(B,cart(real,N)),G0),s(B,i(s(fun(A,B),H0),s(A,X))))) & s(A,X) = s(A,i(s(fun(B,A),K0),s(B,i(s(fun(A,B),H0),s(A,X))))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),H0),s(A,X))))),s(fun(B,bool),T0)))))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(B,A),K0),s(B,Y))))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),H0),s(A,i(s(fun(B,A),K0),s(B,Y))))) = s(B,Y))) -> s(cart(real,N),i(s(fun(fun(B,cart(real,N)),cart(real,N)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,N)),cart(real,N))),vsum),s(fun(B,bool),T0))),s(fun(B,cart(real,N)),G0))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))) # label(aVSUMu_EQu_GENERALu_INVERSES) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2992 (all Q140276 all X all Y all Z0 s(bool,i(s(fun(fun(cart(real,Q140276),bool),bool),collinear),s(fun(cart(real,Q140276),bool),i(s(fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool)),i(s(fun(cart(real,Q140276),fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool))),insert),s(cart(real,Q140276),i(s(fun(num,cart(real,Q140276)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q140276),bool),i(s(fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool)),i(s(fun(cart(real,Q140276),fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool))),insert),s(cart(real,Q140276),i(s(fun(cart(real,Q140276),cart(real,Q140276)),i(s(fun(cart(real,Q140276),fun(cart(real,Q140276),cart(real,Q140276))),vectoru_sub),s(cart(real,Q140276),X))),s(cart(real,Q140276),Y))))),s(fun(cart(real,Q140276),bool),i(s(fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool)),i(s(fun(cart(real,Q140276),fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool))),insert),s(cart(real,Q140276),i(s(fun(cart(real,Q140276),cart(real,Q140276)),i(s(fun(cart(real,Q140276),fun(cart(real,Q140276),cart(real,Q140276))),vectoru_sub),s(cart(real,Q140276),Z0))),s(cart(real,Q140276),Y))))),s(fun(cart(real,Q140276),bool),empty))))))))) = s(bool,i(s(fun(fun(cart(real,Q140276),bool),bool),collinear),s(fun(cart(real,Q140276),bool),i(s(fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool)),i(s(fun(cart(real,Q140276),fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool))),insert),s(cart(real,Q140276),X))),s(fun(cart(real,Q140276),bool),i(s(fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool)),i(s(fun(cart(real,Q140276),fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool))),insert),s(cart(real,Q140276),Y))),s(fun(cart(real,Q140276),bool),i(s(fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool)),i(s(fun(cart(real,Q140276),fun(fun(cart(real,Q140276),bool),fun(cart(real,Q140276),bool))),insert),s(cart(real,Q140276),Z0))),s(fun(cart(real,Q140276),bool),empty)))))))))) # label(aCOLLINEARu_3) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2993 (all Q140023 all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,Q140023),bool),bool),i(s(fun(fun(cart(real,Q140023),bool),fun(fun(cart(real,Q140023),bool),bool)),subset),s(fun(cart(real,Q140023),bool),S0))),s(fun(cart(real,Q140023),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,Q140023),bool),bool),collinear),s(fun(cart(real,Q140023),bool),T0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q140023),bool),bool),collinear),s(fun(cart(real,Q140023),bool),S0)))))) # label(aCOLLINEARu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2994 (all Q121316 all Q121317 all X all Y all YI_ s(real,i(s(fun(prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))),real),distance),s(prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,finite_sum(Q121316,Q121317)),prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317)))),i(s(fun(cart(real,finite_sum(Q121316,Q121317)),fun(cart(real,finite_sum(Q121316,Q121317)),prod(cart(real,finite_sum(Q121316,Q121317)),cart(real,finite_sum(Q121316,Q121317))))),c_),s(cart(real,finite_sum(Q121316,Q121317)),i(s(fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,Q121316),fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317)))),pastecart),s(cart(real,Q121316),X))),s(cart(real,Q121317),Y))))),s(cart(real,finite_sum(Q121316,Q121317)),i(s(fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317))),i(s(fun(cart(real,Q121316),fun(cart(real,Q121317),cart(real,finite_sum(Q121316,Q121317)))),pastecart),s(cart(real,Q121316),X))),s(cart(real,Q121317),YI_))))))) = s(real,i(s(fun(prod(cart(real,Q121317),cart(real,Q121317)),real),distance),s(prod(cart(real,Q121317),cart(real,Q121317)),i(s(fun(cart(real,Q121317),prod(cart(real,Q121317),cart(real,Q121317))),i(s(fun(cart(real,Q121317),fun(cart(real,Q121317),prod(cart(real,Q121317),cart(real,Q121317)))),c_),s(cart(real,Q121317),Y))),s(cart(real,Q121317),YI_)))))) # label(aDISTu_PASTECARTu_CANCELu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2995 (all N all I0 all J0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0))) = s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> s(num,J0) = s(num,I0))) # label(aBASISu_INJ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2996 p(s(bool,i(s(fun(num,bool),p0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) <-> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(n10,bool),num),dimindex),s(fun(n10,bool),univ)))))) -> p(s(bool,i(s(fun(num,bool),p0),s(num,I0)))))) # label(aFORALLu_DIMINDEXu_1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2997 (all N all S0 all X exists Y exists Z0 ((all W (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),W))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) -> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),Z0))),s(cart(real,N),W)))))) & s(cart(real,N),X) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),Y))),s(cart(real,N),Z0))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))))) # label(aORTHOGONALu_SUBSPACEu_DECOMPu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2998 (all N all F0 all FI_ (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),FI_)))) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> (s(fun(cart(real,N),cart(real,N)),i1) = s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),FI_))),s(fun(cart(real,N),cart(real,N)),F0))) <-> s(fun(cart(real,N),cart(real,N)),i1) = s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,N)),FI_)))))) # label(aLINEARu_INVERSEu_LEFT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 2999 (all A all N all F0 all U all V (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),V)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),U)))) & -p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),V)))) -> s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) -> s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),V))),s(fun(A,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),U))),s(fun(A,bool),V))))),s(fun(A,cart(real,N)),F0))))) # label(aVSUMu_UNIONu_LZERO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3000 (all Q106640 all Q106632 all U_0 ((all F0 all X s(real,i(s(fun(cart(real,Q106632),real),vectoru_norm),s(cart(real,Q106632),i(s(fun(Q106640,cart(real,Q106632)),F0),s(Q106640,X))))) = s(real,i(s(fun(Q106640,real),i(s(fun(fun(Q106640,cart(real,Q106632)),fun(Q106640,real)),U_0),s(fun(Q106640,cart(real,Q106632)),F0))),s(Q106640,X)))) -> (all F0 all S0 (p(s(bool,i(s(fun(fun(Q106640,bool),bool),finite),s(fun(Q106640,bool),S0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q106632),real),vectoru_norm),s(cart(real,Q106632),i(s(fun(fun(Q106640,cart(real,Q106632)),cart(real,Q106632)),i(s(fun(fun(Q106640,bool),fun(fun(Q106640,cart(real,Q106632)),cart(real,Q106632))),vsum),s(fun(Q106640,bool),S0))),s(fun(Q106640,cart(real,Q106632)),F0))))))),s(real,i(s(fun(fun(Q106640,real),real),i(s(fun(fun(Q106640,bool),fun(fun(Q106640,real),real)),sum),s(fun(Q106640,bool),S0))),s(fun(Q106640,real),i(s(fun(fun(Q106640,cart(real,Q106632)),fun(Q106640,real)),U_0),s(fun(Q106640,cart(real,Q106632)),F0)))))))))))) # label(aVSUMu_NORM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3001 (all Q127738 all S0 all T0 (s(fun(cart(real,Q127738),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(cart(real,Q127738),bool)),span),s(fun(cart(real,Q127738),bool),S0))) = s(fun(cart(real,Q127738),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(cart(real,Q127738),bool)),span),s(fun(cart(real,Q127738),bool),T0))) <-> p(s(bool,i(s(fun(fun(cart(real,Q127738),bool),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(fun(cart(real,Q127738),bool),bool)),subset),s(fun(cart(real,Q127738),bool),S0))),s(fun(cart(real,Q127738),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(cart(real,Q127738),bool)),span),s(fun(cart(real,Q127738),bool),T0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q127738),bool),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(fun(cart(real,Q127738),bool),bool)),subset),s(fun(cart(real,Q127738),bool),T0))),s(fun(cart(real,Q127738),bool),i(s(fun(fun(cart(real,Q127738),bool),fun(cart(real,Q127738),bool)),span),s(fun(cart(real,Q127738),bool),S0)))))))) # label(aSPANu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3002 (all N all M all U_0 ((all A5 all I0 all J0 s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(num,I0))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0)))) -> (all A5 all I0 s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),A5))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(num,I0)))))))) # label(arow) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3003 (all Q122368 all S0 p(s(bool,i(s(fun(fun(cart(real,Q122368),bool),bool),i(s(fun(fun(cart(real,Q122368),bool),fun(fun(cart(real,Q122368),bool),bool)),subset),s(fun(cart(real,Q122368),bool),S0))),s(fun(cart(real,Q122368),bool),i(s(fun(fun(cart(real,Q122368),bool),fun(cart(real,Q122368),bool)),span),s(fun(cart(real,Q122368),bool),S0))))))) # label(aSPANu_INC) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3004 (all Q102930 all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q102930),real),vectoru_norm),s(cart(real,Q102930),X))))),s(real,i(s(fun(cart(real,Q102930),real),vectoru_norm),s(cart(real,Q102930),Y))))))),s(real,e0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,Q102930),real),vectoru_norm),s(cart(real,Q102930),i(s(fun(cart(real,Q102930),cart(real,Q102930)),i(s(fun(cart(real,Q102930),fun(cart(real,Q102930),cart(real,Q102930))),vectoru_add),s(cart(real,Q102930),X))),s(cart(real,Q102930),Y))))))),s(real,e0)))))) # label(aNORMu_TRIANGLEu_LT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3005 (all N all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),T0))),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))) -> s(fun(cart(real,N),bool),T0) = s(fun(cart(real,N),bool),S0))) # label(aSPANNINGu_SUBSETu_INDEPENDENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3006 (all Q102535 all A5 all B0 all X (s(cart(real,Q102535),i(s(fun(cart(real,Q102535),cart(real,Q102535)),i(s(fun(real,fun(cart(real,Q102535),cart(real,Q102535))),r_),s(real,A5))),s(cart(real,Q102535),X))) = s(cart(real,Q102535),i(s(fun(cart(real,Q102535),cart(real,Q102535)),i(s(fun(real,fun(cart(real,Q102535),cart(real,Q102535))),r_),s(real,B0))),s(cart(real,Q102535),X))) & s(cart(real,Q102535),i(s(fun(num,cart(real,Q102535)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(real,Q102535),X) -> s(real,B0) = s(real,A5))) # label(aVECTORu_MULu_RCANCELu_IMP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3007 (all N p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),infinite),s(fun(cart(real,N),bool),univ))))) # label(aEUCLIDEANu_SPACEu_INFINITE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3008 (all Q103311 all Q103313 all X all Y (s(real,i(s(fun(cart(real,Q103311),real),i(s(fun(cart(real,Q103311),fun(cart(real,Q103311),real)),dot),s(cart(real,Q103311),X))),s(cart(real,Q103311),X))) = s(real,i(s(fun(cart(real,Q103313),real),i(s(fun(cart(real,Q103313),fun(cart(real,Q103313),real)),dot),s(cart(real,Q103313),Y))),s(cart(real,Q103313),Y))) <-> s(real,i(s(fun(cart(real,Q103311),real),vectoru_norm),s(cart(real,Q103311),X))) = s(real,i(s(fun(cart(real,Q103313),real),vectoru_norm),s(cart(real,Q103313),Y))))) # label(aNORMu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3009 (all Q99948 s(cart(real,Q99948),i(s(fun(cart(real,Q99948),cart(real,Q99948)),i(s(fun(real,fun(cart(real,Q99948),cart(real,Q99948))),r_),s(real,c))),s(cart(real,Q99948),i(s(fun(num,cart(real,Q99948)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q99948),i(s(fun(num,cart(real,Q99948)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aVECTORu_MULu_RZERO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3010 (all Q121218 all Q121215 all X s(real,i(s(fun(cart(real,Q121215),real),vectoru_norm),s(cart(real,Q121215),X))) = s(real,i(s(fun(cart(real,finite_sum(Q121215,Q121218)),real),vectoru_norm),s(cart(real,finite_sum(Q121215,Q121218)),i(s(fun(cart(real,Q121218),cart(real,finite_sum(Q121215,Q121218))),i(s(fun(cart(real,Q121215),fun(cart(real,Q121218),cart(real,finite_sum(Q121215,Q121218)))),pastecart),s(cart(real,Q121215),X))),s(cart(real,Q121218),i(s(fun(num,cart(real,Q121218)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) # label(aNORMu_PASTECARTu_0u_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3011 (all Q126331 all U_0 ((all V all N0 ((exists B0 (p(s(bool,i(s(fun(fun(cart(real,Q126331),bool),bool),i(s(fun(fun(cart(real,Q126331),bool),fun(fun(cart(real,Q126331),bool),bool)),subset),s(fun(cart(real,Q126331),bool),B0))),s(fun(cart(real,Q126331),bool),V)))) & p(s(bool,i(s(fun(fun(cart(real,Q126331),bool),bool),independent),s(fun(cart(real,Q126331),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,Q126331),bool),bool),i(s(fun(fun(cart(real,Q126331),bool),fun(fun(cart(real,Q126331),bool),bool)),subset),s(fun(cart(real,Q126331),bool),V))),s(fun(cart(real,Q126331),bool),i(s(fun(fun(cart(real,Q126331),bool),fun(cart(real,Q126331),bool)),span),s(fun(cart(real,Q126331),bool),B0)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126331),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126331),bool),B0))),s(num,N0)))))) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126331),bool),fun(num,bool)),U_0),s(fun(cart(real,Q126331),bool),V))),s(num,N0)))))) -> (all V s(num,i(s(fun(fun(cart(real,Q126331),bool),num),dim),s(fun(cart(real,Q126331),bool),V))) = s(num,i(s(fun(fun(num,bool),num),h_),s(fun(num,bool),i(s(fun(fun(cart(real,Q126331),bool),fun(num,bool)),U_0),s(fun(cart(real,Q126331),bool),V)))))))) # label(adim) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3012 (all Q141403 all A5 all B0 all C0 (p(s(bool,i(s(fun(prod(cart(real,Q141403),cart(real,Q141403)),bool),i(s(fun(cart(real,Q141403),fun(prod(cart(real,Q141403),cart(real,Q141403)),bool)),between),s(cart(real,Q141403),A5))),s(prod(cart(real,Q141403),cart(real,Q141403)),i(s(fun(cart(real,Q141403),prod(cart(real,Q141403),cart(real,Q141403))),i(s(fun(cart(real,Q141403),fun(cart(real,Q141403),prod(cart(real,Q141403),cart(real,Q141403)))),c_),s(cart(real,Q141403),B0))),s(cart(real,Q141403),C0)))))) & p(s(bool,i(s(fun(prod(cart(real,Q141403),cart(real,Q141403)),bool),i(s(fun(cart(real,Q141403),fun(prod(cart(real,Q141403),cart(real,Q141403)),bool)),between),s(cart(real,Q141403),B0))),s(prod(cart(real,Q141403),cart(real,Q141403)),i(s(fun(cart(real,Q141403),prod(cart(real,Q141403),cart(real,Q141403))),i(s(fun(cart(real,Q141403),fun(cart(real,Q141403),prod(cart(real,Q141403),cart(real,Q141403)))),c_),s(cart(real,Q141403),A5))),s(cart(real,Q141403),C0)))))) -> s(cart(real,Q141403),A5) = s(cart(real,Q141403),B0))) # label(aBETWEENu_ANTISYM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3013 (all N all S0 s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),fun(cart(real,N),bool))),delete),s(fun(cart(real,N),bool),S0))),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) # label(aSPANu_DELETEu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3014 (all Q110667 all X (s(cart(real,Q110667),X) = s(cart(real,Q110667),i(s(fun(num,cart(real,Q110667)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> p(s(bool,i(s(fun(cart(real,Q110667),bool),i(s(fun(cart(real,Q110667),fun(cart(real,Q110667),bool)),orthogonal),s(cart(real,Q110667),X))),s(cart(real,Q110667),X)))))) # label(aORTHOGONALu_REFL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3015 (all N all M all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0)))) & s(fun(cart(real,M),cart(real,M)),i1) = s(fun(cart(real,M),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M))),i(s(fun(fun(cart(real,N),cart(real,M)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M)))),o),s(fun(cart(real,N),cart(real,M)),G0))),s(fun(cart(real,M),cart(real,N)),F0))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (exists B0 all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))))))) # label(aLINEARu_INVERTIBLEu_BOUNDEDu_BELOW) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3016 (all Q111564 all Q111562 all U_0 ((all C0 all F0 all X s(cart(real,Q111562),i(s(fun(cart(real,Q111562),cart(real,Q111562)),i(s(fun(real,fun(cart(real,Q111562),cart(real,Q111562))),r_),s(real,C0))),s(cart(real,Q111562),i(s(fun(cart(real,Q111564),cart(real,Q111562)),F0),s(cart(real,Q111564),X))))) = s(cart(real,Q111562),i(s(fun(cart(real,Q111564),cart(real,Q111562)),i(s(fun(fun(cart(real,Q111564),cart(real,Q111562)),fun(cart(real,Q111564),cart(real,Q111562))),i(s(fun(real,fun(fun(cart(real,Q111564),cart(real,Q111562)),fun(cart(real,Q111564),cart(real,Q111562)))),U_0),s(real,C0))),s(fun(cart(real,Q111564),cart(real,Q111562)),F0))),s(cart(real,Q111564),X)))) -> (all F0 all C0 (p(s(bool,i(s(fun(fun(cart(real,Q111564),cart(real,Q111562)),bool),linear),s(fun(cart(real,Q111564),cart(real,Q111562)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q111564),cart(real,Q111562)),bool),linear),s(fun(cart(real,Q111564),cart(real,Q111562)),i(s(fun(fun(cart(real,Q111564),cart(real,Q111562)),fun(cart(real,Q111564),cart(real,Q111562))),i(s(fun(real,fun(fun(cart(real,Q111564),cart(real,Q111562)),fun(cart(real,Q111564),cart(real,Q111562)))),U_0),s(real,C0))),s(fun(cart(real,Q111564),cart(real,Q111562)),F0)))))))))) # label(aLINEARu_COMPOSEu_CMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3017 (all Q99856 s(cart(real,Q99856),i(s(fun(cart(real,Q99856),cart(real,Q99856)),i(s(fun(real,fun(cart(real,Q99856),cart(real,Q99856))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,a0))),s(real,b0))))),s(cart(real,Q99856),x))) = s(cart(real,Q99856),i(s(fun(cart(real,Q99856),cart(real,Q99856)),i(s(fun(cart(real,Q99856),fun(cart(real,Q99856),cart(real,Q99856))),vectoru_add),s(cart(real,Q99856),i(s(fun(cart(real,Q99856),cart(real,Q99856)),i(s(fun(real,fun(cart(real,Q99856),cart(real,Q99856))),r_),s(real,a0))),s(cart(real,Q99856),x))))),s(cart(real,Q99856),i(s(fun(cart(real,Q99856),cart(real,Q99856)),i(s(fun(real,fun(cart(real,Q99856),cart(real,Q99856))),r_),s(real,b0))),s(cart(real,Q99856),x)))))) # label(aVECTORu_ADDu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3018 (all N all S0 (-p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))))) # label(aPAIRWISEu_ORTHOGONALu_INDEPENDENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3019 (all N all A5 (s(cart(real,N),A5) != s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> (exists S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))) & s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))) = s(fun(cart(real,N),bool),univ) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),S0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & -p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,N),bool),S0)))))))) # label(aVECTORu_INu_ORTHOGONALu_BASIS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3020 (all Q122754 all S0 (s(fun(cart(real,Q122754),bool),S0) = s(fun(cart(real,Q122754),bool),i(s(fun(fun(cart(real,Q122754),bool),fun(cart(real,Q122754),bool)),span),s(fun(cart(real,Q122754),bool),S0))) <-> p(s(bool,i(s(fun(fun(cart(real,Q122754),bool),bool),subspace),s(fun(cart(real,Q122754),bool),S0)))))) # label(aSPANu_EQu_SELF) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3021 (all Q120015 all Q120021 all N0 s(cart(real,Q120021),i(s(fun(num,cart(real,Q120021)),vec),s(num,N0))) = s(cart(real,Q120021),i(s(fun(cart(real,finite_sum(Q120021,Q120015)),cart(real,Q120021)),fstcart),s(cart(real,finite_sum(Q120021,Q120015)),i(s(fun(num,cart(real,finite_sum(Q120021,Q120015))),vec),s(num,N0)))))) # label(aFSTCARTu_VEC) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3022 (all Q112352 all Q112333 all Q112351 all H0 all X all Y all Z0 (p(s(bool,i(s(fun(fun(cart(real,Q112333),fun(cart(real,Q112351),cart(real,Q112352))),bool),bilinear),s(fun(cart(real,Q112333),fun(cart(real,Q112351),cart(real,Q112352))),H0)))) -> s(cart(real,Q112352),i(s(fun(cart(real,Q112352),cart(real,Q112352)),i(s(fun(cart(real,Q112352),fun(cart(real,Q112352),cart(real,Q112352))),vectoru_add),s(cart(real,Q112352),i(s(fun(cart(real,Q112351),cart(real,Q112352)),i(s(fun(cart(real,Q112333),fun(cart(real,Q112351),cart(real,Q112352))),H0),s(cart(real,Q112333),X))),s(cart(real,Q112351),Y))))),s(cart(real,Q112352),i(s(fun(cart(real,Q112351),cart(real,Q112352)),i(s(fun(cart(real,Q112333),fun(cart(real,Q112351),cart(real,Q112352))),H0),s(cart(real,Q112333),X))),s(cart(real,Q112351),Z0))))) = s(cart(real,Q112352),i(s(fun(cart(real,Q112351),cart(real,Q112352)),i(s(fun(cart(real,Q112333),fun(cart(real,Q112351),cart(real,Q112352))),H0),s(cart(real,Q112333),X))),s(cart(real,Q112351),i(s(fun(cart(real,Q112351),cart(real,Q112351)),i(s(fun(cart(real,Q112351),fun(cart(real,Q112351),cart(real,Q112351))),vectoru_add),s(cart(real,Q112351),Y))),s(cart(real,Q112351),Z0))))))) # label(aBILINEARu_RADD) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3023 (all N all X all Y s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),Y))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y)))) # label(aVECTORu_ADDu_SYM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3024 (all N all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))) -> s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))) = s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),S0))))) # label(aDIMu_EQu_CARD) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3025 (all Q102231 all A5 all X s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_abs),s(real,A5))))),s(real,i(s(fun(cart(real,Q102231),real),vectoru_norm),s(cart(real,Q102231),X))))) = s(real,i(s(fun(cart(real,Q102231),real),vectoru_norm),s(cart(real,Q102231),i(s(fun(cart(real,Q102231),cart(real,Q102231)),i(s(fun(real,fun(cart(real,Q102231),cart(real,Q102231))),r_),s(real,A5))),s(cart(real,Q102231),X)))))) # label(aNORMu_MUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.85 3026 (all N all M all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & (all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) -> s(cart(real,M),Y) = s(cart(real,M),X))) -> s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,M),bool),bool),dependent),s(fun(cart(real,M),bool),S0))))) # label(aDEPENDENTu_LINEARu_IMAGEu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3027 (all N all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(cart(real,N),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),transp),s(cart(cart(real,N),N),b))))),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(num,cart(real,N))),d_),s(cart(cart(real,N),N),a))),s(num,I0))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(num,cart(real,N))),d_),s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),a))),s(cart(cart(real,N),N),b))))),s(num,I0))))) # label(aMATRIXu_MULu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3028 (all Q113333 all Q113332 all F0 all FI_ ((all X all Y s(real,i(s(fun(cart(real,Q113333),real),i(s(fun(cart(real,Q113333),fun(cart(real,Q113333),real)),dot),s(cart(real,Q113333),i(s(fun(cart(real,Q113332),cart(real,Q113333)),FI_),s(cart(real,Q113332),X))))),s(cart(real,Q113333),Y))) = s(real,i(s(fun(cart(real,Q113332),real),i(s(fun(cart(real,Q113332),fun(cart(real,Q113332),real)),dot),s(cart(real,Q113332),X))),s(cart(real,Q113332),i(s(fun(cart(real,Q113333),cart(real,Q113332)),F0),s(cart(real,Q113333),Y)))))) & p(s(bool,i(s(fun(fun(cart(real,Q113333),cart(real,Q113332)),bool),linear),s(fun(cart(real,Q113333),cart(real,Q113332)),F0)))) -> s(fun(cart(real,Q113332),cart(real,Q113333)),i(s(fun(fun(cart(real,Q113333),cart(real,Q113332)),fun(cart(real,Q113332),cart(real,Q113333))),adjoint),s(fun(cart(real,Q113333),cart(real,Q113332)),F0))) = s(fun(cart(real,Q113332),cart(real,Q113333)),FI_))) # label(aADJOINTu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3029 (all M all N all U_0 ((all Y all X s(cart(real,N),Y) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,M),cart(real,N))),U_0),s(cart(real,N),Y))),s(cart(real,M),X)))) -> (all Y s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))) = s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,M),cart(real,N))),U_0),s(cart(real,N),Y)))))))) # label(aONORMu_CONST) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3030 (all N all F0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> ((all Y exists X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),Y)) <-> (all X all Y (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y))) -> s(cart(real,N),X) = s(cart(real,N),Y)))))) # label(aLINEARu_SURJECTIVEu_IFFu_INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3031 (all N all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))))) # label(aINDEPENDENTu_IMPu_FINITE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3032 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),realu_inv),s(real,X))))) = s(real,i(s(fun(real,real),realu_inv),s(real,i(s(fun(real,real),sqrt),s(real,X))))))) # label(aSQRTu_INV) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3033 (all P all M all N all H0 (p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0)))) -> (exists B0 all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,P),real),vectoru_norm),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),X))),s(cart(real,N),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))))))))))) # label(aBILINEARu_BOUNDED) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3034 (all N all M all A5 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(cart(real,N),M),A5)))) # label(aMATRIXu_NEGu_MINUS1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3035 (all N all M all A5 (s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),A5))) <-> s(cart(cart(real,N),M),A5) = s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aMATRIXu_NEGu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3036 (all Q120961 all Q120963 all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q120963),real),vectoru_norm),s(cart(real,Q120963),i(s(fun(cart(real,finite_sum(Q120961,Q120963)),cart(real,Q120963)),sndcart),s(cart(real,finite_sum(Q120961,Q120963)),X))))))),s(real,i(s(fun(cart(real,finite_sum(Q120961,Q120963)),real),vectoru_norm),s(cart(real,finite_sum(Q120961,Q120963)),X))))))) # label(aNORMu_SNDCART) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3037 (all N all S0 all T0 all X all Y all XI_ all YI_ ((all A5 all B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),B0))),s(fun(cart(real,N),bool),T0)))) -> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),A5))),s(cart(real,N),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),YI_))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))) & s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),XI_))),s(cart(real,N),YI_))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),XI_))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) -> s(cart(real,N),Y) = s(cart(real,N),YI_) & s(cart(real,N),X) = s(cart(real,N),XI_))) # label(aORTHOGONALu_SUBSPACEu_DECOMPu_UNIQUE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3038 (all N all M all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),T0)))) & s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),S0))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),subspace),s(fun(cart(real,M),bool),S0)))) -> (exists F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & (all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),S0)))) -> s(cart(real,M),X) = s(cart(real,M),Y))) & s(fun(cart(real,N),bool),T0) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))))) # label(aSUBSPACEu_ISOMORPHISM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3039 (all N all U_0 ((all C0 all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),C0))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),C0),s(cart(real,N),X))))),s(cart(real,N),X)))) -> (all C0 all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0)))) -> s(real,i(s(fun(cart(real,N),real),C0),s(cart(real,N),X))) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) -> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),C0))))),s(fun(cart(real,N),bool),S0))))))))) # label(aSPANu_IMAGEu_SCALE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3040 (all N all M all U_0 ((all X all A5 all I0 s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),A5))))) = s(cart(real,M),i(s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(cart(real,N),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(cart(real,N),X))),s(cart(cart(real,N),M),A5))),s(num,I0)))) -> (all A5 all X s(cart(real,M),i(s(fun(fun(num,cart(real,M)),cart(real,M)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,M)),cart(real,M))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,M))),i(s(fun(cart(real,N),fun(cart(cart(real,N),M),fun(num,cart(real,M)))),U_0),s(cart(real,N),X))),s(cart(cart(real,N),M),A5))))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X)))))) # label(aMATRIXu_MULu_VSUM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3041 (all S0 all T0 s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(fun(real,bool),fun(fun(real,bool),bool)),subset),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),S0))))),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),T0))))) = s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(fun(cart(real,n10),bool),fun(fun(cart(real,n10),bool),bool)),subset),s(fun(cart(real,n10),bool),S0))),s(fun(cart(real,n10),bool),T0)))) # label(aSUBSETu_DROPu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3042 (all N all A5 ((exists B0 s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),B0))),s(cart(cart(real,N),N),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) <-> p(s(bool,i(s(fun(cart(cart(real,N),N),bool),invertible),s(cart(cart(real,N),N),A5)))))) # label(aINVERTIBLEu_LEFTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3043 (all M all N all U_0 ((all A5 all X all I0 s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(cart(real,N),X))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))),s(num,I0)))) -> (all A5 all X s(cart(real,M),i(s(fun(fun(num,real),cart(real,M)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X)))))) # label(aMATRIXu_MULu_DOT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3044 (all Q121694 all Q121697 all U_0 ((all F0 all S0 all GENR_PVARR_297 (p(s(bool,i(s(fun(cart(real,Q121694),bool),i(s(fun(fun(cart(real,Q121697),bool),fun(cart(real,Q121694),bool)),i(s(fun(fun(cart(real,Q121694),cart(real,Q121697)),fun(fun(cart(real,Q121697),bool),fun(cart(real,Q121694),bool))),U_0),s(fun(cart(real,Q121694),cart(real,Q121697)),F0))),s(fun(cart(real,Q121697),bool),S0))),s(cart(real,Q121694),GENR_PVARR_297)))) <-> (exists X p(s(bool,i(s(fun(cart(real,Q121694),bool),i(s(fun(bool,fun(cart(real,Q121694),bool)),i(s(fun(cart(real,Q121694),fun(bool,fun(cart(real,Q121694),bool))),setspec),s(cart(real,Q121694),GENR_PVARR_297))),s(bool,i(s(fun(fun(cart(real,Q121697),bool),bool),i(s(fun(cart(real,Q121697),fun(fun(cart(real,Q121697),bool),bool)),in),s(cart(real,Q121697),i(s(fun(cart(real,Q121694),cart(real,Q121697)),F0),s(cart(real,Q121694),X))))),s(fun(cart(real,Q121697),bool),S0))))),s(cart(real,Q121694),X))))))) -> (all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q121697),bool),bool),subspace),s(fun(cart(real,Q121697),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q121694),cart(real,Q121697)),bool),linear),s(fun(cart(real,Q121694),cart(real,Q121697)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121694),bool),bool),subspace),s(fun(cart(real,Q121694),bool),i(s(fun(fun(cart(real,Q121694),bool),fun(cart(real,Q121694),bool)),gspec),s(fun(cart(real,Q121694),bool),i(s(fun(fun(cart(real,Q121697),bool),fun(cart(real,Q121694),bool)),i(s(fun(fun(cart(real,Q121694),cart(real,Q121697)),fun(fun(cart(real,Q121697),bool),fun(cart(real,Q121694),bool))),U_0),s(fun(cart(real,Q121694),cart(real,Q121697)),F0))),s(fun(cart(real,Q121697),bool),S0)))))))))))) # label(aSUBSPACEu_LINEARu_PREIMAGE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3045 (all N all K0 all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> (exists V ((p(s(bool,V)) <-> s(num,K0) = s(num,I0)) & s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,K0))))),s(num,I0))))))) # label(aBASISu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3046 (all Q105715 all Q105728 all U_0 ((all F0 all G0 all X s(cart(real,Q105728),i(s(fun(cart(real,Q105728),cart(real,Q105728)),i(s(fun(cart(real,Q105728),fun(cart(real,Q105728),cart(real,Q105728))),vectoru_add),s(cart(real,Q105728),i(s(fun(Q105715,cart(real,Q105728)),F0),s(Q105715,X))))),s(cart(real,Q105728),i(s(fun(Q105715,cart(real,Q105728)),G0),s(Q105715,X))))) = s(cart(real,Q105728),i(s(fun(Q105715,cart(real,Q105728)),i(s(fun(fun(Q105715,cart(real,Q105728)),fun(Q105715,cart(real,Q105728))),i(s(fun(fun(Q105715,cart(real,Q105728)),fun(fun(Q105715,cart(real,Q105728)),fun(Q105715,cart(real,Q105728)))),U_0),s(fun(Q105715,cart(real,Q105728)),F0))),s(fun(Q105715,cart(real,Q105728)),G0))),s(Q105715,X)))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(Q105715,bool),bool),finite),s(fun(Q105715,bool),S0)))) -> s(cart(real,Q105728),i(s(fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728)),i(s(fun(fun(Q105715,bool),fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728))),vsum),s(fun(Q105715,bool),S0))),s(fun(Q105715,cart(real,Q105728)),i(s(fun(fun(Q105715,cart(real,Q105728)),fun(Q105715,cart(real,Q105728))),i(s(fun(fun(Q105715,cart(real,Q105728)),fun(fun(Q105715,cart(real,Q105728)),fun(Q105715,cart(real,Q105728)))),U_0),s(fun(Q105715,cart(real,Q105728)),F0))),s(fun(Q105715,cart(real,Q105728)),G0))))) = s(cart(real,Q105728),i(s(fun(cart(real,Q105728),cart(real,Q105728)),i(s(fun(cart(real,Q105728),fun(cart(real,Q105728),cart(real,Q105728))),vectoru_add),s(cart(real,Q105728),i(s(fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728)),i(s(fun(fun(Q105715,bool),fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728))),vsum),s(fun(Q105715,bool),S0))),s(fun(Q105715,cart(real,Q105728)),F0))))),s(cart(real,Q105728),i(s(fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728)),i(s(fun(fun(Q105715,bool),fun(fun(Q105715,cart(real,Q105728)),cart(real,Q105728))),vsum),s(fun(Q105715,bool),S0))),s(fun(Q105715,cart(real,Q105728)),G0))))))))) # label(aVSUMu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3047 (all A all N all U_0 ((all F0 all I0 all X s(real,i(s(fun(A,real),i(s(fun(num,fun(A,real)),i(s(fun(fun(A,cart(real,N)),fun(num,fun(A,real))),U_0),s(fun(A,cart(real,N)),F0))),s(num,I0))),s(A,X))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))))),s(num,I0)))) -> (all S0 all F0 all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(num,fun(A,real)),i(s(fun(fun(A,cart(real,N)),fun(num,fun(A,real))),U_0),s(fun(A,cart(real,N)),F0))),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))),s(num,I0))))))) # label(aVSUMu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3048 (all Q140034 all X p(s(bool,i(s(fun(fun(cart(real,Q140034),bool),bool),collinear),s(fun(cart(real,Q140034),bool),i(s(fun(fun(cart(real,Q140034),bool),fun(cart(real,Q140034),bool)),i(s(fun(cart(real,Q140034),fun(fun(cart(real,Q140034),bool),fun(cart(real,Q140034),bool))),insert),s(cart(real,Q140034),X))),s(fun(cart(real,Q140034),bool),empty))))))) # label(aCOLLINEARu_SING) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3049 (all N all M all A5 all B0 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0)))) # label(aMATRIXu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3050 (all X all Y s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,X))),s(real,Y))))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),fun(cart(real,n10),cart(real,n10))),vectoru_add),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,Y)))))) # label(aLIFTu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3051 (all N all M all F0 all S0 ((all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) -> s(cart(real,M),Y) = s(cart(real,M),X))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> s(bool,i(s(fun(fun(cart(real,M),bool),bool),independent),s(fun(cart(real,M),bool),S0))) = s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))))) # label(aINDEPENDENTu_LINEARu_IMAGEu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3052 (all A all P0 ((all F0 p(s(bool,i(s(fun(fun(A,real),bool),P0),s(fun(A,real),F0))))) <-> (all F0 p(s(bool,i(s(fun(fun(A,real),bool),P0),s(fun(A,real),i(s(fun(fun(A,cart(real,n10)),fun(A,real)),i(s(fun(fun(cart(real,n10),real),fun(fun(A,cart(real,n10)),fun(A,real))),o),s(fun(cart(real,n10),real),drop))),s(fun(A,cart(real,n10)),F0))))))))) # label(aFORALLu_DROPu_FUN) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3053 (all N all V all B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),V))))),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),B0)))))))) # label(aSPANu_CARDu_GEu_DIM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3054 (all N all U_0 ((all C0 all X all I0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(real,fun(cart(real,N),fun(num,real))),U_0),s(real,C0))),s(cart(real,N),X))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0)))))) -> (all C0 all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(real,fun(cart(real,N),fun(num,real))),U_0),s(real,C0))),s(cart(real,N),X)))))))) # label(avectoru_mul) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3055 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) <-> s(real,X) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) # label(aSQRTu_POW2) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3056 (all N all U_0 ((all GENR_PVARR_312 (p(s(bool,i(s(fun(cart(real,N),bool),U_0),s(cart(real,N),GENR_PVARR_312)))) <-> (exists I0 exists V (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_312))),s(bool,V))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0))))))))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),U_0)))))))) # label(aFINITEu_STDBASIS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3057 (all N all S0 ((p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),S0)))))) # label(aDEPENDENTu_BIGGERSETu_GENERAL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3058 (all Q99745 all X s(cart(real,Q99745),X) = s(cart(real,Q99745),i(s(fun(cart(real,Q99745),cart(real,Q99745)),i(s(fun(real,fun(cart(real,Q99745),cart(real,Q99745))),r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(real,Q99745),X)))) # label(aVECTORu_MULu_LID) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3059 (all X all C0 s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,C0))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,X)))))) # label(aLIFTu_CMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3060 (all Q122165 s(fun(cart(real,Q122165),bool),i(s(fun(fun(cart(real,Q122165),bool),fun(cart(real,Q122165),bool)),span),s(fun(cart(real,Q122165),bool),empty))) = s(fun(cart(real,Q122165),bool),i(s(fun(fun(cart(real,Q122165),bool),fun(cart(real,Q122165),bool)),i(s(fun(cart(real,Q122165),fun(fun(cart(real,Q122165),bool),fun(cart(real,Q122165),bool))),insert),s(cart(real,Q122165),i(s(fun(num,cart(real,Q122165)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q122165),bool),empty)))) # label(aSPANu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3061 (all Q105645 all Q105652 all U_0 ((all C0 all F0 all X s(cart(real,Q105652),i(s(fun(cart(real,Q105652),cart(real,Q105652)),i(s(fun(real,fun(cart(real,Q105652),cart(real,Q105652))),r_),s(real,C0))),s(cart(real,Q105652),i(s(fun(Q105645,cart(real,Q105652)),F0),s(Q105645,X))))) = s(cart(real,Q105652),i(s(fun(Q105645,cart(real,Q105652)),i(s(fun(fun(Q105645,cart(real,Q105652)),fun(Q105645,cart(real,Q105652))),i(s(fun(real,fun(fun(Q105645,cart(real,Q105652)),fun(Q105645,cart(real,Q105652)))),U_0),s(real,C0))),s(fun(Q105645,cart(real,Q105652)),F0))),s(Q105645,X)))) -> (all F0 all C0 all S0 s(cart(real,Q105652),i(s(fun(fun(Q105645,cart(real,Q105652)),cart(real,Q105652)),i(s(fun(fun(Q105645,bool),fun(fun(Q105645,cart(real,Q105652)),cart(real,Q105652))),vsum),s(fun(Q105645,bool),S0))),s(fun(Q105645,cart(real,Q105652)),i(s(fun(fun(Q105645,cart(real,Q105652)),fun(Q105645,cart(real,Q105652))),i(s(fun(real,fun(fun(Q105645,cart(real,Q105652)),fun(Q105645,cart(real,Q105652)))),U_0),s(real,C0))),s(fun(Q105645,cart(real,Q105652)),F0))))) = s(cart(real,Q105652),i(s(fun(cart(real,Q105652),cart(real,Q105652)),i(s(fun(real,fun(cart(real,Q105652),cart(real,Q105652))),r_),s(real,C0))),s(cart(real,Q105652),i(s(fun(fun(Q105645,cart(real,Q105652)),cart(real,Q105652)),i(s(fun(fun(Q105645,bool),fun(fun(Q105645,cart(real,Q105652)),cart(real,Q105652))),vsum),s(fun(Q105645,bool),S0))),s(fun(Q105645,cart(real,Q105652)),F0)))))))) # label(aVSUMu_LMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3062 (all Q142205 all A5 all B0 all X (p(s(bool,i(s(fun(fun(cart(real,Q142205),bool),bool),collinear),s(fun(cart(real,Q142205),bool),i(s(fun(fun(cart(real,Q142205),bool),fun(cart(real,Q142205),bool)),i(s(fun(cart(real,Q142205),fun(fun(cart(real,Q142205),bool),fun(cart(real,Q142205),bool))),insert),s(cart(real,Q142205),X))),s(fun(cart(real,Q142205),bool),i(s(fun(fun(cart(real,Q142205),bool),fun(cart(real,Q142205),bool)),i(s(fun(cart(real,Q142205),fun(fun(cart(real,Q142205),bool),fun(cart(real,Q142205),bool))),insert),s(cart(real,Q142205),A5))),s(fun(cart(real,Q142205),bool),i(s(fun(fun(cart(real,Q142205),bool),fun(cart(real,Q142205),bool)),i(s(fun(cart(real,Q142205),fun(fun(cart(real,Q142205),bool),fun(cart(real,Q142205),bool))),insert),s(cart(real,Q142205),B0))),s(fun(cart(real,Q142205),bool),empty)))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q142205),cart(real,Q142205)),real),distance),s(prod(cart(real,Q142205),cart(real,Q142205)),i(s(fun(cart(real,Q142205),prod(cart(real,Q142205),cart(real,Q142205))),i(s(fun(cart(real,Q142205),fun(cart(real,Q142205),prod(cart(real,Q142205),cart(real,Q142205)))),c_),s(cart(real,Q142205),X))),s(cart(real,Q142205),B0))))))),s(real,i(s(fun(prod(cart(real,Q142205),cart(real,Q142205)),real),distance),s(prod(cart(real,Q142205),cart(real,Q142205)),i(s(fun(cart(real,Q142205),prod(cart(real,Q142205),cart(real,Q142205))),i(s(fun(cart(real,Q142205),fun(cart(real,Q142205),prod(cart(real,Q142205),cart(real,Q142205)))),c_),s(cart(real,Q142205),A5))),s(cart(real,Q142205),B0)))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q142205),cart(real,Q142205)),real),distance),s(prod(cart(real,Q142205),cart(real,Q142205)),i(s(fun(cart(real,Q142205),prod(cart(real,Q142205),cart(real,Q142205))),i(s(fun(cart(real,Q142205),fun(cart(real,Q142205),prod(cart(real,Q142205),cart(real,Q142205)))),c_),s(cart(real,Q142205),X))),s(cart(real,Q142205),A5))))))),s(real,i(s(fun(prod(cart(real,Q142205),cart(real,Q142205)),real),distance),s(prod(cart(real,Q142205),cart(real,Q142205)),i(s(fun(cart(real,Q142205),prod(cart(real,Q142205),cart(real,Q142205))),i(s(fun(cart(real,Q142205),fun(cart(real,Q142205),prod(cart(real,Q142205),cart(real,Q142205)))),c_),s(cart(real,Q142205),A5))),s(cart(real,Q142205),B0)))))))) -> p(s(bool,i(s(fun(prod(cart(real,Q142205),cart(real,Q142205)),bool),i(s(fun(cart(real,Q142205),fun(prod(cart(real,Q142205),cart(real,Q142205)),bool)),between),s(cart(real,Q142205),X))),s(prod(cart(real,Q142205),cart(real,Q142205)),i(s(fun(cart(real,Q142205),prod(cart(real,Q142205),cart(real,Q142205))),i(s(fun(cart(real,Q142205),fun(cart(real,Q142205),prod(cart(real,Q142205),cart(real,Q142205)))),c_),s(cart(real,Q142205),A5))),s(cart(real,Q142205),B0)))))))) # label(aCOLLINEARu_DISTu_BETWEEN) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3063 (all N all M all A5 p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),finite),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),columns),s(cart(cart(real,N),M),A5))))))) # label(aFINITEu_COLUMNS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3064 (all Q105385 all X (s(real,i(s(fun(cart(real,Q105385),real),vectoru_norm),s(cart(real,Q105385),X))) = s(real,i(s(fun(prod(cart(real,Q105385),cart(real,Q105385)),real),distance),s(prod(cart(real,Q105385),cart(real,Q105385)),i(s(fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385))),i(s(fun(cart(real,Q105385),fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385)))),c_),s(cart(real,Q105385),X))),s(cart(real,Q105385),i(s(fun(num,cart(real,Q105385)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) & s(real,i(s(fun(cart(real,Q105385),real),vectoru_norm),s(cart(real,Q105385),X))) = s(real,i(s(fun(prod(cart(real,Q105385),cart(real,Q105385)),real),distance),s(prod(cart(real,Q105385),cart(real,Q105385)),i(s(fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385))),i(s(fun(cart(real,Q105385),fun(cart(real,Q105385),prod(cart(real,Q105385),cart(real,Q105385)))),c_),s(cart(real,Q105385),i(s(fun(num,cart(real,Q105385)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q105385),X))))))) # label(aDISTu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3065 (all Q104636 all X all Y (s(real,i(s(fun(cart(real,Q104636),real),i(s(fun(cart(real,Q104636),fun(cart(real,Q104636),real)),dot),s(cart(real,Q104636),X))),s(cart(real,Q104636),X))) = s(real,i(s(fun(cart(real,Q104636),real),i(s(fun(cart(real,Q104636),fun(cart(real,Q104636),real)),dot),s(cart(real,Q104636),Y))),s(cart(real,Q104636),Y))) & s(real,i(s(fun(cart(real,Q104636),real),i(s(fun(cart(real,Q104636),fun(cart(real,Q104636),real)),dot),s(cart(real,Q104636),X))),s(cart(real,Q104636),Y))) = s(real,i(s(fun(cart(real,Q104636),real),i(s(fun(cart(real,Q104636),fun(cart(real,Q104636),real)),dot),s(cart(real,Q104636),X))),s(cart(real,Q104636),X))) <-> s(cart(real,Q104636),X) = s(cart(real,Q104636),Y))) # label(aVECTORu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3066 (all N all P0 ((all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),P0),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),P0),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,N),cart(real,N)),F0))),s(fun(cart(real,N),bool),S0)))))))) -> (all F0 ((all X all Y (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) -> s(cart(real,N),X) = s(cart(real,N),Y))) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> (all S0 s(bool,i(s(fun(fun(cart(real,N),bool),bool),P0),s(fun(cart(real,N),bool),S0))) = s(bool,i(s(fun(fun(cart(real,N),bool),bool),P0),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,N),cart(real,N)),F0))),s(fun(cart(real,N),bool),S0)))))))))) # label(aWLOGu_LINEARu_INJECTIVEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3067 (all Q100205 all X all Y s(real,i(s(fun(cart(real,Q100205),real),i(s(fun(cart(real,Q100205),fun(cart(real,Q100205),real)),dot),s(cart(real,Q100205),Y))),s(cart(real,Q100205),X))) = s(real,i(s(fun(cart(real,Q100205),real),i(s(fun(cart(real,Q100205),fun(cart(real,Q100205),real)),dot),s(cart(real,Q100205),X))),s(cart(real,Q100205),Y)))) # label(aDOTu_SYM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3068 (all N all M all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (all X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))),s(cart(real,M),X)))))) # label(aMATRIXu_WORKS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3069 (all N all A5 all B0 all X (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),B0))),s(cart(real,N),X))))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),A5))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),A5))))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),B0))),s(cart(real,N),X))))) <-> p(s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(cart(real,N),fun(prod(cart(real,N),cart(real,N)),bool)),between),s(cart(real,N),X))),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),B0)))))))) # label(aBETWEENu_NORM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3070 (all N all M all A5 s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),columns),s(cart(cart(real,N),M),A5))) = s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5)))))) # label(aROWSu_TRANSP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3071 (all N0 (p(s(bool,i(s(fun(num,bool),even),s(num,N0)))) -> s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(num,N0))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),div),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) # label(aSQRTu_EVENu_POW2) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3072 (all Q109577 all Q109575 all U_0 ((all A5 all X exists V (s(cart(real,Q109577),i(s(fun(cart(real,Q109577),cart(real,Q109577)),i(s(fun(cart(real,Q109577),fun(cart(real,Q109577),cart(real,Q109577))),i(s(fun(bool,fun(cart(real,Q109577),fun(cart(real,Q109577),cart(real,Q109577)))),cond),s(bool,V))),s(cart(real,Q109577),y))),s(cart(real,Q109577),i(s(fun(Q109575,cart(real,Q109577)),f),s(Q109575,X))))) = s(cart(real,Q109577),i(s(fun(Q109575,cart(real,Q109577)),i(s(fun(Q109575,fun(Q109575,cart(real,Q109577))),U_0),s(Q109575,A5))),s(Q109575,X))) & (p(s(bool,V)) <-> s(Q109575,X) = s(Q109575,A5)))) -> (all S0 all A5 (p(s(bool,i(s(fun(fun(Q109575,bool),bool),finite),s(fun(Q109575,bool),S0)))) & p(s(bool,i(s(fun(fun(Q109575,bool),bool),i(s(fun(Q109575,fun(fun(Q109575,bool),bool)),in),s(Q109575,A5))),s(fun(Q109575,bool),S0)))) -> s(cart(real,Q109577),i(s(fun(fun(Q109575,cart(real,Q109577)),cart(real,Q109577)),i(s(fun(fun(Q109575,bool),fun(fun(Q109575,cart(real,Q109577)),cart(real,Q109577))),vsum),s(fun(Q109575,bool),S0))),s(fun(Q109575,cart(real,Q109577)),i(s(fun(Q109575,fun(Q109575,cart(real,Q109577))),U_0),s(Q109575,A5))))) = s(cart(real,Q109577),i(s(fun(cart(real,Q109577),cart(real,Q109577)),i(s(fun(cart(real,Q109577),fun(cart(real,Q109577),cart(real,Q109577))),vectoru_add),s(cart(real,Q109577),i(s(fun(fun(Q109575,cart(real,Q109577)),cart(real,Q109577)),i(s(fun(fun(Q109575,bool),fun(fun(Q109575,cart(real,Q109577)),cart(real,Q109577))),vsum),s(fun(Q109575,bool),S0))),s(fun(Q109575,cart(real,Q109577)),f))))),s(cart(real,Q109577),i(s(fun(cart(real,Q109577),cart(real,Q109577)),i(s(fun(cart(real,Q109577),fun(cart(real,Q109577),cart(real,Q109577))),vectoru_sub),s(cart(real,Q109577),y))),s(cart(real,Q109577),i(s(fun(Q109575,cart(real,Q109577)),f),s(Q109575,A5))))))))))) # label(aVSUMu_CASESu_1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3073 (all N all K0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,K0))) != s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aBASISu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3074 (all N all M all A5 all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) -> s(cart(real,N),i(s(fun(cart(cart(real,M),N),cart(real,N)),i(s(fun(num,fun(cart(cart(real,M),N),cart(real,N))),column),s(num,I0))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) = s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),A5))))) # label(aCOLUMNu_TRANSP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3075 (all Q111683 all U_0 ((all X s(cart(real,Q111683),i(s(fun(cart(real,Q111683),cart(real,Q111683)),U_0),s(cart(real,Q111683),X))) = s(cart(real,Q111683),X)) -> p(s(bool,i(s(fun(fun(cart(real,Q111683),cart(real,Q111683)),bool),linear),s(fun(cart(real,Q111683),cart(real,Q111683)),U_0)))))) # label(aLINEARu_ID) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3076 (all Q122108 all X all C0 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q122108),bool),bool),i(s(fun(cart(real,Q122108),fun(fun(cart(real,Q122108),bool),bool)),in),s(cart(real,Q122108),X))),s(fun(cart(real,Q122108),bool),i(s(fun(fun(cart(real,Q122108),bool),fun(cart(real,Q122108),bool)),span),s(fun(cart(real,Q122108),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,Q122108),bool),bool),i(s(fun(cart(real,Q122108),fun(fun(cart(real,Q122108),bool),bool)),in),s(cart(real,Q122108),i(s(fun(cart(real,Q122108),cart(real,Q122108)),i(s(fun(real,fun(cart(real,Q122108),cart(real,Q122108))),r_),s(real,C0))),s(cart(real,Q122108),X))))),s(fun(cart(real,Q122108),bool),i(s(fun(fun(cart(real,Q122108),bool),fun(cart(real,Q122108),bool)),span),s(fun(cart(real,Q122108),bool),S0)))))))) # label(aSPANu_CLAUSESu_conjunct3) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3077 (all N all M all A5 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,M),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_mul),s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),M),A5)) # label(aMATRIXu_MULu_LID) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3078 (all Q112240 all Q112239 all F0 all S0 ((all X (p(s(bool,i(s(fun(fun(cart(real,Q112239),bool),bool),i(s(fun(cart(real,Q112239),fun(fun(cart(real,Q112239),bool),bool)),in),s(cart(real,Q112239),X))),s(fun(cart(real,Q112239),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q112239),bool),bool),i(s(fun(cart(real,Q112239),fun(fun(cart(real,Q112239),bool),bool)),in),s(cart(real,Q112239),i(s(fun(cart(real,Q112239),cart(real,Q112239)),vectoru_neg),s(cart(real,Q112239),X))))),s(fun(cart(real,Q112239),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q112239),cart(real,Q112240)),bool),linear),s(fun(cart(real,Q112239),cart(real,Q112240)),F0)))) -> (all X (p(s(bool,i(s(fun(fun(cart(real,Q112240),bool),bool),i(s(fun(cart(real,Q112240),fun(fun(cart(real,Q112240),bool),bool)),in),s(cart(real,Q112240),X))),s(fun(cart(real,Q112240),bool),i(s(fun(fun(cart(real,Q112239),bool),fun(cart(real,Q112240),bool)),i(s(fun(fun(cart(real,Q112239),cart(real,Q112240)),fun(fun(cart(real,Q112239),bool),fun(cart(real,Q112240),bool))),image),s(fun(cart(real,Q112239),cart(real,Q112240)),F0))),s(fun(cart(real,Q112239),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,Q112240),bool),bool),i(s(fun(cart(real,Q112240),fun(fun(cart(real,Q112240),bool),bool)),in),s(cart(real,Q112240),i(s(fun(cart(real,Q112240),cart(real,Q112240)),vectoru_neg),s(cart(real,Q112240),X))))),s(fun(cart(real,Q112240),bool),i(s(fun(fun(cart(real,Q112239),bool),fun(cart(real,Q112240),bool)),i(s(fun(fun(cart(real,Q112239),cart(real,Q112240)),fun(fun(cart(real,Q112239),bool),fun(cart(real,Q112240),bool))),image),s(fun(cart(real,Q112239),cart(real,Q112240)),F0))),s(fun(cart(real,Q112239),bool),S0)))))))))) # label(aSYMMETRICu_LINEARu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3079 (all Q111967 all Q111971 all Q111963 all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q111963),cart(real,Q111967)),bool),linear),s(fun(cart(real,Q111963),cart(real,Q111967)),F0)))) & p(s(bool,i(s(fun(fun(Q111971,bool),bool),finite),s(fun(Q111971,bool),S0)))) -> s(cart(real,Q111967),i(s(fun(fun(Q111971,cart(real,Q111967)),cart(real,Q111967)),i(s(fun(fun(Q111971,bool),fun(fun(Q111971,cart(real,Q111967)),cart(real,Q111967))),vsum),s(fun(Q111971,bool),S0))),s(fun(Q111971,cart(real,Q111967)),i(s(fun(fun(Q111971,cart(real,Q111963)),fun(Q111971,cart(real,Q111967))),i(s(fun(fun(cart(real,Q111963),cart(real,Q111967)),fun(fun(Q111971,cart(real,Q111963)),fun(Q111971,cart(real,Q111967)))),o),s(fun(cart(real,Q111963),cart(real,Q111967)),F0))),s(fun(Q111971,cart(real,Q111963)),G0))))) = s(cart(real,Q111967),i(s(fun(cart(real,Q111963),cart(real,Q111967)),F0),s(cart(real,Q111963),i(s(fun(fun(Q111971,cart(real,Q111963)),cart(real,Q111963)),i(s(fun(fun(Q111971,bool),fun(fun(Q111971,cart(real,Q111963)),cart(real,Q111963))),vsum),s(fun(Q111971,bool),S0))),s(fun(Q111971,cart(real,Q111963)),G0))))))) # label(aLINEARu_VSUM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3080 (all Q121430 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q121430),bool),bool),independent),s(fun(cart(real,Q121430),bool),S0)))) <-> -p(s(bool,i(s(fun(fun(cart(real,Q121430),bool),bool),dependent),s(fun(cart(real,Q121430),bool),S0)))))) # label(aindependent) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3081 (all N all M all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & (all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) -> s(cart(real,M),Y) = s(cart(real,M),X))) -> s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),S0))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))))) # label(aDIMu_INJECTIVEu_LINEARu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3082 (all Q138980 all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q138980),real),infnorm),s(cart(real,Q138980),X))))))) # label(aINFNORMu_POSu_LE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3083 (all Q128763 all Q128793 all F0 all B0 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q128763),cart(real,Q128793)),bool),linear),s(fun(cart(real,Q128763),cart(real,Q128793)),F0)))) & p(s(bool,i(s(fun(fun(cart(real,Q128763),bool),bool),i(s(fun(fun(cart(real,Q128763),bool),fun(fun(cart(real,Q128763),bool),bool)),subset),s(fun(cart(real,Q128763),bool),S0))),s(fun(cart(real,Q128763),bool),i(s(fun(fun(cart(real,Q128763),bool),fun(cart(real,Q128763),bool)),span),s(fun(cart(real,Q128763),bool),B0)))))) & (all X (p(s(bool,i(s(fun(fun(cart(real,Q128763),bool),bool),i(s(fun(cart(real,Q128763),fun(fun(cart(real,Q128763),bool),bool)),in),s(cart(real,Q128763),X))),s(fun(cart(real,Q128763),bool),B0)))) -> s(cart(real,Q128793),i(s(fun(cart(real,Q128763),cart(real,Q128793)),F0),s(cart(real,Q128763),X))) = s(cart(real,Q128793),i(s(fun(num,cart(real,Q128793)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) -> (all X (p(s(bool,i(s(fun(fun(cart(real,Q128763),bool),bool),i(s(fun(cart(real,Q128763),fun(fun(cart(real,Q128763),bool),bool)),in),s(cart(real,Q128763),X))),s(fun(cart(real,Q128763),bool),S0)))) -> s(cart(real,Q128793),i(s(fun(num,cart(real,Q128793)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q128793),i(s(fun(cart(real,Q128763),cart(real,Q128793)),F0),s(cart(real,Q128763),X))))))) # label(aLINEARu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3084 (all N all U_0 ((all K0 all X s(cart(real,n10),i(s(fun(cart(real,N),cart(real,n10)),i(s(fun(num,fun(cart(real,N),cart(real,n10))),U_0),s(num,K0))),s(cart(real,N),X))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,K0)))))) -> (all K0 p(s(bool,i(s(fun(fun(cart(real,N),cart(real,n10)),bool),linear),s(fun(cart(real,N),cart(real,n10)),i(s(fun(num,fun(cart(real,N),cart(real,n10))),U_0),s(num,K0))))))))) # label(aLINEARu_LIFTu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3085 (all Q99936 s(cart(real,Q99936),i(s(fun(cart(real,Q99936),cart(real,Q99936)),i(s(fun(cart(real,Q99936),fun(cart(real,Q99936),cart(real,Q99936))),vectoru_sub),s(cart(real,Q99936),x))),s(cart(real,Q99936),i(s(fun(num,cart(real,Q99936)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q99936),x)) # label(aVECTORu_SUBu_RZERO) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3086 (all N all M all A5 all B0 all X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,M),N),cart(cart(real,M),N))),matrixu_add),s(cart(cart(real,M),N),A5))),s(cart(cart(real,M),N),B0))))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),B0))),s(cart(real,M),X)))))) # label(aMATRIXu_VECTORu_MULu_ADDu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.86 3087 (all Q110858 all A5 all X all C0 (p(s(bool,i(s(fun(cart(real,Q110858),bool),i(s(fun(cart(real,Q110858),fun(cart(real,Q110858),bool)),orthogonal),s(cart(real,Q110858),A5))),s(cart(real,Q110858),X)))) -> p(s(bool,i(s(fun(cart(real,Q110858),bool),i(s(fun(cart(real,Q110858),fun(cart(real,Q110858),bool)),orthogonal),s(cart(real,Q110858),A5))),s(cart(real,Q110858),i(s(fun(cart(real,Q110858),cart(real,Q110858)),i(s(fun(real,fun(cart(real,Q110858),cart(real,Q110858))),r_),s(real,C0))),s(cart(real,Q110858),X)))))))) # label(aORTHOGONALu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3088 (all N all A5 all B0 all C0 all D0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),C0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),D0))),s(fun(cart(real,N),bool),empty)))))))))) & s(cart(real,N),B0) != s(cart(real,N),C0) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),C0))),s(fun(cart(real,N),bool),empty)))))))))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),D0))),s(fun(cart(real,N),bool),empty)))))))))))) # label(aCOLLINEARu_3u_TRANS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3089 (all M all P all N all A5 all B0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(cart(cart(real,N),M),num),rank),s(cart(cart(real,N),M),A5))))),s(num,i(s(fun(cart(cart(real,P),N),num),rank),s(cart(cart(real,P),N),B0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(cart(cart(real,P),M),num),rank),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))))) # label(aRANKu_SYLVESTER) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3090 (all N all C0 all X all I0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X))))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0)))))) # label(aVECTORu_MULu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3091 (all Q100240 all X all Y all Z0 s(real,i(s(fun(cart(real,Q100240),real),i(s(fun(cart(real,Q100240),fun(cart(real,Q100240),real)),dot),s(cart(real,Q100240),i(s(fun(cart(real,Q100240),cart(real,Q100240)),i(s(fun(cart(real,Q100240),fun(cart(real,Q100240),cart(real,Q100240))),vectoru_add),s(cart(real,Q100240),X))),s(cart(real,Q100240),Y))))),s(cart(real,Q100240),Z0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q100240),real),i(s(fun(cart(real,Q100240),fun(cart(real,Q100240),real)),dot),s(cart(real,Q100240),X))),s(cart(real,Q100240),Z0))))),s(real,i(s(fun(cart(real,Q100240),real),i(s(fun(cart(real,Q100240),fun(cart(real,Q100240),real)),dot),s(cart(real,Q100240),Y))),s(cart(real,Q100240),Z0)))))) # label(aDOTu_LADD) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3092 (all M all N all A5 all C0 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(real,fun(cart(cart(real,M),N),cart(cart(real,M),N))),r_r_),s(real,C0))),s(cart(cart(real,M),N),A5))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),A5)))))) # label(aTRANSPu_MATRIXu_CMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3093 (all Q120993 all Q120995 all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q120995),cart(real,Q120995)),real),distance),s(prod(cart(real,Q120995),cart(real,Q120995)),i(s(fun(cart(real,Q120995),prod(cart(real,Q120995),cart(real,Q120995))),i(s(fun(cart(real,Q120995),fun(cart(real,Q120995),prod(cart(real,Q120995),cart(real,Q120995)))),c_),s(cart(real,Q120995),i(s(fun(cart(real,finite_sum(Q120993,Q120995)),cart(real,Q120995)),sndcart),s(cart(real,finite_sum(Q120993,Q120995)),X))))),s(cart(real,Q120995),i(s(fun(cart(real,finite_sum(Q120993,Q120995)),cart(real,Q120995)),sndcart),s(cart(real,finite_sum(Q120993,Q120995)),Y))))))))),s(real,i(s(fun(prod(cart(real,finite_sum(Q120993,Q120995)),cart(real,finite_sum(Q120993,Q120995))),real),distance),s(prod(cart(real,finite_sum(Q120993,Q120995)),cart(real,finite_sum(Q120993,Q120995))),i(s(fun(cart(real,finite_sum(Q120993,Q120995)),prod(cart(real,finite_sum(Q120993,Q120995)),cart(real,finite_sum(Q120993,Q120995)))),i(s(fun(cart(real,finite_sum(Q120993,Q120995)),fun(cart(real,finite_sum(Q120993,Q120995)),prod(cart(real,finite_sum(Q120993,Q120995)),cart(real,finite_sum(Q120993,Q120995))))),c_),s(cart(real,finite_sum(Q120993,Q120995)),X))),s(cart(real,finite_sum(Q120993,Q120995)),Y))))))))) # label(aDISTu_SNDCART) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3094 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y))))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,Y))))))) # label(aSQRTu_DIV) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3095 (all N all M all F0 ((all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) -> s(cart(real,M),Y) = s(cart(real,M),X))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (exists B0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,B0)))) & (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))),s(real,B0))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))))))))) # label(aLINEARu_INJECTIVEu_BOUNDEDu_BELOWu_POS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3096 (all A s(A,y) = s(A,i(s(fun(num,A),i(s(fun(cart(A,n20),fun(num,A)),d_),s(cart(A,n20),i(s(fun(list(A),cart(A,n20)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,y))),s(list(A),nil))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aVECTORu_2u_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3097 (all N all M all A5 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),N),cart(cart(real,N),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(cart(cart(real,N),M),A5)) # label(aMATRIXu_MULu_RID) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3098 (all N all S0 ((p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),g_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),S0)))))) # label(aDEPENDENTu_BIGGERSET) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3099 (all N s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),x))),s(cart(real,N),y))))),s(cart(real,N),z))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),x))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),y))),s(cart(real,N),z)))))) # label(aVECTORu_ADDu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3100 (all Q122036 all A5 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q122036),bool),bool),i(s(fun(cart(real,Q122036),fun(fun(cart(real,Q122036),bool),bool)),in),s(cart(real,Q122036),A5))),s(fun(cart(real,Q122036),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q122036),bool),bool),i(s(fun(cart(real,Q122036),fun(fun(cart(real,Q122036),bool),bool)),in),s(cart(real,Q122036),A5))),s(fun(cart(real,Q122036),bool),i(s(fun(fun(cart(real,Q122036),bool),fun(cart(real,Q122036),bool)),span),s(fun(cart(real,Q122036),bool),S0)))))))) # label(aSPANu_CLAUSESu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3101 (all N all F0 ((all X all Y (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) -> s(cart(real,N),X) = s(cart(real,N),Y))) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> (all Y exists X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),Y)))) # label(aLINEARu_INJECTIVEu_IMPu_SURJECTIVE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3102 (all Q103280 all Q103282 all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,Q103280),real),i(s(fun(cart(real,Q103280),fun(cart(real,Q103280),real)),dot),s(cart(real,Q103280),X))),s(cart(real,Q103280),X))))),s(real,i(s(fun(cart(real,Q103282),real),i(s(fun(cart(real,Q103282),fun(cart(real,Q103282),real)),dot),s(cart(real,Q103282),Y))),s(cart(real,Q103282),Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,Q103280),real),vectoru_norm),s(cart(real,Q103280),X))))),s(real,i(s(fun(cart(real,Q103282),real),vectoru_norm),s(cart(real,Q103282),Y)))))) # label(aNORMu_LT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3103 (all Q139083 s(real,i(s(fun(cart(real,Q139083),real),infnorm),s(cart(real,Q139083),i(s(fun(num,cart(real,Q139083)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aINFNORMu_0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3104 (all N all M all F0 all B0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> ((all X (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,B0)))))) <-> (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X)))))))))))) # label(aNORMu_BOUNDu_GENERALIZE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3105 (all Q132081 all S0 all X ((all Y (p(s(bool,i(s(fun(fun(cart(real,Q132081),bool),bool),i(s(fun(cart(real,Q132081),fun(fun(cart(real,Q132081),bool),bool)),in),s(cart(real,Q132081),Y))),s(fun(cart(real,Q132081),bool),S0)))) -> p(s(bool,i(s(fun(cart(real,Q132081),bool),i(s(fun(cart(real,Q132081),fun(cart(real,Q132081),bool)),orthogonal),s(cart(real,Q132081),X))),s(cart(real,Q132081),Y)))))) -> (all Y (p(s(bool,i(s(fun(fun(cart(real,Q132081),bool),bool),i(s(fun(cart(real,Q132081),fun(fun(cart(real,Q132081),bool),bool)),in),s(cart(real,Q132081),Y))),s(fun(cart(real,Q132081),bool),i(s(fun(fun(cart(real,Q132081),bool),fun(cart(real,Q132081),bool)),span),s(fun(cart(real,Q132081),bool),S0)))))) -> p(s(bool,i(s(fun(cart(real,Q132081),bool),i(s(fun(cart(real,Q132081),fun(cart(real,Q132081),bool)),orthogonal),s(cart(real,Q132081),X))),s(cart(real,Q132081),Y)))))))) # label(aORTHOGONALu_TOu_SPAN) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3106 (all Q121103 all Q121104 all X all Y s(real,i(s(fun(cart(real,finite_sum(Q121103,Q121104)),real),vectoru_norm),s(cart(real,finite_sum(Q121103,Q121104)),i(s(fun(cart(real,Q121104),cart(real,finite_sum(Q121103,Q121104))),i(s(fun(cart(real,Q121103),fun(cart(real,Q121104),cart(real,finite_sum(Q121103,Q121104)))),pastecart),s(cart(real,Q121103),X))),s(cart(real,Q121104),Y))))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q121103),real),vectoru_norm),s(cart(real,Q121103),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q121104),real),vectoru_norm),s(cart(real,Q121104),Y))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) # label(aNORMu_PASTECART) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3107 (all Q122839 all U_0 ((all A5 all X s(cart(real,Q122839),i(s(fun(cart(real,Q122839),cart(real,Q122839)),i(s(fun(cart(real,Q122839),fun(cart(real,Q122839),cart(real,Q122839))),vectoru_add),s(cart(real,Q122839),A5))),s(cart(real,Q122839),X))) = s(cart(real,Q122839),i(s(fun(cart(real,Q122839),cart(real,Q122839)),i(s(fun(cart(real,Q122839),fun(cart(real,Q122839),cart(real,Q122839))),U_0),s(cart(real,Q122839),A5))),s(cart(real,Q122839),X)))) -> (all S0 all A5 (p(s(bool,i(s(fun(fun(cart(real,Q122839),bool),bool),subspace),s(fun(cart(real,Q122839),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q122839),bool),bool),i(s(fun(cart(real,Q122839),fun(fun(cart(real,Q122839),bool),bool)),in),s(cart(real,Q122839),A5))),s(fun(cart(real,Q122839),bool),S0)))) -> s(fun(cart(real,Q122839),bool),i(s(fun(fun(cart(real,Q122839),bool),fun(cart(real,Q122839),bool)),i(s(fun(fun(cart(real,Q122839),cart(real,Q122839)),fun(fun(cart(real,Q122839),bool),fun(cart(real,Q122839),bool))),image),s(fun(cart(real,Q122839),cart(real,Q122839)),i(s(fun(cart(real,Q122839),fun(cart(real,Q122839),cart(real,Q122839))),U_0),s(cart(real,Q122839),A5))))),s(fun(cart(real,Q122839),bool),S0))) = s(fun(cart(real,Q122839),bool),S0))))) # label(aSUBSPACEu_TRANSLATIONu_SELF) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3108 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),sqrt),s(real,X)))))))) # label(aSQRTu_POSu_LE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3109 (all Q107219 all Q107222 all U_0 ((all A5 all X exists V ((s(Q107219,X) = s(Q107219,A5) <-> p(s(bool,V))) & s(cart(real,Q107222),i(s(fun(cart(real,Q107222),cart(real,Q107222)),i(s(fun(cart(real,Q107222),fun(cart(real,Q107222),cart(real,Q107222))),i(s(fun(bool,fun(cart(real,Q107222),fun(cart(real,Q107222),cart(real,Q107222)))),cond),s(bool,V))),s(cart(real,Q107222),b0))),s(cart(real,Q107222),i(s(fun(num,cart(real,Q107222)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q107222),i(s(fun(Q107219,cart(real,Q107222)),i(s(fun(Q107219,fun(Q107219,cart(real,Q107222))),U_0),s(Q107219,A5))),s(Q107219,X))))) -> (all S0 all A5 s(cart(real,Q107222),i(s(fun(cart(real,Q107222),cart(real,Q107222)),i(s(fun(cart(real,Q107222),fun(cart(real,Q107222),cart(real,Q107222))),i(s(fun(bool,fun(cart(real,Q107222),fun(cart(real,Q107222),cart(real,Q107222)))),cond),s(bool,i(s(fun(fun(Q107219,bool),bool),i(s(fun(Q107219,fun(fun(Q107219,bool),bool)),in),s(Q107219,A5))),s(fun(Q107219,bool),S0))))),s(cart(real,Q107222),b0))),s(cart(real,Q107222),i(s(fun(num,cart(real,Q107222)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q107222),i(s(fun(fun(Q107219,cart(real,Q107222)),cart(real,Q107222)),i(s(fun(fun(Q107219,bool),fun(fun(Q107219,cart(real,Q107222)),cart(real,Q107222))),vsum),s(fun(Q107219,bool),S0))),s(fun(Q107219,cart(real,Q107222)),i(s(fun(Q107219,fun(Q107219,cart(real,Q107222))),U_0),s(Q107219,A5)))))))) # label(aVSUMu_DELTA) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3110 (all Q138882 all N all U_1 ((all I0 s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,Q138882),fun(num,real)),d_),s(cart(real,Q138882),x))),s(num,I0))))) = s(real,i(s(fun(num,real),U_1),s(num,I0)))) -> (all U_0 ((all GENR_PVARR_375 ((exists I0 exists V (p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_375))),s(bool,V))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,Q138882),fun(num,real)),d_),s(cart(real,Q138882),x))),s(num,I0)))))))) & (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(real,bool),U_0),s(real,GENR_PVARR_375)))))) -> s(fun(real,bool),i(s(fun(fun(num,bool),fun(real,bool)),i(s(fun(fun(num,real),fun(fun(num,bool),fun(real,bool))),image),s(fun(num,real),U_1))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))) = s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),U_0))))))) # label(aINFNORMu_SETu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3111 (all N all U_0 ((all A5 all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),A5))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),U_0),s(cart(real,N),A5))),s(cart(real,N),X)))) -> (all A5 all X all L s(bool,i(s(fun(list(cart(real,N)),bool),i(s(fun(cart(real,N),fun(list(cart(real,N)),bool)),mem),s(cart(real,N),X))),s(list(cart(real,N)),L))) = s(bool,i(s(fun(list(cart(real,N)),bool),i(s(fun(cart(real,N),fun(list(cart(real,N)),bool)),mem),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),A5))),s(cart(real,N),X))))),s(list(cart(real,N)),i(s(fun(list(cart(real,N)),list(cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(list(cart(real,N)),list(cart(real,N)))),map0),s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),U_0),s(cart(real,N),A5))))),s(list(cart(real,N)),L)))))))) # label(aMEMu_TRANSLATION) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3112 (all N all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))))) # label(aINDEPENDENTu_BOUNDu_GENERAL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3113 (all Q121516 all X all C0 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q121516),bool),bool),subspace),s(fun(cart(real,Q121516),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q121516),bool),bool),i(s(fun(cart(real,Q121516),fun(fun(cart(real,Q121516),bool),bool)),in),s(cart(real,Q121516),X))),s(fun(cart(real,Q121516),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121516),bool),bool),i(s(fun(cart(real,Q121516),fun(fun(cart(real,Q121516),bool),bool)),in),s(cart(real,Q121516),i(s(fun(cart(real,Q121516),cart(real,Q121516)),i(s(fun(real,fun(cart(real,Q121516),cart(real,Q121516))),r_),s(real,C0))),s(cart(real,Q121516),X))))),s(fun(cart(real,Q121516),bool),S0)))))) # label(aSUBSPACEu_MUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3114 (all X p(s(bool,i(s(fun(real,bool),p0),s(real,X))))) <-> (all X p(s(bool,i(s(fun(real,bool),p0),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))))) # label(aFORALLu_DROP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3115 (all X s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X)))) # label(adrop) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3116 (all N all U_0 ((all GENR_PVARR_374 (p(s(bool,i(s(fun(real,bool),U_0),s(real,GENR_PVARR_374)))) <-> (exists I0 exists V (p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_374))),s(bool,V))),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),x))),s(num,I0)))))))) & (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) <-> p(s(bool,V))))))) -> s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),U_0))))) = s(real,i(s(fun(cart(real,N),real),infnorm),s(cart(real,N),x))))) # label(ainfnorm) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3117 (all N all M all A5 all X all C0 s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,C0))),s(cart(real,M),X)))))) # label(aMATRIXu_VECTORu_MULu_RMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3118 (all Q111583 all Q111590 all U_0 ((all F0 all X s(cart(real,Q111590),i(s(fun(cart(real,Q111583),cart(real,Q111590)),i(s(fun(fun(cart(real,Q111583),cart(real,Q111590)),fun(cart(real,Q111583),cart(real,Q111590))),U_0),s(fun(cart(real,Q111583),cart(real,Q111590)),F0))),s(cart(real,Q111583),X))) = s(cart(real,Q111590),i(s(fun(cart(real,Q111590),cart(real,Q111590)),vectoru_neg),s(cart(real,Q111590),i(s(fun(cart(real,Q111583),cart(real,Q111590)),F0),s(cart(real,Q111583),X)))))) -> (all F0 (p(s(bool,i(s(fun(fun(cart(real,Q111583),cart(real,Q111590)),bool),linear),s(fun(cart(real,Q111583),cart(real,Q111590)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q111583),cart(real,Q111590)),bool),linear),s(fun(cart(real,Q111583),cart(real,Q111590)),i(s(fun(fun(cart(real,Q111583),cart(real,Q111590)),fun(cart(real,Q111583),cart(real,Q111590))),U_0),s(fun(cart(real,Q111583),cart(real,Q111590)),F0)))))))))) # label(aLINEARu_COMPOSEu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3119 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),sqrt),s(real,X)))))))) # label(aSQRTu_POSu_LT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3120 (all N all M all U_0 ((all A5 all X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),U_0),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X)))) -> (all A5 s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),U_0),s(cart(cart(real,M),N),A5))))),s(fun(cart(real,M),bool),univ)))))))) # label(aRANKu_DIMu_IM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3121 (all N all A5 all AI_ (s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),A5))),s(cart(cart(real,N),N),AI_))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) <-> s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),N),cart(cart(real,N),N)),i(s(fun(cart(cart(real,N),N),fun(cart(cart(real,N),N),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,N),N),AI_))),s(cart(cart(real,N),N),A5))))) # label(aMATRIXu_LEFTu_RIGHTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3122 (all N all M all U_0 ((all A5 all X s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X)))) -> (all A5 s(cart(cart(real,N),M),i(s(fun(fun(cart(real,N),cart(real,M)),cart(cart(real,N),M)),matrix),s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,N),M),A5)))) # label(aMATRIXu_OFu_MATRIXu_VECTORu_MUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3123 (all Q100029 s(cart(real,Q100029),i(s(fun(cart(real,Q100029),cart(real,Q100029)),vectoru_neg),s(cart(real,Q100029),i(s(fun(cart(real,Q100029),cart(real,Q100029)),i(s(fun(real,fun(cart(real,Q100029),cart(real,Q100029))),r_),s(real,c))),s(cart(real,Q100029),x))))) = s(cart(real,Q100029),i(s(fun(cart(real,Q100029),cart(real,Q100029)),i(s(fun(real,fun(cart(real,Q100029),cart(real,Q100029))),r_),s(real,i(s(fun(real,real),realu_neg),s(real,c))))),s(cart(real,Q100029),x)))) # label(aVECTORu_MULu_LNEG) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3124 (all Q110681 all X all Y s(bool,i(s(fun(cart(real,Q110681),bool),i(s(fun(cart(real,Q110681),fun(cart(real,Q110681),bool)),orthogonal),s(cart(real,Q110681),Y))),s(cart(real,Q110681),X))) = s(bool,i(s(fun(cart(real,Q110681),bool),i(s(fun(cart(real,Q110681),fun(cart(real,Q110681),bool)),orthogonal),s(cart(real,Q110681),X))),s(cart(real,Q110681),Y)))) # label(aORTHOGONALu_SYM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3125 (all N all V all B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),B0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),V)))))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))))) # label(aCARDu_LEu_DIMu_SPANNING) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3126 (all Q121390 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(num,cart(real,Q121390)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q121390),bool),S0)))) & (all C0 all X (p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(real,fun(cart(real,Q121390),cart(real,Q121390))),r_),s(real,C0))),s(cart(real,Q121390),X))))),s(fun(cart(real,Q121390),bool),S0)))))) & (all X all Y (p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),Y))),s(fun(cart(real,Q121390),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),X))),s(fun(cart(real,Q121390),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),i(s(fun(cart(real,Q121390),fun(fun(cart(real,Q121390),bool),bool)),in),s(cart(real,Q121390),i(s(fun(cart(real,Q121390),cart(real,Q121390)),i(s(fun(cart(real,Q121390),fun(cart(real,Q121390),cart(real,Q121390))),vectoru_add),s(cart(real,Q121390),X))),s(cart(real,Q121390),Y))))),s(fun(cart(real,Q121390),bool),S0)))))) <-> p(s(bool,i(s(fun(fun(cart(real,Q121390),bool),bool),subspace),s(fun(cart(real,Q121390),bool),S0)))))) # label(asubspace) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3127 (all Q105678 all Q105681 all U_0 ((all C0 all V all X s(cart(real,Q105681),i(s(fun(cart(real,Q105681),cart(real,Q105681)),i(s(fun(real,fun(cart(real,Q105681),cart(real,Q105681))),r_),s(real,i(s(fun(Q105678,real),C0),s(Q105678,X))))),s(cart(real,Q105681),V))) = s(cart(real,Q105681),i(s(fun(Q105678,cart(real,Q105681)),i(s(fun(cart(real,Q105681),fun(Q105678,cart(real,Q105681))),i(s(fun(fun(Q105678,real),fun(cart(real,Q105681),fun(Q105678,cart(real,Q105681)))),U_0),s(fun(Q105678,real),C0))),s(cart(real,Q105681),V))),s(Q105678,X)))) -> (all C0 all S0 all V s(cart(real,Q105681),i(s(fun(cart(real,Q105681),cart(real,Q105681)),i(s(fun(real,fun(cart(real,Q105681),cart(real,Q105681))),r_),s(real,i(s(fun(fun(Q105678,real),real),i(s(fun(fun(Q105678,bool),fun(fun(Q105678,real),real)),sum),s(fun(Q105678,bool),S0))),s(fun(Q105678,real),C0))))),s(cart(real,Q105681),V))) = s(cart(real,Q105681),i(s(fun(fun(Q105678,cart(real,Q105681)),cart(real,Q105681)),i(s(fun(fun(Q105678,bool),fun(fun(Q105678,cart(real,Q105681)),cart(real,Q105681))),vsum),s(fun(Q105678,bool),S0))),s(fun(Q105678,cart(real,Q105681)),i(s(fun(cart(real,Q105681),fun(Q105678,cart(real,Q105681))),i(s(fun(fun(Q105678,real),fun(cart(real,Q105681),fun(Q105678,cart(real,Q105681)))),U_0),s(fun(Q105678,real),C0))),s(cart(real,Q105681),V)))))))) # label(aVSUMu_RMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3128 (all N all M all U_0 ((all A5 all GENR_PVARR_292 ((exists I0 exists V ((p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(bool,fun(cart(real,M),bool)),i(s(fun(cart(real,M),fun(bool,fun(cart(real,M),bool))),setspec),s(cart(real,M),GENR_PVARR_292))),s(bool,V))),s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),A5)))))))) <-> p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,M),GENR_PVARR_292)))))) -> (all A5 s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),gspec),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),U_0),s(cart(cart(real,N),M),A5))))) = s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),columns),s(cart(cart(real,N),M),A5)))))) # label(acolumns) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3129 (all M all N all P all U_1 ((all H0 all F0 all G0 all K0 s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_1),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_sub),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,K0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) -> (all U_0 ((all H0 all F0 all G0 all K0 s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,K0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0))))))) = s(cart(real,P),i(s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0)))) -> (all F0 all G0 all H0 all M0 all N0 (p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0)))) -> s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),i(s(fun(bool,fun(cart(real,P),fun(cart(real,P),cart(real,P)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),vectoru_sub),s(cart(real,P),i(s(fun(cart(real,P),cart(real,P)),i(s(fun(cart(real,P),fun(cart(real,P),cart(real,P))),vectoru_sub),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0),s(cart(real,M),i(s(fun(num,cart(real,M)),F0),s(num,M0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,M0))))))))),s(cart(real,P),i(s(fun(fun(num,cart(real,P)),cart(real,P)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,P)),cart(real,P))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_1),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))))))))),s(cart(real,P),i(s(fun(num,cart(real,P)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,P),i(s(fun(fun(num,cart(real,P)),cart(real,P)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,P)),cart(real,P))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,P)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,P))),i(s(fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P)))),i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),fun(fun(num,cart(real,M)),fun(fun(num,cart(real,N)),fun(num,cart(real,P))))),U_0),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),H0))),s(fun(num,cart(real,M)),F0))),s(fun(num,cart(real,N)),G0))))))))))) # label(aBILINEARu_VSUMu_PARTIALu_SUC) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3130 (all N all I0 all J0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & s(num,I0) != s(num,J0) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0))) != s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))) # label(aBASISu_NE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3131 (all Q143335 all P0 all F0 all S0 ((all G0 all T0 (p(s(bool,i(s(fun(fun(cart(real,Q143335),cart(real,Q143335)),bool),linear),s(fun(cart(real,Q143335),cart(real,Q143335)),G0)))) & p(s(bool,i(s(fun(fun(cart(real,Q143335),bool),bool),P0),s(fun(cart(real,Q143335),bool),T0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q143335),bool),bool),P0),s(fun(cart(real,Q143335),bool),i(s(fun(fun(cart(real,Q143335),bool),fun(cart(real,Q143335),bool)),i(s(fun(fun(cart(real,Q143335),cart(real,Q143335)),fun(fun(cart(real,Q143335),bool),fun(cart(real,Q143335),bool))),image),s(fun(cart(real,Q143335),cart(real,Q143335)),G0))),s(fun(cart(real,Q143335),bool),T0)))))))) & (all X all Y (s(cart(real,Q143335),i(s(fun(cart(real,Q143335),cart(real,Q143335)),F0),s(cart(real,Q143335),Y))) = s(cart(real,Q143335),i(s(fun(cart(real,Q143335),cart(real,Q143335)),F0),s(cart(real,Q143335),X))) -> s(cart(real,Q143335),Y) = s(cart(real,Q143335),X))) & p(s(bool,i(s(fun(fun(cart(real,Q143335),cart(real,Q143335)),bool),linear),s(fun(cart(real,Q143335),cart(real,Q143335)),F0)))) -> s(bool,i(s(fun(fun(cart(real,Q143335),bool),bool),P0),s(fun(cart(real,Q143335),bool),i(s(fun(fun(cart(real,Q143335),bool),fun(cart(real,Q143335),bool)),i(s(fun(fun(cart(real,Q143335),cart(real,Q143335)),fun(fun(cart(real,Q143335),bool),fun(cart(real,Q143335),bool))),image),s(fun(cart(real,Q143335),cart(real,Q143335)),F0))),s(fun(cart(real,Q143335),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,Q143335),bool),bool),P0),s(fun(cart(real,Q143335),bool),S0))))) # label(aWLOGu_LINEARu_INJECTIVEu_IMAGEu_ALT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3132 (all Q140433 all X all Y ((exists C0 s(cart(real,Q140433),i(s(fun(cart(real,Q140433),cart(real,Q140433)),i(s(fun(real,fun(cart(real,Q140433),cart(real,Q140433))),r_),s(real,C0))),s(cart(real,Q140433),X))) = s(cart(real,Q140433),Y)) | s(cart(real,Q140433),i(s(fun(num,cart(real,Q140433)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q140433),X) <-> p(s(bool,i(s(fun(fun(cart(real,Q140433),bool),bool),collinear),s(fun(cart(real,Q140433),bool),i(s(fun(fun(cart(real,Q140433),bool),fun(cart(real,Q140433),bool)),i(s(fun(cart(real,Q140433),fun(fun(cart(real,Q140433),bool),fun(cart(real,Q140433),bool))),insert),s(cart(real,Q140433),i(s(fun(num,cart(real,Q140433)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q140433),bool),i(s(fun(fun(cart(real,Q140433),bool),fun(cart(real,Q140433),bool)),i(s(fun(cart(real,Q140433),fun(fun(cart(real,Q140433),bool),fun(cart(real,Q140433),bool))),insert),s(cart(real,Q140433),X))),s(fun(cart(real,Q140433),bool),i(s(fun(fun(cart(real,Q140433),bool),fun(cart(real,Q140433),bool)),i(s(fun(cart(real,Q140433),fun(fun(cart(real,Q140433),bool),fun(cart(real,Q140433),bool))),insert),s(cart(real,Q140433),Y))),s(fun(cart(real,Q140433),bool),empty)))))))))))) # label(aCOLLINEARu_LEMMAu_ALT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.87 3133 (all M all N all U_0 ((all X all F0 all J0 all I0 s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real))),i(s(fun(cart(real,M),fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real)))),U_0),s(cart(real,M),X))),s(fun(cart(real,M),cart(real,N)),F0))),s(num,J0))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),d_),s(cart(real,M),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0))))))),s(num,J0)))))) -> (all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (all X all J0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0)))) -> s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))))),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real))),i(s(fun(cart(real,M),fun(fun(cart(real,M),cart(real,N)),fun(num,fun(num,real)))),U_0),s(cart(real,M),X))),s(fun(cart(real,M),cart(real,N)),F0))),s(num,J0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(num,J0))))))))) # label(aLINEARu_COMPONENTWISE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3134 (all N p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),univ))))) # label(aSUBSPACEu_UNIV) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3135 (all N all M all A5 all B0 s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,M),N),cart(cart(real,M),N))),matrixu_add),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0)))))) # label(aTRANSPu_MATRIXu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3136 (all N all M all P0 all Q0 ((all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),P0),s(fun(cart(real,M),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),Q0),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0)))))))) & (all G0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),Q0),s(fun(cart(real,N),bool),T0)))) -> p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),P0),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,M),bool)),i(s(fun(fun(cart(real,N),cart(real,M)),fun(fun(cart(real,N),bool),fun(cart(real,M),bool))),image),s(fun(cart(real,N),cart(real,M)),G0))),s(fun(cart(real,N),bool),T0)))))))) -> (all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & (all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) -> s(cart(real,M),X) = s(cart(real,M),Y))) -> (all S0 s(bool,i(s(fun(fun(cart(real,M),bool),bool),P0),s(fun(cart(real,M),bool),S0))) = s(bool,i(s(fun(fun(cart(real,N),bool),bool),Q0),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0)))))))))) # label(aWLOGu_LINEARu_INJECTIVEu_IMAGEu_2) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3137 (all M all N all A5 all X all Y s(real,i(s(fun(cart(real,M),real),i(s(fun(cart(real,M),fun(cart(real,M),real)),dot),s(cart(real,M),X))),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),Y))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(cart(real,M),fun(cart(cart(real,N),M),cart(real,N))),vectoru_matrixu_mul),s(cart(real,M),X))),s(cart(cart(real,N),M),A5))))),s(cart(real,N),Y)))) # label(aDOTu_LMULu_MATRIX) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3138 (all N all U_0 ((all N0 all I0 s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))) = s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),U_0),s(num,N0))),s(num,I0)))) -> (all N0 s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),U_0),s(num,N0))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,N0)))))) # label(avec) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3139 (all Q141441 all A5 all B0 all C0 all D0 (p(s(bool,i(s(fun(prod(cart(real,Q141441),cart(real,Q141441)),bool),i(s(fun(cart(real,Q141441),fun(prod(cart(real,Q141441),cart(real,Q141441)),bool)),between),s(cart(real,Q141441),A5))),s(prod(cart(real,Q141441),cart(real,Q141441)),i(s(fun(cart(real,Q141441),prod(cart(real,Q141441),cart(real,Q141441))),i(s(fun(cart(real,Q141441),fun(cart(real,Q141441),prod(cart(real,Q141441),cart(real,Q141441)))),c_),s(cart(real,Q141441),B0))),s(cart(real,Q141441),C0)))))) & p(s(bool,i(s(fun(prod(cart(real,Q141441),cart(real,Q141441)),bool),i(s(fun(cart(real,Q141441),fun(prod(cart(real,Q141441),cart(real,Q141441)),bool)),between),s(cart(real,Q141441),D0))),s(prod(cart(real,Q141441),cart(real,Q141441)),i(s(fun(cart(real,Q141441),prod(cart(real,Q141441),cart(real,Q141441))),i(s(fun(cart(real,Q141441),fun(cart(real,Q141441),prod(cart(real,Q141441),cart(real,Q141441)))),c_),s(cart(real,Q141441),A5))),s(cart(real,Q141441),C0)))))) -> p(s(bool,i(s(fun(prod(cart(real,Q141441),cart(real,Q141441)),bool),i(s(fun(cart(real,Q141441),fun(prod(cart(real,Q141441),cart(real,Q141441)),bool)),between),s(cart(real,Q141441),D0))),s(prod(cart(real,Q141441),cart(real,Q141441)),i(s(fun(cart(real,Q141441),prod(cart(real,Q141441),cart(real,Q141441))),i(s(fun(cart(real,Q141441),fun(cart(real,Q141441),prod(cart(real,Q141441),cart(real,Q141441)))),c_),s(cart(real,Q141441),B0))),s(cart(real,Q141441),C0)))))))) # label(aBETWEENu_TRANS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3140 (all N all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),union),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0)))))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0)))) | p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),T0))),s(fun(cart(real,N),bool),S0)))))) # label(aSUBSPACEu_UNIONu_CHAIN) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3141 (all N all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),X))),s(cart(real,N),Y))))))))))) # label(aNORMu_TRIANGLEu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3142 (all N all M all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (all X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))) # label(aMATRIXu_VECTORu_MUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3143 (all N all M all A5 all X all Y s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_sub),s(cart(real,M),X))),s(cart(real,M),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),Y)))))) # label(aMATRIXu_VECTORu_MULu_SUBu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3144 (all T0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,real),T0)))) # label(aSUMu_2) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3145 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> s(real,i(s(fun(real,real),sqrt),s(real,X))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,X))),s(real,i(s(fun(real,real),sqrt),s(real,X))))))) # label(aREALu_DIVu_SQRT) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3146 (all Q118371 all Q118373 all Q118374 all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,Q118373),cart(real,Q118374)),bool),linear),s(fun(cart(real,Q118373),cart(real,Q118374)),G0)))) & p(s(bool,i(s(fun(fun(cart(real,Q118374),cart(real,Q118371)),bool),linear),s(fun(cart(real,Q118374),cart(real,Q118371)),F0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(cart(real,Q118373),cart(real,Q118371)),real),onorm),s(fun(cart(real,Q118373),cart(real,Q118371)),i(s(fun(fun(cart(real,Q118373),cart(real,Q118374)),fun(cart(real,Q118373),cart(real,Q118371))),i(s(fun(fun(cart(real,Q118374),cart(real,Q118371)),fun(fun(cart(real,Q118373),cart(real,Q118374)),fun(cart(real,Q118373),cart(real,Q118371)))),o),s(fun(cart(real,Q118374),cart(real,Q118371)),F0))),s(fun(cart(real,Q118373),cart(real,Q118374)),G0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(fun(cart(real,Q118374),cart(real,Q118371)),real),onorm),s(fun(cart(real,Q118374),cart(real,Q118371)),F0))))),s(real,i(s(fun(fun(cart(real,Q118373),cart(real,Q118374)),real),onorm),s(fun(cart(real,Q118373),cart(real,Q118374)),G0)))))))))) # label(aONORMu_COMPOSE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3147 (all N all M all A5 (s(fun(cart(real,M),bool),univ) = s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),bool)),columns),s(cart(cart(real,N),M),A5))))) <-> (exists B0 s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),B0))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aMATRIXu_RIGHTu_INVERTIBLEu_SPANu_COLUMNS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3148 (all N all F0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> ((exists G0 (s(fun(cart(real,N),cart(real,N)),i1) = s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),G0))),s(fun(cart(real,N),cart(real,N)),F0))) & s(fun(cart(real,N),cart(real,N)),i1) = s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,N)),G0))) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),G0)))))) <-> p(s(bool,i(s(fun(cart(cart(real,N),N),bool),invertible),s(cart(cart(real,N),N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(cart(real,N),N)),matrix),s(fun(cart(real,N),cart(real,N)),F0))))))))) # label(aMATRIXu_INVERTIBLE) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3149 (all M all N all X all C0 s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),X))))) = s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(real,fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),r_),s(real,C0))),s(cart(real,finite_sum(M,N)),X)))))) # label(aSNDCARTu_CMUL) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3150 (all N all M all A5 s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,N),bool)),columns),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))) = s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),rows),s(cart(cart(real,N),M),A5)))) # label(aCOLUMNSu_TRANSP) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3151 (all N all M all A5 all B0 s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,M),N),cart(cart(real,M),N))),matrixu_sub),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),B0)))))) # label(aTRANSPu_MATRIXu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3152 (all N all M all F0 all B0 (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),independent),s(fun(cart(real,M),bool),B0)))) -> (exists G0 ((all X (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),B0)))) -> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),G0),s(cart(real,M),X))))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),G0)))))))) # label(aLINEARu_INDEPENDENTu_EXTEND) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3153 (all Q131992 all U_0 ((all X all GENR_PVARR_327 (p(s(bool,i(s(fun(cart(real,Q131992),bool),i(s(fun(cart(real,Q131992),fun(cart(real,Q131992),bool)),U_0),s(cart(real,Q131992),X))),s(cart(real,Q131992),GENR_PVARR_327)))) <-> (exists Y p(s(bool,i(s(fun(cart(real,Q131992),bool),i(s(fun(bool,fun(cart(real,Q131992),bool)),i(s(fun(cart(real,Q131992),fun(bool,fun(cart(real,Q131992),bool))),setspec),s(cart(real,Q131992),GENR_PVARR_327))),s(bool,i(s(fun(cart(real,Q131992),bool),i(s(fun(cart(real,Q131992),fun(cart(real,Q131992),bool)),orthogonal),s(cart(real,Q131992),X))),s(cart(real,Q131992),Y))))),s(cart(real,Q131992),Y))))))) -> (all X p(s(bool,i(s(fun(fun(cart(real,Q131992),bool),bool),subspace),s(fun(cart(real,Q131992),bool),i(s(fun(fun(cart(real,Q131992),bool),fun(cart(real,Q131992),bool)),gspec),s(fun(cart(real,Q131992),bool),i(s(fun(cart(real,Q131992),fun(cart(real,Q131992),bool)),U_0),s(cart(real,Q131992),X))))))))))) # label(aSUBSPACEu_ORTHOGONALu_TOu_VECTOR) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3154 (all U_0 ((all X all I0 s(real,X) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))),s(num,I0)))) -> (all X s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))) = s(cart(real,n10),i(s(fun(fun(num,real),cart(real,n10)),lambda),s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X)))))))) # label(alift) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3155 (all N all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(cart(real,N),N),fun(cart(real,N),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(real,N),X))) = s(cart(real,N),X)) # label(aMATRIXu_VECTORu_MULu_LID) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3156 (all M all N all A5 s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,N),bool)),columns),s(cart(cart(real,M),N),A5)))))) # label(arank) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3157 (all A all N all U_2 ((all P0 all X (-p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_2),s(fun(A,bool),P0))),s(A,X)))))) -> (all U_1 ((all S0 all P0 all GENR_PVARR_279 ((exists X exists V ((p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(A,bool),P0),s(A,X)))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_279))),s(bool,V))),s(A,X)))))) <-> p(s(bool,i(s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),P0))),s(A,GENR_PVARR_279)))))) -> (all U_0 ((all P0 all F0 all G0 all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),i(s(fun(bool,fun(cart(real,N),fun(cart(real,N),cart(real,N)))),cond),s(bool,i(s(fun(A,bool),P0),s(A,X))))),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))))),s(cart(real,N),i(s(fun(A,cart(real,N)),G0),s(A,X))))) = s(cart(real,N),i(s(fun(A,cart(real,N)),i(s(fun(fun(A,cart(real,N)),fun(A,cart(real,N))),i(s(fun(fun(A,cart(real,N)),fun(fun(A,cart(real,N)),fun(A,cart(real,N)))),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),fun(fun(A,cart(real,N)),fun(A,cart(real,N))))),U_0),s(fun(A,bool),P0))),s(fun(A,cart(real,N)),F0))),s(fun(A,cart(real,N)),G0))),s(A,X)))) -> (all S0 all P0 all F0 all G0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),P0))))))),s(fun(A,cart(real,N)),F0))))),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),U_1),s(fun(A,bool),S0))),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),U_2),s(fun(A,bool),P0))))))))),s(fun(A,cart(real,N)),G0))))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),i(s(fun(fun(A,cart(real,N)),fun(A,cart(real,N))),i(s(fun(fun(A,cart(real,N)),fun(fun(A,cart(real,N)),fun(A,cart(real,N)))),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),fun(fun(A,cart(real,N)),fun(A,cart(real,N))))),U_0),s(fun(A,bool),P0))),s(fun(A,cart(real,N)),F0))),s(fun(A,cart(real,N)),G0))))))))))))) # label(aVSUMu_CASES) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3158 (all M all N all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))))))) & (all B0 ((all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))))),s(real,B0)))))))) # label(aONORM) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3159 (all A all N all U_1 ((all F0 all I0 all X s(real,i(s(fun(A,real),i(s(fun(num,fun(A,real)),i(s(fun(fun(A,cart(real,N)),fun(num,fun(A,real))),U_1),s(fun(A,cart(real,N)),F0))),s(num,I0))),s(A,X))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))))),s(num,I0)))) -> (all U_0 ((all S0 all F0 all I0 s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),S0))),s(fun(A,real),i(s(fun(num,fun(A,real)),i(s(fun(fun(A,cart(real,N)),fun(num,fun(A,real))),U_1),s(fun(A,cart(real,N)),F0))),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(fun(A,cart(real,N)),fun(num,real)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),fun(num,real))),U_0),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))),s(num,I0)))) -> (all S0 all F0 s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(fun(A,cart(real,N)),fun(num,real)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),fun(num,real))),U_0),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0)))))))))) # label(avsum) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3160 (all N all M s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),a))),s(cart(cart(real,N),M),b))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),b))),s(cart(cart(real,N),M),a)))) # label(aMATRIXu_ADDu_ACu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3161 (all Q107857 all U_0 ((all K0 s(cart(real,Q107857),i(s(fun(cart(real,Q107857),cart(real,Q107857)),i(s(fun(cart(real,Q107857),fun(cart(real,Q107857),cart(real,Q107857))),vectoru_sub),s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),f),s(num,K0))))),s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),U_0),s(num,K0)))) -> (all M0 all N0 s(cart(real,Q107857),i(s(fun(cart(real,Q107857),cart(real,Q107857)),i(s(fun(cart(real,Q107857),fun(cart(real,Q107857),cart(real,Q107857))),i(s(fun(bool,fun(cart(real,Q107857),fun(cart(real,Q107857),cart(real,Q107857)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,Q107857),i(s(fun(cart(real,Q107857),cart(real,Q107857)),i(s(fun(cart(real,Q107857),fun(cart(real,Q107857),cart(real,Q107857))),vectoru_sub),s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),f),s(num,M0))))),s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(cart(real,Q107857),i(s(fun(num,cart(real,Q107857)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q107857),i(s(fun(fun(num,cart(real,Q107857)),cart(real,Q107857)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107857)),cart(real,Q107857))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107857)),U_0)))))) # label(aVSUMu_DIFFS) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3162 (all N all A5 all B0 all X all Y (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,B0))),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,A5))),s(cart(real,N),X))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,B0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,A5)))) -> s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))),s(cart(real,N),X))))) # label(aNORMu_CROSSu_MULTIPLY) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3163 (all Q112492 all Q112477 all Q112491 all H0 all X all Y (p(s(bool,i(s(fun(fun(cart(real,Q112477),fun(cart(real,Q112491),cart(real,Q112492))),bool),bilinear),s(fun(cart(real,Q112477),fun(cart(real,Q112491),cart(real,Q112492))),H0)))) -> s(cart(real,Q112492),i(s(fun(cart(real,Q112492),cart(real,Q112492)),vectoru_neg),s(cart(real,Q112492),i(s(fun(cart(real,Q112491),cart(real,Q112492)),i(s(fun(cart(real,Q112477),fun(cart(real,Q112491),cart(real,Q112492))),H0),s(cart(real,Q112477),X))),s(cart(real,Q112491),Y))))) = s(cart(real,Q112492),i(s(fun(cart(real,Q112491),cart(real,Q112492)),i(s(fun(cart(real,Q112477),fun(cart(real,Q112491),cart(real,Q112492))),H0),s(cart(real,Q112477),X))),s(cart(real,Q112491),i(s(fun(cart(real,Q112491),cart(real,Q112491)),vectoru_neg),s(cart(real,Q112491),Y))))))) # label(aBILINEARu_RNEG) # label(axiom) # label(non_clause). [assumption]. 15.81/15.88 3164 (all Q117843 all Q117844 all F0 (p(s(bool,i(s(fun(fun(cart(real,Q117843),cart(real,Q117844)),bool),linear),s(fun(cart(real,Q117843),cart(real,Q117844)),F0)))) -> s(cart(cart(real,Q117844),Q117843),i(s(fun(fun(cart(real,Q117844),cart(real,Q117843)),cart(cart(real,Q117844),Q117843)),matrix),s(fun(cart(real,Q117844),cart(real,Q117843)),i(s(fun(fun(cart(real,Q117843),cart(real,Q117844)),fun(cart(real,Q117844),cart(real,Q117843))),adjoint),s(fun(cart(real,Q117843),cart(real,Q117844)),F0))))) = s(cart(cart(real,Q117844),Q117843),i(s(fun(cart(cart(real,Q117843),Q117844),cart(cart(real,Q117844),Q117843)),transp),s(cart(cart(real,Q117843),Q117844),i(s(fun(fun(cart(real,Q117843),cart(real,Q117844)),cart(cart(real,Q117843),Q117844)),matrix),s(fun(cart(real,Q117843),cart(real,Q117844)),F0))))))) # label(aMATRIXu_ADJOINT) # label(axiom) # label(non_clause). [assumption]. 15.91/15.88 3165 (all Q104777 all X all Y all Z0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q104777),cart(real,Q104777)),real),distance),s(prod(cart(real,Q104777),cart(real,Q104777)),i(s(fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777))),i(s(fun(cart(real,Q104777),fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777)))),c_),s(cart(real,Q104777),Y))),s(cart(real,Q104777),Z0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,Q104777),cart(real,Q104777)),real),distance),s(prod(cart(real,Q104777),cart(real,Q104777)),i(s(fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777))),i(s(fun(cart(real,Q104777),fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777)))),c_),s(cart(real,Q104777),X))),s(cart(real,Q104777),Y))))))),s(real,i(s(fun(prod(cart(real,Q104777),cart(real,Q104777)),real),distance),s(prod(cart(real,Q104777),cart(real,Q104777)),i(s(fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777))),i(s(fun(cart(real,Q104777),fun(cart(real,Q104777),prod(cart(real,Q104777),cart(real,Q104777)))),c_),s(cart(real,Q104777),X))),s(cart(real,Q104777),Z0))))))))))) # label(aDISTu_TRIANGLEu_ALT) # label(axiom) # label(non_clause). [assumption]. 15.91/15.88 3166 (all Q115612 all Q115613 all C0 s(cart(cart(real,Q115612),Q115613),i(s(fun(num,cart(cart(real,Q115612),Q115613)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(cart(real,Q115612),Q115613),i(s(fun(cart(cart(real,Q115612),Q115613),cart(cart(real,Q115612),Q115613)),i(s(fun(real,fun(cart(cart(real,Q115612),Q115613),cart(cart(real,Q115612),Q115613))),r_r_),s(real,C0))),s(cart(cart(real,Q115612),Q115613),i(s(fun(num,cart(cart(real,Q115612),Q115613)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aMATRIXu_CMULu_RZERO) # label(axiom) # label(non_clause). [assumption]. 15.91/15.88 3167 (all Q121402 all S0 s(fun(cart(real,Q121402),bool),i(s(fun(fun(cart(real,Q121402),bool),fun(cart(real,Q121402),bool)),i(s(fun(fun(fun(cart(real,Q121402),bool),bool),fun(fun(cart(real,Q121402),bool),fun(cart(real,Q121402),bool))),hull),s(fun(fun(cart(real,Q121402),bool),bool),subspace))),s(fun(cart(real,Q121402),bool),S0))) = s(fun(cart(real,Q121402),bool),i(s(fun(fun(cart(real,Q121402),bool),fun(cart(real,Q121402),bool)),span),s(fun(cart(real,Q121402),bool),S0)))) # label(aspan) # label(axiom) # label(non_clause). [assumption]. 15.91/15.88 3168 (all N all M all A5 all B0 all X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,M),N),cart(cart(real,M),N))),matrixu_sub),s(cart(cart(real,M),N),A5))),s(cart(cart(real,M),N),B0))))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),B0))),s(cart(real,M),X)))))) # label(aMATRIXu_VECTORu_MULu_SUBu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.91/15.88 3169 (all N all U_1 ((all F0 all G0 all K0 s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_1),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),F0),s(num,K0))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0)))))) -> (all U_0 ((all F0 all G0 all K0 s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_0),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))),s(num,K0))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,K0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,K0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) -> (all F0 all G0 all M0 all N0 s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_0),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),i(s(fun(bool,fun(cart(real,N),fun(cart(real,N),cart(real,N)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,N0))))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(num,real),F0),s(num,M0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),G0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))))),s(cart(real,N),i(s(fun(fun(num,cart(real,N)),cart(real,N)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,N)),cart(real,N))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,N)),i(s(fun(fun(num,cart(real,N)),fun(num,cart(real,N))),i(s(fun(fun(num,real),fun(fun(num,cart(real,N)),fun(num,cart(real,N)))),U_1),s(fun(num,real),F0))),s(fun(num,cart(real,N)),G0))))))))),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))))) # label(aVSUMu_PARTIALu_PRE) # label(axiom) # label(non_clause). [assumption]. 15.91/15.88 3170 (all N all A all F0 all P0 all S0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,i(s(fun(A,A),P0),s(A,X))))),s(fun(A,bool),S0)))))) & (all Y (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,Y))),s(fun(A,bool),S0)))) -> (exists X (s(A,i(s(fun(A,A),P0),s(A,X))) = s(A,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))))) & (all X all XI_ (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(A,Y) = s(A,i(s(fun(A,A),P0),s(A,X))) & s(A,i(s(fun(A,A),P0),s(A,XI_))) = s(A,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0)))) -> s(A,X) = s(A,XI_))))) -> s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),i(s(fun(fun(A,A),fun(A,cart(real,N))),i(s(fun(fun(A,cart(real,N)),fun(fun(A,A),fun(A,cart(real,N)))),o),s(fun(A,cart(real,N)),F0))),s(fun(A,A),P0))))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))) # label(aVSUMu_BIJECTION) # label(axiom) # label(non_clause). [assumption]. 15.91/15.88 3171 (all Q121570 all X all S0 (p(s(bool,i(s(fun(fun(cart(real,Q121570),bool),bool),i(s(fun(cart(real,Q121570),fun(fun(cart(real,Q121570),bool),bool)),in),s(cart(real,Q121570),X))),s(fun(cart(real,Q121570),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q121570),bool),bool),subspace),s(fun(cart(real,Q121570),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121570),bool),bool),i(s(fun(cart(real,Q121570),fun(fun(cart(real,Q121570),bool),bool)),in),s(cart(real,Q121570),i(s(fun(cart(real,Q121570),cart(real,Q121570)),vectoru_neg),s(cart(real,Q121570),X))))),s(fun(cart(real,Q121570),bool),S0)))))) # label(aSUBSPACEu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.91/15.88 3172 (all Q123857 all U_0 ((all A5 all B0 all C0 all GENR_PVARR_303 ((exists U exists V exists W exists V0 (p(s(bool,i(s(fun(cart(real,Q123857),bool),i(s(fun(bool,fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(bool,fun(cart(real,Q123857),bool))),setspec),s(cart(real,Q123857),GENR_PVARR_303))),s(bool,V0))),s(cart(real,Q123857),i(s(fun(cart(real,Q123857),cart(real,Q123857)),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),cart(real,Q123857))),vectoru_add),s(cart(real,Q123857),i(s(fun(cart(real,Q123857),cart(real,Q123857)),i(s(fun(real,fun(cart(real,Q123857),cart(real,Q123857))),r_),s(real,U))),s(cart(real,Q123857),A5))))),s(cart(real,Q123857),i(s(fun(cart(real,Q123857),cart(real,Q123857)),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),cart(real,Q123857))),vectoru_add),s(cart(real,Q123857),i(s(fun(cart(real,Q123857),cart(real,Q123857)),i(s(fun(real,fun(cart(real,Q123857),cart(real,Q123857))),r_),s(real,V))),s(cart(real,Q123857),B0))))),s(cart(real,Q123857),i(s(fun(cart(real,Q123857),cart(real,Q123857)),i(s(fun(real,fun(cart(real,Q123857),cart(real,Q123857))),r_),s(real,W))),s(cart(real,Q123857),C0)))))))))) & (p(s(bool,V0)) <-> p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,V))),s(fun(real,bool),univ)))) & p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,W))),s(fun(real,bool),univ)))) & p(s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,U))),s(fun(real,bool),univ))))))) <-> p(s(bool,i(s(fun(cart(real,Q123857),bool),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),bool))),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),bool)))),U_0),s(cart(real,Q123857),A5))),s(cart(real,Q123857),B0))),s(cart(real,Q123857),C0))),s(cart(real,Q123857),GENR_PVARR_303)))))) -> (all A5 all B0 all C0 s(fun(cart(real,Q123857),bool),i(s(fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool)),gspec),s(fun(cart(real,Q123857),bool),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),bool))),i(s(fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),fun(cart(real,Q123857),bool)))),U_0),s(cart(real,Q123857),A5))),s(cart(real,Q123857),B0))),s(cart(real,Q123857),C0))))) = s(fun(cart(real,Q123857),bool),i(s(fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool)),span),s(fun(cart(real,Q123857),bool),i(s(fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool))),insert),s(cart(real,Q123857),A5))),s(fun(cart(real,Q123857),bool),i(s(fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool))),insert),s(cart(real,Q123857),B0))),s(fun(cart(real,Q123857),bool),i(s(fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool)),i(s(fun(cart(real,Q123857),fun(fun(cart(real,Q123857),bool),fun(cart(real,Q123857),bool))),insert),s(cart(real,Q123857),C0))),s(fun(cart(real,Q123857),bool),empty)))))))))))) # label(aSPANu_3) # label(axiom) # label(non_clause). [assumption]. 15.91/15.88 3173 (all N all M all U_0 ((all S0 all F0 all GENR_PVARR_353 ((exists X exists V ((p(s(bool,V)) <-> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),S0))))) & p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(bool,fun(cart(real,M),bool)),i(s(fun(cart(real,M),fun(bool,fun(cart(real,M),bool))),setspec),s(cart(real,M),GENR_PVARR_353))),s(bool,V))),s(cart(real,M),X)))))) <-> p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool)),i(s(fun(fun(cart(real,M),bool),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool))),U_0),s(fun(cart(real,M),bool),S0))),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,M),GENR_PVARR_353)))))) -> (all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),subspace),s(fun(cart(real,M),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))))),s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),gspec),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool)),i(s(fun(fun(cart(real,M),bool),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool))),U_0),s(fun(cart(real,M),bool),S0))),s(fun(cart(real,M),cart(real,N)),F0))))))))) = s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),S0))))))) # label(aDIMu_IMAGEu_KERNELu_GEN) # label(axiom) # label(non_clause). [assumption]. 15.91/15.88 3174 (all Q122419 p(s(bool,i(s(fun(fun(cart(real,Q122419),bool),bool),i(s(fun(cart(real,Q122419),fun(fun(cart(real,Q122419),bool),bool)),in),s(cart(real,Q122419),i(s(fun(num,cart(real,Q122419)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q122419),bool),i(s(fun(fun(cart(real,Q122419),bool),fun(cart(real,Q122419),bool)),span),s(fun(cart(real,Q122419),bool),s0))))))) # label(aSPANu_0) # label(axiom) # label(non_clause). [assumption]. 15.91/15.88 3175 (all Q105536 all Q105541 all X all F0 all S0 (p(s(bool,i(s(fun(fun(Q105536,bool),bool),finite),s(fun(Q105536,bool),S0)))) -> s(cart(real,Q105541),i(s(fun(cart(real,Q105541),cart(real,Q105541)),i(s(fun(cart(real,Q105541),fun(cart(real,Q105541),cart(real,Q105541))),i(s(fun(bool,fun(cart(real,Q105541),fun(cart(real,Q105541),cart(real,Q105541)))),cond),s(bool,i(s(fun(fun(Q105536,bool),bool),i(s(fun(Q105536,fun(fun(Q105536,bool),bool)),in),s(Q105536,X))),s(fun(Q105536,bool),S0))))),s(cart(real,Q105541),i(s(fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541)),i(s(fun(fun(Q105536,bool),fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541))),vsum),s(fun(Q105536,bool),S0))),s(fun(Q105536,cart(real,Q105541)),F0))))),s(cart(real,Q105541),i(s(fun(cart(real,Q105541),cart(real,Q105541)),i(s(fun(cart(real,Q105541),fun(cart(real,Q105541),cart(real,Q105541))),vectoru_add),s(cart(real,Q105541),i(s(fun(Q105536,cart(real,Q105541)),F0),s(Q105536,X))))),s(cart(real,Q105541),i(s(fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541)),i(s(fun(fun(Q105536,bool),fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541))),vsum),s(fun(Q105536,bool),S0))),s(fun(Q105536,cart(real,Q105541)),F0))))))) = s(cart(real,Q105541),i(s(fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541)),i(s(fun(fun(Q105536,bool),fun(fun(Q105536,cart(real,Q105541)),cart(real,Q105541))),vsum),s(fun(Q105536,bool),i(s(fun(fun(Q105536,bool),fun(Q105536,bool)),i(s(fun(Q105536,fun(fun(Q105536,bool),fun(Q105536,bool))),insert),s(Q105536,X))),s(fun(Q105536,bool),S0))))),s(fun(Q105536,cart(real,Q105541)),F0))))) # label(aVSUMu_CLAUSESu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3176 (all Q105555 all Q105569 all F0 all S0 (p(s(bool,i(s(fun(fun(Q105555,bool),bool),finite),s(fun(Q105555,bool),S0)))) -> s(cart(real,Q105569),i(s(fun(fun(Q105555,cart(real,Q105569)),cart(real,Q105569)),i(s(fun(fun(Q105555,bool),fun(fun(Q105555,cart(real,Q105569)),cart(real,Q105569))),i(s(fun(fun(cart(real,Q105569),fun(cart(real,Q105569),cart(real,Q105569))),fun(fun(Q105555,bool),fun(fun(Q105555,cart(real,Q105569)),cart(real,Q105569)))),iterate),s(fun(cart(real,Q105569),fun(cart(real,Q105569),cart(real,Q105569))),vectoru_add))),s(fun(Q105555,bool),S0))),s(fun(Q105555,cart(real,Q105569)),F0))) = s(cart(real,Q105569),i(s(fun(fun(Q105555,cart(real,Q105569)),cart(real,Q105569)),i(s(fun(fun(Q105555,bool),fun(fun(Q105555,cart(real,Q105569)),cart(real,Q105569))),vsum),s(fun(Q105555,bool),S0))),s(fun(Q105555,cart(real,Q105569)),F0))))) # label(aVSUM) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3177 (all N all M all F0 ((all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) -> s(cart(real,M),Y) = s(cart(real,M),X))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (exists G0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0)))) & s(fun(cart(real,M),cart(real,M)),i1) = s(fun(cart(real,M),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M))),i(s(fun(fun(cart(real,N),cart(real,M)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M)))),o),s(fun(cart(real,N),cart(real,M)),G0))),s(fun(cart(real,M),cart(real,N)),F0))))))) # label(aLINEARu_INJECTIVEu_LEFTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3178 (all N all F0 (p(s(bool,i(s(fun(fun(cart(real,n10),cart(real,N)),bool),linear),s(fun(cart(real,n10),cart(real,N)),F0)))) -> (all X s(cart(real,N),i(s(fun(cart(real,n10),cart(real,N)),F0),s(cart(real,n10),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(cart(real,N),i(s(fun(cart(cart(real,n10),N),cart(real,N)),i(s(fun(num,fun(cart(cart(real,n10),N),cart(real,N))),column),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(cart(cart(real,n10),N),i(s(fun(fun(cart(real,n10),cart(real,N)),cart(cart(real,n10),N)),matrix),s(fun(cart(real,n10),cart(real,N)),F0)))))))))) # label(aLINEARu_FROMu_REALS) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3179 (all N all U_0 ((all GENR_PVARR_318 (p(s(bool,i(s(fun(cart(real,N),bool),U_0),s(cart(real,N),GENR_PVARR_318)))) <-> (exists I0 exists V (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_318))),s(bool,V))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))) & (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) <-> p(s(bool,V))))))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),U_0)))))))) # label(aINDEPENDENTu_STDBASIS) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3180 (all A ((exists V p(s(bool,i(s(fun(cart(A,n20),bool),p0),s(cart(A,n20),V))))) <-> (exists X exists Y p(s(bool,i(s(fun(cart(A,n20),bool),p0),s(cart(A,n20),i(s(fun(list(A),cart(A,n20)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Y))),s(list(A),nil))))))))))))) # label(aEXISTSu_VECTORu_2) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3181 (all S0 s(fun(cart(real,n10),bool),S0) = s(fun(cart(real,n10),bool),i(s(fun(fun(cart(real,n10),bool),fun(cart(real,n10),bool)),i(s(fun(fun(cart(real,n10),cart(real,n10)),fun(fun(cart(real,n10),bool),fun(cart(real,n10),bool))),image),s(fun(cart(real,n10),cart(real,n10)),i(s(fun(fun(cart(real,n10),real),fun(cart(real,n10),cart(real,n10))),i(s(fun(fun(real,cart(real,n10)),fun(fun(cart(real,n10),real),fun(cart(real,n10),cart(real,n10)))),o),s(fun(real,cart(real,n10)),lift))),s(fun(cart(real,n10),real),drop))))),s(fun(cart(real,n10),bool),S0)))) # label(aIMAGEu_LIFTu_DROPu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3182 (all N all F0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) & (all Y exists X s(cart(real,N),Y) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X)))) -> (exists FI_ ((all X s(cart(real,N),X) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),FI_),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X)))))) & (all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),FI_),s(cart(real,N),X))))) = s(cart(real,N),X)) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),FI_)))))))) # label(aLINEARu_SURJECTIVEu_ISOMORPHISM) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3183 (all A s(A,i(s(fun(num,A),i(s(fun(cart(A,n3),fun(num,A)),d_),s(cart(A,n3),i(s(fun(list(A),cart(A,n3)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,y))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,z))),s(list(A),nil))))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(A,z)) # label(aVECTORu_3u_conjunct2) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3184 (all N all S0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,N0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> (exists B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),B0))),s(num,N0)))))))) # label(aLOWDIMu_EXPANDu_BASIS) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3185 (exists X p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),X))))) <-> (exists X p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))))) # label(aEXISTSu_LIFT) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3186 (all Q122358 all X (p(s(bool,i(s(fun(fun(cart(real,Q122358),bool),bool),i(s(fun(cart(real,Q122358),fun(fun(cart(real,Q122358),bool),bool)),in),s(cart(real,Q122358),X))),s(fun(cart(real,Q122358),bool),s0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q122358),bool),bool),i(s(fun(cart(real,Q122358),fun(fun(cart(real,Q122358),bool),bool)),in),s(cart(real,Q122358),X))),s(fun(cart(real,Q122358),bool),i(s(fun(fun(cart(real,Q122358),bool),fun(cart(real,Q122358),bool)),span),s(fun(cart(real,Q122358),bool),s0)))))))) # label(aSPANu_SUPERSET) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3187 (all X all S0 s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(cart(real,n10),fun(fun(cart(real,n10),bool),bool)),in),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),S0))))) = s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,X))),s(fun(real,bool),S0)))) # label(aLIFTu_INu_IMAGEu_LIFT) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3188 (all Q111053 all A5 all X (p(s(bool,i(s(fun(cart(real,Q111053),bool),i(s(fun(cart(real,Q111053),fun(cart(real,Q111053),bool)),orthogonal),s(cart(real,Q111053),A5))),s(cart(real,Q111053),X)))) -> p(s(bool,i(s(fun(cart(real,Q111053),bool),i(s(fun(cart(real,Q111053),fun(cart(real,Q111053),bool)),orthogonal),s(cart(real,Q111053),A5))),s(cart(real,Q111053),i(s(fun(cart(real,Q111053),cart(real,Q111053)),vectoru_neg),s(cart(real,Q111053),X)))))))) # label(aORTHOGONALu_CLAUSESu_conjunct2) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3189 (all Q112388 all Q112385 all Q112376 all H0 all C0 all X all Y (p(s(bool,i(s(fun(fun(cart(real,Q112385),fun(cart(real,Q112376),cart(real,Q112388))),bool),bilinear),s(fun(cart(real,Q112385),fun(cart(real,Q112376),cart(real,Q112388))),H0)))) -> s(cart(real,Q112388),i(s(fun(cart(real,Q112376),cart(real,Q112388)),i(s(fun(cart(real,Q112385),fun(cart(real,Q112376),cart(real,Q112388))),H0),s(cart(real,Q112385),i(s(fun(cart(real,Q112385),cart(real,Q112385)),i(s(fun(real,fun(cart(real,Q112385),cart(real,Q112385))),r_),s(real,C0))),s(cart(real,Q112385),X))))),s(cart(real,Q112376),Y))) = s(cart(real,Q112388),i(s(fun(cart(real,Q112388),cart(real,Q112388)),i(s(fun(real,fun(cart(real,Q112388),cart(real,Q112388))),r_),s(real,C0))),s(cart(real,Q112388),i(s(fun(cart(real,Q112376),cart(real,Q112388)),i(s(fun(cart(real,Q112385),fun(cart(real,Q112376),cart(real,Q112388))),H0),s(cart(real,Q112385),X))),s(cart(real,Q112376),Y))))))) # label(aBILINEARu_LMUL) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3190 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) # label(aREALu_LSQRTu_LE) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3191 (all M all N all U_0 ((all F0 all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,M),X)))) -> (all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,N))),U_0),s(fun(cart(real,M),cart(real,N)),F0))))) = s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))))))) # label(aONORMu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3192 (all N s(fun(cart(real,N),bool),univ) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),univ)))) # label(aSPANu_UNIV) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3193 (all Q120795 all Q120800 all X all Y all N0 (s(cart(real,Q120795),X) = s(cart(real,Q120795),i(s(fun(num,cart(real,Q120795)),vec),s(num,N0))) & s(cart(real,Q120800),i(s(fun(num,cart(real,Q120800)),vec),s(num,N0))) = s(cart(real,Q120800),Y) <-> s(cart(real,finite_sum(Q120795,Q120800)),i(s(fun(cart(real,Q120800),cart(real,finite_sum(Q120795,Q120800))),i(s(fun(cart(real,Q120795),fun(cart(real,Q120800),cart(real,finite_sum(Q120795,Q120800)))),pastecart),s(cart(real,Q120795),X))),s(cart(real,Q120800),Y))) = s(cart(real,finite_sum(Q120795,Q120800)),i(s(fun(num,cart(real,finite_sum(Q120795,Q120800))),vec),s(num,N0))))) # label(aPASTECARTu_EQu_VEC) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3194 (all N all S0 all H0 ((all C0 all X all Y (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(cart(real,N),bool),H0),s(cart(real,N),Y)))) -> p(s(bool,i(s(fun(cart(real,N),bool),H0),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X))))),s(cart(real,N),Y)))))))) & p(s(bool,i(s(fun(cart(real,N),bool),H0),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) -> (all X (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) -> p(s(bool,i(s(fun(cart(real,N),bool),H0),s(cart(real,N),X)))))))) # label(aSPANu_INDUCTu_ALT) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3195 (all Q106879 all M0 exists V ((p(s(bool,V)) <-> s(num,M0) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))) & s(cart(real,Q106879),i(s(fun(cart(real,Q106879),cart(real,Q106879)),i(s(fun(cart(real,Q106879),fun(cart(real,Q106879),cart(real,Q106879))),i(s(fun(bool,fun(cart(real,Q106879),fun(cart(real,Q106879),cart(real,Q106879)))),cond),s(bool,V))),s(cart(real,Q106879),i(s(fun(num,cart(real,Q106879)),f),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q106879),i(s(fun(num,cart(real,Q106879)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q106879),i(s(fun(fun(num,cart(real,Q106879)),cart(real,Q106879)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q106879)),cart(real,Q106879))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(num,cart(real,Q106879)),f))))) # label(aVSUMu_CLAUSESu_NUMSEGu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3196 (all N all M all F0 all B0 (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),finite),s(fun(cart(real,M),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),B0)))))) & (all X all Y (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),B0)))) & s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),B0)))) -> s(cart(real,M),X) = s(cart(real,M),Y))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (all X (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0)))))) -> (s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) -> s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,M),X)))))) # label(aLINEARu_INDEPu_IMAGEu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3197 (all N all X all E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,E0)))) -> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))))),s(real,E0)))))))) # label(aNORMu_BOUNDu_COMPONENTu_LT) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3198 (all Q99834 s(cart(real,Q99834),i(s(fun(cart(real,Q99834),cart(real,Q99834)),i(s(fun(cart(real,Q99834),fun(cart(real,Q99834),cart(real,Q99834))),vectoru_sub),s(cart(real,Q99834),i(s(fun(cart(real,Q99834),cart(real,Q99834)),i(s(fun(real,fun(cart(real,Q99834),cart(real,Q99834))),r_),s(real,c))),s(cart(real,Q99834),x))))),s(cart(real,Q99834),i(s(fun(cart(real,Q99834),cart(real,Q99834)),i(s(fun(real,fun(cart(real,Q99834),cart(real,Q99834))),r_),s(real,c))),s(cart(real,Q99834),y))))) = s(cart(real,Q99834),i(s(fun(cart(real,Q99834),cart(real,Q99834)),i(s(fun(real,fun(cart(real,Q99834),cart(real,Q99834))),r_),s(real,c))),s(cart(real,Q99834),i(s(fun(cart(real,Q99834),cart(real,Q99834)),i(s(fun(cart(real,Q99834),fun(cart(real,Q99834),cart(real,Q99834))),vectoru_sub),s(cart(real,Q99834),x))),s(cart(real,Q99834),y)))))) # label(aVECTORu_SUBu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3199 (all M all P all N all A5 all B0 all C0 s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(cart(cart(real,P),M),fun(cart(cart(real,P),M),cart(cart(real,P),M))),matrixu_sub),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),C0))))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),B0))),s(cart(cart(real,P),N),C0))))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))),s(cart(cart(real,P),N),C0)))) # label(aMATRIXu_SUBu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3200 (all N all X all Y all Z0 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),X))),s(cart(real,N),Z0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),X))),s(cart(real,N),Y))))))),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),Y))),s(cart(real,N),Z0))))))))))) # label(aDISTu_TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3201 (all Q139133 all X all Y s(real,i(s(fun(cart(real,Q139133),real),infnorm),s(cart(real,Q139133),i(s(fun(cart(real,Q139133),cart(real,Q139133)),i(s(fun(cart(real,Q139133),fun(cart(real,Q139133),cart(real,Q139133))),vectoru_sub),s(cart(real,Q139133),X))),s(cart(real,Q139133),Y))))) = s(real,i(s(fun(cart(real,Q139133),real),infnorm),s(cart(real,Q139133),i(s(fun(cart(real,Q139133),cart(real,Q139133)),i(s(fun(cart(real,Q139133),fun(cart(real,Q139133),cart(real,Q139133))),vectoru_sub),s(cart(real,Q139133),Y))),s(cart(real,Q139133),X)))))) # label(aINFNORMu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3202 (all N all A5 all B0 all X (p(s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(cart(real,N),fun(prod(cart(real,N),cart(real,N)),bool)),between),s(cart(real,N),X))),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),B0)))))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),empty)))))))))))) # label(aBETWEENu_IMPu_COLLINEAR) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3203 (all Q111643 all Q111652 all U_0 ((all F0 all G0 all X s(cart(real,Q111652),i(s(fun(cart(real,Q111652),cart(real,Q111652)),i(s(fun(cart(real,Q111652),fun(cart(real,Q111652),cart(real,Q111652))),vectoru_sub),s(cart(real,Q111652),i(s(fun(cart(real,Q111643),cart(real,Q111652)),F0),s(cart(real,Q111643),X))))),s(cart(real,Q111652),i(s(fun(cart(real,Q111643),cart(real,Q111652)),G0),s(cart(real,Q111643),X))))) = s(cart(real,Q111652),i(s(fun(cart(real,Q111643),cart(real,Q111652)),i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(cart(real,Q111643),cart(real,Q111652))),i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(cart(real,Q111643),cart(real,Q111652)))),U_0),s(fun(cart(real,Q111643),cart(real,Q111652)),F0))),s(fun(cart(real,Q111643),cart(real,Q111652)),G0))),s(cart(real,Q111643),X)))) -> (all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),bool),linear),s(fun(cart(real,Q111643),cart(real,Q111652)),G0)))) & p(s(bool,i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),bool),linear),s(fun(cart(real,Q111643),cart(real,Q111652)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),bool),linear),s(fun(cart(real,Q111643),cart(real,Q111652)),i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(cart(real,Q111643),cart(real,Q111652))),i(s(fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(fun(cart(real,Q111643),cart(real,Q111652)),fun(cart(real,Q111643),cart(real,Q111652)))),U_0),s(fun(cart(real,Q111643),cart(real,Q111652)),F0))),s(fun(cart(real,Q111643),cart(real,Q111652)),G0)))))))))) # label(aLINEARu_COMPOSEu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3204 (all Q122563 all X all S0 (p(s(bool,i(s(fun(fun(cart(real,Q122563),bool),bool),i(s(fun(cart(real,Q122563),fun(fun(cart(real,Q122563),bool),bool)),in),s(cart(real,Q122563),X))),s(fun(cart(real,Q122563),bool),i(s(fun(fun(cart(real,Q122563),bool),fun(cart(real,Q122563),bool)),span),s(fun(cart(real,Q122563),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,Q122563),bool),bool),i(s(fun(cart(real,Q122563),fun(fun(cart(real,Q122563),bool),bool)),in),s(cart(real,Q122563),i(s(fun(cart(real,Q122563),cart(real,Q122563)),vectoru_neg),s(cart(real,Q122563),X))))),s(fun(cart(real,Q122563),bool),i(s(fun(fun(cart(real,Q122563),bool),fun(cart(real,Q122563),bool)),span),s(fun(cart(real,Q122563),bool),S0)))))))) # label(aSPANu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3205 (all N all M all A5 all B0 (s(cart(cart(real,N),M),A5) = s(cart(cart(real,N),M),B0) <-> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),B0))) = s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),A5))))))) # label(aMATRIXu_EQUALu_COLUMNS) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3206 (all Q100273 all X all Y all Z0 s(real,i(s(fun(cart(real,Q100273),real),i(s(fun(cart(real,Q100273),fun(cart(real,Q100273),real)),dot),s(cart(real,Q100273),X))),s(cart(real,Q100273),i(s(fun(cart(real,Q100273),cart(real,Q100273)),i(s(fun(cart(real,Q100273),fun(cart(real,Q100273),cart(real,Q100273))),vectoru_add),s(cart(real,Q100273),Y))),s(cart(real,Q100273),Z0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q100273),real),i(s(fun(cart(real,Q100273),fun(cart(real,Q100273),real)),dot),s(cart(real,Q100273),X))),s(cart(real,Q100273),Y))))),s(real,i(s(fun(cart(real,Q100273),real),i(s(fun(cart(real,Q100273),fun(cart(real,Q100273),real)),dot),s(cart(real,Q100273),X))),s(cart(real,Q100273),Z0)))))) # label(aDOTu_RADD) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3207 (all M all P all N all A5 all B0 all C0 s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),M),cart(cart(real,P),M)),i(s(fun(cart(cart(real,P),M),fun(cart(cart(real,P),M),cart(cart(real,P),M))),matrixu_add),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),C0))))),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),B0))),s(cart(cart(real,P),N),C0))))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))),s(cart(cart(real,P),N),C0)))) # label(aMATRIXu_ADDu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3208 (all N all S0 all V (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),V)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))) -> (exists B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),V)))))))) # label(aMAXIMALu_INDEPENDENTu_SUBSETu_EXTEND) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3209 (all Q132154 all S0 all T0 ((all X all Y (p(s(bool,i(s(fun(fun(cart(real,Q132154),bool),bool),i(s(fun(cart(real,Q132154),fun(fun(cart(real,Q132154),bool),bool)),in),s(cart(real,Q132154),Y))),s(fun(cart(real,Q132154),bool),i(s(fun(fun(cart(real,Q132154),bool),fun(cart(real,Q132154),bool)),span),s(fun(cart(real,Q132154),bool),T0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q132154),bool),bool),i(s(fun(cart(real,Q132154),fun(fun(cart(real,Q132154),bool),bool)),in),s(cart(real,Q132154),X))),s(fun(cart(real,Q132154),bool),i(s(fun(fun(cart(real,Q132154),bool),fun(cart(real,Q132154),bool)),span),s(fun(cart(real,Q132154),bool),S0)))))) -> p(s(bool,i(s(fun(cart(real,Q132154),bool),i(s(fun(cart(real,Q132154),fun(cart(real,Q132154),bool)),orthogonal),s(cart(real,Q132154),X))),s(cart(real,Q132154),Y)))))) <-> (all X all Y (p(s(bool,i(s(fun(fun(cart(real,Q132154),bool),bool),i(s(fun(cart(real,Q132154),fun(fun(cart(real,Q132154),bool),bool)),in),s(cart(real,Q132154),Y))),s(fun(cart(real,Q132154),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,Q132154),bool),bool),i(s(fun(cart(real,Q132154),fun(fun(cart(real,Q132154),bool),bool)),in),s(cart(real,Q132154),X))),s(fun(cart(real,Q132154),bool),S0)))) -> p(s(bool,i(s(fun(cart(real,Q132154),bool),i(s(fun(cart(real,Q132154),fun(cart(real,Q132154),bool)),orthogonal),s(cart(real,Q132154),X))),s(cart(real,Q132154),Y)))))))) # label(aORTHOGONALu_TOu_SPANSu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3210 (all Q118614 all Q118625 all U_0 ((all F0 all G0 all X s(cart(real,Q118625),i(s(fun(cart(real,Q118625),cart(real,Q118625)),i(s(fun(cart(real,Q118625),fun(cart(real,Q118625),cart(real,Q118625))),vectoru_add),s(cart(real,Q118625),i(s(fun(cart(real,Q118614),cart(real,Q118625)),F0),s(cart(real,Q118614),X))))),s(cart(real,Q118625),i(s(fun(cart(real,Q118614),cart(real,Q118625)),G0),s(cart(real,Q118614),X))))) = s(cart(real,Q118625),i(s(fun(cart(real,Q118614),cart(real,Q118625)),i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(cart(real,Q118614),cart(real,Q118625))),i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(cart(real,Q118614),cart(real,Q118625)))),U_0),s(fun(cart(real,Q118614),cart(real,Q118625)),F0))),s(fun(cart(real,Q118614),cart(real,Q118625)),G0))),s(cart(real,Q118614),X)))) -> (all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),bool),linear),s(fun(cart(real,Q118614),cart(real,Q118625)),F0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),real),onorm),s(fun(cart(real,Q118614),cart(real,Q118625)),F0))))),s(real,i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),real),onorm),s(fun(cart(real,Q118614),cart(real,Q118625)),G0))))))),s(real,e0)))) & p(s(bool,i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),bool),linear),s(fun(cart(real,Q118614),cart(real,Q118625)),G0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),real),onorm),s(fun(cart(real,Q118614),cart(real,Q118625)),i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(cart(real,Q118614),cart(real,Q118625))),i(s(fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(fun(cart(real,Q118614),cart(real,Q118625)),fun(cart(real,Q118614),cart(real,Q118625)))),U_0),s(fun(cart(real,Q118614),cart(real,Q118625)),F0))),s(fun(cart(real,Q118614),cart(real,Q118625)),G0))))))),s(real,e0)))))))) # label(aONORMu_TRIANGLEu_LT) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3211 (all Q131708 all V s(cart(cart(real,Q131708),n10),i(s(fun(cart(real,Q131708),cart(cart(real,Q131708),n10)),rowvector),s(cart(real,Q131708),V))) = s(cart(cart(real,Q131708),n10),i(s(fun(cart(cart(real,n10),Q131708),cart(cart(real,Q131708),n10)),transp),s(cart(cart(real,n10),Q131708),i(s(fun(cart(real,Q131708),cart(cart(real,n10),Q131708)),columnvector),s(cart(real,Q131708),V)))))) # label(aTRANSPu_COLUMNVECTOR) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3212 (all N all M all F0 all X all Y (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & (all X s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))) -> s(bool,i(s(fun(cart(real,M),bool),i(s(fun(cart(real,M),fun(cart(real,M),bool)),orthogonal),s(cart(real,M),X))),s(cart(real,M),Y))) = s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))))))) # label(aORTHOGONALu_LINEARu_IMAGEu_EQ) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3213 (all N all M all U_0 ((all A5 all GENR_PVARR_291 ((exists I0 exists V ((p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_291))),s(bool,V))),s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,N))),row),s(num,I0))),s(cart(cart(real,N),M),A5)))))))) <-> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),GENR_PVARR_291)))))) -> (all A5 s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),U_0),s(cart(cart(real,N),M),A5))))) = s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),rows),s(cart(cart(real,N),M),A5)))))) # label(arows) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3214 (all Q126544 all V all B0 (s(fun(cart(real,Q126544),bool),i(s(fun(fun(cart(real,Q126544),bool),fun(cart(real,Q126544),bool)),span),s(fun(cart(real,Q126544),bool),B0))) = s(fun(cart(real,Q126544),bool),V) & p(s(bool,i(s(fun(fun(cart(real,Q126544),bool),bool),independent),s(fun(cart(real,Q126544),bool),B0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126544),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126544),bool),B0))),s(num,i(s(fun(fun(cart(real,Q126544),bool),num),dim),s(fun(cart(real,Q126544),bool),V)))))))) # label(aBASISu_HASu_SIZEu_DIM) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3215 (all Q116425 all Q116423 all Q116424 all A5 all B0 s(cart(cart(real,Q116424),Q116425),i(s(fun(cart(cart(real,Q116425),Q116424),cart(cart(real,Q116424),Q116425)),transp),s(cart(cart(real,Q116425),Q116424),i(s(fun(cart(cart(real,Q116425),Q116423),cart(cart(real,Q116425),Q116424)),i(s(fun(cart(cart(real,Q116423),Q116424),fun(cart(cart(real,Q116425),Q116423),cart(cart(real,Q116425),Q116424))),matrixu_mul),s(cart(cart(real,Q116423),Q116424),A5))),s(cart(cart(real,Q116425),Q116423),B0))))) = s(cart(cart(real,Q116424),Q116425),i(s(fun(cart(cart(real,Q116424),Q116423),cart(cart(real,Q116424),Q116425)),i(s(fun(cart(cart(real,Q116423),Q116425),fun(cart(cart(real,Q116424),Q116423),cart(cart(real,Q116424),Q116425))),matrixu_mul),s(cart(cart(real,Q116423),Q116425),i(s(fun(cart(cart(real,Q116425),Q116423),cart(cart(real,Q116423),Q116425)),transp),s(cart(cart(real,Q116425),Q116423),B0))))),s(cart(cart(real,Q116424),Q116423),i(s(fun(cart(cart(real,Q116423),Q116424),cart(cart(real,Q116424),Q116423)),transp),s(cart(cart(real,Q116423),Q116424),A5)))))) # label(aMATRIXu_TRANSPu_MUL) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3216 (all Q111747 all Q111736 all Q111733 all U_1 ((all F0 all X all A5 s(cart(real,Q111733),i(s(fun(Q111747,cart(real,Q111733)),i(s(fun(cart(real,Q111736),fun(Q111747,cart(real,Q111733))),i(s(fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),fun(Q111747,cart(real,Q111733)))),U_1),s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0))),s(cart(real,Q111736),X))),s(Q111747,A5))) = s(cart(real,Q111733),i(s(fun(cart(real,Q111736),cart(real,Q111733)),i(s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0),s(Q111747,A5))),s(cart(real,Q111736),X)))) -> (all U_0 ((all S0 all F0 all X s(cart(real,Q111733),i(s(fun(fun(Q111747,cart(real,Q111733)),cart(real,Q111733)),i(s(fun(fun(Q111747,bool),fun(fun(Q111747,cart(real,Q111733)),cart(real,Q111733))),vsum),s(fun(Q111747,bool),S0))),s(fun(Q111747,cart(real,Q111733)),i(s(fun(cart(real,Q111736),fun(Q111747,cart(real,Q111733))),i(s(fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),fun(Q111747,cart(real,Q111733)))),U_1),s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0))),s(cart(real,Q111736),X))))) = s(cart(real,Q111733),i(s(fun(cart(real,Q111736),cart(real,Q111733)),i(s(fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),cart(real,Q111733))),i(s(fun(fun(Q111747,bool),fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),cart(real,Q111733)))),U_0),s(fun(Q111747,bool),S0))),s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0))),s(cart(real,Q111736),X)))) -> (all F0 all S0 (p(s(bool,i(s(fun(fun(Q111747,bool),bool),finite),s(fun(Q111747,bool),S0)))) & (all A5 (p(s(bool,i(s(fun(fun(Q111747,bool),bool),i(s(fun(Q111747,fun(fun(Q111747,bool),bool)),in),s(Q111747,A5))),s(fun(Q111747,bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q111736),cart(real,Q111733)),bool),linear),s(fun(cart(real,Q111736),cart(real,Q111733)),i(s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0),s(Q111747,A5)))))))) -> p(s(bool,i(s(fun(fun(cart(real,Q111736),cart(real,Q111733)),bool),linear),s(fun(cart(real,Q111736),cart(real,Q111733)),i(s(fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),cart(real,Q111733))),i(s(fun(fun(Q111747,bool),fun(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),fun(cart(real,Q111736),cart(real,Q111733)))),U_0),s(fun(Q111747,bool),S0))),s(fun(Q111747,fun(cart(real,Q111736),cart(real,Q111733))),F0)))))))))))) # label(aLINEARu_COMPOSEu_VSUM) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3217 (all Q107636 all Q107660 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q107636,bool),bool),finite),s(fun(Q107636,bool),S0)))) & p(s(bool,i(s(fun(fun(Q107636,bool),bool),finite),s(fun(Q107636,bool),T0)))) & (all X (p(s(bool,i(s(fun(fun(Q107636,bool),bool),i(s(fun(Q107636,fun(fun(Q107636,bool),bool)),in),s(Q107636,X))),s(fun(Q107636,bool),i(s(fun(fun(Q107636,bool),fun(Q107636,bool)),i(s(fun(fun(Q107636,bool),fun(fun(Q107636,bool),fun(Q107636,bool))),inter),s(fun(Q107636,bool),S0))),s(fun(Q107636,bool),T0)))))) -> s(cart(real,Q107660),i(s(fun(num,cart(real,Q107660)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q107660),i(s(fun(Q107636,cart(real,Q107660)),F0),s(Q107636,X))))) -> s(cart(real,Q107660),i(s(fun(cart(real,Q107660),cart(real,Q107660)),i(s(fun(cart(real,Q107660),fun(cart(real,Q107660),cart(real,Q107660))),vectoru_add),s(cart(real,Q107660),i(s(fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660)),i(s(fun(fun(Q107636,bool),fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660))),vsum),s(fun(Q107636,bool),S0))),s(fun(Q107636,cart(real,Q107660)),F0))))),s(cart(real,Q107660),i(s(fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660)),i(s(fun(fun(Q107636,bool),fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660))),vsum),s(fun(Q107636,bool),T0))),s(fun(Q107636,cart(real,Q107660)),F0))))) = s(cart(real,Q107660),i(s(fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660)),i(s(fun(fun(Q107636,bool),fun(fun(Q107636,cart(real,Q107660)),cart(real,Q107660))),vsum),s(fun(Q107636,bool),i(s(fun(fun(Q107636,bool),fun(Q107636,bool)),i(s(fun(fun(Q107636,bool),fun(fun(Q107636,bool),fun(Q107636,bool))),union),s(fun(Q107636,bool),S0))),s(fun(Q107636,bool),T0))))),s(fun(Q107636,cart(real,Q107660)),F0))))) # label(aVSUMu_UNIONu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3218 (all A all N all S0 all T0 all F0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))) -> s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),T0))),s(fun(A,cart(real,N)),F0))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),union),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,cart(real,N)),F0))))),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),i(s(fun(fun(A,bool),fun(fun(A,bool),fun(A,bool))),inter),s(fun(A,bool),S0))),s(fun(A,bool),T0))))),s(fun(A,cart(real,N)),F0))))))) # label(aVSUMu_INCLu_EXCL) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3219 (all M all N all A5 (s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(cart(real,M),N),A5) <-> s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))))) # label(aRANKu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3220 (all Q121494 all X all Y all S0 (p(s(bool,i(s(fun(fun(cart(real,Q121494),bool),bool),i(s(fun(cart(real,Q121494),fun(fun(cart(real,Q121494),bool),bool)),in),s(cart(real,Q121494),X))),s(fun(cart(real,Q121494),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q121494),bool),bool),i(s(fun(cart(real,Q121494),fun(fun(cart(real,Q121494),bool),bool)),in),s(cart(real,Q121494),Y))),s(fun(cart(real,Q121494),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q121494),bool),bool),subspace),s(fun(cart(real,Q121494),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121494),bool),bool),i(s(fun(cart(real,Q121494),fun(fun(cart(real,Q121494),bool),bool)),in),s(cart(real,Q121494),i(s(fun(cart(real,Q121494),cart(real,Q121494)),i(s(fun(cart(real,Q121494),fun(cart(real,Q121494),cart(real,Q121494))),vectoru_add),s(cart(real,Q121494),X))),s(cart(real,Q121494),Y))))),s(fun(cart(real,Q121494),bool),S0)))))) # label(aSUBSPACEu_ADD) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3221 (all A s(A,i(s(fun(num,A),i(s(fun(cart(A,n10),fun(num,A)),d_),s(cart(A,n10),i(s(fun(list(A),cart(A,n10)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),nil))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(A,x)) # label(aVECTORu_1) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3222 (all M all N all A5 all X p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,N),bool)),columns),s(cart(cart(real,M),N),A5))))))))) # label(aMATRIXu_VECTORu_MULu_INu_COLUMNSPACE) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3223 (all N all M all U_1 ((all C0 all A5 all I0 all J0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))) = s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(real,fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(real,C0))),s(cart(cart(real,N),M),A5))),s(num,I0))),s(num,J0)))) -> (all U_0 ((all C0 all A5 all I0 s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(real,fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(real,C0))),s(cart(cart(real,N),M),A5))),s(num,I0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(real,fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(real,C0))),s(cart(cart(real,N),M),A5))),s(num,I0)))))) -> (all C0 all A5 s(cart(cart(real,N),M),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),M)),lambda),s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(real,fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(real,C0))),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5)))))))) # label(amatrixu_cmul) # label(axiom) # label(non_clause). [assumption]. 15.91/15.89 3224 (all N all A5 all B0 all C0 all D0 (s(cart(real,N),A5) != s(cart(real,N),B0) -> (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),C0))),s(fun(cart(real,N),bool),empty)))))))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),D0))),s(fun(cart(real,N),bool),empty)))))))))) <-> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),collinear),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),C0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),D0))),s(fun(cart(real,N),bool),empty))))))))))))))) # label(aCOLLINEARu_4u_3) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3225 (all Q122668 all Q122679 all S0 all F0 all T0 ((all X (p(s(bool,i(s(fun(fun(Q122668,bool),bool),i(s(fun(Q122668,fun(fun(Q122668,bool),bool)),in),s(Q122668,X))),s(fun(Q122668,bool),T0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q122679),bool),bool),i(s(fun(cart(real,Q122679),fun(fun(cart(real,Q122679),bool),bool)),in),s(cart(real,Q122679),i(s(fun(Q122668,cart(real,Q122679)),F0),s(Q122668,X))))),s(fun(cart(real,Q122679),bool),i(s(fun(fun(cart(real,Q122679),bool),fun(cart(real,Q122679),bool)),span),s(fun(cart(real,Q122679),bool),S0)))))))) & p(s(bool,i(s(fun(fun(Q122668,bool),bool),finite),s(fun(Q122668,bool),T0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q122679),bool),bool),i(s(fun(cart(real,Q122679),fun(fun(cart(real,Q122679),bool),bool)),in),s(cart(real,Q122679),i(s(fun(fun(Q122668,cart(real,Q122679)),cart(real,Q122679)),i(s(fun(fun(Q122668,bool),fun(fun(Q122668,cart(real,Q122679)),cart(real,Q122679))),vsum),s(fun(Q122668,bool),T0))),s(fun(Q122668,cart(real,Q122679)),F0))))),s(fun(cart(real,Q122679),bool),i(s(fun(fun(cart(real,Q122679),bool),fun(cart(real,Q122679),bool)),span),s(fun(cart(real,Q122679),bool),S0)))))))) # label(aSPANu_VSUM) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3226 (all N all X all S0 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),i(s(fun(bool,fun(num,fun(num,num))),cond),s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0)))))) # label(aDIMu_INSERT) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3227 (all Q142613 all A5 all B0 ((s(cart(real,Q142613),B0) = s(cart(real,Q142613),i(s(fun(prod(cart(real,Q142613),cart(real,Q142613)),cart(real,Q142613)),midpoint),s(prod(cart(real,Q142613),cart(real,Q142613)),i(s(fun(cart(real,Q142613),prod(cart(real,Q142613),cart(real,Q142613))),i(s(fun(cart(real,Q142613),fun(cart(real,Q142613),prod(cart(real,Q142613),cart(real,Q142613)))),c_),s(cart(real,Q142613),A5))),s(cart(real,Q142613),B0))))) <-> s(cart(real,Q142613),A5) = s(cart(real,Q142613),B0)) & (s(cart(real,Q142613),B0) = s(cart(real,Q142613),A5) <-> s(cart(real,Q142613),A5) = s(cart(real,Q142613),i(s(fun(prod(cart(real,Q142613),cart(real,Q142613)),cart(real,Q142613)),midpoint),s(prod(cart(real,Q142613),cart(real,Q142613)),i(s(fun(cart(real,Q142613),prod(cart(real,Q142613),cart(real,Q142613))),i(s(fun(cart(real,Q142613),fun(cart(real,Q142613),prod(cart(real,Q142613),cart(real,Q142613)))),c_),s(cart(real,Q142613),A5))),s(cart(real,Q142613),B0)))))) & (s(cart(real,Q142613),A5) = s(cart(real,Q142613),B0) <-> s(cart(real,Q142613),B0) = s(cart(real,Q142613),i(s(fun(prod(cart(real,Q142613),cart(real,Q142613)),cart(real,Q142613)),midpoint),s(prod(cart(real,Q142613),cart(real,Q142613)),i(s(fun(cart(real,Q142613),prod(cart(real,Q142613),cart(real,Q142613))),i(s(fun(cart(real,Q142613),fun(cart(real,Q142613),prod(cart(real,Q142613),cart(real,Q142613)))),c_),s(cart(real,Q142613),A5))),s(cart(real,Q142613),B0)))))) & (s(cart(real,Q142613),A5) = s(cart(real,Q142613),B0) <-> s(cart(real,Q142613),i(s(fun(prod(cart(real,Q142613),cart(real,Q142613)),cart(real,Q142613)),midpoint),s(prod(cart(real,Q142613),cart(real,Q142613)),i(s(fun(cart(real,Q142613),prod(cart(real,Q142613),cart(real,Q142613))),i(s(fun(cart(real,Q142613),fun(cart(real,Q142613),prod(cart(real,Q142613),cart(real,Q142613)))),c_),s(cart(real,Q142613),A5))),s(cart(real,Q142613),B0))))) = s(cart(real,Q142613),A5)))) # label(aMIDPOINTu_EQu_ENDPOINT) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3228 (all Q122389 all S0 all T0 p(s(bool,i(s(fun(fun(cart(real,Q122389),bool),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(fun(cart(real,Q122389),bool),bool)),subset),s(fun(cart(real,Q122389),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool)),i(s(fun(fun(cart(real,Q122389),bool),fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool))),union),s(fun(cart(real,Q122389),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool)),span),s(fun(cart(real,Q122389),bool),S0))))),s(fun(cart(real,Q122389),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool)),span),s(fun(cart(real,Q122389),bool),T0))))))),s(fun(cart(real,Q122389),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool)),span),s(fun(cart(real,Q122389),bool),i(s(fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool)),i(s(fun(fun(cart(real,Q122389),bool),fun(fun(cart(real,Q122389),bool),fun(cart(real,Q122389),bool))),union),s(fun(cart(real,Q122389),bool),S0))),s(fun(cart(real,Q122389),bool),T0))))))))) # label(aSPANu_UNIONu_SUBSET) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3229 (all Q105987 all Q106012 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q105987,bool),bool),finite),s(fun(Q105987,bool),S0)))) & p(s(bool,i(s(fun(fun(Q105987,bool),bool),i(s(fun(fun(Q105987,bool),fun(fun(Q105987,bool),bool)),subset),s(fun(Q105987,bool),T0))),s(fun(Q105987,bool),S0)))) -> s(cart(real,Q106012),i(s(fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012)),i(s(fun(fun(Q105987,bool),fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012))),vsum),s(fun(Q105987,bool),i(s(fun(fun(Q105987,bool),fun(Q105987,bool)),i(s(fun(fun(Q105987,bool),fun(fun(Q105987,bool),fun(Q105987,bool))),diff),s(fun(Q105987,bool),S0))),s(fun(Q105987,bool),T0))))),s(fun(Q105987,cart(real,Q106012)),F0))) = s(cart(real,Q106012),i(s(fun(cart(real,Q106012),cart(real,Q106012)),i(s(fun(cart(real,Q106012),fun(cart(real,Q106012),cart(real,Q106012))),vectoru_sub),s(cart(real,Q106012),i(s(fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012)),i(s(fun(fun(Q105987,bool),fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012))),vsum),s(fun(Q105987,bool),S0))),s(fun(Q105987,cart(real,Q106012)),F0))))),s(cart(real,Q106012),i(s(fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012)),i(s(fun(fun(Q105987,bool),fun(fun(Q105987,cart(real,Q106012)),cart(real,Q106012))),vsum),s(fun(Q105987,bool),T0))),s(fun(Q105987,cart(real,Q106012)),F0))))))) # label(aVSUMu_DIFF) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3230 (all Q103249 all Q103251 all X all Y s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q103249),real),vectoru_norm),s(cart(real,Q103249),X))))),s(real,i(s(fun(cart(real,Q103251),real),vectoru_norm),s(cart(real,Q103251),Y))))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q103249),real),i(s(fun(cart(real,Q103249),fun(cart(real,Q103249),real)),dot),s(cart(real,Q103249),X))),s(cart(real,Q103249),X))))),s(real,i(s(fun(cart(real,Q103251),real),i(s(fun(cart(real,Q103251),fun(cart(real,Q103251),real)),dot),s(cart(real,Q103251),Y))),s(cart(real,Q103251),Y)))))) # label(aNORMu_LE) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3231 (all N all M all C0 all A5 all I0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))),s(num,I0))))),s(num,j))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,j)))))) # label(aMATRIXu_CMULu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3232 (all N all X all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))),s(cart(real,N),X)))) <-> s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aORTHOGONALu_BASIS) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3233 (all N all V all B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),V)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),B0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),V)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),B0)))))) # label(aINDEPENDENTu_CARDu_LEu_DIM) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3234 (all A all B all Q107444 all U_2 ((all X all F0 (p(s(bool,i(s(fun(fun(prod(A,B),cart(real,Q107444)),bool),i(s(fun(fun(A,fun(B,cart(real,Q107444))),fun(fun(prod(A,B),cart(real,Q107444)),bool)),U_2),s(fun(A,fun(B,cart(real,Q107444))),X))),s(fun(prod(A,B),cart(real,Q107444)),F0)))) <-> (all I0 all J0 p(s(bool,i(s(fun(cart(real,Q107444),bool),i(s(fun(cart(real,Q107444),fun(cart(real,Q107444),bool)),geq),s(cart(real,Q107444),i(s(fun(prod(A,B),cart(real,Q107444)),F0),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,I0))),s(B,J0))))))),s(cart(real,Q107444),i(s(fun(B,cart(real,Q107444)),i(s(fun(A,fun(B,cart(real,Q107444))),X),s(A,I0))),s(B,J0))))))))) -> (all U_1 ((all S0 all T0 all GENR_PVARR_283 ((exists I0 exists J0 exists V (p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(bool,fun(prod(A,B),bool)),i(s(fun(prod(A,B),fun(bool,fun(prod(A,B),bool))),setspec),s(prod(A,B),GENR_PVARR_283))),s(bool,V))),s(prod(A,B),i(s(fun(B,prod(A,B)),i(s(fun(A,fun(B,prod(A,B))),c_),s(A,I0))),s(B,J0)))))) & (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,J0))),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0)))) <-> p(s(bool,V))))) <-> p(s(bool,i(s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))),s(prod(A,B),GENR_PVARR_283)))))) -> (all U_0 ((all T0 all X all I0 s(cart(real,Q107444),i(s(fun(fun(B,cart(real,Q107444)),cart(real,Q107444)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,Q107444)),cart(real,Q107444))),vsum),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0))))),s(fun(B,cart(real,Q107444)),i(s(fun(A,fun(B,cart(real,Q107444))),X),s(A,I0))))) = s(cart(real,Q107444),i(s(fun(A,cart(real,Q107444)),i(s(fun(fun(A,fun(B,cart(real,Q107444))),fun(A,cart(real,Q107444))),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,cart(real,Q107444))),fun(A,cart(real,Q107444)))),U_0),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,cart(real,Q107444))),X))),s(A,I0)))) -> (all S0 all T0 all X (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all I0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,I0))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(fun(B,bool),bool),finite),s(fun(B,bool),i(s(fun(A,fun(B,bool)),T0),s(A,I0)))))))) -> s(cart(real,Q107444),i(s(fun(fun(prod(A,B),cart(real,Q107444)),cart(real,Q107444)),i(s(fun(fun(prod(A,B),bool),fun(fun(prod(A,B),cart(real,Q107444)),cart(real,Q107444))),vsum),s(fun(prod(A,B),bool),i(s(fun(fun(prod(A,B),bool),fun(prod(A,B),bool)),gspec),s(fun(prod(A,B),bool),i(s(fun(fun(A,fun(B,bool)),fun(prod(A,B),bool)),i(s(fun(fun(A,bool),fun(fun(A,fun(B,bool)),fun(prod(A,B),bool))),U_1),s(fun(A,bool),S0))),s(fun(A,fun(B,bool)),T0))))))),s(fun(prod(A,B),cart(real,Q107444)),i(s(fun(fun(fun(prod(A,B),cart(real,Q107444)),bool),fun(prod(A,B),cart(real,Q107444))),gabs),s(fun(fun(prod(A,B),cart(real,Q107444)),bool),i(s(fun(fun(A,fun(B,cart(real,Q107444))),fun(fun(prod(A,B),cart(real,Q107444)),bool)),U_2),s(fun(A,fun(B,cart(real,Q107444))),X))))))) = s(cart(real,Q107444),i(s(fun(fun(A,cart(real,Q107444)),cart(real,Q107444)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107444)),cart(real,Q107444))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q107444)),i(s(fun(fun(A,fun(B,cart(real,Q107444))),fun(A,cart(real,Q107444))),i(s(fun(fun(A,fun(B,bool)),fun(fun(A,fun(B,cart(real,Q107444))),fun(A,cart(real,Q107444)))),U_0),s(fun(A,fun(B,bool)),T0))),s(fun(A,fun(B,cart(real,Q107444))),X))))))))))))) # label(aVSUMu_VSUMu_PRODUCT) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3235 (all N all U_0 ((all X all Y all I0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y))),s(num,I0)))) -> (all X all Y s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y)))))))) # label(avectoru_add) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3236 (all N all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))))),s(real,i(s(fun(cart(real,N),real),infnorm),s(cart(real,N),X))))))))) # label(aNORMu_LEu_INFNORM) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3237 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(real,real),sqrt),s(real,Y)))))))) # label(aREALu_LEu_RSQRT) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3238 (all X s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))) = s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),vectoru_neg),s(cart(real,n10),X)))))) # label(aDROPu_NEG) # label(axiom) # label(non_clause). [assumption]. 15.93/15.90 3239 (all Q105942 all Q105967 all F0 all S0 all T0 (p(s(bool,i(s(fun(fun(Q105942,bool),bool),finite),s(fun(Q105942,bool),T0)))) & p(s(bool,i(s(fun(fun(Q105942,bool),bool),i(s(fun(fun(Q105942,bool),fun(fun(Q105942,bool),bool)),disjoint),s(fun(Q105942,bool),S0))),s(fun(Q105942,bool),T0)))) & p(s(bool,i(s(fun(fun(Q105942,bool),bool),finite),s(fun(Q105942,bool),S0)))) -> s(cart(real,Q105967),i(s(fun(cart(real,Q105967),cart(real,Q105967)),i(s(fun(cart(real,Q105967),fun(cart(real,Q105967),cart(real,Q105967))),vectoru_add),s(cart(real,Q105967),i(s(fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967)),i(s(fun(fun(Q105942,bool),fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967))),vsum),s(fun(Q105942,bool),S0))),s(fun(Q105942,cart(real,Q105967)),F0))))),s(cart(real,Q105967),i(s(fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967)),i(s(fun(fun(Q105942,bool),fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967))),vsum),s(fun(Q105942,bool),T0))),s(fun(Q105942,cart(real,Q105967)),F0))))) = s(cart(real,Q105967),i(s(fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967)),i(s(fun(fun(Q105942,bool),fun(fun(Q105942,cart(real,Q105967)),cart(real,Q105967))),vsum),s(fun(Q105942,bool),i(s(fun(fun(Q105942,bool),fun(Q105942,bool)),i(s(fun(fun(Q105942,bool),fun(fun(Q105942,bool),fun(Q105942,bool))),union),s(fun(Q105942,bool),S0))),s(fun(Q105942,bool),T0))))),s(fun(Q105942,cart(real,Q105967)),F0))))) # label(aVSUMu_UNION) # label(axiom) # label(non_clause). [assumption]. 15.94/15.99 3240 (all N all M all U_0 ((all A5 all J0 all I0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))) = s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(num,J0))),s(num,I0)))) -> (all A5 all J0 s(cart(real,M),i(s(fun(fun(num,real),cart(real,M)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(num,J0))))) = s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,J0))),s(cart(cart(real,N),M),A5)))))) # label(acolumn) # label(axiom) # label(non_clause). [assumption]. 15.94/15.99 3241 (all N all F0 all A5 all B0 all E1 all E2 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,B0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,A5))))),s(fun(cart(real,N),bool),E1)))) & (all E0 all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X)))) -> (exists D0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D0)))) & (all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,Y))),s(real,X))))))),s(real,D0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,Y))))),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,X))))))))),s(real,E0)))))))))) & (all Y (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),E1)))) -> (exists E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) & (all YI_ (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),YI_))),s(cart(real,N),Y))))))),s(real,E0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),YI_))),s(fun(cart(real,N),bool),E1)))))))))) & -(exists X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,X))))),s(fun(cart(real,N),bool),E1)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,X))))),s(fun(cart(real,N),bool),E2)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X)))))) & (all Y (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),E2)))) -> (exists E0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,E0)))) & (all YI_ (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,N),cart(real,N)),real),distance),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),YI_))),s(cart(real,N),Y))))))),s(real,E0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),YI_))),s(fun(cart(real,N),bool),E2)))))))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,B0))))),s(fun(cart(real,N),bool),E2)))) -> (exists X (-p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,X))))),s(fun(cart(real,N),bool),E2)))) & -p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(real,cart(real,N)),F0),s(real,X))))),s(fun(cart(real,N),bool),E1)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,B0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,A5))),s(real,X)))))))) # label(aCONNECTEDu_REALu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 15.94/15.99 3242 (all Q100537 all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q100537),real),i(s(fun(cart(real,Q100537),fun(cart(real,Q100537),real)),dot),s(cart(real,Q100537),X))),s(cart(real,Q100537),X)))))) <-> s(cart(real,Q100537),i(s(fun(num,cart(real,Q100537)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(real,Q100537),X))) # label(aDOTu_POSu_LT) # label(axiom) # label(non_clause). [assumption]. 15.94/15.99 3243 (all Q121075 all Q121076 all X1 all X2 all Y1 all Y2 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,Q121075),real),i(s(fun(cart(real,Q121075),fun(cart(real,Q121075),real)),dot),s(cart(real,Q121075),X1))),s(cart(real,Q121075),Y1))))),s(real,i(s(fun(cart(real,Q121076),real),i(s(fun(cart(real,Q121076),fun(cart(real,Q121076),real)),dot),s(cart(real,Q121076),X2))),s(cart(real,Q121076),Y2))))) = s(real,i(s(fun(cart(real,finite_sum(Q121075,Q121076)),real),i(s(fun(cart(real,finite_sum(Q121075,Q121076)),fun(cart(real,finite_sum(Q121075,Q121076)),real)),dot),s(cart(real,finite_sum(Q121075,Q121076)),i(s(fun(cart(real,Q121076),cart(real,finite_sum(Q121075,Q121076))),i(s(fun(cart(real,Q121075),fun(cart(real,Q121076),cart(real,finite_sum(Q121075,Q121076)))),pastecart),s(cart(real,Q121075),X1))),s(cart(real,Q121076),X2))))),s(cart(real,finite_sum(Q121075,Q121076)),i(s(fun(cart(real,Q121076),cart(real,finite_sum(Q121075,Q121076))),i(s(fun(cart(real,Q121075),fun(cart(real,Q121076),cart(real,finite_sum(Q121075,Q121076)))),pastecart),s(cart(real,Q121075),Y1))),s(cart(real,Q121076),Y2)))))) # label(aDOTu_PASTECART) # label(axiom) # label(non_clause). [assumption]. 15.94/15.99 3244 (all N all M all U_1 ((all A5 all J0 all X all I0 s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),i(s(fun(num,fun(cart(real,M),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(real,M),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,J0))),s(cart(real,M),X))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),d_),s(cart(real,M),X))),s(num,I0)))))) -> (all U_0 ((all A5 all X all J0 s(real,i(s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,M),X))),s(num,J0))) = s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))))),s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),i(s(fun(num,fun(cart(real,M),fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(num,fun(cart(real,M),fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(num,J0))),s(cart(real,M),X)))))) -> (all A5 all X s(cart(real,N),i(s(fun(cart(cart(real,N),M),cart(real,N)),i(s(fun(cart(real,M),fun(cart(cart(real,N),M),cart(real,N))),vectoru_matrixu_mul),s(cart(real,M),X))),s(cart(cart(real,N),M),A5))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(cart(real,M),fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(cart(real,M),fun(num,real))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,M),X)))))))))) # label(avectoru_matrixu_mul) # label(axiom) # label(non_clause). [assumption]. 15.94/15.99 3245 (all N all M all F0 ((all X all Y s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_add),s(cart(real,M),X))),s(cart(real,M),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y)))))) & (all C0 all X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,C0))),s(cart(real,M),X))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))) <-> p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))))) # label(alinear) # label(axiom) # label(non_clause). [assumption]. 15.94/15.99 3246 (all M all N all P all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0)))) & (all I0 all J0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0))))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0))))))) & p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0)))) -> s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0) = s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0))) # label(aBILINEARu_EQu_STDBASIS) # label(axiom) # label(non_clause). [assumption]. 15.94/16.00 3247 (all N all F0 all G0 (s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),G0))),s(fun(cart(real,N),cart(real,N)),F0))) = s(fun(cart(real,N),cart(real,N)),i1) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),G0)))))) # label(aLEFTu_INVERSEu_LINEAR) # label(axiom) # label(non_clause). [assumption]. 15.94/16.00 3248 (all M all N all X all Y s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_sub),s(cart(real,finite_sum(M,N)),X))),s(cart(real,finite_sum(M,N)),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),X))))),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),Y)))))) # label(aSNDCARTu_SUB) # label(axiom) # label(non_clause). [assumption]. 15.94/16.00 3249 (all N all A5 all B0 all X (p(s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(cart(real,N),fun(prod(cart(real,N),cart(real,N)),bool)),between),s(cart(real,N),B0))),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),A5))),s(cart(real,N),X)))))) & s(cart(real,N),B0) != s(cart(real,N),A5) -> (exists D0 (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),B0))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,D0))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),B0))),s(cart(real,N),A5))))))) = s(cart(real,N),X) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,D0)))))))) # label(aBETWEENu_EXISTSu_EXTENSION) # label(axiom) # label(non_clause). [assumption]. 15.94/16.00 3250 (all A all P0 ((exists F0 p(s(bool,i(s(fun(fun(A,cart(real,n10)),bool),P0),s(fun(A,cart(real,n10)),F0))))) <-> (exists F0 p(s(bool,i(s(fun(fun(A,cart(real,n10)),bool),P0),s(fun(A,cart(real,n10)),i(s(fun(fun(A,real),fun(A,cart(real,n10))),i(s(fun(fun(real,cart(real,n10)),fun(fun(A,real),fun(A,cart(real,n10)))),o),s(fun(real,cart(real,n10)),lift))),s(fun(A,real),F0))))))))) # label(aEXISTSu_LIFTu_FUN) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3251 (all N all F0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> ((all X (s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) -> s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),X))) <-> (all X (s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),adjoint),s(fun(cart(real,N),cart(real,N)),F0))),s(cart(real,N),X))) -> s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),X)))))) # label(aADJOINTu_INJECTIVEu_INJECTIVEu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3252 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,Y)))))) # label(aREALu_LTu_LSQRT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3253 (all M all N all A5 s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(cart(cart(real,M),M),num),rank),s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),A5))))),s(cart(cart(real,M),N),A5)))))) # label(aRANKu_GRAM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3254 (all N all M all U_0 ((all A5 all GENR_PVARR_368 ((exists X exists V ((s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(bool,fun(cart(real,M),bool)),i(s(fun(cart(real,M),fun(bool,fun(cart(real,M),bool))),setspec),s(cart(real,M),GENR_PVARR_368))),s(bool,V))),s(cart(real,M),X)))))) <-> p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),U_0),s(cart(cart(real,M),N),A5))),s(cart(real,M),GENR_PVARR_368)))))) -> (all A5 s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))))),s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),gspec),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),U_0),s(cart(cart(real,M),N),A5))))))))) = s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) # label(aRANKu_NULLSPACE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3255 (all A s(A,i(s(fun(num,A),i(s(fun(cart(A,n3),fun(num,A)),d_),s(cart(A,n3),i(s(fun(list(A),cart(A,n3)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,x))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,y))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,z))),s(list(A),nil))))))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(A,x)) # label(aVECTORu_3u_conjunct0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3256 (all N all M all F0 all S0 ((all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),S0)))))) -> s(cart(real,M),Y) = s(cart(real,M),X))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),independent),s(fun(cart(real,M),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0)))))))) # label(aINDEPENDENTu_INJECTIVEu_IMAGEu_GEN) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3257 (all X s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))) = s(cart(real,n10),X)) # label(aLIFTu_DROPu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3258 (all N all S0 s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0)))) # label(aDIMu_SPAN) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3259 (all Q108650 all U_0 ((all F0 all M0 all I0 s(cart(real,Q108650),i(s(fun(num,cart(real,Q108650)),i(s(fun(num,fun(num,cart(real,Q108650))),i(s(fun(fun(num,cart(real,Q108650)),fun(num,fun(num,cart(real,Q108650)))),U_0),s(fun(num,cart(real,Q108650)),F0))),s(num,M0))),s(num,I0))) = s(cart(real,Q108650),i(s(fun(num,cart(real,Q108650)),F0),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,I0))),s(num,M0)))))) -> (all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0)))) -> s(cart(real,Q108650),i(s(fun(fun(num,cart(real,Q108650)),cart(real,Q108650)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108650)),cart(real,Q108650))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q108650)),F0))) = s(cart(real,Q108650),i(s(fun(fun(num,cart(real,Q108650)),cart(real,Q108650)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108650)),cart(real,Q108650))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,N0))),s(num,M0))))))),s(fun(num,cart(real,Q108650)),i(s(fun(num,fun(num,cart(real,Q108650))),i(s(fun(fun(num,cart(real,Q108650)),fun(num,fun(num,cart(real,Q108650)))),U_0),s(fun(num,cart(real,Q108650)),F0))),s(num,M0))))))))) # label(aVSUMu_OFFSETu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3260 (all Q132106 all S0 all X ((all Y (p(s(bool,i(s(fun(fun(cart(real,Q132106),bool),bool),i(s(fun(cart(real,Q132106),fun(fun(cart(real,Q132106),bool),bool)),in),s(cart(real,Q132106),Y))),s(fun(cart(real,Q132106),bool),S0)))) -> p(s(bool,i(s(fun(cart(real,Q132106),bool),i(s(fun(cart(real,Q132106),fun(cart(real,Q132106),bool)),orthogonal),s(cart(real,Q132106),X))),s(cart(real,Q132106),Y)))))) <-> (all Y (p(s(bool,i(s(fun(fun(cart(real,Q132106),bool),bool),i(s(fun(cart(real,Q132106),fun(fun(cart(real,Q132106),bool),bool)),in),s(cart(real,Q132106),Y))),s(fun(cart(real,Q132106),bool),i(s(fun(fun(cart(real,Q132106),bool),fun(cart(real,Q132106),bool)),span),s(fun(cart(real,Q132106),bool),S0)))))) -> p(s(bool,i(s(fun(cart(real,Q132106),bool),i(s(fun(cart(real,Q132106),fun(cart(real,Q132106),bool)),orthogonal),s(cart(real,Q132106),X))),s(cart(real,Q132106),Y)))))))) # label(aORTHOGONALu_TOu_SPANu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3261 (all A all P0 ((all F0 p(s(bool,i(s(fun(fun(A,cart(real,n10)),bool),P0),s(fun(A,cart(real,n10)),F0))))) <-> (all F0 p(s(bool,i(s(fun(fun(A,cart(real,n10)),bool),P0),s(fun(A,cart(real,n10)),i(s(fun(fun(A,real),fun(A,cart(real,n10))),i(s(fun(fun(real,cart(real,n10)),fun(fun(A,real),fun(A,cart(real,n10)))),o),s(fun(real,cart(real,n10)),lift))),s(fun(A,real),F0))))))))) # label(aFORALLu_LIFTu_FUN) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3262 (all Q117856 all U_0 ((all X s(cart(real,Q117856),i(s(fun(cart(real,Q117856),cart(real,Q117856)),U_0),s(cart(real,Q117856),X))) = s(cart(real,Q117856),X)) -> s(cart(cart(real,Q117856),Q117856),i(s(fun(num,cart(cart(real,Q117856),Q117856)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(cart(cart(real,Q117856),Q117856),i(s(fun(fun(cart(real,Q117856),cart(real,Q117856)),cart(cart(real,Q117856),Q117856)),matrix),s(fun(cart(real,Q117856),cart(real,Q117856)),U_0))))) # label(aMATRIXu_ID) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3263 (all Q104818 all X all Y (s(cart(real,Q104818),Y) = s(cart(real,Q104818),X) <-> s(real,i(s(fun(prod(cart(real,Q104818),cart(real,Q104818)),real),distance),s(prod(cart(real,Q104818),cart(real,Q104818)),i(s(fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818))),i(s(fun(cart(real,Q104818),fun(cart(real,Q104818),prod(cart(real,Q104818),cart(real,Q104818)))),c_),s(cart(real,Q104818),X))),s(cart(real,Q104818),Y))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aDISTu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3264 (all Q105328 all Q105334 all W all X all Y all Z0 (s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(prod(cart(real,Q105328),cart(real,Q105328)),real),distance),s(prod(cart(real,Q105328),cart(real,Q105328)),i(s(fun(cart(real,Q105328),prod(cart(real,Q105328),cart(real,Q105328))),i(s(fun(cart(real,Q105328),fun(cart(real,Q105328),prod(cart(real,Q105328),cart(real,Q105328)))),c_),s(cart(real,Q105328),W))),s(cart(real,Q105328),X))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(prod(cart(real,Q105334),cart(real,Q105334)),real),distance),s(prod(cart(real,Q105334),cart(real,Q105334)),i(s(fun(cart(real,Q105334),prod(cart(real,Q105334),cart(real,Q105334))),i(s(fun(cart(real,Q105334),fun(cart(real,Q105334),prod(cart(real,Q105334),cart(real,Q105334)))),c_),s(cart(real,Q105334),Y))),s(cart(real,Q105334),Z0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) <-> s(real,i(s(fun(prod(cart(real,Q105334),cart(real,Q105334)),real),distance),s(prod(cart(real,Q105334),cart(real,Q105334)),i(s(fun(cart(real,Q105334),prod(cart(real,Q105334),cart(real,Q105334))),i(s(fun(cart(real,Q105334),fun(cart(real,Q105334),prod(cart(real,Q105334),cart(real,Q105334)))),c_),s(cart(real,Q105334),Y))),s(cart(real,Q105334),Z0))))) = s(real,i(s(fun(prod(cart(real,Q105328),cart(real,Q105328)),real),distance),s(prod(cart(real,Q105328),cart(real,Q105328)),i(s(fun(cart(real,Q105328),prod(cart(real,Q105328),cart(real,Q105328))),i(s(fun(cart(real,Q105328),fun(cart(real,Q105328),prod(cart(real,Q105328),cart(real,Q105328)))),c_),s(cart(real,Q105328),W))),s(cart(real,Q105328),X))))))) # label(aDISTu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3265 (all N all V all B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),V)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),V))))),s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),V))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0)))))))) # label(aCARDu_GEu_DIMu_INDEPENDENT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3266 (all Q102307 all X (s(cart(real,Q102307),i(s(fun(num,cart(real,Q102307)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(real,Q102307),X) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q102307),real),vectoru_norm),s(cart(real,Q102307),X)))))))) # label(aNORMu_POSu_LT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3267 (all Q115629 all Q115630 all A5 s(cart(cart(real,Q115629),Q115630),i(s(fun(cart(cart(real,Q115629),Q115630),cart(cart(real,Q115629),Q115630)),i(s(fun(real,fun(cart(cart(real,Q115629),Q115630),cart(cart(real,Q115629),Q115630))),r_r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,Q115629),Q115630),A5))) = s(cart(cart(real,Q115629),Q115630),i(s(fun(num,cart(cart(real,Q115629),Q115630)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aMATRIXu_CMULu_LZERO) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3268 (exists X p(s(bool,i(s(fun(real,bool),p0),s(real,X))))) <-> (exists X p(s(bool,i(s(fun(real,bool),p0),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))))) # label(aEXISTSu_DROP) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3269 (all Q109210 all F0 all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,N0))),s(num,P0)))) -> s(cart(real,Q109210),i(s(fun(cart(real,Q109210),cart(real,Q109210)),i(s(fun(cart(real,Q109210),fun(cart(real,Q109210),cart(real,Q109210))),vectoru_add),s(cart(real,Q109210),i(s(fun(fun(num,cart(real,Q109210)),cart(real,Q109210)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109210)),cart(real,Q109210))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q109210)),F0))))),s(cart(real,Q109210),i(s(fun(fun(num,cart(real,Q109210)),cart(real,Q109210)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109210)),cart(real,Q109210))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,P0))))),s(fun(num,cart(real,Q109210)),F0))))) = s(cart(real,Q109210),i(s(fun(fun(num,cart(real,Q109210)),cart(real,Q109210)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109210)),cart(real,Q109210))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,P0))))),s(fun(num,cart(real,Q109210)),F0))))) # label(aVSUMu_COMBINEu_R) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3270 (all N all A5 exists S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0)))) & s(fun(cart(real,N),bool),univ) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),S0)))))) # label(aVECTORu_INu_ORTHOGONALu_SPANNINGSET) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3271 (all N all P all M all A5 s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),i(s(fun(num,cart(cart(real,P),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(cart(real,P),M),i(s(fun(num,cart(cart(real,P),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aMATRIXu_MULu_RZERO) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3272 (all M all N all X all C0 s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(real,fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),r_),s(real,C0))),s(cart(real,finite_sum(M,N)),X))))) = s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(real,fun(cart(real,M),cart(real,M))),r_),s(real,C0))),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),X)))))) # label(aFSTCARTu_CMUL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3273 (all N s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),y))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),x))),s(cart(real,N),y))))) = s(cart(real,N),x)) # label(aVECTORu_SUBu_ADD2) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3274 (all M all N all P all A5 all B0 all X s(cart(real,M),i(s(fun(cart(real,P),cart(real,M)),i(s(fun(cart(cart(real,P),M),fun(cart(real,P),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))),s(cart(real,P),X))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),i(s(fun(cart(real,P),cart(real,N)),i(s(fun(cart(cart(real,P),N),fun(cart(real,P),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,P),N),B0))),s(cart(real,P),X)))))) # label(aMATRIXu_VECTORu_MULu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3275 (all N all U_0 ((all C0 all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),U_0),s(real,C0))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,C0))),s(cart(real,N),X)))) -> (all C0 p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),U_0),s(real,C0))))))))) # label(aLINEARu_SCALING) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3276 (all N all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,a0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,a0)))))) # label(aNORMu_LEu_SQUARE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3277 (all N all M all F0 ((exists A5 all X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X)))) <-> p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))))) # label(aLINEARu_MATRIXu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3278 (all Q122488 all X all C0 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q122488),bool),bool),i(s(fun(cart(real,Q122488),fun(fun(cart(real,Q122488),bool),bool)),in),s(cart(real,Q122488),X))),s(fun(cart(real,Q122488),bool),i(s(fun(fun(cart(real,Q122488),bool),fun(cart(real,Q122488),bool)),span),s(fun(cart(real,Q122488),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,Q122488),bool),bool),i(s(fun(cart(real,Q122488),fun(fun(cart(real,Q122488),bool),bool)),in),s(cart(real,Q122488),i(s(fun(cart(real,Q122488),cart(real,Q122488)),i(s(fun(real,fun(cart(real,Q122488),cart(real,Q122488))),r_),s(real,C0))),s(cart(real,Q122488),X))))),s(fun(cart(real,Q122488),bool),i(s(fun(fun(cart(real,Q122488),bool),fun(cart(real,Q122488),bool)),span),s(fun(cart(real,Q122488),bool),S0)))))))) # label(aSPANu_MUL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3279 (all Q100059 s(cart(real,Q100059),i(s(fun(cart(real,Q100059),cart(real,Q100059)),vectoru_neg),s(cart(real,Q100059),i(s(fun(num,cart(real,Q100059)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q100059),i(s(fun(num,cart(real,Q100059)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aVECTORu_NEGu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3280 (all N all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0)))))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0)))))))) # label(aSUBSETu_LEu_DIM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3281 (all N all M all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (exists B0 ((all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,B0)))))))) # label(aLINEARu_BOUNDEDu_POS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3282 (all Q100593 all X s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(cart(real,Q100593),real),i(s(fun(cart(real,Q100593),fun(cart(real,Q100593),real)),dot),s(cart(real,Q100593),X))),s(cart(real,Q100593),X))))) = s(real,i(s(fun(cart(real,Q100593),real),vectoru_norm),s(cart(real,Q100593),X)))) # label(avectoru_norm) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3283 (all A all B all N all S0 all T0 all F0 all G0 all H0 ((all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))) = s(cart(real,N),i(s(fun(B,cart(real,N)),G0),s(B,i(s(fun(A,B),H0),s(A,X))))) & p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,i(s(fun(A,B),H0),s(A,X))))),s(fun(B,bool),T0)))))) & (all Y (p(s(bool,i(s(fun(fun(B,bool),bool),i(s(fun(B,fun(fun(B,bool),bool)),in),s(B,Y))),s(fun(B,bool),T0)))) -> (all X all XI_ (s(B,Y) = s(B,i(s(fun(A,B),H0),s(A,XI_))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,XI_))),s(fun(A,bool),S0)))) & s(B,i(s(fun(A,B),H0),s(A,X))) = s(B,Y) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> s(A,X) = s(A,XI_))) & (exists X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,Y) = s(B,i(s(fun(A,B),H0),s(A,X))))))) -> s(cart(real,N),i(s(fun(fun(B,cart(real,N)),cart(real,N)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,N)),cart(real,N))),vsum),s(fun(B,bool),T0))),s(fun(B,cart(real,N)),G0))) = s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))) # label(aVSUMu_EQu_GENERAL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3284 (all Q102162 all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q102162),real),vectoru_norm),s(cart(real,Q102162),X))))))) # label(aNORMu_POSu_LE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3285 (all Q108694 all F0 all M0 all N0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,N0))),s(num,M0)))) -> s(cart(real,Q108694),i(s(fun(fun(num,cart(real,Q108694)),cart(real,Q108694)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108694)),cart(real,Q108694))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q108694)),F0))) = s(cart(real,Q108694),i(s(fun(num,cart(real,Q108694)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aVSUMu_TRIVu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3286 (all Q110652 all X (p(s(bool,i(s(fun(cart(real,Q110652),bool),i(s(fun(cart(real,Q110652),fun(cart(real,Q110652),bool)),orthogonal),s(cart(real,Q110652),X))),s(cart(real,Q110652),i(s(fun(num,cart(real,Q110652)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) & p(s(bool,i(s(fun(cart(real,Q110652),bool),i(s(fun(cart(real,Q110652),fun(cart(real,Q110652),bool)),orthogonal),s(cart(real,Q110652),i(s(fun(num,cart(real,Q110652)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q110652),X)))))) # label(aORTHOGONALu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3287 (all Q111931 all Q111930 all F0 all X all Y (p(s(bool,i(s(fun(fun(cart(real,Q111930),cart(real,Q111931)),bool),linear),s(fun(cart(real,Q111930),cart(real,Q111931)),F0)))) -> s(cart(real,Q111931),i(s(fun(cart(real,Q111930),cart(real,Q111931)),F0),s(cart(real,Q111930),i(s(fun(cart(real,Q111930),cart(real,Q111930)),i(s(fun(cart(real,Q111930),fun(cart(real,Q111930),cart(real,Q111930))),vectoru_sub),s(cart(real,Q111930),X))),s(cart(real,Q111930),Y))))) = s(cart(real,Q111931),i(s(fun(cart(real,Q111931),cart(real,Q111931)),i(s(fun(cart(real,Q111931),fun(cart(real,Q111931),cart(real,Q111931))),vectoru_sub),s(cart(real,Q111931),i(s(fun(cart(real,Q111930),cart(real,Q111931)),F0),s(cart(real,Q111930),X))))),s(cart(real,Q111931),i(s(fun(cart(real,Q111930),cart(real,Q111931)),F0),s(cart(real,Q111930),Y))))))) # label(aLINEARu_SUB) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3288 (all N all M all A5 all B0 all I0 all J0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),B0))),s(num,I0))))),s(num,J0))))) = s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))),s(num,I0))))),s(num,J0)))) # label(aMATRIXu_ADDu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3289 (all N all M all A5 all B0 all C0 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))),s(cart(cart(real,N),M),C0))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),B0))),s(cart(cart(real,N),M),C0)))))) # label(aMATRIXu_ADDu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3290 (all N all M all A5 all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> s(cart(real,M),i(s(fun(cart(cart(real,N),M),cart(real,M)),i(s(fun(num,fun(cart(cart(real,N),M),cart(real,M))),column),s(num,I0))),s(cart(cart(real,N),M),A5))) = s(cart(real,M),i(s(fun(cart(cart(real,M),N),cart(real,M)),i(s(fun(num,fun(cart(cart(real,M),N),cart(real,M))),row),s(num,I0))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))))) # label(aROWu_TRANSP) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3291 (all N all A5 all S0 exists V ((-p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0)))) <-> p(s(bool,V))) & s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),i(s(fun(bool,fun(bool,fun(bool,bool))),cond),s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0))))),s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),S0))))),s(bool,V))) = s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0))))))) # label(aINDEPENDENTu_INSERT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3292 (all Q110589 all Y all Z0 ((all X s(real,i(s(fun(cart(real,Q110589),real),i(s(fun(cart(real,Q110589),fun(cart(real,Q110589),real)),dot),s(cart(real,Q110589),X))),s(cart(real,Q110589),Y))) = s(real,i(s(fun(cart(real,Q110589),real),i(s(fun(cart(real,Q110589),fun(cart(real,Q110589),real)),dot),s(cart(real,Q110589),X))),s(cart(real,Q110589),Z0)))) <-> s(cart(real,Q110589),Z0) = s(cart(real,Q110589),Y))) # label(aVECTORu_EQu_LDOT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3293 (all N all U_0 ((all A5 all GENR_PVARR_335 ((exists X exists V ((s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),A5))),s(cart(real,N),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_335))),s(bool,V))),s(cart(real,N),X)))))) <-> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),U_0),s(cart(real,N),A5))),s(cart(real,N),GENR_PVARR_335)))))) -> (all S0 (s(fun(cart(real,N),bool),univ) != s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))) -> (exists A5 (s(cart(real,N),A5) != s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),U_0),s(cart(real,N),A5)))))))))))))) # label(aSPANu_NOTu_UNIVu_SUBSETu_HYPERPLANE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3294 (all B all A all Q107061 all U_1 ((all S0 all F0 all Y all GENR_PVARR_281 (p(s(bool,i(s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))),s(A,GENR_PVARR_281)))) <-> (exists X exists V ((p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) & s(B,Y) = s(B,i(s(fun(A,B),F0),s(A,X))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(A,bool),i(s(fun(bool,fun(A,bool)),i(s(fun(A,fun(bool,fun(A,bool))),setspec),s(A,GENR_PVARR_281))),s(bool,V))),s(A,X)))))))) -> (all U_0 ((all S0 all F0 all G0 all Y s(cart(real,Q107061),i(s(fun(fun(A,cart(real,Q107061)),cart(real,Q107061)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107061)),cart(real,Q107061))),vsum),s(fun(A,bool),i(s(fun(fun(A,bool),fun(A,bool)),gspec),s(fun(A,bool),i(s(fun(B,fun(A,bool)),i(s(fun(fun(A,B),fun(B,fun(A,bool))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(B,fun(A,bool)))),U_1),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(B,Y))))))),s(fun(A,cart(real,Q107061)),G0))) = s(cart(real,Q107061),i(s(fun(B,cart(real,Q107061)),i(s(fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061))),i(s(fun(fun(A,B),fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061)))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061))))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,cart(real,Q107061)),G0))),s(B,Y)))) -> (all F0 all G0 all S0 (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) -> s(cart(real,Q107061),i(s(fun(fun(B,cart(real,Q107061)),cart(real,Q107061)),i(s(fun(fun(B,bool),fun(fun(B,cart(real,Q107061)),cart(real,Q107061))),vsum),s(fun(B,bool),i(s(fun(fun(A,bool),fun(B,bool)),i(s(fun(fun(A,B),fun(fun(A,bool),fun(B,bool))),image),s(fun(A,B),F0))),s(fun(A,bool),S0))))),s(fun(B,cart(real,Q107061)),i(s(fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061))),i(s(fun(fun(A,B),fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061)))),i(s(fun(fun(A,bool),fun(fun(A,B),fun(fun(A,cart(real,Q107061)),fun(B,cart(real,Q107061))))),U_0),s(fun(A,bool),S0))),s(fun(A,B),F0))),s(fun(A,cart(real,Q107061)),G0))))) = s(cart(real,Q107061),i(s(fun(fun(A,cart(real,Q107061)),cart(real,Q107061)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107061)),cart(real,Q107061))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,Q107061)),G0))))))))) # label(aVSUMu_IMAGEu_GEN) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3295 (all N all M all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))))))),s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),S0)))))))) # label(aDIMu_LINEARu_IMAGEu_LE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3296 (all Q119381 all K0 all X (p(s(bool,i(s(fun(fun(Q119381,bool),bool),finite),s(fun(Q119381,bool),K0)))) -> s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(fun(Q119381,real),real),i(s(fun(fun(Q119381,bool),fun(fun(Q119381,real),real)),sum),s(fun(Q119381,bool),K0))),s(fun(Q119381,real),X))))) = s(cart(real,n10),i(s(fun(fun(Q119381,cart(real,n10)),cart(real,n10)),i(s(fun(fun(Q119381,bool),fun(fun(Q119381,cart(real,n10)),cart(real,n10))),vsum),s(fun(Q119381,bool),K0))),s(fun(Q119381,cart(real,n10)),i(s(fun(fun(Q119381,real),fun(Q119381,cart(real,n10))),i(s(fun(fun(real,cart(real,n10)),fun(fun(Q119381,real),fun(Q119381,cart(real,n10)))),o),s(fun(real,cart(real,n10)),lift))),s(fun(Q119381,real),X))))))) # label(aLIFTu_SUM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3297 (all M all N all A5 ((exists AI_ (s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),AI_))),s(cart(cart(real,N),M),A5))) = s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) & s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),AI_))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) <-> p(s(bool,i(s(fun(cart(cart(real,N),M),bool),invertible),s(cart(cart(real,N),M),A5)))))) # label(ainvertible) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3298 (all Q114621 all Q114622 all A5 s(cart(cart(real,Q114621),Q114622),A5) = s(cart(cart(real,Q114621),Q114622),i(s(fun(cart(cart(real,Q114621),Q114622),cart(cart(real,Q114621),Q114622)),i(s(fun(cart(cart(real,Q114621),Q114622),fun(cart(cart(real,Q114621),Q114622),cart(cart(real,Q114621),Q114622))),matrixu_add),s(cart(cart(real,Q114621),Q114622),A5))),s(cart(cart(real,Q114621),Q114622),i(s(fun(num,cart(cart(real,Q114621),Q114622)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) # label(aMATRIXu_ADDu_RID) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3299 (all N all M all A5 p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),bool)),rows),s(cart(cart(real,N),M),A5))))))) # label(aFINITEu_ROWS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3300 (all Q139200 all X s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,Q139200),real),infnorm),s(cart(real,Q139200),X))))) = s(real,i(s(fun(cart(real,Q139200),real),infnorm),s(cart(real,Q139200),X)))) # label(aREALu_ABSu_INFNORM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3301 (all Q100419 all X all Y s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(cart(real,Q100419),real),i(s(fun(cart(real,Q100419),fun(cart(real,Q100419),real)),dot),s(cart(real,Q100419),X))),s(cart(real,Q100419),Y))))) = s(real,i(s(fun(cart(real,Q100419),real),i(s(fun(cart(real,Q100419),fun(cart(real,Q100419),real)),dot),s(cart(real,Q100419),i(s(fun(cart(real,Q100419),cart(real,Q100419)),vectoru_neg),s(cart(real,Q100419),X))))),s(cart(real,Q100419),Y)))) # label(aDOTu_LNEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.00 3302 (all Q109622 all T0 s(cart(real,Q109622),i(s(fun(fun(num,cart(real,Q109622)),cart(real,Q109622)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109622)),cart(real,Q109622))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(fun(num,cart(real,Q109622)),T0))) = s(cart(real,Q109622),i(s(fun(cart(real,Q109622),cart(real,Q109622)),i(s(fun(cart(real,Q109622),fun(cart(real,Q109622),cart(real,Q109622))),vectoru_add),s(cart(real,Q109622),i(s(fun(num,cart(real,Q109622)),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(cart(real,Q109622),i(s(fun(num,cart(real,Q109622)),T0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) # label(aVSUMu_2) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3303 (all Q111705 p(s(bool,i(s(fun(fun(cart(real,Q111705),cart(real,Q111705)),bool),linear),s(fun(cart(real,Q111705),cart(real,Q111705)),vectoru_neg))))) # label(aLINEARu_NEGATION) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3304 (all Q119985 all Q119987 p(s(bool,i(s(fun(fun(cart(real,finite_sum(Q119985,Q119987)),cart(real,Q119987)),bool),linear),s(fun(cart(real,finite_sum(Q119985,Q119987)),cart(real,Q119987)),sndcart))))) # label(aLINEARu_SNDCART) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3305 (all N all M all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (exists B0 all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,B0))),s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))))))))))) # label(aLINEARu_BOUNDED) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3306 (all N all S0 s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,N),bool),S0)))))) # label(aDIMu_INSERTu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3307 (all Q122739 all S0 all X all Y (p(s(bool,i(s(fun(fun(cart(real,Q122739),bool),bool),i(s(fun(cart(real,Q122739),fun(fun(cart(real,Q122739),bool),bool)),in),s(cart(real,Q122739),X))),s(fun(cart(real,Q122739),bool),i(s(fun(fun(cart(real,Q122739),bool),fun(cart(real,Q122739),bool)),span),s(fun(cart(real,Q122739),bool),S0)))))) -> s(bool,i(s(fun(fun(cart(real,Q122739),bool),bool),i(s(fun(cart(real,Q122739),fun(fun(cart(real,Q122739),bool),bool)),in),s(cart(real,Q122739),Y))),s(fun(cart(real,Q122739),bool),i(s(fun(fun(cart(real,Q122739),bool),fun(cart(real,Q122739),bool)),span),s(fun(cart(real,Q122739),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,Q122739),bool),bool),i(s(fun(cart(real,Q122739),fun(fun(cart(real,Q122739),bool),bool)),in),s(cart(real,Q122739),i(s(fun(cart(real,Q122739),cart(real,Q122739)),i(s(fun(cart(real,Q122739),fun(cart(real,Q122739),cart(real,Q122739))),vectoru_add),s(cart(real,Q122739),X))),s(cart(real,Q122739),Y))))),s(fun(cart(real,Q122739),bool),i(s(fun(fun(cart(real,Q122739),bool),fun(cart(real,Q122739),bool)),span),s(fun(cart(real,Q122739),bool),S0))))))) # label(aSPANu_ADDu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3308 (all Q110704 all X all Y s(bool,i(s(fun(cart(real,Q110704),bool),i(s(fun(cart(real,Q110704),fun(cart(real,Q110704),bool)),orthogonal),s(cart(real,Q110704),i(s(fun(cart(real,Q110704),cart(real,Q110704)),vectoru_neg),s(cart(real,Q110704),X))))),s(cart(real,Q110704),Y))) = s(bool,i(s(fun(cart(real,Q110704),bool),i(s(fun(cart(real,Q110704),fun(cart(real,Q110704),bool)),orthogonal),s(cart(real,Q110704),X))),s(cart(real,Q110704),Y)))) # label(aORTHOGONALu_LNEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3309 (all N all M all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (all X all Y s(real,i(s(fun(cart(real,M),real),i(s(fun(cart(real,M),fun(cart(real,M),real)),dot),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,N),Y))))),s(cart(real,M),X))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),Y))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))) & (all X all Y s(real,i(s(fun(cart(real,M),real),i(s(fun(cart(real,M),fun(cart(real,M),real)),dot),s(cart(real,M),X))),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,N),Y))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),Y)))))) # label(aADJOINTu_CLAUSES) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3310 (all Q99628 all X s(cart(real,Q99628),i(s(fun(cart(real,Q99628),cart(real,Q99628)),i(s(fun(cart(real,Q99628),fun(cart(real,Q99628),cart(real,Q99628))),vectoru_add),s(cart(real,Q99628),X))),s(cart(real,Q99628),i(s(fun(cart(real,Q99628),cart(real,Q99628)),vectoru_neg),s(cart(real,Q99628),X))))) = s(cart(real,Q99628),i(s(fun(num,cart(real,Q99628)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aVECTORu_ADDu_RINV) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3311 (all N all X all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X)))))))) # label(aCOMPONENTu_LEu_NORM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3312 (all N all U_1 ((all U all V s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V))))),s(cart(real,N),V))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_1),s(fun(cart(real,N),real),U))),s(cart(real,N),V)))) -> (all U_0 ((all S0 all GENR_PVARR_307 (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),U_0),s(fun(cart(real,N),bool),S0))),s(cart(real,N),GENR_PVARR_307)))) <-> (exists Y exists V ((p(s(bool,V)) <-> (exists U s(cart(real,N),Y) = s(cart(real,N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(real,N)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),cart(real,N)),cart(real,N))),vsum),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_1),s(fun(cart(real,N),real),U))))))) & p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_307))),s(bool,V))),s(cart(real,N),Y)))))))) -> (all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))) -> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),U_0),s(fun(cart(real,N),bool),S0))))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))))))) # label(aSPANu_FINITE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3313 (all A all F0 all G0 all H0 (s(fun(A,A),i(s(fun(fun(A,A),fun(A,A)),i(s(fun(fun(A,A),fun(fun(A,A),fun(A,A))),o),s(fun(A,A),F0))),s(fun(A,A),G0))) = s(fun(A,A),i1) & s(fun(A,A),i(s(fun(fun(A,A),fun(A,A)),i(s(fun(fun(A,A),fun(fun(A,A),fun(A,A))),o),s(fun(A,A),G0))),s(fun(A,A),H0))) = s(fun(A,A),i1) -> s(fun(A,A),F0) = s(fun(A,A),H0))) # label(aLEFTu_RIGHTu_INVERSEu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3314 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y)))))))) # label(aSQRTu_MONOu_LT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3315 (all Q105155 all X all XI_ all Y all YI_ p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q105155),cart(real,Q105155)),real),distance),s(prod(cart(real,Q105155),cart(real,Q105155)),i(s(fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155))),i(s(fun(cart(real,Q105155),fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155)))),c_),s(cart(real,Q105155),i(s(fun(cart(real,Q105155),cart(real,Q105155)),i(s(fun(cart(real,Q105155),fun(cart(real,Q105155),cart(real,Q105155))),vectoru_add),s(cart(real,Q105155),X))),s(cart(real,Q105155),Y))))),s(cart(real,Q105155),i(s(fun(cart(real,Q105155),cart(real,Q105155)),i(s(fun(cart(real,Q105155),fun(cart(real,Q105155),cart(real,Q105155))),vectoru_add),s(cart(real,Q105155),XI_))),s(cart(real,Q105155),YI_))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,Q105155),cart(real,Q105155)),real),distance),s(prod(cart(real,Q105155),cart(real,Q105155)),i(s(fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155))),i(s(fun(cart(real,Q105155),fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155)))),c_),s(cart(real,Q105155),X))),s(cart(real,Q105155),XI_))))))),s(real,i(s(fun(prod(cart(real,Q105155),cart(real,Q105155)),real),distance),s(prod(cart(real,Q105155),cart(real,Q105155)),i(s(fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155))),i(s(fun(cart(real,Q105155),fun(cart(real,Q105155),prod(cart(real,Q105155),cart(real,Q105155)))),c_),s(cart(real,Q105155),Y))),s(cart(real,Q105155),YI_))))))))))) # label(aDISTu_TRIANGLEu_ADD) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3316 (all N all A5 all S0 ((exists K0 p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),x))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,K0))),s(cart(real,N),A5))))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))))) <-> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),x))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0)))))))))) # label(aSPANu_BREAKDOWNu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3317 (all Q141274 all A5 all X all B0 (s(real,i(s(fun(prod(cart(real,Q141274),cart(real,Q141274)),real),distance),s(prod(cart(real,Q141274),cart(real,Q141274)),i(s(fun(cart(real,Q141274),prod(cart(real,Q141274),cart(real,Q141274))),i(s(fun(cart(real,Q141274),fun(cart(real,Q141274),prod(cart(real,Q141274),cart(real,Q141274)))),c_),s(cart(real,Q141274),A5))),s(cart(real,Q141274),B0))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(prod(cart(real,Q141274),cart(real,Q141274)),real),distance),s(prod(cart(real,Q141274),cart(real,Q141274)),i(s(fun(cart(real,Q141274),prod(cart(real,Q141274),cart(real,Q141274))),i(s(fun(cart(real,Q141274),fun(cart(real,Q141274),prod(cart(real,Q141274),cart(real,Q141274)))),c_),s(cart(real,Q141274),A5))),s(cart(real,Q141274),X))))))),s(real,i(s(fun(prod(cart(real,Q141274),cart(real,Q141274)),real),distance),s(prod(cart(real,Q141274),cart(real,Q141274)),i(s(fun(cart(real,Q141274),prod(cart(real,Q141274),cart(real,Q141274))),i(s(fun(cart(real,Q141274),fun(cart(real,Q141274),prod(cart(real,Q141274),cart(real,Q141274)))),c_),s(cart(real,Q141274),X))),s(cart(real,Q141274),B0))))))) <-> p(s(bool,i(s(fun(prod(cart(real,Q141274),cart(real,Q141274)),bool),i(s(fun(cart(real,Q141274),fun(prod(cart(real,Q141274),cart(real,Q141274)),bool)),between),s(cart(real,Q141274),X))),s(prod(cart(real,Q141274),cart(real,Q141274)),i(s(fun(cart(real,Q141274),prod(cart(real,Q141274),cart(real,Q141274))),i(s(fun(cart(real,Q141274),fun(cart(real,Q141274),prod(cart(real,Q141274),cart(real,Q141274)))),c_),s(cart(real,Q141274),A5))),s(cart(real,Q141274),B0)))))))) # label(abetween) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3318 (all Q114667 all Q114668 all A5 s(cart(cart(real,Q114667),Q114668),i(s(fun(cart(cart(real,Q114667),Q114668),cart(cart(real,Q114667),Q114668)),i(s(fun(cart(cart(real,Q114667),Q114668),fun(cart(cart(real,Q114667),Q114668),cart(cart(real,Q114667),Q114668))),matrixu_add),s(cart(cart(real,Q114667),Q114668),A5))),s(cart(cart(real,Q114667),Q114668),i(s(fun(cart(cart(real,Q114667),Q114668),cart(cart(real,Q114667),Q114668)),matrixu_neg),s(cart(cart(real,Q114667),Q114668),A5))))) = s(cart(cart(real,Q114667),Q114668),i(s(fun(num,cart(cart(real,Q114667),Q114668)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aMATRIXu_ADDu_RNEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3319 (all N all M all A5 all B0 all C0 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),B0)))))) # label(aMATRIXu_CMULu_SUBu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3320 (all X all Y s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(prod(cart(real,n10),cart(real,n10)),real),distance),s(prod(cart(real,n10),cart(real,n10)),i(s(fun(cart(real,n10),prod(cart(real,n10),cart(real,n10))),i(s(fun(cart(real,n10),fun(cart(real,n10),prod(cart(real,n10),cart(real,n10)))),c_),s(cart(real,n10),X))),s(cart(real,n10),Y)))))) # label(aDISTu_REAL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3321 (all N all F0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) & (all Y exists X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),Y)) -> (all X all Y (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) -> s(cart(real,N),Y) = s(cart(real,N),X))))) # label(aLINEARu_SURJECTIVEu_IMPu_INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3322 (all N all F0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> ((all X all Y (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),adjoint),s(fun(cart(real,N),cart(real,N)),F0))),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),adjoint),s(fun(cart(real,N),cart(real,N)),F0))),s(cart(real,N),X))) -> s(cart(real,N),X) = s(cart(real,N),Y))) <-> (all X all Y (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),F0),s(cart(real,N),Y))) -> s(cart(real,N),Y) = s(cart(real,N),X)))))) # label(aADJOINTu_INJECTIVEu_INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3323 (all Q110508 all I0 all J0 (s(num,I0) != s(num,J0) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,i(s(fun(cart(real,Q110508),real),i(s(fun(cart(real,Q110508),fun(cart(real,Q110508),real)),dot),s(cart(real,Q110508),i(s(fun(num,cart(real,Q110508)),basis),s(num,I0))))),s(cart(real,Q110508),i(s(fun(num,cart(real,Q110508)),basis),s(num,J0))))))) # label(aDOTu_BASISu_BASISu_UNEQUAL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3324 (all N all U_0 ((all GENR_PVARR_313 (p(s(bool,i(s(fun(cart(real,N),bool),U_0),s(cart(real,N),GENR_PVARR_313)))) <-> (exists I0 exists V (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_313))),s(bool,V))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0)))))) & (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) <-> p(s(bool,V))))))) -> s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))) = s(num,i(s(fun(fun(cart(real,N),bool),num),card),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),U_0))))))) # label(aCARDu_STDBASIS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3325 (all Q139366 all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q139366),real),infnorm),s(cart(real,Q139366),X))))),s(real,i(s(fun(cart(real,Q139366),real),vectoru_norm),s(cart(real,Q139366),X))))))) # label(aINFNORMu_LEu_NORM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3326 (all N all A5 all B0 all C0 all X all Y all Z0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),C0))),s(fun(cart(real,N),bool),empty)))))))))) & s(cart(real,N),B0) != s(cart(real,N),A5) & s(cart(real,N),A5) != s(cart(real,N),C0) & s(cart(real,N),B0) != s(cart(real,N),C0) -> (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,X))),s(cart(real,N),A5))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Y))),s(cart(real,N),B0))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Z0))),s(cart(real,N),C0))))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(real,Y) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & s(real,Z0) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,X)))) # label(aINDEPENDENTu_3) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3327 (all Q106736 all Q106745 all U_0 ((all F0 all A5 s(real,i(s(fun(Q106736,real),i(s(fun(fun(Q106736,cart(real,Q106745)),fun(Q106736,real)),U_0),s(fun(Q106736,cart(real,Q106745)),F0))),s(Q106736,A5))) = s(real,i(s(fun(cart(real,Q106745),real),vectoru_norm),s(cart(real,Q106745),i(s(fun(Q106736,cart(real,Q106745)),F0),s(Q106736,A5)))))) -> (all S0 all F0 all B0 (p(s(bool,i(s(fun(fun(Q106736,bool),bool),finite),s(fun(Q106736,bool),S0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(Q106736,real),real),i(s(fun(fun(Q106736,bool),fun(fun(Q106736,real),real)),sum),s(fun(Q106736,bool),S0))),s(fun(Q106736,real),i(s(fun(fun(Q106736,cart(real,Q106745)),fun(Q106736,real)),U_0),s(fun(Q106736,cart(real,Q106745)),F0))))))),s(real,B0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q106745),real),vectoru_norm),s(cart(real,Q106745),i(s(fun(fun(Q106736,cart(real,Q106745)),cart(real,Q106745)),i(s(fun(fun(Q106736,bool),fun(fun(Q106736,cart(real,Q106745)),cart(real,Q106745))),vsum),s(fun(Q106736,bool),S0))),s(fun(Q106736,cart(real,Q106745)),F0))))))),s(real,B0)))))))) # label(aVSUMu_NORMu_TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3328 (all N all U_0 ((all A5 all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),A5))),s(cart(real,N),X))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),U_0),s(cart(real,N),A5))),s(cart(real,N),X)))) -> (all S0 all A5 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0)))) -> (s(fun(cart(real,N),bool),S0) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),U_0),s(cart(real,N),A5))))),s(fun(cart(real,N),bool),S0))) <-> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0))))))))) # label(aSUBSPACEu_TRANSLATIONu_SELFu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3329 (all Q111058 all A5 all X all Y (p(s(bool,i(s(fun(cart(real,Q111058),bool),i(s(fun(cart(real,Q111058),fun(cart(real,Q111058),bool)),orthogonal),s(cart(real,Q111058),X))),s(cart(real,Q111058),A5)))) & p(s(bool,i(s(fun(cart(real,Q111058),bool),i(s(fun(cart(real,Q111058),fun(cart(real,Q111058),bool)),orthogonal),s(cart(real,Q111058),Y))),s(cart(real,Q111058),A5)))) -> p(s(bool,i(s(fun(cart(real,Q111058),bool),i(s(fun(cart(real,Q111058),fun(cart(real,Q111058),bool)),orthogonal),s(cart(real,Q111058),i(s(fun(cart(real,Q111058),cart(real,Q111058)),i(s(fun(cart(real,Q111058),fun(cart(real,Q111058),cart(real,Q111058))),vectoru_sub),s(cart(real,Q111058),X))),s(cart(real,Q111058),Y))))),s(cart(real,Q111058),A5)))))) # label(aORTHOGONALu_CLAUSESu_conjunct9) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3330 (all X (s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,n10),X))) # label(aDROPu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3331 (all Q139356 all X (s(cart(real,Q139356),i(s(fun(num,cart(real,Q139356)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(real,Q139356),X) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(cart(real,Q139356),real),infnorm),s(cart(real,Q139356),X)))))))) # label(aINFNORMu_POSu_LT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3332 (all Q141372 all A5 all B0 all X s(bool,i(s(fun(prod(cart(real,Q141372),cart(real,Q141372)),bool),i(s(fun(cart(real,Q141372),fun(prod(cart(real,Q141372),cart(real,Q141372)),bool)),between),s(cart(real,Q141372),X))),s(prod(cart(real,Q141372),cart(real,Q141372)),i(s(fun(cart(real,Q141372),prod(cart(real,Q141372),cart(real,Q141372))),i(s(fun(cart(real,Q141372),fun(cart(real,Q141372),prod(cart(real,Q141372),cart(real,Q141372)))),c_),s(cart(real,Q141372),A5))),s(cart(real,Q141372),B0))))) = s(bool,i(s(fun(prod(cart(real,Q141372),cart(real,Q141372)),bool),i(s(fun(cart(real,Q141372),fun(prod(cart(real,Q141372),cart(real,Q141372)),bool)),between),s(cart(real,Q141372),X))),s(prod(cart(real,Q141372),cart(real,Q141372)),i(s(fun(cart(real,Q141372),prod(cart(real,Q141372),cart(real,Q141372))),i(s(fun(cart(real,Q141372),fun(cart(real,Q141372),prod(cart(real,Q141372),cart(real,Q141372)))),c_),s(cart(real,Q141372),B0))),s(cart(real,Q141372),A5)))))) # label(aBETWEENu_SYM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3333 (all N all U_0 ((all U all V s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),U))),s(cart(real,N),V))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V))))),s(cart(real,N),V)))) -> (all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))) -> (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),S0)))) <-> (exists U (s(cart(real,N),i(s(fun(fun(cart(real,N),cart(real,N)),cart(real,N)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),cart(real,N)),cart(real,N))),vsum),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),real),fun(cart(real,N),cart(real,N))),U_0),s(fun(cart(real,N),real),U))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & (exists V (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),V))),s(fun(cart(real,N),bool),S0)))) & s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(real,i(s(fun(cart(real,N),real),U),s(cart(real,N),V)))))))))))) # label(aDEPENDENTu_FINITE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3334 (all Q106605 all Q106610 all F0 all X s(cart(real,Q106605),i(s(fun(Q106610,cart(real,Q106605)),F0),s(Q106610,X))) = s(cart(real,Q106605),i(s(fun(fun(Q106610,cart(real,Q106605)),cart(real,Q106605)),i(s(fun(fun(Q106610,bool),fun(fun(Q106610,cart(real,Q106605)),cart(real,Q106605))),vsum),s(fun(Q106610,bool),i(s(fun(fun(Q106610,bool),fun(Q106610,bool)),i(s(fun(Q106610,fun(fun(Q106610,bool),fun(Q106610,bool))),insert),s(Q106610,X))),s(fun(Q106610,bool),empty))))),s(fun(Q106610,cart(real,Q106605)),F0)))) # label(aVSUMu_SING) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3335 (all Q131723 all V s(cart(cart(real,n10),Q131723),i(s(fun(cart(real,Q131723),cart(cart(real,n10),Q131723)),columnvector),s(cart(real,Q131723),V))) = s(cart(cart(real,n10),Q131723),i(s(fun(cart(cart(real,Q131723),n10),cart(cart(real,n10),Q131723)),transp),s(cart(cart(real,Q131723),n10),i(s(fun(cart(real,Q131723),cart(cart(real,Q131723),n10)),rowvector),s(cart(real,Q131723),V)))))) # label(aTRANSPu_ROWVECTOR) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3336 (all P0 (p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) & p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(num,bool),P0),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) <-> (all I0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) -> p(s(bool,i(s(fun(num,bool),P0),s(num,I0)))))))) # label(aFORALLu_3) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3337 (all A ((exists X exists Y exists Z0 p(s(bool,i(s(fun(cart(A,n3),bool),p0),s(cart(A,n3),i(s(fun(list(A),cart(A,n3)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Y))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Z0))),s(list(A),nil))))))))))))) <-> (exists V p(s(bool,i(s(fun(cart(A,n3),bool),p0),s(cart(A,n3),V))))))) # label(aEXISTSu_VECTORu_3) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3338 (all Q105615 all Q105619 all U_0 ((all X s(cart(real,Q105619),i(s(fun(num,cart(real,Q105619)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q105619),i(s(fun(Q105615,cart(real,Q105619)),U_0),s(Q105615,X)))) -> s(cart(real,Q105619),i(s(fun(num,cart(real,Q105619)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q105619),i(s(fun(fun(Q105615,cart(real,Q105619)),cart(real,Q105619)),i(s(fun(fun(Q105615,bool),fun(fun(Q105615,cart(real,Q105619)),cart(real,Q105619))),vsum),s(fun(Q105615,bool),s0))),s(fun(Q105615,cart(real,Q105619)),U_0))))) # label(aVSUMu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3339 (all M all N all A5 all B0 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,M),N),cart(cart(real,M),N))),matrixu_add),s(cart(cart(real,M),N),A5))),s(cart(cart(real,M),N),B0))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))))),s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),B0))))))))) # label(aRANKu_TRIANGLE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3340 (all Q111612 all Q111621 all U_0 ((all F0 all G0 all X s(cart(real,Q111621),i(s(fun(cart(real,Q111612),cart(real,Q111621)),i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(cart(real,Q111612),cart(real,Q111621))),i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(cart(real,Q111612),cart(real,Q111621)))),U_0),s(fun(cart(real,Q111612),cart(real,Q111621)),F0))),s(fun(cart(real,Q111612),cart(real,Q111621)),G0))),s(cart(real,Q111612),X))) = s(cart(real,Q111621),i(s(fun(cart(real,Q111621),cart(real,Q111621)),i(s(fun(cart(real,Q111621),fun(cart(real,Q111621),cart(real,Q111621))),vectoru_add),s(cart(real,Q111621),i(s(fun(cart(real,Q111612),cart(real,Q111621)),F0),s(cart(real,Q111612),X))))),s(cart(real,Q111621),i(s(fun(cart(real,Q111612),cart(real,Q111621)),G0),s(cart(real,Q111612),X)))))) -> (all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),bool),linear),s(fun(cart(real,Q111612),cart(real,Q111621)),F0)))) & p(s(bool,i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),bool),linear),s(fun(cart(real,Q111612),cart(real,Q111621)),G0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),bool),linear),s(fun(cart(real,Q111612),cart(real,Q111621)),i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(cart(real,Q111612),cart(real,Q111621))),i(s(fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(fun(cart(real,Q111612),cart(real,Q111621)),fun(cart(real,Q111612),cart(real,Q111621)))),U_0),s(fun(cart(real,Q111612),cart(real,Q111621)),F0))),s(fun(cart(real,Q111612),cart(real,Q111621)),G0)))))))))) # label(aLINEARu_COMPOSEu_ADD) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3341 (all Q139075 all X (s(cart(real,Q139075),i(s(fun(num,cart(real,Q139075)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q139075),X) <-> s(real,i(s(fun(cart(real,Q139075),real),infnorm),s(cart(real,Q139075),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aINFNORMu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3342 (all Q100443 all X all Y s(real,i(s(fun(real,real),realu_neg),s(real,i(s(fun(cart(real,Q100443),real),i(s(fun(cart(real,Q100443),fun(cart(real,Q100443),real)),dot),s(cart(real,Q100443),X))),s(cart(real,Q100443),Y))))) = s(real,i(s(fun(cart(real,Q100443),real),i(s(fun(cart(real,Q100443),fun(cart(real,Q100443),real)),dot),s(cart(real,Q100443),X))),s(cart(real,Q100443),i(s(fun(cart(real,Q100443),cart(real,Q100443)),vectoru_neg),s(cart(real,Q100443),Y)))))) # label(aDOTu_RNEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3343 (all N all K0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0)))) -> s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,K0))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) # label(aNORMu_BASIS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3344 (all Q100076 (s(cart(real,Q100076),i(s(fun(num,cart(real,Q100076)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q100076),i(s(fun(cart(real,Q100076),cart(real,Q100076)),vectoru_neg),s(cart(real,Q100076),x))) <-> s(cart(real,Q100076),x) = s(cart(real,Q100076),i(s(fun(num,cart(real,Q100076)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aVECTORu_NEGu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3345 (all N all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,N),bool),empty)))))) <-> s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))))) # label(aDIMu_EQu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3346 (all N0 s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))) = s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,N0)))))) # label(aDROPu_VEC) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3347 (all Q142675 all Q142689 all F0 all A5 all B0 (p(s(bool,i(s(fun(fun(cart(real,Q142689),cart(real,Q142675)),bool),linear),s(fun(cart(real,Q142689),cart(real,Q142675)),F0)))) -> s(cart(real,Q142675),i(s(fun(prod(cart(real,Q142675),cart(real,Q142675)),cart(real,Q142675)),midpoint),s(prod(cart(real,Q142675),cart(real,Q142675)),i(s(fun(cart(real,Q142675),prod(cart(real,Q142675),cart(real,Q142675))),i(s(fun(cart(real,Q142675),fun(cart(real,Q142675),prod(cart(real,Q142675),cart(real,Q142675)))),c_),s(cart(real,Q142675),i(s(fun(cart(real,Q142689),cart(real,Q142675)),F0),s(cart(real,Q142689),A5))))),s(cart(real,Q142675),i(s(fun(cart(real,Q142689),cart(real,Q142675)),F0),s(cart(real,Q142689),B0))))))) = s(cart(real,Q142675),i(s(fun(cart(real,Q142689),cart(real,Q142675)),F0),s(cart(real,Q142689),i(s(fun(prod(cart(real,Q142689),cart(real,Q142689)),cart(real,Q142689)),midpoint),s(prod(cart(real,Q142689),cart(real,Q142689)),i(s(fun(cart(real,Q142689),prod(cart(real,Q142689),cart(real,Q142689))),i(s(fun(cart(real,Q142689),fun(cart(real,Q142689),prod(cart(real,Q142689),cart(real,Q142689)))),c_),s(cart(real,Q142689),A5))),s(cart(real,Q142689),B0))))))))) # label(aMIDPOINTu_LINEARu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3348 (all Q100000 s(cart(real,Q100000),i(s(fun(cart(real,Q100000),cart(real,Q100000)),i(s(fun(cart(real,Q100000),fun(cart(real,Q100000),cart(real,Q100000))),vectoru_sub),s(cart(real,Q100000),i(s(fun(num,cart(real,Q100000)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q100000),x))) = s(cart(real,Q100000),i(s(fun(cart(real,Q100000),cart(real,Q100000)),vectoru_neg),s(cart(real,Q100000),x)))) # label(aVECTORu_SUBu_LZERO) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3349 (all Q142390 all X s(cart(real,Q142390),X) = s(cart(real,Q142390),i(s(fun(prod(cart(real,Q142390),cart(real,Q142390)),cart(real,Q142390)),midpoint),s(prod(cart(real,Q142390),cart(real,Q142390)),i(s(fun(cart(real,Q142390),prod(cart(real,Q142390),cart(real,Q142390))),i(s(fun(cart(real,Q142390),fun(cart(real,Q142390),prod(cart(real,Q142390),cart(real,Q142390)))),c_),s(cart(real,Q142390),X))),s(cart(real,Q142390),X)))))) # label(aMIDPOINTu_REFL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3350 (all M all N all A5 s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aMATRIXu_VECTORu_MULu_RZERO) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3351 (all Q105293 all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(prod(cart(real,Q105293),cart(real,Q105293)),real),distance),s(prod(cart(real,Q105293),cart(real,Q105293)),i(s(fun(cart(real,Q105293),prod(cart(real,Q105293),cart(real,Q105293))),i(s(fun(cart(real,Q105293),fun(cart(real,Q105293),prod(cart(real,Q105293),cart(real,Q105293)))),c_),s(cart(real,Q105293),X))),s(cart(real,Q105293),Y))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) <-> s(cart(real,Q105293),Y) = s(cart(real,Q105293),X))) # label(aDISTu_LEu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3352 (all Q141483 all A5 all B0 all C0 all D0 (p(s(bool,i(s(fun(prod(cart(real,Q141483),cart(real,Q141483)),bool),i(s(fun(cart(real,Q141483),fun(prod(cart(real,Q141483),cart(real,Q141483)),bool)),between),s(cart(real,Q141483),D0))),s(prod(cart(real,Q141483),cart(real,Q141483)),i(s(fun(cart(real,Q141483),prod(cart(real,Q141483),cart(real,Q141483))),i(s(fun(cart(real,Q141483),fun(cart(real,Q141483),prod(cart(real,Q141483),cart(real,Q141483)))),c_),s(cart(real,Q141483),A5))),s(cart(real,Q141483),B0)))))) & p(s(bool,i(s(fun(prod(cart(real,Q141483),cart(real,Q141483)),bool),i(s(fun(cart(real,Q141483),fun(prod(cart(real,Q141483),cart(real,Q141483)),bool)),between),s(cart(real,Q141483),A5))),s(prod(cart(real,Q141483),cart(real,Q141483)),i(s(fun(cart(real,Q141483),prod(cart(real,Q141483),cart(real,Q141483))),i(s(fun(cart(real,Q141483),fun(cart(real,Q141483),prod(cart(real,Q141483),cart(real,Q141483)))),c_),s(cart(real,Q141483),B0))),s(cart(real,Q141483),C0)))))) -> p(s(bool,i(s(fun(prod(cart(real,Q141483),cart(real,Q141483)),bool),i(s(fun(cart(real,Q141483),fun(prod(cart(real,Q141483),cart(real,Q141483)),bool)),between),s(cart(real,Q141483),A5))),s(prod(cart(real,Q141483),cart(real,Q141483)),i(s(fun(cart(real,Q141483),prod(cart(real,Q141483),cart(real,Q141483))),i(s(fun(cart(real,Q141483),fun(cart(real,Q141483),prod(cart(real,Q141483),cart(real,Q141483)))),c_),s(cart(real,Q141483),C0))),s(cart(real,Q141483),D0)))))))) # label(aBETWEENu_TRANSu_2) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3353 (all P0 ((all S0 p(s(bool,i(s(fun(fun(cart(real,n10),bool),bool),P0),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),S0))))))) <-> (all S0 p(s(bool,i(s(fun(fun(cart(real,n10),bool),bool),P0),s(fun(cart(real,n10),bool),S0))))))) # label(aFORALLu_LIFTu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3354 (all Q121985 all S0 s(fun(cart(real,Q121985),bool),i(s(fun(fun(cart(real,Q121985),bool),fun(cart(real,Q121985),bool)),span),s(fun(cart(real,Q121985),bool),i(s(fun(fun(cart(real,Q121985),bool),fun(cart(real,Q121985),bool)),span),s(fun(cart(real,Q121985),bool),S0))))) = s(fun(cart(real,Q121985),bool),i(s(fun(fun(cart(real,Q121985),bool),fun(cart(real,Q121985),bool)),span),s(fun(cart(real,Q121985),bool),S0)))) # label(aSPANu_SPAN) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3355 (all M all N all A5 all B0 all X s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(real,fun(cart(cart(real,M),N),cart(cart(real,M),N))),r_r_),s(real,A5))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(real,fun(cart(cart(real,M),N),cart(cart(real,M),N))),r_r_),s(real,B0))),s(cart(cart(real,M),N),X))))) = s(cart(cart(real,M),N),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),N)),i(s(fun(real,fun(cart(cart(real,M),N),cart(cart(real,M),N))),r_r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,A5))),s(real,B0))))),s(cart(cart(real,M),N),X)))) # label(aMATRIXu_CMULu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3356 (all Q105798 all Q105801 all U_0 ((all C0 all N0 s(cart(real,Q105801),i(s(fun(Q105798,cart(real,Q105801)),i(s(fun(cart(real,Q105801),fun(Q105798,cart(real,Q105801))),U_0),s(cart(real,Q105801),C0))),s(Q105798,N0))) = s(cart(real,Q105801),C0)) -> (all C0 all S0 (p(s(bool,i(s(fun(fun(Q105798,bool),bool),finite),s(fun(Q105798,bool),S0)))) -> s(cart(real,Q105801),i(s(fun(fun(Q105798,cart(real,Q105801)),cart(real,Q105801)),i(s(fun(fun(Q105798,bool),fun(fun(Q105798,cart(real,Q105801)),cart(real,Q105801))),vsum),s(fun(Q105798,bool),S0))),s(fun(Q105798,cart(real,Q105801)),i(s(fun(cart(real,Q105801),fun(Q105798,cart(real,Q105801))),U_0),s(cart(real,Q105801),C0))))) = s(cart(real,Q105801),i(s(fun(cart(real,Q105801),cart(real,Q105801)),i(s(fun(real,fun(cart(real,Q105801),cart(real,Q105801))),r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(Q105798,bool),num),card),s(fun(Q105798,bool),S0))))))),s(cart(real,Q105801),C0))))))) # label(aVSUMu_CONST) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3357 (all N all M all F0 all X all L ((all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) -> s(cart(real,M),Y) = s(cart(real,M),X))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> s(bool,i(s(fun(list(cart(real,N)),bool),i(s(fun(cart(real,N),fun(list(cart(real,N)),bool)),mem),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(list(cart(real,N)),i(s(fun(list(cart(real,M)),list(cart(real,N))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(list(cart(real,M)),list(cart(real,N)))),map0),s(fun(cart(real,M),cart(real,N)),F0))),s(list(cart(real,M)),L))))) = s(bool,i(s(fun(list(cart(real,M)),bool),i(s(fun(cart(real,M),fun(list(cart(real,M)),bool)),mem),s(cart(real,M),X))),s(list(cart(real,M)),L))))) # label(aMEMu_LINEARu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3358 (all Q106054 all Q106053 all F0 all S0 all A5 (p(s(bool,i(s(fun(fun(Q106053,bool),bool),finite),s(fun(Q106053,bool),S0)))) & p(s(bool,i(s(fun(fun(Q106053,bool),bool),i(s(fun(Q106053,fun(fun(Q106053,bool),bool)),in),s(Q106053,A5))),s(fun(Q106053,bool),S0)))) -> s(cart(real,Q106054),i(s(fun(fun(Q106053,cart(real,Q106054)),cart(real,Q106054)),i(s(fun(fun(Q106053,bool),fun(fun(Q106053,cart(real,Q106054)),cart(real,Q106054))),vsum),s(fun(Q106053,bool),i(s(fun(Q106053,fun(Q106053,bool)),i(s(fun(fun(Q106053,bool),fun(Q106053,fun(Q106053,bool))),delete),s(fun(Q106053,bool),S0))),s(Q106053,A5))))),s(fun(Q106053,cart(real,Q106054)),F0))) = s(cart(real,Q106054),i(s(fun(cart(real,Q106054),cart(real,Q106054)),i(s(fun(cart(real,Q106054),fun(cart(real,Q106054),cart(real,Q106054))),vectoru_sub),s(cart(real,Q106054),i(s(fun(fun(Q106053,cart(real,Q106054)),cart(real,Q106054)),i(s(fun(fun(Q106053,bool),fun(fun(Q106053,cart(real,Q106054)),cart(real,Q106054))),vsum),s(fun(Q106053,bool),S0))),s(fun(Q106053,cart(real,Q106054)),F0))))),s(cart(real,Q106054),i(s(fun(Q106053,cart(real,Q106054)),F0),s(Q106053,A5))))))) # label(aVSUMu_DELETE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3359 (all Q142414 all A5 all B0 s(cart(real,Q142414),i(s(fun(prod(cart(real,Q142414),cart(real,Q142414)),cart(real,Q142414)),midpoint),s(prod(cart(real,Q142414),cart(real,Q142414)),i(s(fun(cart(real,Q142414),prod(cart(real,Q142414),cart(real,Q142414))),i(s(fun(cart(real,Q142414),fun(cart(real,Q142414),prod(cart(real,Q142414),cart(real,Q142414)))),c_),s(cart(real,Q142414),A5))),s(cart(real,Q142414),B0))))) = s(cart(real,Q142414),i(s(fun(prod(cart(real,Q142414),cart(real,Q142414)),cart(real,Q142414)),midpoint),s(prod(cart(real,Q142414),cart(real,Q142414)),i(s(fun(cart(real,Q142414),prod(cart(real,Q142414),cart(real,Q142414))),i(s(fun(cart(real,Q142414),fun(cart(real,Q142414),prod(cart(real,Q142414),cart(real,Q142414)))),c_),s(cart(real,Q142414),B0))),s(cart(real,Q142414),A5)))))) # label(aMIDPOINTu_SYM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3360 (all N all M all F0 all S0 ((all X all Y (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),S0)))) & s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) -> s(cart(real,M),X) = s(cart(real,M),Y))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),dependent),s(fun(cart(real,M),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),dependent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0)))))))) # label(aDEPENDENTu_LINEARu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3361 (all N0 s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(num,real),realu_ofu_num),s(num,N0))))) = s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,N0)))) # label(aLIFTu_NUM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3362 (all Q100563 all Y ((all X s(real,i(s(fun(cart(real,Q100563),real),i(s(fun(cart(real,Q100563),fun(cart(real,Q100563),real)),dot),s(cart(real,Q100563),X))),s(cart(real,Q100563),Y))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) <-> s(cart(real,Q100563),i(s(fun(num,cart(real,Q100563)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q100563),Y))) # label(aFORALLu_DOTu_EQu_0u_conjunct0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.01 3363 (all N all U_0 ((all T0 all S0 all GENR_PVARR_367 ((exists Y exists V ((p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),T0)))) & (all X (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),S0)))) -> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),X))),s(cart(real,N),Y)))))) <-> p(s(bool,V))) & p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_367))),s(bool,V))),s(cart(real,N),Y)))))) <-> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),U_0),s(fun(cart(real,N),bool),T0))),s(fun(cart(real,N),bool),S0))),s(cart(real,N),GENR_PVARR_367)))))) -> (all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),T0)))) -> s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),U_0),s(fun(cart(real,N),bool),T0))),s(fun(cart(real,N),bool),S0))))))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))) = s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0))))))) # label(aDIMu_SUBSPACEu_ORTHOGONALu_TOu_VECTORS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3364 (all X s(real,X) = s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) # label(aLIFTu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3365 (all X all S0 s(bool,i(s(fun(fun(cart(real,n10),bool),bool),i(s(fun(cart(real,n10),fun(fun(cart(real,n10),bool),bool)),in),s(cart(real,n10),X))),s(fun(cart(real,n10),bool),i(s(fun(fun(real,bool),fun(cart(real,n10),bool)),i(s(fun(fun(real,cart(real,n10)),fun(fun(real,bool),fun(cart(real,n10),bool))),image),s(fun(real,cart(real,n10)),lift))),s(fun(real,bool),S0))))) = s(bool,i(s(fun(fun(real,bool),bool),i(s(fun(real,fun(fun(real,bool),bool)),in),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))),s(fun(real,bool),S0)))) # label(aINu_IMAGEu_LIFTu_DROPu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3366 (all N all M all F0 all X all Y (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & (all X s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))) = s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X)))) -> s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))))) = s(real,i(s(fun(cart(real,M),real),i(s(fun(cart(real,M),fun(cart(real,M),real)),dot),s(cart(real,M),X))),s(cart(real,M),Y))))) # label(aPRESERVESu_NORMu_PRESERVESu_DOT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3367 (all A all N all U_0 ((all F0 all X s(real,i(s(fun(A,real),i(s(fun(fun(A,cart(real,N)),fun(A,real)),U_0),s(fun(A,cart(real,N)),F0))),s(A,X))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X)))))) -> (all F0 all P0 all E0 ((all Q0 (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(fun(A,bool),fun(fun(A,bool),bool)),subset),s(fun(A,bool),Q0))),s(fun(A,bool),P0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),Q0))),s(fun(A,cart(real,N)),F0))))))),s(real,E0)))))) & p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),P0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(fun(A,real),real),i(s(fun(fun(A,bool),fun(fun(A,real),real)),sum),s(fun(A,bool),P0))),s(fun(A,real),i(s(fun(fun(A,cart(real,N)),fun(A,real)),U_0),s(fun(A,cart(real,N)),F0))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(real,E0)))))))))))) # label(aVSUMu_NORMu_ALLSUBSETSu_BOUND) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3368 (all M all N all A5 ((all X (s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) -> s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),X))) <-> (exists B0 s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),B0))),s(cart(cart(real,N),M),A5)))))) # label(aMATRIXu_LEFTu_INVERTIBLEu_KER) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3369 (all Q121236 all Q121234 all Y s(real,i(s(fun(cart(real,Q121234),real),vectoru_norm),s(cart(real,Q121234),Y))) = s(real,i(s(fun(cart(real,finite_sum(Q121236,Q121234)),real),vectoru_norm),s(cart(real,finite_sum(Q121236,Q121234)),i(s(fun(cart(real,Q121234),cart(real,finite_sum(Q121236,Q121234))),i(s(fun(cart(real,Q121236),fun(cart(real,Q121234),cart(real,finite_sum(Q121236,Q121234)))),pastecart),s(cart(real,Q121236),i(s(fun(num,cart(real,Q121236)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(real,Q121234),Y)))))) # label(aNORMu_PASTECARTu_0u_conjunct1) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3370 (all N all S0 all T0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0))))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0)))) -> s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),T0))) = s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))) # label(aDIMu_EQu_SPAN) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3371 (all N all M all A5 all B0 all C0 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,B0))),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,C0))),s(cart(cart(real,N),M),A5))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(real,fun(cart(cart(real,N),M),cart(cart(real,N),M))),r_r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,B0))),s(real,C0))))),s(cart(cart(real,N),M),A5)))) # label(aMATRIXu_CMULu_SUBu_RDISTRIB) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3372 (all Q125680 all X (s(cart(real,Q125680),X) != s(cart(real,Q125680),i(s(fun(num,cart(real,Q125680)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> p(s(bool,i(s(fun(fun(cart(real,Q125680),bool),bool),independent),s(fun(cart(real,Q125680),bool),i(s(fun(fun(cart(real,Q125680),bool),fun(cart(real,Q125680),bool)),i(s(fun(cart(real,Q125680),fun(fun(cart(real,Q125680),bool),fun(cart(real,Q125680),bool))),insert),s(cart(real,Q125680),X))),s(fun(cart(real,Q125680),bool),empty)))))))) # label(aINDEPENDENTu_SING) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3373 (all N all U_1 ((all S0 all GENR_PVARR_338 (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),U_1),s(fun(cart(real,N),bool),S0))),s(cart(real,N),GENR_PVARR_338)))) <-> (exists Z0 exists V ((p(s(bool,V)) <-> (all X (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) -> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),Z0))),s(cart(real,N),X))))))) & p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_338))),s(bool,V))),s(cart(real,N),Z0)))))))) -> (all U_0 ((all S0 all X all F0 (p(s(bool,i(s(fun(fun(prod(cart(real,N),cart(real,N)),bool),bool),i(s(fun(cart(real,N),fun(fun(prod(cart(real,N),cart(real,N)),bool),bool)),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),fun(fun(prod(cart(real,N),cart(real,N)),bool),bool))),U_0),s(fun(cart(real,N),bool),S0))),s(cart(real,N),X))),s(fun(prod(cart(real,N),cart(real,N)),bool),F0)))) <-> (all Y all Z0 exists V (p(s(bool,i(s(fun(bool,bool),i(s(fun(bool,fun(bool,bool)),geq),s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),F0),s(prod(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),prod(cart(real,N),cart(real,N))),i(s(fun(cart(real,N),fun(cart(real,N),prod(cart(real,N),cart(real,N)))),c_),s(cart(real,N),Y))),s(cart(real,N),Z0))))))),s(bool,V)))) & (p(s(bool,V)) <-> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Z0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),U_1),s(fun(cart(real,N),bool),S0)))))))) & s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),Y))),s(cart(real,N),Z0))) = s(cart(real,N),X)))))) -> (all S0 all X ((all X0 all Y (p(s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(fun(fun(prod(cart(real,N),cart(real,N)),bool),bool),fun(prod(cart(real,N),cart(real,N)),bool)),gabs),s(fun(fun(prod(cart(real,N),cart(real,N)),bool),bool),i(s(fun(cart(real,N),fun(fun(prod(cart(real,N),cart(real,N)),bool),bool)),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),fun(fun(prod(cart(real,N),cart(real,N)),bool),bool))),U_0),s(fun(cart(real,N),bool),S0))),s(cart(real,N),X))))),s(prod(cart(real,N),cart(real,N)),X0)))) & p(s(bool,i(s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(fun(fun(prod(cart(real,N),cart(real,N)),bool),bool),fun(prod(cart(real,N),cart(real,N)),bool)),gabs),s(fun(fun(prod(cart(real,N),cart(real,N)),bool),bool),i(s(fun(cart(real,N),fun(fun(prod(cart(real,N),cart(real,N)),bool),bool)),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),fun(fun(prod(cart(real,N),cart(real,N)),bool),bool))),U_0),s(fun(cart(real,N),bool),S0))),s(cart(real,N),X))))),s(prod(cart(real,N),cart(real,N)),Y)))) -> s(prod(cart(real,N),cart(real,N)),Y) = s(prod(cart(real,N),cart(real,N)),X0))) & p(s(bool,i(s(fun(fun(prod(cart(real,N),cart(real,N)),bool),bool),q_),s(fun(prod(cart(real,N),cart(real,N)),bool),i(s(fun(fun(fun(prod(cart(real,N),cart(real,N)),bool),bool),fun(prod(cart(real,N),cart(real,N)),bool)),gabs),s(fun(fun(prod(cart(real,N),cart(real,N)),bool),bool),i(s(fun(cart(real,N),fun(fun(prod(cart(real,N),cart(real,N)),bool),bool)),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),fun(fun(prod(cart(real,N),cart(real,N)),bool),bool))),U_0),s(fun(cart(real,N),bool),S0))),s(cart(real,N),X)))))))))))))) # label(aORTHOGONALu_SUBSPACEu_DECOMP) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3374 (all Q122457 all X all Y all S0 (p(s(bool,i(s(fun(fun(cart(real,Q122457),bool),bool),i(s(fun(cart(real,Q122457),fun(fun(cart(real,Q122457),bool),bool)),in),s(cart(real,Q122457),X))),s(fun(cart(real,Q122457),bool),i(s(fun(fun(cart(real,Q122457),bool),fun(cart(real,Q122457),bool)),span),s(fun(cart(real,Q122457),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q122457),bool),bool),i(s(fun(cart(real,Q122457),fun(fun(cart(real,Q122457),bool),bool)),in),s(cart(real,Q122457),Y))),s(fun(cart(real,Q122457),bool),i(s(fun(fun(cart(real,Q122457),bool),fun(cart(real,Q122457),bool)),span),s(fun(cart(real,Q122457),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,Q122457),bool),bool),i(s(fun(cart(real,Q122457),fun(fun(cart(real,Q122457),bool),bool)),in),s(cart(real,Q122457),i(s(fun(cart(real,Q122457),cart(real,Q122457)),i(s(fun(cart(real,Q122457),fun(cart(real,Q122457),cart(real,Q122457))),vectoru_add),s(cart(real,Q122457),X))),s(cart(real,Q122457),Y))))),s(fun(cart(real,Q122457),bool),i(s(fun(fun(cart(real,Q122457),bool),fun(cart(real,Q122457),bool)),span),s(fun(cart(real,Q122457),bool),S0)))))))) # label(aSPANu_ADD) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3375 (all N all P all M all A5 s(cart(cart(real,P),M),i(s(fun(num,cart(cart(real,P),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),i(s(fun(num,cart(cart(real,N),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(cart(cart(real,P),N),A5)))) # label(aMATRIXu_MULu_LZERO) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3376 (all M all N all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> ((all X all Y (s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,N),Y))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,N),cart(real,M))),adjoint),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,N),X))) -> s(cart(real,N),Y) = s(cart(real,N),X))) <-> (all Y exists X s(cart(real,N),Y) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))) # label(aADJOINTu_INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3377 (all N all U_0 ((all A5 all GENR_PVARR_340 (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),U_0),s(cart(real,N),A5))),s(cart(real,N),GENR_PVARR_340)))) <-> (exists X exists V (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_340))),s(bool,V))),s(cart(real,N),X)))) & (s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),A5))),s(cart(real,N),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> p(s(bool,V))))))) -> (all A5 p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),U_0),s(cart(real,N),A5))))))))))) # label(aSUBSPACEu_HYPERPLANE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3378 (all N all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0)))) -> (exists B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),B0)))) & s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0))) = s(fun(cart(real,N),bool),S0))))) # label(aORTHOGONALu_SPANNINGSETu_SUBSPACE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3379 (all N all F0 all G0 (s(fun(cart(real,N),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N))),i(s(fun(fun(cart(real,N),cart(real,N)),fun(fun(cart(real,N),cart(real,N)),fun(cart(real,N),cart(real,N)))),o),s(fun(cart(real,N),cart(real,N)),F0))),s(fun(cart(real,N),cart(real,N)),G0))) = s(fun(cart(real,N),cart(real,N)),i1) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),cart(real,N)),bool),linear),s(fun(cart(real,N),cart(real,N)),G0)))))) # label(aRIGHTu_INVERSEu_LINEAR) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3380 (all N all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,a0)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),X))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,a0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,a0)))))) # label(aNORMu_LTu_SQUARE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3381 (all M all N all X s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),vectoru_neg),s(cart(real,finite_sum(M,N)),X))))) = s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),vectoru_neg),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),X)))))) # label(aFSTCARTu_NEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3382 (all Q99503 all Q99508 s(Q99503,i(s(fun(Q99503,Q99503),i(s(fun(Q99503,fun(Q99503,Q99503)),i(s(fun(bool,fun(Q99503,fun(Q99503,Q99503))),cond),s(bool,b0))),s(Q99503,i(s(fun(num,Q99503),i(s(fun(cart(Q99503,Q99508),fun(num,Q99503)),d_),s(cart(Q99503,Q99508),x))),s(num,i0))))),s(Q99503,i(s(fun(num,Q99503),i(s(fun(cart(Q99503,Q99508),fun(num,Q99503)),d_),s(cart(Q99503,Q99508),y))),s(num,i0))))) = s(Q99503,i(s(fun(num,Q99503),i(s(fun(cart(Q99503,Q99508),fun(num,Q99503)),d_),s(cart(Q99503,Q99508),i(s(fun(cart(Q99503,Q99508),cart(Q99503,Q99508)),i(s(fun(cart(Q99503,Q99508),fun(cart(Q99503,Q99508),cart(Q99503,Q99508))),i(s(fun(bool,fun(cart(Q99503,Q99508),fun(cart(Q99503,Q99508),cart(Q99503,Q99508)))),cond),s(bool,b0))),s(cart(Q99503,Q99508),x))),s(cart(Q99503,Q99508),y))))),s(num,i0)))) # label(aCONDu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3383 (all Q126603 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q126603),bool),bool),finite),s(fun(cart(real,Q126603),bool),S0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,Q126603),bool),num),dim),s(fun(cart(real,Q126603),bool),S0))))),s(num,i(s(fun(fun(cart(real,Q126603),bool),num),card),s(fun(cart(real,Q126603),bool),S0)))))))) # label(aDIMu_LEu_CARD) # label(axiom) # label(non_clause). [assumption]. 16.04/16.02 3384 (all Q105011 all X1 all X2 all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105011),cart(real,Q105011)),real),distance),s(prod(cart(real,Q105011),cart(real,Q105011)),i(s(fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011))),i(s(fun(cart(real,Q105011),fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011)))),c_),s(cart(real,Q105011),X2))),s(cart(real,Q105011),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105011),cart(real,Q105011)),real),distance),s(prod(cart(real,Q105011),cart(real,Q105011)),i(s(fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011))),i(s(fun(cart(real,Q105011),fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011)))),c_),s(cart(real,Q105011),X1))),s(cart(real,Q105011),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,e0))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(prod(cart(real,Q105011),cart(real,Q105011)),real),distance),s(prod(cart(real,Q105011),cart(real,Q105011)),i(s(fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011))),i(s(fun(cart(real,Q105011),fun(cart(real,Q105011),prod(cart(real,Q105011),cart(real,Q105011)))),c_),s(cart(real,Q105011),X1))),s(cart(real,Q105011),X2))))))),s(real,e0)))))) # label(aDISTu_TRIANGLEu_HALFu_L) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3385 (all A all Q107754 all U_0 ((all F0 all T0 s(cart(real,Q107754),i(s(fun(fun(A,cart(real,Q107754)),cart(real,Q107754)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107754)),cart(real,Q107754))),vsum),s(fun(A,bool),T0))),s(fun(A,cart(real,Q107754)),F0))) = s(cart(real,Q107754),i(s(fun(fun(A,bool),cart(real,Q107754)),i(s(fun(fun(A,cart(real,Q107754)),fun(fun(A,bool),cart(real,Q107754))),U_0),s(fun(A,cart(real,Q107754)),F0))),s(fun(A,bool),T0)))) -> (all F0 all S0 ((all T0 (p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T0))),s(fun(fun(A,bool),bool),S0)))) -> p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),T0)))))) & (all T1 all T2 all X (s(fun(A,bool),T1) != s(fun(A,bool),T2) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T2)))) & p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),T1)))) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T2))),s(fun(fun(A,bool),bool),S0)))) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),i(s(fun(fun(A,bool),fun(fun(fun(A,bool),bool),bool)),in),s(fun(A,bool),T1))),s(fun(fun(A,bool),bool),S0)))) -> s(cart(real,Q107754),i(s(fun(num,cart(real,Q107754)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q107754),i(s(fun(A,cart(real,Q107754)),F0),s(A,X))))) & p(s(bool,i(s(fun(fun(fun(A,bool),bool),bool),finite),s(fun(fun(A,bool),bool),S0)))) -> s(cart(real,Q107754),i(s(fun(fun(fun(A,bool),cart(real,Q107754)),cart(real,Q107754)),i(s(fun(fun(fun(A,bool),bool),fun(fun(fun(A,bool),cart(real,Q107754)),cart(real,Q107754))),vsum),s(fun(fun(A,bool),bool),S0))),s(fun(fun(A,bool),cart(real,Q107754)),i(s(fun(fun(A,cart(real,Q107754)),fun(fun(A,bool),cart(real,Q107754))),U_0),s(fun(A,cart(real,Q107754)),F0))))) = s(cart(real,Q107754),i(s(fun(fun(A,cart(real,Q107754)),cart(real,Q107754)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,Q107754)),cart(real,Q107754))),vsum),s(fun(A,bool),i(s(fun(fun(fun(A,bool),bool),fun(A,bool)),unions),s(fun(fun(A,bool),bool),S0))))),s(fun(A,cart(real,Q107754)),F0))))))) # label(aVSUMu_UNIONSu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3386 (all Q102346 all X (s(real,i(s(fun(cart(real,Q102346),real),vectoru_norm),s(cart(real,Q102346),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(cart(real,Q102346),X) = s(cart(real,Q102346),i(s(fun(num,cart(real,Q102346)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aNORMu_EQu_0u_IMP) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3387 (all Q112656 all Q112637 all Q112655 all H0 all X all Y all Z0 (p(s(bool,i(s(fun(fun(cart(real,Q112637),fun(cart(real,Q112655),cart(real,Q112656))),bool),bilinear),s(fun(cart(real,Q112637),fun(cart(real,Q112655),cart(real,Q112656))),H0)))) -> s(cart(real,Q112656),i(s(fun(cart(real,Q112655),cart(real,Q112656)),i(s(fun(cart(real,Q112637),fun(cart(real,Q112655),cart(real,Q112656))),H0),s(cart(real,Q112637),X))),s(cart(real,Q112655),i(s(fun(cart(real,Q112655),cart(real,Q112655)),i(s(fun(cart(real,Q112655),fun(cart(real,Q112655),cart(real,Q112655))),vectoru_sub),s(cart(real,Q112655),Y))),s(cart(real,Q112655),Z0))))) = s(cart(real,Q112656),i(s(fun(cart(real,Q112656),cart(real,Q112656)),i(s(fun(cart(real,Q112656),fun(cart(real,Q112656),cart(real,Q112656))),vectoru_sub),s(cart(real,Q112656),i(s(fun(cart(real,Q112655),cart(real,Q112656)),i(s(fun(cart(real,Q112637),fun(cart(real,Q112655),cart(real,Q112656))),H0),s(cart(real,Q112637),X))),s(cart(real,Q112655),Y))))),s(cart(real,Q112656),i(s(fun(cart(real,Q112655),cart(real,Q112656)),i(s(fun(cart(real,Q112637),fun(cart(real,Q112655),cart(real,Q112656))),H0),s(cart(real,Q112637),X))),s(cart(real,Q112655),Z0))))))) # label(aBILINEARu_RSUB) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3388 (all N all M all U_0 ((all A5 all X s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X)))) -> (all A5 all X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(fun(cart(real,N),cart(real,M)),fun(cart(real,M),cart(real,N))),adjoint),s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),U_0),s(cart(cart(real,N),M),A5))))),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),transp),s(cart(cart(real,N),M),A5))))),s(cart(real,M),X)))))) # label(aADJOINTu_MATRIX) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3389 (all N all M all A5 all X all Y (s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5)))))))) -> p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(cart(real,M),fun(cart(real,M),bool)),orthogonal),s(cart(real,M),X))),s(cart(real,M),Y)))))) # label(aORTHOGONALu_NULLSPACEu_ROWSPACE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3390 (all Q118203 all Q118204 all F0 (p(s(bool,i(s(fun(fun(cart(real,Q118203),cart(real,Q118204)),bool),linear),s(fun(cart(real,Q118203),cart(real,Q118204)),F0)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(fun(cart(real,Q118203),cart(real,Q118204)),real),onorm),s(fun(cart(real,Q118203),cart(real,Q118204)),F0)))))))) # label(aONORMu_POSu_LE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3391 (all Q125545 all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,Q125545),bool),bool),i(s(fun(fun(cart(real,Q125545),bool),fun(fun(cart(real,Q125545),bool),bool)),subset),s(fun(cart(real,Q125545),bool),S0))),s(fun(cart(real,Q125545),bool),i(s(fun(fun(cart(real,Q125545),bool),fun(cart(real,Q125545),bool)),span),s(fun(cart(real,Q125545),bool),T0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q125545),bool),bool),independent),s(fun(cart(real,Q125545),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q125545),bool),bool),finite),s(fun(cart(real,Q125545),bool),T0)))) -> p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(fun(cart(real,Q125545),bool),num),card),s(fun(cart(real,Q125545),bool),S0))))),s(num,i(s(fun(fun(cart(real,Q125545),bool),num),card),s(fun(cart(real,Q125545),bool),T0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q125545),bool),bool),finite),s(fun(cart(real,Q125545),bool),S0)))))) # label(aINDEPENDENTu_SPANu_BOUND) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3392 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,Y)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,X))),s(real,i(s(fun(real,real),sqrt),s(real,Y)))))))) # label(aREALu_LTu_RSQRT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3393 (all N all U_0 ((all K0 all GENR_PVARR_341 (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(num,fun(cart(real,N),bool)),U_0),s(num,K0))),s(cart(real,N),GENR_PVARR_341)))) <-> (exists X exists V (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_341))),s(bool,V))),s(cart(real,N),X)))) & (s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,K0))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> p(s(bool,V))))))) -> (all K0 p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(num,fun(cart(real,N),bool)),U_0),s(num,K0))))))))))) # label(aSUBSPACEu_SPECIALu_HYPERPLANE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3394 (all Q107387 all F0 all M0 all N0 all P0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) -> s(cart(real,Q107387),i(s(fun(fun(num,cart(real,Q107387)),cart(real,Q107387)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107387)),cart(real,Q107387))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))),s(fun(num,cart(real,Q107387)),F0))) = s(cart(real,Q107387),i(s(fun(cart(real,Q107387),cart(real,Q107387)),i(s(fun(cart(real,Q107387),fun(cart(real,Q107387),cart(real,Q107387))),vectoru_add),s(cart(real,Q107387),i(s(fun(fun(num,cart(real,Q107387)),cart(real,Q107387)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107387)),cart(real,Q107387))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107387)),F0))))),s(cart(real,Q107387),i(s(fun(fun(num,cart(real,Q107387)),cart(real,Q107387)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107387)),cart(real,Q107387))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,P0))))))),s(fun(num,cart(real,Q107387)),F0))))))) # label(aVSUMu_ADDu_SPLIT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3395 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X))) = s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_lt),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,i(s(fun(real,real),sqrt),s(real,X))))))) # label(aSQRTu_LTu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3396 (all Q108721 all U_0 ((all C0 all N0 s(cart(real,Q108721),C0) = s(cart(real,Q108721),i(s(fun(num,cart(real,Q108721)),i(s(fun(cart(real,Q108721),fun(num,cart(real,Q108721))),U_0),s(cart(real,Q108721),C0))),s(num,N0)))) -> (all C0 all M0 all N0 s(cart(real,Q108721),i(s(fun(cart(real,Q108721),cart(real,Q108721)),i(s(fun(real,fun(cart(real,Q108721),cart(real,Q108721))),r_),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),m_),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,M0))))))),s(cart(real,Q108721),C0))) = s(cart(real,Q108721),i(s(fun(fun(num,cart(real,Q108721)),cart(real,Q108721)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108721)),cart(real,Q108721))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q108721)),i(s(fun(cart(real,Q108721),fun(num,cart(real,Q108721))),U_0),s(cart(real,Q108721),C0)))))))) # label(aVSUMu_CONSTu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3397 (all Q120589 all Q120590 all X1 all Y1 all C0 s(cart(real,finite_sum(Q120589,Q120590)),i(s(fun(cart(real,finite_sum(Q120589,Q120590)),cart(real,finite_sum(Q120589,Q120590))),i(s(fun(real,fun(cart(real,finite_sum(Q120589,Q120590)),cart(real,finite_sum(Q120589,Q120590)))),r_),s(real,C0))),s(cart(real,finite_sum(Q120589,Q120590)),i(s(fun(cart(real,Q120590),cart(real,finite_sum(Q120589,Q120590))),i(s(fun(cart(real,Q120589),fun(cart(real,Q120590),cart(real,finite_sum(Q120589,Q120590)))),pastecart),s(cart(real,Q120589),X1))),s(cart(real,Q120590),Y1))))) = s(cart(real,finite_sum(Q120589,Q120590)),i(s(fun(cart(real,Q120590),cart(real,finite_sum(Q120589,Q120590))),i(s(fun(cart(real,Q120589),fun(cart(real,Q120590),cart(real,finite_sum(Q120589,Q120590)))),pastecart),s(cart(real,Q120589),i(s(fun(cart(real,Q120589),cart(real,Q120589)),i(s(fun(real,fun(cart(real,Q120589),cart(real,Q120589))),r_),s(real,C0))),s(cart(real,Q120589),X1))))),s(cart(real,Q120590),i(s(fun(cart(real,Q120590),cart(real,Q120590)),i(s(fun(real,fun(cart(real,Q120590),cart(real,Q120590))),r_),s(real,C0))),s(cart(real,Q120590),Y1)))))) # label(aPASTECARTu_CMUL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3398 (all N all I0 all J0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,I0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,I0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,J0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,J0)))) -> (p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,I0))))),s(cart(real,N),i(s(fun(num,cart(real,N)),basis),s(num,J0)))))) <-> s(num,J0) != s(num,I0)))) # label(aORTHOGONALu_BASISu_BASIS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3399 (all Q107910 all U_0 ((all K0 s(cart(real,Q107910),i(s(fun(cart(real,Q107910),cart(real,Q107910)),i(s(fun(cart(real,Q107910),fun(cart(real,Q107910),cart(real,Q107910))),vectoru_sub),s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,K0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),f),s(num,K0))))) = s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),U_0),s(num,K0)))) -> (all M0 all N0 s(cart(real,Q107910),i(s(fun(fun(num,cart(real,Q107910)),cart(real,Q107910)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107910)),cart(real,Q107910))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107910)),U_0))) = s(cart(real,Q107910),i(s(fun(cart(real,Q107910),cart(real,Q107910)),i(s(fun(cart(real,Q107910),fun(cart(real,Q107910),cart(real,Q107910))),i(s(fun(bool,fun(cart(real,Q107910),fun(cart(real,Q107910),cart(real,Q107910)))),cond),s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,M0))),s(num,N0))))),s(cart(real,Q107910),i(s(fun(cart(real,Q107910),cart(real,Q107910)),i(s(fun(cart(real,Q107910),fun(cart(real,Q107910),cart(real,Q107910))),vectoru_sub),s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),f),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,N0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),f),s(num,M0))))))),s(cart(real,Q107910),i(s(fun(num,cart(real,Q107910)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))))) # label(aVSUMu_DIFFSu_ALT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3400 (all Q122205 all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,Q122205),bool),bool),independent),s(fun(cart(real,Q122205),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,Q122205),bool),bool),i(s(fun(fun(cart(real,Q122205),bool),fun(fun(cart(real,Q122205),bool),bool)),subset),s(fun(cart(real,Q122205),bool),S0))),s(fun(cart(real,Q122205),bool),T0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q122205),bool),bool),independent),s(fun(cart(real,Q122205),bool),S0)))))) # label(aINDEPENDENTu_MONO) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3401 (all N all M all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),subspace),s(fun(cart(real,M),bool),S0)))) -> ((all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),Y))),s(fun(cart(real,M),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),S0)))) -> s(cart(real,M),X) = s(cart(real,M),Y))) <-> (all X (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),S0)))) & s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,M),X)))))) # label(aLINEARu_INJECTIVEu_0u_SUBSPACE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3402 (all M all N all A5 all B0 ((all X s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),B0))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),A5))),s(cart(real,N),X)))) <-> s(cart(cart(real,N),M),A5) = s(cart(cart(real,N),M),B0))) # label(aMATRIXu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3403 (all N all X all Y (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),X))),s(cart(real,N),Y))))) <-> s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(cart(real,N),Y))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))),s(cart(real,N),X))))) # label(aNORMu_TRIANGLEu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3404 (all Q108775 all F0 all M0 all N0 s(cart(real,Q108775),i(s(fun(fun(num,cart(real,Q108775)),cart(real,Q108775)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108775)),cart(real,Q108775))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,N0))),s(num,M0))))),s(fun(num,cart(real,Q108775)),i(s(fun(fun(num,num),fun(num,cart(real,Q108775))),i(s(fun(fun(num,cart(real,Q108775)),fun(fun(num,num),fun(num,cart(real,Q108775)))),o),s(fun(num,cart(real,Q108775)),F0))),s(fun(num,num),suc))))) = s(cart(real,Q108775),i(s(fun(fun(num,cart(real,Q108775)),cart(real,Q108775)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q108775)),cart(real,Q108775))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),suc),s(num,N0))))),s(num,i(s(fun(num,num),suc),s(num,M0))))))),s(fun(num,cart(real,Q108775)),F0)))) # label(aVSUMu_SUC) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3405 (all N all M all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> ((exists B0 s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),B0))),s(cart(cart(real,M),N),i(s(fun(fun(cart(real,M),cart(real,N)),cart(cart(real,M),N)),matrix),s(fun(cart(real,M),cart(real,N)),F0))))) = s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))) <-> (exists G0 (s(fun(cart(real,M),cart(real,M)),i1) = s(fun(cart(real,M),cart(real,M)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M))),i(s(fun(fun(cart(real,N),cart(real,M)),fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),cart(real,M)))),o),s(fun(cart(real,N),cart(real,M)),G0))),s(fun(cart(real,M),cart(real,N)),F0))) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0))))))))) # label(aMATRIXu_LEFTu_INVERTIBLE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3406 (all N all U_1 ((all V all I0 all J0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),V))),s(num,I0))) = s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(real,N),fun(num,fun(num,real))),U_1),s(cart(real,N),V))),s(num,I0))),s(num,J0)))) -> (all U_0 ((all V all I0 s(cart(real,n10),i(s(fun(fun(num,real),cart(real,n10)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(real,N),fun(num,fun(num,real))),U_1),s(cart(real,N),V))),s(num,I0))))) = s(cart(real,n10),i(s(fun(num,cart(real,n10)),i(s(fun(cart(real,N),fun(num,cart(real,n10))),U_0),s(cart(real,N),V))),s(num,I0)))) -> (all V s(cart(cart(real,n10),N),i(s(fun(cart(real,N),cart(cart(real,n10),N)),columnvector),s(cart(real,N),V))) = s(cart(cart(real,n10),N),i(s(fun(fun(num,cart(real,n10)),cart(cart(real,n10),N)),lambda),s(fun(num,cart(real,n10)),i(s(fun(cart(real,N),fun(num,cart(real,n10))),U_0),s(cart(real,N),V)))))))))) # label(acolumnvector) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3407 (all N all M all A5 all X (s(cart(real,M),X) = s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),bool)),rows),s(cart(cart(real,M),N),A5)))))))) & s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))) # label(aNULLSPACEu_INTERu_ROWSPACE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3408 (all Q103338 all X (s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,Q103338),real),i(s(fun(cart(real,Q103338),fun(cart(real,Q103338),real)),dot),s(cart(real,Q103338),X))),s(cart(real,Q103338),X))) <-> s(real,i(s(fun(cart(real,Q103338),real),vectoru_norm),s(cart(real,Q103338),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) # label(aNORMu_EQu_1) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3409 (all Q126364 all V exists B0 (p(s(bool,i(s(fun(fun(cart(real,Q126364),bool),bool),i(s(fun(fun(cart(real,Q126364),bool),fun(fun(cart(real,Q126364),bool),bool)),subset),s(fun(cart(real,Q126364),bool),B0))),s(fun(cart(real,Q126364),bool),V)))) & p(s(bool,i(s(fun(fun(cart(real,Q126364),bool),bool),independent),s(fun(cart(real,Q126364),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,Q126364),bool),bool),i(s(fun(fun(cart(real,Q126364),bool),fun(fun(cart(real,Q126364),bool),bool)),subset),s(fun(cart(real,Q126364),bool),V))),s(fun(cart(real,Q126364),bool),i(s(fun(fun(cart(real,Q126364),bool),fun(cart(real,Q126364),bool)),span),s(fun(cart(real,Q126364),bool),B0)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126364),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126364),bool),B0))),s(num,i(s(fun(fun(cart(real,Q126364),bool),num),dim),s(fun(cart(real,Q126364),bool),V)))))))) # label(aBASISu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3410 (all N all S0 (s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))) != s(fun(cart(real,N),bool),univ) -> (exists A5 ((all X (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) -> s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),A5))),s(cart(real,N),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) & s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(real,N),A5))))) # label(aSPANu_NOTu_UNIVu_ORTHOGONAL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3411 (all A all N all F0 all S0 all Y (p(s(bool,i(s(fun(fun(A,bool),bool),finite),s(fun(A,bool),S0)))) & (all X (p(s(bool,i(s(fun(fun(A,bool),bool),i(s(fun(A,fun(fun(A,bool),bool)),in),s(A,X))),s(fun(A,bool),S0)))) -> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),i(s(fun(A,cart(real,N)),F0),s(A,X))))),s(cart(real,N),Y)))))) -> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),i(s(fun(fun(A,cart(real,N)),cart(real,N)),i(s(fun(fun(A,bool),fun(fun(A,cart(real,N)),cart(real,N))),vsum),s(fun(A,bool),S0))),s(fun(A,cart(real,N)),F0))))),s(cart(real,N),Y)))))) # label(aORTHOGONALu_LVSUM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3412 (all M all N all A5 p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))))),s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),min),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))))) # label(aRANKu_BOUND) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3413 (all Q111807 all Q111809 all F0 (p(s(bool,i(s(fun(fun(cart(real,Q111807),cart(real,Q111809)),bool),linear),s(fun(cart(real,Q111807),cart(real,Q111809)),F0)))) -> s(cart(real,Q111809),i(s(fun(cart(real,Q111807),cart(real,Q111809)),F0),s(cart(real,Q111807),i(s(fun(num,cart(real,Q111807)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(real,Q111809),i(s(fun(num,cart(real,Q111809)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) # label(aLINEARu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3414 (all Q120760 all Q120763 all Q120761 all U_0 ((all X all Y all I0 s(cart(real,finite_sum(Q120760,Q120761)),i(s(fun(Q120763,cart(real,finite_sum(Q120760,Q120761))),i(s(fun(fun(Q120763,cart(real,Q120761)),fun(Q120763,cart(real,finite_sum(Q120760,Q120761)))),i(s(fun(fun(Q120763,cart(real,Q120760)),fun(fun(Q120763,cart(real,Q120761)),fun(Q120763,cart(real,finite_sum(Q120760,Q120761))))),U_0),s(fun(Q120763,cart(real,Q120760)),X))),s(fun(Q120763,cart(real,Q120761)),Y))),s(Q120763,I0))) = s(cart(real,finite_sum(Q120760,Q120761)),i(s(fun(cart(real,Q120761),cart(real,finite_sum(Q120760,Q120761))),i(s(fun(cart(real,Q120760),fun(cart(real,Q120761),cart(real,finite_sum(Q120760,Q120761)))),pastecart),s(cart(real,Q120760),i(s(fun(Q120763,cart(real,Q120760)),X),s(Q120763,I0))))),s(cart(real,Q120761),i(s(fun(Q120763,cart(real,Q120761)),Y),s(Q120763,I0)))))) -> (all K0 all X all Y (p(s(bool,i(s(fun(fun(Q120763,bool),bool),finite),s(fun(Q120763,bool),K0)))) -> s(cart(real,finite_sum(Q120760,Q120761)),i(s(fun(cart(real,Q120761),cart(real,finite_sum(Q120760,Q120761))),i(s(fun(cart(real,Q120760),fun(cart(real,Q120761),cart(real,finite_sum(Q120760,Q120761)))),pastecart),s(cart(real,Q120760),i(s(fun(fun(Q120763,cart(real,Q120760)),cart(real,Q120760)),i(s(fun(fun(Q120763,bool),fun(fun(Q120763,cart(real,Q120760)),cart(real,Q120760))),vsum),s(fun(Q120763,bool),K0))),s(fun(Q120763,cart(real,Q120760)),X))))),s(cart(real,Q120761),i(s(fun(fun(Q120763,cart(real,Q120761)),cart(real,Q120761)),i(s(fun(fun(Q120763,bool),fun(fun(Q120763,cart(real,Q120761)),cart(real,Q120761))),vsum),s(fun(Q120763,bool),K0))),s(fun(Q120763,cart(real,Q120761)),Y))))) = s(cart(real,finite_sum(Q120760,Q120761)),i(s(fun(fun(Q120763,cart(real,finite_sum(Q120760,Q120761))),cart(real,finite_sum(Q120760,Q120761))),i(s(fun(fun(Q120763,bool),fun(fun(Q120763,cart(real,finite_sum(Q120760,Q120761))),cart(real,finite_sum(Q120760,Q120761)))),vsum),s(fun(Q120763,bool),K0))),s(fun(Q120763,cart(real,finite_sum(Q120760,Q120761))),i(s(fun(fun(Q120763,cart(real,Q120761)),fun(Q120763,cart(real,finite_sum(Q120760,Q120761)))),i(s(fun(fun(Q120763,cart(real,Q120760)),fun(fun(Q120763,cart(real,Q120761)),fun(Q120763,cart(real,finite_sum(Q120760,Q120761))))),U_0),s(fun(Q120763,cart(real,Q120760)),X))),s(fun(Q120763,cart(real,Q120761)),Y))))))))) # label(aPASTECARTu_VSUM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3415 (all Q117930 all F0 (p(s(bool,i(s(fun(fun(cart(real,Q117930),cart(real,Q117930)),bool),linear),s(fun(cart(real,Q117930),cart(real,Q117930)),F0)))) -> (s(cart(cart(real,Q117930),Q117930),i(s(fun(fun(cart(real,Q117930),cart(real,Q117930)),cart(cart(real,Q117930),Q117930)),matrix),s(fun(cart(real,Q117930),cart(real,Q117930)),F0))) = s(cart(cart(real,Q117930),Q117930),i(s(fun(cart(cart(real,Q117930),Q117930),cart(cart(real,Q117930),Q117930)),transp),s(cart(cart(real,Q117930),Q117930),i(s(fun(fun(cart(real,Q117930),cart(real,Q117930)),cart(cart(real,Q117930),Q117930)),matrix),s(fun(cart(real,Q117930),cart(real,Q117930)),F0))))) <-> s(fun(cart(real,Q117930),cart(real,Q117930)),F0) = s(fun(cart(real,Q117930),cart(real,Q117930)),i(s(fun(fun(cart(real,Q117930),cart(real,Q117930)),fun(cart(real,Q117930),cart(real,Q117930))),adjoint),s(fun(cart(real,Q117930),cart(real,Q117930)),F0)))))) # label(aMATRIXu_SELFu_ADJOINT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3416 (all A ((all V p(s(bool,i(s(fun(cart(A,n3),bool),p0),s(cart(A,n3),V))))) <-> (all X all Y all Z0 p(s(bool,i(s(fun(cart(A,n3),bool),p0),s(cart(A,n3),i(s(fun(list(A),cart(A,n3)),vector),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,X))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Y))),s(list(A),i(s(fun(list(A),list(A)),i(s(fun(A,fun(list(A),list(A))),cons),s(A,Z0))),s(list(A),nil))))))))))))))) # label(aFORALLu_VECTORu_3) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3417 (all X all Y (s(cart(real,n10),X) = s(cart(real,n10),Y) <-> s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),Y))) = s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X))))) # label(aDROPu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3418 (all Q104506 all X all Y s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104506),real),vectoru_norm),s(cart(real,Q104506),i(s(fun(cart(real,Q104506),cart(real,Q104506)),i(s(fun(cart(real,Q104506),fun(cart(real,Q104506),cart(real,Q104506))),vectoru_add),s(cart(real,Q104506),X))),s(cart(real,Q104506),Y))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104506),real),vectoru_norm),s(cart(real,Q104506),X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(cart(real,Q104506),real),vectoru_norm),s(cart(real,Q104506),Y))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(cart(real,Q104506),real),i(s(fun(cart(real,Q104506),fun(cart(real,Q104506),real)),dot),s(cart(real,Q104506),X))),s(cart(real,Q104506),Y)))) # label(aDOTu_NORM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3419 (all M all N all A5 s(num,i(s(fun(cart(cart(real,N),M),num),rank),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),A5))))) = s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5)))) # label(aRANKu_TRANSP) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3420 (all M all N all A5 all K0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ)))))) -> s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),i(s(fun(num,cart(real,M)),basis),s(num,K0))))) = s(cart(real,N),i(s(fun(cart(cart(real,M),N),cart(real,N)),i(s(fun(num,fun(cart(cart(real,M),N),cart(real,N))),column),s(num,K0))),s(cart(cart(real,M),N),A5))))) # label(aMATRIXu_VECTORu_MULu_BASIS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3421 (all Q142636 all A5 all B0 (p(s(bool,i(s(fun(prod(cart(real,Q142636),cart(real,Q142636)),bool),i(s(fun(cart(real,Q142636),fun(prod(cart(real,Q142636),cart(real,Q142636)),bool)),between),s(cart(real,Q142636),i(s(fun(prod(cart(real,Q142636),cart(real,Q142636)),cart(real,Q142636)),midpoint),s(prod(cart(real,Q142636),cart(real,Q142636)),i(s(fun(cart(real,Q142636),prod(cart(real,Q142636),cart(real,Q142636))),i(s(fun(cart(real,Q142636),fun(cart(real,Q142636),prod(cart(real,Q142636),cart(real,Q142636)))),c_),s(cart(real,Q142636),A5))),s(cart(real,Q142636),B0))))))),s(prod(cart(real,Q142636),cart(real,Q142636)),i(s(fun(cart(real,Q142636),prod(cart(real,Q142636),cart(real,Q142636))),i(s(fun(cart(real,Q142636),fun(cart(real,Q142636),prod(cart(real,Q142636),cart(real,Q142636)))),c_),s(cart(real,Q142636),A5))),s(cart(real,Q142636),B0)))))) & p(s(bool,i(s(fun(prod(cart(real,Q142636),cart(real,Q142636)),bool),i(s(fun(cart(real,Q142636),fun(prod(cart(real,Q142636),cart(real,Q142636)),bool)),between),s(cart(real,Q142636),i(s(fun(prod(cart(real,Q142636),cart(real,Q142636)),cart(real,Q142636)),midpoint),s(prod(cart(real,Q142636),cart(real,Q142636)),i(s(fun(cart(real,Q142636),prod(cart(real,Q142636),cart(real,Q142636))),i(s(fun(cart(real,Q142636),fun(cart(real,Q142636),prod(cart(real,Q142636),cart(real,Q142636)))),c_),s(cart(real,Q142636),A5))),s(cart(real,Q142636),B0))))))),s(prod(cart(real,Q142636),cart(real,Q142636)),i(s(fun(cart(real,Q142636),prod(cart(real,Q142636),cart(real,Q142636))),i(s(fun(cart(real,Q142636),fun(cart(real,Q142636),prod(cart(real,Q142636),cart(real,Q142636)))),c_),s(cart(real,Q142636),B0))),s(cart(real,Q142636),A5)))))))) # label(aBETWEENu_MIDPOINT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3422 (all N all S0 all T0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),S0))),s(fun(cart(real,N),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),T0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))),s(fun(cart(real,N),bool),T0)))))) # label(aSPANu_SUBSETu_SUBSPACE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3423 (all Q111690 p(s(bool,i(s(fun(fun(cart(real,Q111690),cart(real,Q111690)),bool),linear),s(fun(cart(real,Q111690),cart(real,Q111690)),i1))))) # label(aLINEARu_I) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3424 (all Q107324 all U_0 ((all F0 all G0 all I0 s(cart(real,Q107324),i(s(fun(num,cart(real,Q107324)),i(s(fun(fun(num,cart(real,Q107324)),fun(num,cart(real,Q107324))),i(s(fun(fun(num,cart(real,Q107324)),fun(fun(num,cart(real,Q107324)),fun(num,cart(real,Q107324)))),U_0),s(fun(num,cart(real,Q107324)),F0))),s(fun(num,cart(real,Q107324)),G0))),s(num,I0))) = s(cart(real,Q107324),i(s(fun(cart(real,Q107324),cart(real,Q107324)),i(s(fun(cart(real,Q107324),fun(cart(real,Q107324),cart(real,Q107324))),vectoru_sub),s(cart(real,Q107324),i(s(fun(num,cart(real,Q107324)),F0),s(num,I0))))),s(cart(real,Q107324),i(s(fun(num,cart(real,Q107324)),G0),s(num,I0)))))) -> (all F0 all G0 all M0 all N0 s(cart(real,Q107324),i(s(fun(fun(num,cart(real,Q107324)),cart(real,Q107324)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107324)),cart(real,Q107324))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107324)),i(s(fun(fun(num,cart(real,Q107324)),fun(num,cart(real,Q107324))),i(s(fun(fun(num,cart(real,Q107324)),fun(fun(num,cart(real,Q107324)),fun(num,cart(real,Q107324)))),U_0),s(fun(num,cart(real,Q107324)),F0))),s(fun(num,cart(real,Q107324)),G0))))) = s(cart(real,Q107324),i(s(fun(cart(real,Q107324),cart(real,Q107324)),i(s(fun(cart(real,Q107324),fun(cart(real,Q107324),cart(real,Q107324))),vectoru_sub),s(cart(real,Q107324),i(s(fun(fun(num,cart(real,Q107324)),cart(real,Q107324)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107324)),cart(real,Q107324))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107324)),F0))))),s(cart(real,Q107324),i(s(fun(fun(num,cart(real,Q107324)),cart(real,Q107324)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q107324)),cart(real,Q107324))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,M0))),s(num,N0))))),s(fun(num,cart(real,Q107324)),G0)))))))) # label(aVSUMu_SUBu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3425 (all Q126398 all V exists B0 (p(s(bool,i(s(fun(fun(cart(real,Q126398),bool),bool),finite),s(fun(cart(real,Q126398),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,Q126398),bool),bool),i(s(fun(fun(cart(real,Q126398),bool),fun(fun(cart(real,Q126398),bool),bool)),subset),s(fun(cart(real,Q126398),bool),B0))),s(fun(cart(real,Q126398),bool),V)))) & p(s(bool,i(s(fun(fun(cart(real,Q126398),bool),bool),i(s(fun(fun(cart(real,Q126398),bool),fun(fun(cart(real,Q126398),bool),bool)),subset),s(fun(cart(real,Q126398),bool),V))),s(fun(cart(real,Q126398),bool),i(s(fun(fun(cart(real,Q126398),bool),fun(cart(real,Q126398),bool)),span),s(fun(cart(real,Q126398),bool),B0)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,Q126398),bool),fun(num,bool)),hasu_size),s(fun(cart(real,Q126398),bool),B0))),s(num,i(s(fun(fun(cart(real,Q126398),bool),num),dim),s(fun(cart(real,Q126398),bool),V)))))) & p(s(bool,i(s(fun(fun(cart(real,Q126398),bool),bool),independent),s(fun(cart(real,Q126398),bool),B0)))))) # label(aBASISu_EXISTSu_FINITE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3426 (all Q99731 all A5 all B0 all X s(cart(real,Q99731),i(s(fun(cart(real,Q99731),cart(real,Q99731)),i(s(fun(real,fun(cart(real,Q99731),cart(real,Q99731))),r_),s(real,A5))),s(cart(real,Q99731),i(s(fun(cart(real,Q99731),cart(real,Q99731)),i(s(fun(real,fun(cart(real,Q99731),cart(real,Q99731))),r_),s(real,B0))),s(cart(real,Q99731),X))))) = s(cart(real,Q99731),i(s(fun(cart(real,Q99731),cart(real,Q99731)),i(s(fun(real,fun(cart(real,Q99731),cart(real,Q99731))),r_),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,A5))),s(real,B0))))),s(cart(real,Q99731),X)))) # label(aVECTORu_MULu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3427 (all M all N (s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))) = s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))) -> (exists F0 exists G0 ((all X s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))) & (all X s(cart(real,M),X) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),G0),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))) & (all Y s(cart(real,N),Y) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),G0),s(cart(real,N),Y)))))) & (all Y s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))) = s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),G0),s(cart(real,N),Y)))))) & p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0)))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))))))) # label(aISOMORPHISMSu_UNIVu_UNIV) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3428 (all N all U_0 ((all A5 all GENR_PVARR_336 ((exists X exists V ((p(s(bool,V)) <-> s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),A5))),s(cart(real,N),X))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) & p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(bool,fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(bool,fun(cart(real,N),bool))),setspec),s(cart(real,N),GENR_PVARR_336))),s(bool,V))),s(cart(real,N),X)))))) <-> p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),U_0),s(cart(real,N),A5))),s(cart(real,N),GENR_PVARR_336)))))) -> (all S0 (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> (exists A5 (s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(real,N),A5) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0))))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),gspec),s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),U_0),s(cart(real,N),A5)))))))))))))) # label(aLOWDIMu_SUBSETu_HYPERPLANE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3429 (all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> s(real,X) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) # label(aSQRTu_POWu_2) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3430 (all N all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))))))) # label(aNORMu_CAUCHYu_SCHWARZu_ABS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3431 (all N all X all Y p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),Y))))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) # label(aNORMu_CAUCHYu_SCHWARZu_DIV) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3432 (all N all M all A5 all B0 s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),matrixu_neg),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_sub),s(cart(cart(real,N),M),B0))),s(cart(cart(real,N),M),A5)))) # label(aMATRIXu_NEGu_SUB) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3433 (all N all C0 (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,C0)))) -> (exists X s(real,C0) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X)))))) # label(aVECTORu_CHOOSEu_SIZE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3434 (all N all U_0 ((all X s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),U_0),s(cart(real,N),X))) = s(cart(real,N),X)) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(fun(cart(real,N),cart(real,N)),real),onorm),s(fun(cart(real,N),cart(real,N)),U_0))))) # label(aONORMu_ID) # label(axiom) # label(non_clause). [assumption]. 16.04/16.03 3435 (all Q142467 all A5 all B0 (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),real),distance),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),A5))),s(cart(real,Q142467),B0))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),real),distance),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),B0))),s(cart(real,Q142467),i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),cart(real,Q142467)),midpoint),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),A5))),s(cart(real,Q142467),B0))))))))) & s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),real),distance),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),A5))),s(cart(real,Q142467),B0))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),real),distance),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),cart(real,Q142467)),midpoint),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),A5))),s(cart(real,Q142467),B0))))))),s(cart(real,Q142467),B0))))) & s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),real),distance),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),A5))),s(cart(real,Q142467),B0))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),real),distance),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),cart(real,Q142467)),midpoint),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),A5))),s(cart(real,Q142467),B0))))))),s(cart(real,Q142467),A5))))) & s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_div),s(real,i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),real),distance),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),A5))),s(cart(real,Q142467),B0))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))) = s(real,i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),real),distance),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),A5))),s(cart(real,Q142467),i(s(fun(prod(cart(real,Q142467),cart(real,Q142467)),cart(real,Q142467)),midpoint),s(prod(cart(real,Q142467),cart(real,Q142467)),i(s(fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467))),i(s(fun(cart(real,Q142467),fun(cart(real,Q142467),prod(cart(real,Q142467),cart(real,Q142467)))),c_),s(cart(real,Q142467),A5))),s(cart(real,Q142467),B0))))))))))) # label(aDISTu_MIDPOINT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3436 (all X s(real,i(s(fun(cart(real,n10),real),vectoru_norm),s(cart(real,n10),X))) = s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(num,real),i(s(fun(cart(real,n10),fun(num,real)),d_),s(cart(real,n10),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))) # label(aNORMu_REAL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3437 (all M all N all X all Y s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),i(s(fun(cart(real,M),fun(cart(real,M),cart(real,M))),vectoru_add),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),X))))),s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),Y))))) = s(cart(real,M),i(s(fun(cart(real,finite_sum(M,N)),cart(real,M)),fstcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_add),s(cart(real,finite_sum(M,N)),X))),s(cart(real,finite_sum(M,N)),Y)))))) # label(aFSTCARTu_ADD) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3438 (all Q121764 all F0 ((all S0 (p(s(bool,i(s(fun(fun(fun(cart(real,Q121764),bool),bool),bool),i(s(fun(fun(cart(real,Q121764),bool),fun(fun(fun(cart(real,Q121764),bool),bool),bool)),in),s(fun(cart(real,Q121764),bool),S0))),s(fun(fun(cart(real,Q121764),bool),bool),F0)))) -> p(s(bool,i(s(fun(fun(cart(real,Q121764),bool),bool),subspace),s(fun(cart(real,Q121764),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,Q121764),bool),bool),subspace),s(fun(cart(real,Q121764),bool),i(s(fun(fun(fun(cart(real,Q121764),bool),bool),fun(cart(real,Q121764),bool)),inters),s(fun(fun(cart(real,Q121764),bool),bool),F0)))))))) # label(aSUBSPACEu_INTERS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3439 (all N all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),S0)))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),finite),s(fun(cart(real,N),bool),S0)))))) # label(aPAIRWISEu_ORTHOGONALu_IMPu_FINITE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3440 (all Q120851 all Q120849 all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q120851),real),vectoru_norm),s(cart(real,Q120851),i(s(fun(cart(real,finite_sum(Q120851,Q120849)),cart(real,Q120851)),fstcart),s(cart(real,finite_sum(Q120851,Q120849)),X))))))),s(real,i(s(fun(cart(real,finite_sum(Q120851,Q120849)),real),vectoru_norm),s(cart(real,finite_sum(Q120851,Q120849)),X))))))) # label(aNORMu_FSTCART) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3441 (all N s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_sub),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),x))),s(cart(real,N),y))))),s(cart(real,N),x))) = s(cart(real,N),y)) # label(aVECTORu_ADDu_SUB) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3442 (all N all S0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),S0)))) -> (exists B0 (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),fun(cart(real,N),bool)),fun(fun(cart(real,N),bool),bool)),pairwise),s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal))),s(fun(cart(real,N),bool),B0)))) & (all X (p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),X))),s(fun(cart(real,N),bool),B0)))) -> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),X))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),B0)))) & s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),B0))) = s(fun(cart(real,N),bool),S0) & p(s(bool,i(s(fun(num,bool),i(s(fun(fun(cart(real,N),bool),fun(num,bool)),hasu_size),s(fun(cart(real,N),bool),B0))),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),S0)))))))))) # label(aORTHONORMALu_BASISu_SUBSPACE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3443 (all Q102367 all X (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q102367),real),vectoru_norm),s(cart(real,Q102367),X))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) <-> s(cart(real,Q102367),i(s(fun(num,cart(real,Q102367)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,Q102367),X))) # label(aNORMu_LEu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3444 (all N all M all S0 all T0 (s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),T0))) = s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),S0))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),subspace),s(fun(cart(real,N),bool),T0)))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),subspace),s(fun(cart(real,M),bool),S0)))) -> (exists F0 (s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0))) = s(fun(cart(real,N),bool),T0) & (all X (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),S0)))) -> s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X))) = s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))))))) # label(aISOMETRYu_SUBSPACES) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3445 (all N all M all U_0 ((all F0 all GENR_PVARR_354 ((exists X exists V ((p(s(bool,V)) <-> s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))) & p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(bool,fun(cart(real,M),bool)),i(s(fun(cart(real,M),fun(bool,fun(cart(real,M),bool))),setspec),s(cart(real,M),GENR_PVARR_354))),s(bool,V))),s(cart(real,M),X)))))) <-> p(s(bool,i(s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(cart(real,M),GENR_PVARR_354)))))) -> (all F0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))) = s(num,i(s(fun(num,num),i(s(fun(num,fun(num,num)),p_),s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),univ))))))),s(num,i(s(fun(fun(cart(real,M),bool),num),dim),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),gspec),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(cart(real,M),bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))))))))))))) # label(aDIMu_IMAGEu_KERNEL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3446 (all Q121280 all Q121279 all X all XI_ all Y s(real,i(s(fun(prod(cart(real,finite_sum(Q121279,Q121280)),cart(real,finite_sum(Q121279,Q121280))),real),distance),s(prod(cart(real,finite_sum(Q121279,Q121280)),cart(real,finite_sum(Q121279,Q121280))),i(s(fun(cart(real,finite_sum(Q121279,Q121280)),prod(cart(real,finite_sum(Q121279,Q121280)),cart(real,finite_sum(Q121279,Q121280)))),i(s(fun(cart(real,finite_sum(Q121279,Q121280)),fun(cart(real,finite_sum(Q121279,Q121280)),prod(cart(real,finite_sum(Q121279,Q121280)),cart(real,finite_sum(Q121279,Q121280))))),c_),s(cart(real,finite_sum(Q121279,Q121280)),i(s(fun(cart(real,Q121280),cart(real,finite_sum(Q121279,Q121280))),i(s(fun(cart(real,Q121279),fun(cart(real,Q121280),cart(real,finite_sum(Q121279,Q121280)))),pastecart),s(cart(real,Q121279),X))),s(cart(real,Q121280),Y))))),s(cart(real,finite_sum(Q121279,Q121280)),i(s(fun(cart(real,Q121280),cart(real,finite_sum(Q121279,Q121280))),i(s(fun(cart(real,Q121279),fun(cart(real,Q121280),cart(real,finite_sum(Q121279,Q121280)))),pastecart),s(cart(real,Q121279),XI_))),s(cart(real,Q121280),Y))))))) = s(real,i(s(fun(prod(cart(real,Q121279),cart(real,Q121279)),real),distance),s(prod(cart(real,Q121279),cart(real,Q121279)),i(s(fun(cart(real,Q121279),prod(cart(real,Q121279),cart(real,Q121279))),i(s(fun(cart(real,Q121279),fun(cart(real,Q121279),prod(cart(real,Q121279),cart(real,Q121279)))),c_),s(cart(real,Q121279),X))),s(cart(real,Q121279),XI_)))))) # label(aDISTu_PASTECARTu_CANCELu_conjunct0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3447 (all M all N all A5 all X s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),i(s(fun(cart(cart(real,N),M),fun(cart(real,N),cart(real,M))),matrixu_vectoru_mul),s(cart(cart(real,N),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,N),M)),transp),s(cart(cart(real,M),N),A5))))),s(cart(real,N),X))) = s(cart(real,M),i(s(fun(cart(cart(real,M),N),cart(real,M)),i(s(fun(cart(real,N),fun(cart(cart(real,M),N),cart(real,M))),vectoru_matrixu_mul),s(cart(real,N),X))),s(cart(cart(real,M),N),A5)))) # label(aVECTORu_MATRIXu_MULu_TRANSP) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3448 (all P0 ((all S0 p(s(bool,i(s(fun(fun(real,bool),bool),P0),s(fun(real,bool),i(s(fun(fun(cart(real,n10),bool),fun(real,bool)),i(s(fun(fun(cart(real,n10),real),fun(fun(cart(real,n10),bool),fun(real,bool))),image),s(fun(cart(real,n10),real),drop))),s(fun(cart(real,n10),bool),S0))))))) <-> (all S0 p(s(bool,i(s(fun(fun(real,bool),bool),P0),s(fun(real,bool),S0))))))) # label(aFORALLu_DROPu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3449 (all N all X (p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) -> (exists Y (s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(real,N),Y) & p(s(bool,i(s(fun(cart(real,N),bool),i(s(fun(cart(real,N),fun(cart(real,N),bool)),orthogonal),s(cart(real,N),X))),s(cart(real,N),Y)))))))) # label(aORTHOGONALu_TOu_VECTORu_EXISTS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3450 (all M all N all A5 (p(s(bool,i(s(fun(cart(cart(real,N),M),bool),invertible),s(cart(cart(real,N),M),A5)))) -> s(cart(cart(real,M),M),i(s(fun(num,cart(cart(real,M),M)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(cart(cart(real,M),M),i(s(fun(cart(cart(real,M),N),cart(cart(real,M),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,M),N),cart(cart(real,M),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),matrixu_inv),s(cart(cart(real,N),M),A5))))) & s(cart(cart(real,N),N),i(s(fun(num,cart(cart(real,N),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(cart(cart(real,N),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),N)),i(s(fun(cart(cart(real,M),N),fun(cart(cart(real,N),M),cart(cart(real,N),N))),matrixu_mul),s(cart(cart(real,M),N),i(s(fun(cart(cart(real,N),M),cart(cart(real,M),N)),matrixu_inv),s(cart(cart(real,N),M),A5))))),s(cart(cart(real,N),M),A5))))) # label(aMATRIXu_INV) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3451 (all Q122592 all X all S0 s(bool,i(s(fun(fun(cart(real,Q122592),bool),bool),i(s(fun(cart(real,Q122592),fun(fun(cart(real,Q122592),bool),bool)),in),s(cart(real,Q122592),X))),s(fun(cart(real,Q122592),bool),i(s(fun(fun(cart(real,Q122592),bool),fun(cart(real,Q122592),bool)),span),s(fun(cart(real,Q122592),bool),S0))))) = s(bool,i(s(fun(fun(cart(real,Q122592),bool),bool),i(s(fun(cart(real,Q122592),fun(fun(cart(real,Q122592),bool),bool)),in),s(cart(real,Q122592),i(s(fun(cart(real,Q122592),cart(real,Q122592)),vectoru_neg),s(cart(real,Q122592),X))))),s(fun(cart(real,Q122592),bool),i(s(fun(fun(cart(real,Q122592),bool),fun(cart(real,Q122592),bool)),span),s(fun(cart(real,Q122592),bool),S0)))))) # label(aSPANu_NEGu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3452 (all M all N all A5 (s(num,i(s(fun(fun(M,bool),num),dimindex),s(fun(M,bool),univ))) != s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) -> (exists X (s(cart(real,M),X) != s(cart(real,M),i(s(fun(num,cart(real,M)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) & s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),i(s(fun(cart(cart(real,M),N),fun(cart(real,M),cart(real,N))),matrixu_vectoru_mul),s(cart(cart(real,M),N),A5))),s(cart(real,M),X))))))) # label(aMATRIXu_NONFULLu_LINEARu_EQUATIONS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3453 (all N all M all F0 all S0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & (all Y exists X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),Y)) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(fun(cart(real,M),bool),fun(fun(cart(real,M),bool),bool)),subset),s(fun(cart(real,M),bool),univ))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),S0)))))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),univ))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,N),bool)),i(s(fun(fun(cart(real,M),cart(real,N)),fun(fun(cart(real,M),bool),fun(cart(real,N),bool))),image),s(fun(cart(real,M),cart(real,N)),F0))),s(fun(cart(real,M),bool),S0)))))))))) # label(aSPANNINGu_SURJECTIVEu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3454 (all Q109598 s(cart(real,Q109598),i(s(fun(num,cart(real,Q109598)),f),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(cart(real,Q109598),i(s(fun(fun(num,cart(real,Q109598)),cart(real,Q109598)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109598)),cart(real,Q109598))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(fun(num,cart(real,Q109598)),f)))) # label(aVSUMu_1) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3455 (all N exists I0 p(s(bool,i(s(fun(fun(num,bool),bool),i(s(fun(num,fun(fun(num,bool),bool)),in),s(num,I0))),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))))) # label(aNUMSEGu_DIMINDEXu_NONEMPTY) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3456 (all M all N all X all Y s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),i(s(fun(cart(real,M),cart(real,M)),vectoru_neg),s(cart(real,M),X))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),Y))))) = s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),vectoru_neg),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,N),cart(real,finite_sum(M,N))),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,finite_sum(M,N)))),pastecart),s(cart(real,M),X))),s(cart(real,N),Y)))))) # label(aPASTECARTu_NEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3457 (all M all N all U_0 ((all F0 all GENR_PVARR_293 ((exists X exists V (p(s(bool,i(s(fun(real,bool),i(s(fun(bool,fun(real,bool)),i(s(fun(real,fun(bool,fun(real,bool))),setspec),s(real,GENR_PVARR_293))),s(bool,V))),s(real,i(s(fun(cart(real,N),real),vectoru_norm),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))))) & (p(s(bool,V)) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))) = s(real,i(s(fun(cart(real,M),real),vectoru_norm),s(cart(real,M),X)))))) <-> p(s(bool,i(s(fun(real,bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(real,bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(real,GENR_PVARR_293)))))) -> (all F0 s(real,i(s(fun(fun(cart(real,M),cart(real,N)),real),onorm),s(fun(cart(real,M),cart(real,N)),F0))) = s(real,i(s(fun(fun(real,bool),real),sup),s(fun(real,bool),i(s(fun(fun(real,bool),fun(real,bool)),gspec),s(fun(real,bool),i(s(fun(fun(cart(real,M),cart(real,N)),fun(real,bool)),U_0),s(fun(cart(real,M),cart(real,N)),F0)))))))))) # label(aonorm) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3458 (all Q116735 all Q116736 all N0 s(cart(cart(real,Q116735),Q116736),i(s(fun(cart(cart(real,Q116736),Q116735),cart(cart(real,Q116735),Q116736)),transp),s(cart(cart(real,Q116736),Q116735),i(s(fun(num,cart(cart(real,Q116736),Q116735)),mat),s(num,N0))))) = s(cart(cart(real,Q116735),Q116736),i(s(fun(num,cart(cart(real,Q116735),Q116736)),mat),s(num,N0)))) # label(aTRANSPu_MAT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3459 (all Q102210 all X all Y s(real,i(s(fun(cart(real,Q102210),real),vectoru_norm),s(cart(real,Q102210),i(s(fun(cart(real,Q102210),cart(real,Q102210)),i(s(fun(cart(real,Q102210),fun(cart(real,Q102210),cart(real,Q102210))),vectoru_sub),s(cart(real,Q102210),X))),s(cart(real,Q102210),Y))))) = s(real,i(s(fun(cart(real,Q102210),real),vectoru_norm),s(cart(real,Q102210),i(s(fun(cart(real,Q102210),cart(real,Q102210)),i(s(fun(cart(real,Q102210),fun(cart(real,Q102210),cart(real,Q102210))),vectoru_sub),s(cart(real,Q102210),Y))),s(cart(real,Q102210),X)))))) # label(aNORMu_SUB) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3460 (all M all N all X s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),vectoru_neg),s(cart(real,finite_sum(M,N)),X))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),vectoru_neg),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),X)))))) # label(aSNDCARTu_NEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3461 (all U_0 ((all X all I0 s(real,X) = s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X))),s(num,I0)))) -> ((all X p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),X))))) <-> (all X p(s(bool,i(s(fun(cart(real,n10),bool),p0),s(cart(real,n10),i(s(fun(fun(num,real),cart(real,n10)),lambda),s(fun(num,real),i(s(fun(real,fun(num,real)),U_0),s(real,X)))))))))))) # label(aFORALLu_REALu_ONE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3462 (all N all M all U_1 ((all A5 all B0 all I0 all J0 s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_add),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),A5))),s(num,I0))))),s(num,J0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),d_),s(cart(cart(real,N),M),B0))),s(num,I0))))),s(num,J0))))) = s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0))),s(num,J0)))) -> (all U_0 ((all A5 all B0 all I0 s(cart(real,N),i(s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0))) = s(cart(real,N),i(s(fun(fun(num,real),cart(real,N)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),i(s(fun(cart(cart(real,N),M),fun(num,fun(num,real))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,fun(num,real)))),U_1),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))),s(num,I0)))))) -> (all A5 all B0 s(cart(cart(real,N),M),i(s(fun(fun(num,cart(real,N)),cart(cart(real,N),M)),lambda),s(fun(num,cart(real,N)),i(s(fun(cart(cart(real,N),M),fun(num,cart(real,N))),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),fun(num,cart(real,N)))),U_0),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0))))) = s(cart(cart(real,N),M),i(s(fun(cart(cart(real,N),M),cart(cart(real,N),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,N),M),cart(cart(real,N),M))),matrixu_add),s(cart(cart(real,N),M),A5))),s(cart(cart(real,N),M),B0)))))))) # label(amatrixu_add) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3463 (all Q117654 all Q117653 all Q117652 all F0 all G0 (p(s(bool,i(s(fun(fun(cart(real,Q117652),cart(real,Q117654)),bool),linear),s(fun(cart(real,Q117652),cart(real,Q117654)),G0)))) & p(s(bool,i(s(fun(fun(cart(real,Q117653),cart(real,Q117652)),bool),linear),s(fun(cart(real,Q117653),cart(real,Q117652)),F0)))) -> s(cart(cart(real,Q117653),Q117654),i(s(fun(cart(cart(real,Q117653),Q117652),cart(cart(real,Q117653),Q117654)),i(s(fun(cart(cart(real,Q117652),Q117654),fun(cart(cart(real,Q117653),Q117652),cart(cart(real,Q117653),Q117654))),matrixu_mul),s(cart(cart(real,Q117652),Q117654),i(s(fun(fun(cart(real,Q117652),cart(real,Q117654)),cart(cart(real,Q117652),Q117654)),matrix),s(fun(cart(real,Q117652),cart(real,Q117654)),G0))))),s(cart(cart(real,Q117653),Q117652),i(s(fun(fun(cart(real,Q117653),cart(real,Q117652)),cart(cart(real,Q117653),Q117652)),matrix),s(fun(cart(real,Q117653),cart(real,Q117652)),F0))))) = s(cart(cart(real,Q117653),Q117654),i(s(fun(fun(cart(real,Q117653),cart(real,Q117654)),cart(cart(real,Q117653),Q117654)),matrix),s(fun(cart(real,Q117653),cart(real,Q117654)),i(s(fun(fun(cart(real,Q117653),cart(real,Q117652)),fun(cart(real,Q117653),cart(real,Q117654))),i(s(fun(fun(cart(real,Q117652),cart(real,Q117654)),fun(fun(cart(real,Q117653),cart(real,Q117652)),fun(cart(real,Q117653),cart(real,Q117654)))),o),s(fun(cart(real,Q117652),cart(real,Q117654)),G0))),s(fun(cart(real,Q117653),cart(real,Q117652)),F0))))))) # label(aMATRIXu_COMPOSE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3464 (all X s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))) = s(real,X)) # label(aLIFTu_DROPu_conjunct1) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3465 (all Q122179 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q122179),bool),bool),independent),s(fun(cart(real,Q122179),bool),S0)))) -> -p(s(bool,i(s(fun(fun(cart(real,Q122179),bool),bool),i(s(fun(cart(real,Q122179),fun(fun(cart(real,Q122179),bool),bool)),in),s(cart(real,Q122179),i(s(fun(num,cart(real,Q122179)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,Q122179),bool),S0)))))) # label(aINDEPENDENTu_NONZERO) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3466 (all Q111863 all Q111862 all F0 all X (p(s(bool,i(s(fun(fun(cart(real,Q111862),cart(real,Q111863)),bool),linear),s(fun(cart(real,Q111862),cart(real,Q111863)),F0)))) -> s(cart(real,Q111863),i(s(fun(cart(real,Q111862),cart(real,Q111863)),F0),s(cart(real,Q111862),i(s(fun(cart(real,Q111862),cart(real,Q111862)),vectoru_neg),s(cart(real,Q111862),X))))) = s(cart(real,Q111863),i(s(fun(cart(real,Q111863),cart(real,Q111863)),vectoru_neg),s(cart(real,Q111863),i(s(fun(cart(real,Q111862),cart(real,Q111863)),F0),s(cart(real,Q111862),X))))))) # label(aLINEARu_NEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3467 (all Q139185 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(cart(real,Q139185),real),infnorm),s(cart(real,Q139185),x))))),s(real,i(s(fun(cart(real,Q139185),real),infnorm),s(cart(real,Q139185),y))))))))),s(real,i(s(fun(cart(real,Q139185),real),infnorm),s(cart(real,Q139185),i(s(fun(cart(real,Q139185),cart(real,Q139185)),i(s(fun(cart(real,Q139185),fun(cart(real,Q139185),cart(real,Q139185))),vectoru_sub),s(cart(real,Q139185),x))),s(cart(real,Q139185),y))))))))) # label(aREALu_ABSu_SUBu_INFNORM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3468 (all X all Y all Z0 (p(s(bool,i(s(fun(cart(real,n20),bool),i(s(fun(cart(real,n20),fun(cart(real,n20),bool)),orthogonal),s(cart(real,n20),X))),s(cart(real,n20),Y)))) & p(s(bool,i(s(fun(cart(real,n20),bool),i(s(fun(cart(real,n20),fun(cart(real,n20),bool)),orthogonal),s(cart(real,n20),X))),s(cart(real,n20),Z0)))) & s(cart(real,n20),X) != s(cart(real,n20),i(s(fun(num,cart(real,n20)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> p(s(bool,i(s(fun(fun(cart(real,n20),bool),bool),collinear),s(fun(cart(real,n20),bool),i(s(fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool)),i(s(fun(cart(real,n20),fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool))),insert),s(cart(real,n20),i(s(fun(num,cart(real,n20)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(fun(cart(real,n20),bool),i(s(fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool)),i(s(fun(cart(real,n20),fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool))),insert),s(cart(real,n20),Y))),s(fun(cart(real,n20),bool),i(s(fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool)),i(s(fun(cart(real,n20),fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool))),insert),s(cart(real,n20),Z0))),s(fun(cart(real,n20),bool),empty)))))))))))) # label(aORTHOGONALu_TOu_ORTHOGONALu_2D) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3469 (all Q115825 all Q115826 s(cart(cart(real,Q115825),Q115826),i(s(fun(cart(cart(real,Q115825),Q115826),cart(cart(real,Q115825),Q115826)),matrixu_neg),s(cart(cart(real,Q115825),Q115826),i(s(fun(num,cart(cart(real,Q115825),Q115826)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(cart(cart(real,Q115825),Q115826),i(s(fun(num,cart(cart(real,Q115825),Q115826)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) # label(aMATRIXu_NEGu_0) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3470 (all Q128822 all Q128829 all F0 all G0 all B0 all S0 (p(s(bool,i(s(fun(fun(cart(real,Q128829),cart(real,Q128822)),bool),linear),s(fun(cart(real,Q128829),cart(real,Q128822)),G0)))) & (all X (p(s(bool,i(s(fun(fun(cart(real,Q128829),bool),bool),i(s(fun(cart(real,Q128829),fun(fun(cart(real,Q128829),bool),bool)),in),s(cart(real,Q128829),X))),s(fun(cart(real,Q128829),bool),B0)))) -> s(cart(real,Q128822),i(s(fun(cart(real,Q128829),cart(real,Q128822)),F0),s(cart(real,Q128829),X))) = s(cart(real,Q128822),i(s(fun(cart(real,Q128829),cart(real,Q128822)),G0),s(cart(real,Q128829),X))))) & p(s(bool,i(s(fun(fun(cart(real,Q128829),bool),bool),i(s(fun(fun(cart(real,Q128829),bool),fun(fun(cart(real,Q128829),bool),bool)),subset),s(fun(cart(real,Q128829),bool),S0))),s(fun(cart(real,Q128829),bool),i(s(fun(fun(cart(real,Q128829),bool),fun(cart(real,Q128829),bool)),span),s(fun(cart(real,Q128829),bool),B0)))))) & p(s(bool,i(s(fun(fun(cart(real,Q128829),cart(real,Q128822)),bool),linear),s(fun(cart(real,Q128829),cart(real,Q128822)),F0)))) -> (all X (p(s(bool,i(s(fun(fun(cart(real,Q128829),bool),bool),i(s(fun(cart(real,Q128829),fun(fun(cart(real,Q128829),bool),bool)),in),s(cart(real,Q128829),X))),s(fun(cart(real,Q128829),bool),S0)))) -> s(cart(real,Q128822),i(s(fun(cart(real,Q128829),cart(real,Q128822)),G0),s(cart(real,Q128829),X))) = s(cart(real,Q128822),i(s(fun(cart(real,Q128829),cart(real,Q128822)),F0),s(cart(real,Q128829),X))))))) # label(aLINEARu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3471 (all N all A5 all B0 all X all Y (s(cart(real,N),B0) != s(cart(real,N),A5) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),independent),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),empty)))))))) -> (s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,X))),s(cart(real,N),A5))))),s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(real,fun(cart(real,N),cart(real,N))),r_),s(real,Y))),s(cart(real,N),B0))))) = s(cart(real,N),i(s(fun(num,cart(real,N)),vec),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) <-> s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,X) & s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(real,Y)))) # label(aINDEPENDENTu_2) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3472 (all M all N all X all Y s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),i(s(fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N))),i(s(fun(cart(real,finite_sum(M,N)),fun(cart(real,finite_sum(M,N)),cart(real,finite_sum(M,N)))),vectoru_add),s(cart(real,finite_sum(M,N)),X))),s(cart(real,finite_sum(M,N)),Y))))) = s(cart(real,N),i(s(fun(cart(real,N),cart(real,N)),i(s(fun(cart(real,N),fun(cart(real,N),cart(real,N))),vectoru_add),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),X))))),s(cart(real,N),i(s(fun(cart(real,finite_sum(M,N)),cart(real,N)),sndcart),s(cart(real,finite_sum(M,N)),Y)))))) # label(aSNDCARTu_ADD) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3473 (all Q99811 s(cart(real,Q99811),i(s(fun(cart(real,Q99811),cart(real,Q99811)),i(s(fun(cart(real,Q99811),fun(cart(real,Q99811),cart(real,Q99811))),vectoru_add),s(cart(real,Q99811),i(s(fun(cart(real,Q99811),cart(real,Q99811)),i(s(fun(real,fun(cart(real,Q99811),cart(real,Q99811))),r_),s(real,c))),s(cart(real,Q99811),x))))),s(cart(real,Q99811),i(s(fun(cart(real,Q99811),cart(real,Q99811)),i(s(fun(real,fun(cart(real,Q99811),cart(real,Q99811))),r_),s(real,c))),s(cart(real,Q99811),y))))) = s(cart(real,Q99811),i(s(fun(cart(real,Q99811),cart(real,Q99811)),i(s(fun(real,fun(cart(real,Q99811),cart(real,Q99811))),r_),s(real,c))),s(cart(real,Q99811),i(s(fun(cart(real,Q99811),cart(real,Q99811)),i(s(fun(cart(real,Q99811),fun(cart(real,Q99811),cart(real,Q99811))),vectoru_add),s(cart(real,Q99811),x))),s(cart(real,Q99811),y)))))) # label(aVECTORu_ADDu_LDISTRIB) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3474 (all Q112310 all Q112309 all Q112292 all H0 all X all Y all Z0 (p(s(bool,i(s(fun(fun(cart(real,Q112309),fun(cart(real,Q112292),cart(real,Q112310))),bool),bilinear),s(fun(cart(real,Q112309),fun(cart(real,Q112292),cart(real,Q112310))),H0)))) -> s(cart(real,Q112310),i(s(fun(cart(real,Q112310),cart(real,Q112310)),i(s(fun(cart(real,Q112310),fun(cart(real,Q112310),cart(real,Q112310))),vectoru_add),s(cart(real,Q112310),i(s(fun(cart(real,Q112292),cart(real,Q112310)),i(s(fun(cart(real,Q112309),fun(cart(real,Q112292),cart(real,Q112310))),H0),s(cart(real,Q112309),X))),s(cart(real,Q112292),Z0))))),s(cart(real,Q112310),i(s(fun(cart(real,Q112292),cart(real,Q112310)),i(s(fun(cart(real,Q112309),fun(cart(real,Q112292),cart(real,Q112310))),H0),s(cart(real,Q112309),Y))),s(cart(real,Q112292),Z0))))) = s(cart(real,Q112310),i(s(fun(cart(real,Q112292),cart(real,Q112310)),i(s(fun(cart(real,Q112309),fun(cart(real,Q112292),cart(real,Q112310))),H0),s(cart(real,Q112309),i(s(fun(cart(real,Q112309),cart(real,Q112309)),i(s(fun(cart(real,Q112309),fun(cart(real,Q112309),cart(real,Q112309))),vectoru_add),s(cart(real,Q112309),X))),s(cart(real,Q112309),Y))))),s(cart(real,Q112292),Z0))))) # label(aBILINEARu_LADD) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3475 (all N all U_0 ((all X all Y all I0 s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),X))),s(num,I0))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),Y))),s(num,I0)))))) -> (all X all Y s(real,i(s(fun(fun(num,real),real),i(s(fun(fun(num,bool),fun(fun(num,real),real)),sum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ))))))),s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),i(s(fun(cart(real,N),fun(cart(real,N),fun(num,real))),U_0),s(cart(real,N),X))),s(cart(real,N),Y))))) = s(real,i(s(fun(cart(real,N),real),i(s(fun(cart(real,N),fun(cart(real,N),real)),dot),s(cart(real,N),X))),s(cart(real,N),Y)))))) # label(adot) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3476 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) -> s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,i(s(fun(real,real),sqrt),s(real,Y))))) = s(real,i(s(fun(real,real),sqrt),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X))),s(real,Y))))))) # label(aSQRTu_MUL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3477 (all Q112022 all Q112025 all Q112011 all U_1 ((all C0 all F0 all V all I0 s(cart(real,Q112022),i(s(fun(Q112025,cart(real,Q112022)),i(s(fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022))),i(s(fun(fun(cart(real,Q112011),cart(real,Q112022)),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022)))),i(s(fun(fun(Q112025,real),fun(fun(cart(real,Q112011),cart(real,Q112022)),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022))))),U_1),s(fun(Q112025,real),C0))),s(fun(cart(real,Q112011),cart(real,Q112022)),F0))),s(fun(Q112025,cart(real,Q112011)),V))),s(Q112025,I0))) = s(cart(real,Q112022),i(s(fun(cart(real,Q112022),cart(real,Q112022)),i(s(fun(real,fun(cart(real,Q112022),cart(real,Q112022))),r_),s(real,i(s(fun(Q112025,real),C0),s(Q112025,I0))))),s(cart(real,Q112022),i(s(fun(cart(real,Q112011),cart(real,Q112022)),F0),s(cart(real,Q112011),i(s(fun(Q112025,cart(real,Q112011)),V),s(Q112025,I0)))))))) -> (all U_0 ((all C0 all V all I0 s(cart(real,Q112011),i(s(fun(Q112025,cart(real,Q112011)),i(s(fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112011))),i(s(fun(fun(Q112025,real),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112011)))),U_0),s(fun(Q112025,real),C0))),s(fun(Q112025,cart(real,Q112011)),V))),s(Q112025,I0))) = s(cart(real,Q112011),i(s(fun(cart(real,Q112011),cart(real,Q112011)),i(s(fun(real,fun(cart(real,Q112011),cart(real,Q112011))),r_),s(real,i(s(fun(Q112025,real),C0),s(Q112025,I0))))),s(cart(real,Q112011),i(s(fun(Q112025,cart(real,Q112011)),V),s(Q112025,I0)))))) -> (all F0 all S0 all C0 all V (p(s(bool,i(s(fun(fun(cart(real,Q112011),cart(real,Q112022)),bool),linear),s(fun(cart(real,Q112011),cart(real,Q112022)),F0)))) & p(s(bool,i(s(fun(fun(Q112025,bool),bool),finite),s(fun(Q112025,bool),S0)))) -> s(cart(real,Q112022),i(s(fun(cart(real,Q112011),cart(real,Q112022)),F0),s(cart(real,Q112011),i(s(fun(fun(Q112025,cart(real,Q112011)),cart(real,Q112011)),i(s(fun(fun(Q112025,bool),fun(fun(Q112025,cart(real,Q112011)),cart(real,Q112011))),vsum),s(fun(Q112025,bool),S0))),s(fun(Q112025,cart(real,Q112011)),i(s(fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112011))),i(s(fun(fun(Q112025,real),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112011)))),U_0),s(fun(Q112025,real),C0))),s(fun(Q112025,cart(real,Q112011)),V))))))) = s(cart(real,Q112022),i(s(fun(fun(Q112025,cart(real,Q112022)),cart(real,Q112022)),i(s(fun(fun(Q112025,bool),fun(fun(Q112025,cart(real,Q112022)),cart(real,Q112022))),vsum),s(fun(Q112025,bool),S0))),s(fun(Q112025,cart(real,Q112022)),i(s(fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022))),i(s(fun(fun(cart(real,Q112011),cart(real,Q112022)),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022)))),i(s(fun(fun(Q112025,real),fun(fun(cart(real,Q112011),cart(real,Q112022)),fun(fun(Q112025,cart(real,Q112011)),fun(Q112025,cart(real,Q112022))))),U_1),s(fun(Q112025,real),C0))),s(fun(cart(real,Q112011),cart(real,Q112022)),F0))),s(fun(Q112025,cart(real,Q112011)),V))))))))))) # label(aLINEARu_VSUMu_MUL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3478 (all Q140000 all S0 ((exists U all X all Y (p(s(bool,i(s(fun(fun(cart(real,Q140000),bool),bool),i(s(fun(cart(real,Q140000),fun(fun(cart(real,Q140000),bool),bool)),in),s(cart(real,Q140000),X))),s(fun(cart(real,Q140000),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,Q140000),bool),bool),i(s(fun(cart(real,Q140000),fun(fun(cart(real,Q140000),bool),bool)),in),s(cart(real,Q140000),Y))),s(fun(cart(real,Q140000),bool),S0)))) -> (exists C0 s(cart(real,Q140000),i(s(fun(cart(real,Q140000),cart(real,Q140000)),i(s(fun(real,fun(cart(real,Q140000),cart(real,Q140000))),r_),s(real,C0))),s(cart(real,Q140000),U))) = s(cart(real,Q140000),i(s(fun(cart(real,Q140000),cart(real,Q140000)),i(s(fun(cart(real,Q140000),fun(cart(real,Q140000),cart(real,Q140000))),vectoru_sub),s(cart(real,Q140000),X))),s(cart(real,Q140000),Y)))))) <-> p(s(bool,i(s(fun(fun(cart(real,Q140000),bool),bool),collinear),s(fun(cart(real,Q140000),bool),S0)))))) # label(acollinear) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3479 (all M all N all F0 ((all Y exists X s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) = s(cart(real,N),Y)) & (all X all Y (s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),Y))) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))) -> s(cart(real,M),X) = s(cart(real,M),Y))) & p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) -> (exists G0 (p(s(bool,i(s(fun(fun(cart(real,N),cart(real,M)),bool),linear),s(fun(cart(real,N),cart(real,M)),G0)))) & (all X s(cart(real,M),X) = s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),G0),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X)))))) & (all Y s(cart(real,N),Y) = s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),i(s(fun(cart(real,N),cart(real,M)),G0),s(cart(real,N),Y)))))))))) # label(aLINEARu_BIJECTIVEu_LEFTu_RIGHTu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3480 (all M all N all Q all P all A5 all B0 all C0 s(cart(cart(real,Q),M),i(s(fun(cart(cart(real,Q),P),cart(cart(real,Q),M)),i(s(fun(cart(cart(real,P),M),fun(cart(cart(real,Q),P),cart(cart(real,Q),M))),matrixu_mul),s(cart(cart(real,P),M),i(s(fun(cart(cart(real,P),N),cart(cart(real,P),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,P),N),cart(cart(real,P),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,P),N),B0))))),s(cart(cart(real,Q),P),C0))) = s(cart(cart(real,Q),M),i(s(fun(cart(cart(real,Q),N),cart(cart(real,Q),M)),i(s(fun(cart(cart(real,N),M),fun(cart(cart(real,Q),N),cart(cart(real,Q),M))),matrixu_mul),s(cart(cart(real,N),M),A5))),s(cart(cart(real,Q),N),i(s(fun(cart(cart(real,Q),P),cart(cart(real,Q),N)),i(s(fun(cart(cart(real,P),N),fun(cart(cart(real,Q),P),cart(cart(real,Q),N))),matrixu_mul),s(cart(cart(real,P),N),B0))),s(cart(cart(real,Q),P),C0)))))) # label(aMATRIXu_MULu_ASSOC) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3481 (all N s(num,i(s(fun(fun(cart(real,N),bool),num),dim),s(fun(cart(real,N),bool),empty))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))) # label(aDIMu_EMPTY) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3482 (all X all Y all Z0 (s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),Z0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),Z0))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))),s(real,i(s(fun(num,real),i(s(fun(cart(real,n20),fun(num,real)),d_),s(cart(real,n20),X))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))))))) <-> p(s(bool,i(s(fun(fun(cart(real,n20),bool),bool),collinear),s(fun(cart(real,n20),bool),i(s(fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool)),i(s(fun(cart(real,n20),fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool))),insert),s(cart(real,n20),X))),s(fun(cart(real,n20),bool),i(s(fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool)),i(s(fun(cart(real,n20),fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool))),insert),s(cart(real,n20),Y))),s(fun(cart(real,n20),bool),i(s(fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool)),i(s(fun(cart(real,n20),fun(fun(cart(real,n20),bool),fun(cart(real,n20),bool))),insert),s(cart(real,n20),Z0))),s(fun(cart(real,n20),bool),empty)))))))))))) # label(aCOLLINEARu_3u_2D) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3483 (all M all N all Q111786 all U_0 ((all F0 all K0 all V all X s(cart(real,Q111786),i(s(fun(cart(real,Q111786),cart(real,Q111786)),i(s(fun(real,fun(cart(real,Q111786),cart(real,Q111786))),r_),s(real,i(s(fun(num,real),i(s(fun(cart(real,N),fun(num,real)),d_),s(cart(real,N),i(s(fun(cart(real,M),cart(real,N)),F0),s(cart(real,M),X))))),s(num,K0))))),s(cart(real,Q111786),V))) = s(cart(real,Q111786),i(s(fun(cart(real,M),cart(real,Q111786)),i(s(fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786))),i(s(fun(num,fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786)))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786))))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(num,K0))),s(cart(real,Q111786),V))),s(cart(real,M),X)))) -> (all F0 all V all K0 (p(s(bool,i(s(fun(fun(cart(real,M),cart(real,N)),bool),linear),s(fun(cart(real,M),cart(real,N)),F0)))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,K0))),s(num,i(s(fun(fun(N,bool),num),dimindex),s(fun(N,bool),univ)))))) & p(s(bool,i(s(fun(num,bool),i(s(fun(num,fun(num,bool)),l_a_),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))),s(num,K0)))) -> p(s(bool,i(s(fun(fun(cart(real,M),cart(real,Q111786)),bool),linear),s(fun(cart(real,M),cart(real,Q111786)),i(s(fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786))),i(s(fun(num,fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786)))),i(s(fun(fun(cart(real,M),cart(real,N)),fun(num,fun(cart(real,Q111786),fun(cart(real,M),cart(real,Q111786))))),U_0),s(fun(cart(real,M),cart(real,N)),F0))),s(num,K0))),s(cart(real,Q111786),V)))))))))) # label(aLINEARu_VMULu_COMPONENT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3484 (all Q102500 all A5 all X all Y (s(cart(real,Q102500),i(s(fun(cart(real,Q102500),cart(real,Q102500)),i(s(fun(real,fun(cart(real,Q102500),cart(real,Q102500))),r_),s(real,A5))),s(cart(real,Q102500),X))) = s(cart(real,Q102500),i(s(fun(cart(real,Q102500),cart(real,Q102500)),i(s(fun(real,fun(cart(real,Q102500),cart(real,Q102500))),r_),s(real,A5))),s(cart(real,Q102500),Y))) & s(real,A5) != s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) -> s(cart(real,Q102500),X) = s(cart(real,Q102500),Y))) # label(aVECTORu_MULu_LCANCELu_IMP) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3485 (all Q112614 all Q112613 all Q112596 all H0 all X all Y all Z0 (p(s(bool,i(s(fun(fun(cart(real,Q112613),fun(cart(real,Q112596),cart(real,Q112614))),bool),bilinear),s(fun(cart(real,Q112613),fun(cart(real,Q112596),cart(real,Q112614))),H0)))) -> s(cart(real,Q112614),i(s(fun(cart(real,Q112596),cart(real,Q112614)),i(s(fun(cart(real,Q112613),fun(cart(real,Q112596),cart(real,Q112614))),H0),s(cart(real,Q112613),i(s(fun(cart(real,Q112613),cart(real,Q112613)),i(s(fun(cart(real,Q112613),fun(cart(real,Q112613),cart(real,Q112613))),vectoru_sub),s(cart(real,Q112613),X))),s(cart(real,Q112613),Y))))),s(cart(real,Q112596),Z0))) = s(cart(real,Q112614),i(s(fun(cart(real,Q112614),cart(real,Q112614)),i(s(fun(cart(real,Q112614),fun(cart(real,Q112614),cart(real,Q112614))),vectoru_sub),s(cart(real,Q112614),i(s(fun(cart(real,Q112596),cart(real,Q112614)),i(s(fun(cart(real,Q112613),fun(cart(real,Q112596),cart(real,Q112614))),H0),s(cart(real,Q112613),X))),s(cart(real,Q112596),Z0))))),s(cart(real,Q112614),i(s(fun(cart(real,Q112596),cart(real,Q112614)),i(s(fun(cart(real,Q112613),fun(cart(real,Q112596),cart(real,Q112614))),H0),s(cart(real,Q112613),Y))),s(cart(real,Q112596),Z0))))))) # label(aBILINEARu_LSUB) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3486 (all X all Y (p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,X))),s(real,i(s(fun(num,real),i(s(fun(real,fun(num,real)),realu_pow),s(real,Y))),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit0),s(num,i(s(fun(num,num),bit1),s(num,u_0)))))))))))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,Y)))) & p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(real,X)))) -> p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),sqrt),s(real,X))))),s(real,Y)))))) # label(aREALu_LEu_LSQRT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3487 (all X all C0 s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,C0))),s(cart(real,n10),X))))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,C0))),s(real,i(s(fun(cart(real,n10),real),drop),s(cart(real,n10),X)))))) # label(aDROPu_CMUL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3488 (all X s(real,i(s(fun(cart(real,n10),real),vectoru_norm),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X))))) = s(real,i(s(fun(real,real),realu_abs),s(real,X)))) # label(aNORMu_LIFT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3489 (all Q103229 p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(real,real),realu_abs),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_sub),s(real,i(s(fun(cart(real,Q103229),real),vectoru_norm),s(cart(real,Q103229),x))))),s(real,i(s(fun(cart(real,Q103229),real),vectoru_norm),s(cart(real,Q103229),y))))))))),s(real,i(s(fun(cart(real,Q103229),real),vectoru_norm),s(cart(real,Q103229),i(s(fun(cart(real,Q103229),cart(real,Q103229)),i(s(fun(cart(real,Q103229),fun(cart(real,Q103229),cart(real,Q103229))),vectoru_sub),s(cart(real,Q103229),x))),s(cart(real,Q103229),y))))))))) # label(aREALu_ABSu_SUBu_NORM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3490 (all Q139282 all A5 all X p(s(bool,i(s(fun(real,bool),i(s(fun(real,fun(real,bool)),realu_le),s(real,i(s(fun(cart(real,Q139282),real),infnorm),s(cart(real,Q139282),i(s(fun(cart(real,Q139282),cart(real,Q139282)),i(s(fun(real,fun(cart(real,Q139282),cart(real,Q139282))),r_),s(real,A5))),s(cart(real,Q139282),X))))))),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,i(s(fun(real,real),realu_abs),s(real,A5))))),s(real,i(s(fun(cart(real,Q139282),real),infnorm),s(cart(real,Q139282),X))))))))) # label(aINFNORMu_MULu_LEMMA) # label(axiom) # label(non_clause). [assumption]. 16.04/16.04 3491 (all S0 p(s(bool,i(s(fun(fun(cart(real,n10),bool),bool),collinear),s(fun(cart(real,n10),bool),S0))))) # label(aCOLLINEARu_1) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3492 (all P all M all N all F0 all G0 all B0 all C0 all S0 (p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0)))) & p(s(bool,i(s(fun(fun(cart(real,M),fun(cart(real,N),cart(real,P))),bool),bilinear),s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0)))) & p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(fun(cart(real,M),bool),fun(fun(cart(real,M),bool),bool)),subset),s(fun(cart(real,M),bool),S0))),s(fun(cart(real,M),bool),i(s(fun(fun(cart(real,M),bool),fun(cart(real,M),bool)),span),s(fun(cart(real,M),bool),B0)))))) & (all X all Y (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),B0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),C0)))) -> s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0),s(cart(real,M),X))),s(cart(real,N),Y))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0),s(cart(real,M),X))),s(cart(real,N),Y))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(fun(cart(real,N),bool),fun(fun(cart(real,N),bool),bool)),subset),s(fun(cart(real,N),bool),t0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),C0)))))) -> (all X all Y (p(s(bool,i(s(fun(fun(cart(real,M),bool),bool),i(s(fun(cart(real,M),fun(fun(cart(real,M),bool),bool)),in),s(cart(real,M),X))),s(fun(cart(real,M),bool),S0)))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),Y))),s(fun(cart(real,N),bool),t0)))) -> s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),G0),s(cart(real,M),X))),s(cart(real,N),Y))) = s(cart(real,P),i(s(fun(cart(real,N),cart(real,P)),i(s(fun(cart(real,M),fun(cart(real,N),cart(real,P))),F0),s(cart(real,M),X))),s(cart(real,N),Y))))))) # label(aBILINEARu_EQ) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3493 (all Q109587 s(cart(real,Q109587),i(s(fun(num,cart(real,Q109587)),f),s(num,n))) = s(cart(real,Q109587),i(s(fun(fun(num,cart(real,Q109587)),cart(real,Q109587)),i(s(fun(fun(num,bool),fun(fun(num,cart(real,Q109587)),cart(real,Q109587))),vsum),s(fun(num,bool),i(s(fun(num,fun(num,bool)),i(s(fun(num,fun(num,fun(num,bool))),o_o_),s(num,n))),s(num,n))))),s(fun(num,cart(real,Q109587)),f)))) # label(aVSUMu_SINGu_NUMSEG) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3494 (all Q109978 all U_0 ((all K0 all I0 exists V ((p(s(bool,V)) <-> s(num,I0) = s(num,K0)) & s(real,i(s(fun(num,real),i(s(fun(num,fun(num,real)),U_0),s(num,K0))),s(num,I0))) = s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),i(s(fun(bool,fun(real,fun(real,real))),cond),s(bool,V))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))) -> (all K0 s(cart(real,Q109978),i(s(fun(num,cart(real,Q109978)),basis),s(num,K0))) = s(cart(real,Q109978),i(s(fun(fun(num,real),cart(real,Q109978)),lambda),s(fun(num,real),i(s(fun(num,fun(num,real)),U_0),s(num,K0)))))))) # label(abasis) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3495 (all N all A5 all B0 all S0 (-p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),S0)))))) & p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),A5))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),B0))),s(fun(cart(real,N),bool),S0)))))))) -> p(s(bool,i(s(fun(fun(cart(real,N),bool),bool),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),bool)),in),s(cart(real,N),B0))),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),span),s(fun(cart(real,N),bool),i(s(fun(fun(cart(real,N),bool),fun(cart(real,N),bool)),i(s(fun(cart(real,N),fun(fun(cart(real,N),bool),fun(cart(real,N),bool))),insert),s(cart(real,N),A5))),s(fun(cart(real,N),bool),S0)))))))))) # label(aINu_SPANu_INSERT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3496 (all Q146857 all Q146876 all F0 ((all X all XI_ (s(Q146857,i(s(fun(Q146876,Q146857),F0),s(Q146876,X))) = s(Q146857,i(s(fun(Q146876,Q146857),F0),s(Q146876,XI_))) -> s(Q146876,XI_) = s(Q146876,X))) <-> (all X s(Q146876,i(s(fun(Q146857,Q146876),i(s(fun(fun(Q146876,Q146857),fun(Q146857,Q146876)),inverse),s(fun(Q146876,Q146857),F0))),s(Q146857,i(s(fun(Q146876,Q146857),F0),s(Q146876,X))))) = s(Q146876,X)))) # label(aINJECTIVEu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3497 (all Q147196 all P0 all S0 (p(s(bool,i(s(fun(fun(Q147196,bool),bool),i(s(fun(fun(Q147196,Q147196),fun(fun(Q147196,bool),bool)),permutes),s(fun(Q147196,Q147196),P0))),s(fun(Q147196,bool),S0)))) -> (all X all Y (s(Q147196,i(s(fun(Q147196,Q147196),P0),s(Q147196,Y))) = s(Q147196,i(s(fun(Q147196,Q147196),P0),s(Q147196,X))) <-> s(Q147196,X) = s(Q147196,Y))))) # label(aPERMUTESu_INJECTIVE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3498 (all Q146998 all A5 s(fun(Q146998,Q146998),i1) = s(fun(Q146998,Q146998),i(s(fun(prod(Q146998,Q146998),fun(Q146998,Q146998)),swap),s(prod(Q146998,Q146998),i(s(fun(Q146998,prod(Q146998,Q146998)),i(s(fun(Q146998,fun(Q146998,prod(Q146998,Q146998))),c_),s(Q146998,A5))),s(Q146998,A5)))))) # label(aSWAPu_REFL) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3499 (all Q147221 all P0 all S0 (p(s(bool,i(s(fun(fun(Q147221,bool),bool),i(s(fun(fun(Q147221,Q147221),fun(fun(Q147221,bool),bool)),permutes),s(fun(Q147221,Q147221),P0))),s(fun(Q147221,bool),S0)))) -> (all Y exists X s(Q147221,Y) = s(Q147221,i(s(fun(Q147221,Q147221),P0),s(Q147221,X)))))) # label(aPERMUTESu_SURJECTIVE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3500 (all Q147144 all P0 all S0 all X (p(s(bool,i(s(fun(fun(Q147144,bool),bool),i(s(fun(fun(Q147144,Q147144),fun(fun(Q147144,bool),bool)),permutes),s(fun(Q147144,Q147144),P0))),s(fun(Q147144,bool),S0)))) -> s(bool,i(s(fun(fun(Q147144,bool),bool),i(s(fun(Q147144,fun(fun(Q147144,bool),bool)),in),s(Q147144,X))),s(fun(Q147144,bool),S0))) = s(bool,i(s(fun(fun(Q147144,bool),bool),i(s(fun(Q147144,fun(fun(Q147144,bool),bool)),in),s(Q147144,i(s(fun(Q147144,Q147144),P0),s(Q147144,X))))),s(fun(Q147144,bool),S0))))) # label(aPERMUTESu_INu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3501 (all Q146759 all S0 all P0 ((all Y ((all X all XI_ (s(Q146759,Y) = s(Q146759,i(s(fun(Q146759,Q146759),P0),s(Q146759,XI_))) & s(Q146759,i(s(fun(Q146759,Q146759),P0),s(Q146759,X))) = s(Q146759,Y) -> s(Q146759,XI_) = s(Q146759,X))) & (exists X s(Q146759,Y) = s(Q146759,i(s(fun(Q146759,Q146759),P0),s(Q146759,X)))))) & (all X (-p(s(bool,i(s(fun(fun(Q146759,bool),bool),i(s(fun(Q146759,fun(fun(Q146759,bool),bool)),in),s(Q146759,X))),s(fun(Q146759,bool),S0)))) -> s(Q146759,i(s(fun(Q146759,Q146759),P0),s(Q146759,X))) = s(Q146759,X))) <-> p(s(bool,i(s(fun(fun(Q146759,bool),bool),i(s(fun(fun(Q146759,Q146759),fun(fun(Q146759,bool),bool)),permutes),s(fun(Q146759,Q146759),P0))),s(fun(Q146759,bool),S0)))))) # label(apermutes) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3502 (all Q146935 all Q146944 all F0 all G0 (s(fun(Q146935,Q146935),i1) = s(fun(Q146935,Q146935),i(s(fun(fun(Q146935,Q146944),fun(Q146935,Q146935)),i(s(fun(fun(Q146944,Q146935),fun(fun(Q146935,Q146944),fun(Q146935,Q146935))),o),s(fun(Q146944,Q146935),F0))),s(fun(Q146935,Q146944),G0))) & s(fun(Q146944,Q146944),i(s(fun(fun(Q146944,Q146935),fun(Q146944,Q146944)),i(s(fun(fun(Q146935,Q146944),fun(fun(Q146944,Q146935),fun(Q146944,Q146944))),o),s(fun(Q146935,Q146944),G0))),s(fun(Q146944,Q146935),F0))) = s(fun(Q146944,Q146944),i1) -> s(fun(Q146935,Q146944),i(s(fun(fun(Q146944,Q146935),fun(Q146935,Q146944)),inverse),s(fun(Q146944,Q146935),F0))) = s(fun(Q146935,Q146944),G0))) # label(aINVERSEu_UNIQUEu_o) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3503 (all Q147019 all A5 all B0 s(fun(Q147019,Q147019),i(s(fun(prod(Q147019,Q147019),fun(Q147019,Q147019)),swap),s(prod(Q147019,Q147019),i(s(fun(Q147019,prod(Q147019,Q147019)),i(s(fun(Q147019,fun(Q147019,prod(Q147019,Q147019))),c_),s(Q147019,B0))),s(Q147019,A5))))) = s(fun(Q147019,Q147019),i(s(fun(prod(Q147019,Q147019),fun(Q147019,Q147019)),swap),s(prod(Q147019,Q147019),i(s(fun(Q147019,prod(Q147019,Q147019)),i(s(fun(Q147019,fun(Q147019,prod(Q147019,Q147019))),c_),s(Q147019,A5))),s(Q147019,B0)))))) # label(aSWAPu_SYM) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3504 (all Q147052 all A5 all B0 s(fun(Q147052,Q147052),i(s(fun(fun(Q147052,Q147052),fun(Q147052,Q147052)),i(s(fun(fun(Q147052,Q147052),fun(fun(Q147052,Q147052),fun(Q147052,Q147052))),o),s(fun(Q147052,Q147052),i(s(fun(prod(Q147052,Q147052),fun(Q147052,Q147052)),swap),s(prod(Q147052,Q147052),i(s(fun(Q147052,prod(Q147052,Q147052)),i(s(fun(Q147052,fun(Q147052,prod(Q147052,Q147052))),c_),s(Q147052,A5))),s(Q147052,B0))))))),s(fun(Q147052,Q147052),i(s(fun(prod(Q147052,Q147052),fun(Q147052,Q147052)),swap),s(prod(Q147052,Q147052),i(s(fun(Q147052,prod(Q147052,Q147052)),i(s(fun(Q147052,fun(Q147052,prod(Q147052,Q147052))),c_),s(Q147052,A5))),s(Q147052,B0))))))) = s(fun(Q147052,Q147052),i1)) # label(aSWAPu_IDEMPOTENT) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3505 (all Q146804 all Q146801 all F0 ((all Y exists X s(Q146801,Y) = s(Q146801,i(s(fun(Q146804,Q146801),F0),s(Q146804,X)))) <-> (all Y s(Q146801,Y) = s(Q146801,i(s(fun(Q146804,Q146801),F0),s(Q146804,i(s(fun(Q146801,Q146804),i(s(fun(fun(Q146804,Q146801),fun(Q146801,Q146804)),inverse),s(fun(Q146804,Q146801),F0))),s(Q146801,Y)))))))) # label(aSURJECTIVEu_INVERSE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3506 (all Q146959 s(fun(Q146959,Q146959),i1) = s(fun(Q146959,Q146959),i(s(fun(fun(Q146959,Q146959),fun(Q146959,Q146959)),inverse),s(fun(Q146959,Q146959),i1)))) # label(aINVERSEu_I) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3507 (all Q147115 all A5 all B0 all X all Y (s(Q147115,Y) = s(Q147115,i(s(fun(Q147115,Q147115),i(s(fun(prod(Q147115,Q147115),fun(Q147115,Q147115)),swap),s(prod(Q147115,Q147115),i(s(fun(Q147115,prod(Q147115,Q147115)),i(s(fun(Q147115,fun(Q147115,prod(Q147115,Q147115))),c_),s(Q147115,A5))),s(Q147115,B0))))),s(Q147115,X))) <-> s(Q147115,X) = s(Q147115,i(s(fun(Q147115,Q147115),i(s(fun(prod(Q147115,Q147115),fun(Q147115,Q147115)),swap),s(prod(Q147115,Q147115),i(s(fun(Q147115,prod(Q147115,Q147115)),i(s(fun(Q147115,fun(Q147115,prod(Q147115,Q147115))),c_),s(Q147115,A5))),s(Q147115,B0))))),s(Q147115,Y))))) # label(aSWAPu_GALOIS) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3508 (all Q147076 all A5 all B0 s(fun(Q147076,Q147076),i(s(fun(fun(Q147076,Q147076),fun(Q147076,Q147076)),inverse),s(fun(Q147076,Q147076),i(s(fun(prod(Q147076,Q147076),fun(Q147076,Q147076)),swap),s(prod(Q147076,Q147076),i(s(fun(Q147076,prod(Q147076,Q147076)),i(s(fun(Q147076,fun(Q147076,prod(Q147076,Q147076))),c_),s(Q147076,A5))),s(Q147076,B0))))))) = s(fun(Q147076,Q147076),i(s(fun(prod(Q147076,Q147076),fun(Q147076,Q147076)),swap),s(prod(Q147076,Q147076),i(s(fun(Q147076,prod(Q147076,Q147076)),i(s(fun(Q147076,fun(Q147076,prod(Q147076,Q147076))),c_),s(Q147076,A5))),s(Q147076,B0)))))) # label(aINVERSEu_SWAP) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3509 (all Q146894 all Q146913 all F0 ((all X all XI_ (s(Q146894,i(s(fun(Q146913,Q146894),F0),s(Q146913,XI_))) = s(Q146894,i(s(fun(Q146913,Q146894),F0),s(Q146913,X))) -> s(Q146913,X) = s(Q146913,XI_))) <-> s(fun(Q146913,Q146913),i(s(fun(fun(Q146913,Q146894),fun(Q146913,Q146913)),i(s(fun(fun(Q146894,Q146913),fun(fun(Q146913,Q146894),fun(Q146913,Q146913))),o),s(fun(Q146894,Q146913),i(s(fun(fun(Q146913,Q146894),fun(Q146894,Q146913)),inverse),s(fun(Q146913,Q146894),F0))))),s(fun(Q146913,Q146894),F0))) = s(fun(Q146913,Q146913),i1))) # label(aINJECTIVEu_INVERSEu_o) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3510 (all Q146981 all J0 all I0 all K0 exists V ((s(Q146981,J0) = s(Q146981,K0) <-> p(s(bool,V))) & (exists VI_ (s(Q146981,i(s(fun(Q146981,Q146981),i(s(fun(prod(Q146981,Q146981),fun(Q146981,Q146981)),swap),s(prod(Q146981,Q146981),i(s(fun(Q146981,prod(Q146981,Q146981)),i(s(fun(Q146981,fun(Q146981,prod(Q146981,Q146981))),c_),s(Q146981,I0))),s(Q146981,J0))))),s(Q146981,K0))) = s(Q146981,i(s(fun(Q146981,Q146981),i(s(fun(Q146981,fun(Q146981,Q146981)),i(s(fun(bool,fun(Q146981,fun(Q146981,Q146981))),cond),s(bool,VI_))),s(Q146981,J0))),s(Q146981,i(s(fun(Q146981,Q146981),i(s(fun(Q146981,fun(Q146981,Q146981)),i(s(fun(bool,fun(Q146981,fun(Q146981,Q146981))),cond),s(bool,V))),s(Q146981,I0))),s(Q146981,K0))))) & (s(Q146981,I0) = s(Q146981,K0) <-> p(s(bool,VI_))))))) # label(aswap) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3511 (all Q146777 all Q146774 all U_0 ((all F0 all X all X0 (p(s(bool,i(s(fun(Q146777,bool),i(s(fun(Q146774,fun(Q146777,bool)),i(s(fun(fun(Q146777,Q146774),fun(Q146774,fun(Q146777,bool))),U_0),s(fun(Q146777,Q146774),F0))),s(Q146774,X))),s(Q146777,X0)))) <-> s(Q146774,i(s(fun(Q146777,Q146774),F0),s(Q146777,X0))) = s(Q146774,X))) -> (all F0 all X s(Q146777,i(s(fun(fun(Q146777,bool),Q146777),h_),s(fun(Q146777,bool),i(s(fun(Q146774,fun(Q146777,bool)),i(s(fun(fun(Q146777,Q146774),fun(Q146774,fun(Q146777,bool))),U_0),s(fun(Q146777,Q146774),F0))),s(Q146774,X))))) = s(Q146777,i(s(fun(Q146774,Q146777),i(s(fun(fun(Q146777,Q146774),fun(Q146774,Q146777)),inverse),s(fun(Q146777,Q146774),F0))),s(Q146774,X)))))) # label(ainverse) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3512 (all Q146838 all Q146839 all F0 ((all Y exists X s(Q146839,Y) = s(Q146839,i(s(fun(Q146838,Q146839),F0),s(Q146838,X)))) <-> s(fun(Q146839,Q146839),i1) = s(fun(Q146839,Q146839),i(s(fun(fun(Q146839,Q146838),fun(Q146839,Q146839)),i(s(fun(fun(Q146838,Q146839),fun(fun(Q146839,Q146838),fun(Q146839,Q146839))),o),s(fun(Q146838,Q146839),F0))),s(fun(Q146839,Q146838),i(s(fun(fun(Q146838,Q146839),fun(Q146839,Q146838)),inverse),s(fun(Q146838,Q146839),F0))))))) # label(aSURJECTIVEu_INVERSEu_o) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3513 (all Q147159 all P0 all S0 (p(s(bool,i(s(fun(fun(Q147159,bool),bool),i(s(fun(fun(Q147159,Q147159),fun(fun(Q147159,bool),bool)),permutes),s(fun(Q147159,Q147159),P0))),s(fun(Q147159,bool),S0)))) -> s(fun(Q147159,bool),S0) = s(fun(Q147159,bool),i(s(fun(fun(Q147159,bool),fun(Q147159,bool)),i(s(fun(fun(Q147159,Q147159),fun(fun(Q147159,bool),fun(Q147159,bool))),image),s(fun(Q147159,Q147159),P0))),s(fun(Q147159,bool),S0))))) # label(aPERMUTESu_IMAGE) # label(axiom) # label(non_clause). [assumption]. 16.04/16.05 3514 -(all Q147264 all P0 all S0 (p(s(bool,i(s(fun(fun(Q147264,bool),bool),i(s(fun(fun(Q147264,Q147264),fun(fun(Q147264,bool),bool)),permutes),s(fun(Q147264,Q147264),P0))),s(fun(Q147264,bool),S0)))) -> s(fun(Q147264,Q147264),i1) = s(fun(Q147264,Q147264),i(s(fun(fun(Q147264,Q147264),fun(Q147264,Q147264)),i(s(fun(fun(Q147264,Q147264),fun(fun(Q147264,Q147264),fun(Q147264,Q147264))),o),s(fun(Q147264,Q147264),P0))),s(fun(Q147264,Q147264),i(s(fun(fun(Q147264,Q147264),fun(Q147264,Q147264)),inverse),s(fun(Q147264,Q147264),P0))))) & s(fun(Q147264,Q147264),i(s(fun(fun(Q147264,Q147264),fun(Q147264,Q147264)),i(s(fun(fun(Q147264,Q147264),fun(fun(Q147264,Q147264),fun(Q147264,Q147264))),o),s(fun(Q147264,Q147264),i(s(fun(fun(Q147264,Q147264),fun(Q147264,Q147264)),inverse),s(fun(Q147264,Q147264),P0))))),s(fun(Q147264,Q147264),P0))) = s(fun(Q147264,Q147264),i1))) # label(aPERMUTESu_INVERSESu_o) # label(negated_conjecture) # label(non_clause). [assumption]. 47.06/47.06 47.06/47.06 ============================== end of process non-clausal formulas === 47.06/47.06 47.06/47.06 ============================== PROCESS INITIAL CLAUSES =============== 47.06/47.06 47.06/47.06 ============================== PREDICATE ELIMINATION ================= 47.06/47.06 47.06/47.06 ============================== end predicate elimination ============= 47.06/47.06 47.06/47.06 Auto_denials: (non-Horn, no changes). 47.06/47.06 47.06/47.06 Term ordering decisions: 47.06/47.06 Function symbol KB weights: bool=1. real=1. num=1. setspec=1. gabs=1. c_=1. in=1. geq=1. int=1. all0=1. u_0=1. numeral=1. gspec=1. hreal=1. image=1. n10=1. finite=1. realu_ofu_num=1. realu_lt=1. realu_le=1. wf=1. map0=1. t=1. pairwise0=1. nadd=1. sum=1. superadmissible=1. card=1. bit1=1. l_a_=1. s0=1. tailadmissible=1. nsum=1. o=1. f=1. subset=1. t0=1. distance=1. fl=1. l_a_u_c=1. vec=1. linear=1. t_=1. dim=1. univ=1. p_=1. admissible=1. vsum=1. o_o_=1. span=1. p0=1. x=1. insert=1. woset=1. empty=1. dimindex=1. intu_ofu_num=1. cond=1. countable=1. realu_mul=1. realu_abs=1. iterate=1. bit0=1. realu_sub=1. hasu_size=1. r_=1. d_=1. vectoru_add=1. l_=1. unions=1. vectoru_norm=1. realu_pow=1. realu_add=1. intu_le=1. intu_lt=1. q0=1. exp0=1. a_u_c=1. orthogonal=1. subspace=1. hull=1. dot=1. mem=1. union=1. inters=1. suc=1. n=1. n20=1. monoidal=1. a0=1. u_match=1. intu_mul=1. m=1. cons=1. intu_add=1. y=1. l_l_=1. h_=1. m_=1. vectoru_sub=1. realu_neg=1. ind0=1. inter=1. nil=1. mod=1. independent=1. b0=1. matrixu_mul=1. intu_abs=1. mat=1. intu_neg=1. q_=1. matrixu_vectoru_mul=1. sup=1. naddu_eq=1. realu_inv=1. delete=1. u_guardedu_pattern=1. realu_div=1. ordinal=1. intu_sub=1. diff=1. div=1. basis=1. intu_pow=1. inf=1. trealu_eq=1. realu_ofu_int=1. destu_nadd=1. neutral=1. hrealu_add=1. f0=1. poset=1. casewise=1. all2=1. g=1. support=1. collinear=1. h0=1. p1=1. u_seqpattern=1. lambda=1. even=1. drop=1. pairwise=1. dist=1. vectoru_neg=1. i1=1. infinite=1. lift=1. n3=1. naddu_le=1. sqrt=1. inseg=1. pastecart=1. naddu_ofu_num=1. hrealu_le=1. y1=1. odd=1. transp=1. length=1. realu_max=1. realu_min=1. disjoint=1. intu_max=1. intu_min=1. l_u_c=1. x1=1. between=1. dependent=1. itset=1. u_unguardedu_pattern=1. append=1. rank=1. t_u_c=1. bilinear=1. hrealu_ofu_num=1. matrixu_add=1. p_u_c=1. ex0=1. naddu_mul=1. r0=1. infnorm=1. realu_sgn=1. onorm=1. adjoint=1. matrix=1. hrealu_mul=1. mku_real=1. naddu_add=1. finrec=1. g_a_=1. r_r_=1. trealu_ofu_num=1. c=1. l_l_l_=1. char=1. fstcart=1. l0=1. linseg=1. sndcart=1. less=1. midpoint=1. mku_hreal=1. trealu_add=1. trealu_le=1. trealu_mul=1. columns=1. psubset=1. z=1. h1=1. pre=1. t1=1. y2=1. chain=1. fst=1. column=1. cross0=1. el=1. l2=1. naddu_rinv=1. op=1. rows=1. setu_ofu_list=1. vector=1. g_=1. matrixu_sub=1. e0=1. inl=1. inr=1. intu_sgn=1. row=1. destu_real=1. intu_ofu_real=1. matrixu_neg=1. q=1. d=1. filter0=1. inverse=1. permutes=1. a=1. b=1. c0=1. destu_hreal=1. finiteu_index=1. invertible=1. iso0=1. realu_gt=1. zrecspace=1. h2=1. hd=1. inj=1. rem=1. swap=1. t2=1. x2=1. constr=1. integer=1. numpair=1. numu_rep=1. tl=1. e_=1. hrealu_inv=1. injp=1. intu_divides=1. last0=1. reverse=1. snd=1. indu_suc=1. mku_pair=1. naddu_inv=1. numsum=1. surj=1. trealu_inv=1. injn=1. itlist=1. listu_ofu_set=1. minimal=1. realu_ge=1. zbot=1. zip0=1. columnvector=1. fact=1. from=1. indu_0=1. inja=1. map2=1. mku_nadd=1. numu_ofu_int=1. one=1. toset=1. trealu_neg=1. d0=1. div0=1. g_a_u_c=1. injf=1. intu_gcd=1. itlist2=1. measure0=1. zconstr=1. a_a_=1. absu_prod=1. intu_mod=1. isu_nadd=1. matrixu_inv=1. min=1. rowvector=1. u_destu_rec=1. butlast=1. choice0=1. clauses=1. destu_cart=1. intu_ge=1. intu_gt=1. li_0=1. mku_finiteu_sum=1. oneu_one=1. replicate=1. repu_prod=1. u=1. u_mku_rec=1. vectoru_matrixu_mul=1. assoc=1. bij=1. bottom=1. destu_finiteu_image=1. destu_finiteu_sum=1. fcons=1. i0=1. intu_coprime=1. max=1. mku_cart=1. numright=1. oneu_abs=1. oneu_rep=1. realu_mod=1. rest=1. ascii=1. fi_=1. gi_=1. j=1. k=1. mku_num=1. none=1. null=1. numfst=1. numleft=1. numsnd=1. numu_gcd=1. numu_mod=1. onto=1. sing=1. some=1. curry=1. decimal=1. destu_num=1. fnil=1. g_u_c=1. let=1. letu_end=1. numu_coprime=1. numu_divides=1. outl=1. outr=1. passoc=1. u_falsityu_=1. u_function=1. uncurry=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. c17=1. c18=1. c19=1. c20=1. c21=1. c22=1. c23=1. c24=1. c25=1. c26=1. c27=1. c28=1. c29=1. c30=1. c31=1. c32=1. c33=1. c34=1. c35=1. c36=1. c37=1. c38=1. c39=1. c40=1. c41=1. c42=1. c43=1. c44=1. c45=1. c46=1. c47=1. c48=1. c49=1. c50=1. c51=1. c52=1. c53=1. c54=1. c55=1. c56=1. c57=1. c58=1. c59=1. fun=1. s=1. i=1. prod=1. cart=1. finite_sum=1. sum0=1. f17=1. f22=1. f23=1. f24=1. f69=1. f70=1. f71=1. f86=1. f87=1. f88=1. f98=1. f99=1. f100=1. f106=1. f128=1. f131=1. f133=1. f148=1. f149=1. f163=1. f164=1. f165=1. f166=1. f184=1. f194=1. f195=1. f196=1. f197=1. f198=1. f199=1. f200=1. f201=1. f202=1. f203=1. f205=1. f209=1. f211=1. f241=1. f242=1. f243=1. f244=1. f245=1. f246=1. f247=1. f248=1. f249=1. f250=1. f251=1. f252=1. f261=1. f262=1. f269=1. f270=1. f271=1. f272=1. f273=1. f281=1. f282=1. f302=1. f311=1. f345=1. f346=1. f347=1. f358=1. f359=1. f374=1. f375=1. f376=1. f377=1. f378=1. f385=1. f390=1. f391=1. f392=1. f399=1. f400=1. f401=1. f406=1. f425=1. f426=1. f428=1. f432=1. f433=1. f434=1. f435=1. f436=1. f459=1. f468=1. f469=1. f470=1. f472=1. f473=1. f474=1. f475=1. f559=1. f560=1. f561=1. f584=1. f585=1. f586=1. f588=1. f589=1. f590=1. f592=1. f593=1. f594=1. f595=1. f645=1. f646=1. f647=1. f648=1. f694=1. f695=1. f696=1. f755=1. f767=1. f768=1. f769=1. f780=1. f817=1. f818=1. f819=1. f820=1. f821=1. f822=1. f823=1. f824=1. f833=1. f861=1. f862=1. f863=1. f864=1. f865=1. f866=1. f868=1. f874=1. f875=1. f876=1. f877=1. f878=1. f904=1. f905=1. f914=1. f915=1. f916=1. f917=1. f918=1. f919=1. f950=1. f951=1. f952=1. f966=1. f967=1. f970=1. f971=1. f992=1. f993=1. f994=1. f1001=1. f1002=1. f1071=1. f1074=1. f1075=1. f1077=1. f1078=1. f1094=1. f1095=1. f1096=1. f1097=1. f1098=1. f1099=1. f1112=1. f1113=1. f1114=1. f1118=1. f1119=1. f1120=1. f1121=1. f1122=1. f1143=1. f1144=1. f1158=1. f1162=1. f1163=1. f1168=1. f1169=1. f1170=1. f1171=1. f1174=1. f1175=1. f1176=1. f1179=1. f1231=1. f1232=1. f1236=1. f1245=1. f1246=1. f1254=1. f1255=1. f1259=1. f1260=1. f1261=1. f1281=1. f1282=1. f1283=1. f1285=1. f1286=1. f1287=1. f1288=1. f1290=1. f1291=1. f1294=1. f1296=1. f1297=1. f1298=1. f1300=1. f1312=1. f1313=1. f1314=1. f1316=1. f1317=1. f1318=1. f1319=1. f1320=1. f1321=1. f1322=1. f1323=1. f1332=1. f1333=1. f1334=1. f1335=1. f1336=1. f1392=1. f1393=1. f1394=1. f1400=1. f1401=1. f1408=1. f1409=1. f1410=1. f1411=1. f1412=1. f1413=1. f1414=1. f1415=1. f1416=1. f1417=1. f1418=1. f1421=1. f1446=1. f1447=1. f1448=1. f1459=1. f1467=1. f1468=1. f1478=1. f1479=1. f1480=1. f1482=1. f1488=1. f1489=1. f1490=1. f1491=1. f1492=1. f1493=1. f1494=1. f1495=1. f1496=1. f1497=1. f1499=1. f1500=1. f1511=1. f1517=1. f1532=1. f1533=1. f1534=1. f1536=1. f1537=1. f1549=1. f1550=1. f1564=1. f1565=1. f1566=1. f1567=1. f1588=1. f1589=1. f1590=1. f1594=1. f1595=1. f1596=1. f1597=1. f1598=1. f1599=1. f1600=1. f1601=1. f1610=1. f1611=1. f1612=1. f1621=1. f1622=1. f1626=1. f1627=1. f1656=1. f1657=1. f1658=1. f1755=1. f1756=1. f1762=1. f1764=1. f1768=1. f1769=1. f1778=1. f1779=1. f1784=1. f1785=1. f1786=1. f1787=1. f1788=1. f1789=1. f1790=1. f1793=1. f1794=1. f1795=1. f1796=1. f1798=1. f1799=1. f1800=1. f1801=1. f1802=1. f1803=1. f1804=1. f1805=1. f1806=1. f1807=1. f1808=1. f1812=1. f1814=1. f1816=1. f1817=1. f1818=1. f1840=1. f1841=1. f1842=1. f1843=1. f1849=1. f1850=1. f1851=1. f1858=1. f1859=1. f1870=1. f1871=1. f1872=1. f1873=1. f1882=1. f1884=1. f1886=1. f1887=1. f1888=1. f1895=1. f1896=1. f1897=1. f1898=1. f1899=1. f1914=1. f1915=1. f1916=1. f1917=1. f1935=1. f1938=1. f1939=1. f1940=1. f1957=1. f1958=1. f1959=1. f1960=1. f1961=1. f1966=1. f1967=1. f1968=1. f1970=1. f1971=1. f1979=1. f1980=1. f1981=1. f1982=1. f1983=1. f1988=1. f1989=1. f1991=1. f1992=1. f1993=1. f2041=1. f2042=1. f2043=1. f2044=1. f2045=1. f2047=1. f2048=1. f2049=1. f2050=1. f2051=1. f2056=1. f2057=1. f2058=1. f2066=1. f2135=1. f2136=1. f2157=1. f2158=1. f2159=1. f2161=1. f2164=1. f2165=1. f2166=1. f2167=1. f2168=1. f2169=1. f2170=1. f2188=1. f2189=1. f2200=1. f2205=1. f2206=1. f2207=1. f2208=1. f2209=1. f2251=1. f2252=1. f2254=1. f2255=1. f2272=1. f2273=1. f2277=1. f2278=1. f2279=1. f2287=1. f2288=1. f2289=1. f2290=1. f2291=1. f2295=1. f2296=1. f2301=1. f2302=1. f2303=1. f2308=1. f2309=1. f2310=1. f2311=1. f2312=1. f2313=1. f2314=1. f2315=1. f2327=1. f2332=1. f2333=1. f2334=1. f2335=1. f2348=1. f2351=1. f2352=1. f2353=1. f2393=1. f2404=1. f2405=1. f2417=1. f2418=1. f2425=1. f2426=1. f2427=1. f2436=1. f2437=1. f2438=1. f2439=1. f2440=1. f2441=1. f2442=1. f2457=1. f2481=1. f2482=1. f2483=1. f2484=1. f2496=1. f2497=1. f2499=1. f2500=1. f2501=1. f2509=1. f2515=1. f2522=1. f2527=1. f2528=1. f2529=1. f2531=1. f2532=1. f2545=1. f2546=1. f2547=1. f2549=1. f2553=1. f2554=1. f2571=1. f2573=1. f2581=1. f2582=1. f2584=1. f2585=1. f2594=1. f2595=1. f2629=1. f2630=1. f2632=1. f2633=1. f2634=1. f2635=1. f2636=1. f2637=1. f2639=1. f2653=1. f2654=1. f2655=1. f2657=1. f2658=1. f2665=1. f2675=1. f2683=1. f2684=1. f2685=1. f2686=1. f2703=1. f2705=1. f2713=1. f2721=1. f2730=1. f2731=1. f2732=1. f2734=1. f2735=1. f2736=1. f2775=1. f2776=1. f2777=1. f2781=1. f2782=1. f2785=1. f2788=1. f2791=1. f2792=1. f2795=1. f2796=1. f2797=1. f2798=1. f2802=1. f2803=1. f2804=1. f2805=1. f2816=1. f2817=1. f2818=1. f2848=1. f2863=1. f2864=1. f2866=1. f2867=1. f2868=1. f2870=1. f2871=1. f2872=1. f2927=1. f2928=1. f2929=1. f2930=1. f2931=1. f2951=1. f2952=1. f2953=1. f2954=1. f2986=1. f2987=1. f2988=1. f2991=1. f3016=1. f3017=1. f3018=1. f3023=1. f3024=1. f3026=1. f3027=1. f3028=1. f3034=1. f3036=1. f3037=1. f3038=1. f3073=1. f3074=1. f3077=1. f3121=1. f3122=1. f3126=1. f3139=1. f3140=1. f3142=1. f3161=1. f3166=1. f3167=1. f3168=1. f3169=1. f3179=1. f3180=1. f3181=1. f3192=1. f3209=1. f3210=1. f3211=1. f3221=1. f3222=1. f3223=1. f3245=1. f3246=1. f3247=1. f3248=1. f3249=1. f3250=1. f3251=1. f3301=1. f3313=1. f3316=1. f3317=1. f3318=1. f3357=1. f3363=1. f3374=1. f3375=1. f3376=1. f3377=1. f3378=1. f3379=1. f3389=1. f3390=1. f3391=1. f3400=1. f3401=1. f3416=1. f3417=1. f3418=1. f3419=1. f3420=1. f3425=1. f3426=1. f3443=1. f3444=1. f3449=1. f3450=1. f3451=1. f3467=1. f3470=1. f3471=1. f3482=1. f3489=1. f3490=1. f3493=1. f3494=1. f3495=1. f3504=1. f3505=1. f3506=1. f3507=1. f3517=1. f3518=1. f3519=1. f3527=1. f3528=1. f3539=1. f3540=1. f3541=1. f3544=1. f3545=1. f3546=1. f3550=1. f3551=1. f3552=1. f3553=1. f3554=1. f3555=1. f3606=1. f3607=1. f3616=1. f3617=1. f3618=1. f3619=1. f3620=1. f3621=1. f3639=1. f3640=1. f3641=1. f3642=1. f3653=1. f3654=1. f3655=1. f3658=1. f3659=1. f3660=1. f3670=1. f3671=1. f3673=1. f3674=1. f3675=1. f3694=1. f3695=1. f3696=1. f3697=1. f3698=1. f3699=1. f3700=1. f3701=1. f3702=1. f3703=1. f3704=1. f3705=1. f3714=1. f3715=1. f3724=1. f3730=1. f3731=1. f3732=1. f3733=1. f3734=1. f3735=1. f3758=1. f3759=1. f3764=1. f3765=1. f3766=1. f3767=1. f3769=1. f3770=1. f3771=1. f3772=1. f3773=1. f3780=1. f3781=1. f3808=1. f3809=1. f3810=1. f3815=1. f3818=1. f3827=1. f3828=1. f3829=1. f3831=1. f3832=1. f3835=1. f3836=1. f3837=1. f3838=1. f3863=1. f3864=1. f3868=1. f3869=1. f3870=1. f3873=1. f3875=1. f3881=1. f3908=1. f3909=1. f3910=1. f3915=1. f3922=1. f3924=1. f3925=1. f3930=1. f3931=1. f3936=1. f3953=1. f3954=1. f3955=1. f3956=1. f3957=1. f3958=1. f3959=1. f3960=1. f3964=1. f3965=1. f3970=1. f3975=1. f3976=1. f3980=1. f3981=1. f3986=1. f3987=1. f3994=1. f3995=1. f3996=1. f3997=1. f3998=1. f4005=1. f4006=1. f4007=1. f4008=1. f4039=1. f4040=1. f4042=1. f4044=1. f4045=1. f4046=1. f4067=1. f4068=1. f4069=1. f4070=1. f4078=1. f4079=1. f4080=1. f4081=1. f4082=1. f4083=1. f4084=1. f4085=1. f4094=1. f4095=1. f4096=1. f4100=1. f4101=1. f4108=1. f4158=1. f4159=1. f4160=1. f4187=1. f4188=1. f4189=1. f4190=1. f4197=1. f4198=1. f4199=1. f4202=1. f4203=1. f4204=1. f4205=1. f4206=1. f4207=1. f4217=1. f4218=1. f4219=1. f4220=1. f4234=1. f4235=1. f4243=1. f4244=1. f4245=1. f4246=1. f4247=1. f4248=1. f4249=1. f4250=1. f4253=1. f4254=1. f4255=1. f4256=1. f4276=1. f4277=1. f4278=1. f4279=1. f4280=1. f4281=1. f4282=1. f4290=1. f4291=1. f4292=1. f4293=1. f4294=1. f4306=1. f4307=1. f4308=1. f4309=1. f4310=1. f4319=1. f4320=1. f4321=1. f4322=1. f4323=1. f4324=1. f4325=1. f4332=1. f4333=1. f4334=1. f4337=1. f4338=1. f4347=1. f4348=1. f4349=1. f4350=1. f4351=1. f4352=1. f4353=1. f4354=1. f4355=1. f4356=1. f4358=1. f4359=1. f4360=1. f4361=1. f4369=1. f4389=1. f4390=1. f4391=1. f4401=1. f4413=1. f4414=1. list=1. recspace=1. finite_image=1. option=1. f16=1. f67=1. f68=1. f72=1. f97=1. f101=1. f102=1. f103=1. f104=1. f129=1. f130=1. f132=1. f151=1. f152=1. f153=1. f154=1. f155=1. f159=1. f160=1. f161=1. f162=1. f210=1. f215=1. f216=1. f217=1. f226=1. f227=1. f228=1. f233=1. f263=1. f264=1. f265=1. f266=1. f267=1. f275=1. f276=1. f277=1. f283=1. f284=1. f285=1. f295=1. f297=1. f298=1. f299=1. f303=1. f305=1. f306=1. f307=1. f308=1. f309=1. f310=1. f342=1. f343=1. f427=1. f429=1. f449=1. f466=1. f467=1. f476=1. f477=1. f514=1. f553=1. f555=1. f556=1. f581=1. f582=1. f583=1. f603=1. f604=1. f606=1. f607=1. f608=1. f642=1. f643=1. f644=1. f756=1. f770=1. f781=1. f782=1. f783=1. f784=1. f785=1. f786=1. f787=1. f797=1. f803=1. f804=1. f816=1. f829=1. f830=1. f831=1. f849=1. f850=1. f851=1. f853=1. f871=1. f872=1. f873=1. f912=1. f949=1. f1007=1. f1008=1. f1009=1. f1010=1. f1011=1. f1012=1. f1013=1. f1030=1. f1031=1. f1033=1. f1034=1. f1050=1. f1051=1. f1052=1. f1068=1. f1069=1. f1070=1. f1072=1. f1073=1. f1092=1. f1103=1. f1104=1. f1145=1. f1173=1. f1187=1. f1188=1. f1189=1. f1190=1. f1191=1. f1192=1. f1233=1. f1234=1. f1235=1. f1256=1. f1257=1. f1258=1. f1310=1. f1311=1. f1315=1. f1370=1. f1404=1. f1405=1. f1406=1. f1419=1. f1420=1. f1422=1. f1423=1. f1424=1. f1425=1. f1443=1. f1444=1. f1445=1. f1462=1. f1463=1. f1464=1. f1472=1. f1473=1. f1474=1. f1475=1. f1506=1. f1507=1. f1508=1. f1509=1. f1510=1. f1512=1. f1538=1. f1539=1. f1540=1. f1541=1. f1547=1. f1548=1. f1560=1. f1561=1. f1562=1. f1563=1. f1571=1. f1572=1. f1573=1. f1591=1. f1592=1. f1608=1. f1609=1. f1623=1. f1624=1. f1625=1. f1700=1. f1701=1. f1702=1. f1763=1. f1766=1. f1767=1. f1770=1. f1771=1. f1780=1. f1781=1. f1813=1. f1852=1. f1874=1. f1875=1. f1876=1. f1877=1. f1878=1. f1879=1. f1880=1. f1936=1. f1937=1. f1955=1. f1956=1. f2067=1. f2068=1. f2069=1. f2070=1. f2071=1. f2072=1. f2073=1. f2074=1. f2098=1. f2111=1. f2112=1. f2113=1. f2114=1. f2115=1. f2116=1. f2117=1. f2118=1. f2148=1. f2149=1. f2150=1. f2162=1. f2163=1. f2180=1. f2181=1. f2182=1. f2198=1. f2199=1. f2201=1. f2202=1. f2203=1. f2204=1. f2219=1. f2220=1. f2221=1. f2267=1. f2268=1. f2269=1. f2270=1. f2271=1. f2276=1. f2280=1. f2281=1. f2282=1. f2283=1. f2284=1. f2285=1. f2286=1. f2292=1. f2293=1. f2294=1. f2317=1. f2331=1. f2391=1. f2392=1. f2403=1. f2406=1. f2443=1. f2444=1. f2447=1. f2498=1. f2502=1. f2503=1. f2504=1. f2505=1. f2506=1. f2507=1. f2508=1. f2510=1. f2511=1. f2512=1. f2565=1. f2572=1. f2588=1. f2589=1. f2596=1. f2638=1. f2640=1. f2668=1. f2669=1. f2670=1. f2687=1. f2688=1. f2700=1. f2701=1. f2702=1. f2708=1. f2709=1. f2710=1. f2711=1. f2712=1. f2714=1. f2715=1. f2716=1. f2726=1. f2727=1. f2728=1. f2779=1. f2780=1. f2783=1. f2784=1. f2786=1. f2787=1. f2789=1. f2790=1. f2799=1. f2800=1. f2808=1. f2809=1. f2810=1. f2840=1. f2841=1. f2842=1. f2860=1. f2861=1. f2862=1. f2955=1. f2956=1. f2961=1. f2970=1. f2971=1. f2997=1. f2998=1. f2999=1. f3000=1. f3014=1. f3015=1. f3020=1. f3021=1. f3022=1. f3042=1. f3043=1. f3044=1. f3045=1. f3125=1. f3156=1. f3157=1. f3160=1. f3162=1. f3163=1. f3164=1. f3183=1. f3184=1. f3214=1. f3215=1. f3216=1. f3217=1. f3319=1. f3320=1. f3321=1. f3323=1. f3358=1. f3359=1. f3364=1. f3373=1. f3380=1. f3381=1. f3385=1. f3386=1. f3447=1. f3448=1. f3547=1. f3548=1. f3636=1. f3637=1. f3638=1. f3755=1. f3756=1. f3761=1. f3762=1. f3763=1. f3819=1. f3882=1. f3883=1. f4047=1. f4048=1. f4097=1. f4098=1. f4099=1. f4259=1. f4260=1. f4261=1. f4262=1. f4263=1. f4268=1. f4269=1. f4343=1. f4344=1. f4345=1. f4346=1. f4367=1. f4368=1. f4372=1. f4377=1. f4378=1. f4379=1. f4380=1. f8=1. f9=1. f10=1. f12=1. f13=1. f14=1. f15=1. f18=1. f19=1. f20=1. f21=1. f76=1. f77=1. f78=1. f79=1. f90=1. f91=1. f92=1. f93=1. f156=1. f157=1. f158=1. f167=1. f168=1. f169=1. f170=1. f171=1. f172=1. f173=1. f185=1. f186=1. f187=1. f191=1. f204=1. f206=1. f207=1. f208=1. f218=1. f219=1. f221=1. f231=1. f232=1. f237=1. f238=1. f239=1. f240=1. f253=1. f286=1. f287=1. f292=1. f293=1. f304=1. f312=1. f313=1. f314=1. f318=1. f327=1. f328=1. f329=1. f333=1. f334=1. f335=1. f336=1. f337=1. f344=1. f348=1. f349=1. f350=1. f379=1. f380=1. f381=1. f382=1. f383=1. f384=1. f386=1. f387=1. f388=1. f389=1. f393=1. f402=1. f403=1. f407=1. f408=1. f409=1. f410=1. f411=1. f413=1. f414=1. f420=1. f421=1. f422=1. f423=1. f424=1. f442=1. f443=1. f444=1. f445=1. f460=1. f461=1. f462=1. f463=1. f464=1. f465=1. f478=1. f479=1. f515=1. f516=1. f517=1. f519=1. f520=1. f547=1. f548=1. f549=1. f557=1. f558=1. f562=1. f563=1. f564=1. f568=1. f569=1. f570=1. f571=1. f572=1. f573=1. f574=1. f577=1. f578=1. f579=1. f580=1. f587=1. f596=1. f597=1. f598=1. f599=1. f600=1. f601=1. f649=1. f670=1. f671=1. f697=1. f698=1. f699=1. f700=1. f701=1. f753=1. f754=1. f757=1. f758=1. f759=1. f760=1. f761=1. f762=1. f771=1. f772=1. f773=1. f774=1. f775=1. f776=1. f777=1. f788=1. f789=1. f790=1. f791=1. f792=1. f798=1. f801=1. f802=1. f805=1. f806=1. f832=1. f835=1. f836=1. f837=1. f838=1. f840=1. f841=1. f842=1. f843=1. f844=1. f854=1. f855=1. f858=1. f859=1. f860=1. f881=1. f882=1. f883=1. f884=1. f885=1. f886=1. f889=1. f890=1. f891=1. f892=1. f893=1. f894=1. f900=1. f901=1. f902=1. f903=1. f906=1. f907=1. f908=1. f909=1. f913=1. f953=1. f954=1. f959=1. f960=1. f961=1. f964=1. f965=1. f972=1. f973=1. f974=1. f975=1. f976=1. f977=1. f978=1. f979=1. f980=1. f991=1. f995=1. f996=1. f1018=1. f1019=1. f1020=1. f1021=1. f1022=1. f1023=1. f1032=1. f1053=1. f1054=1. f1055=1. f1056=1. f1076=1. f1079=1. f1080=1. f1081=1. f1082=1. f1083=1. f1084=1. f1101=1. f1102=1. f1105=1. f1106=1. f1107=1. f1108=1. f1109=1. f1110=1. f1123=1. f1124=1. f1125=1. f1132=1. f1133=1. f1134=1. f1135=1. f1139=1. f1140=1. f1141=1. f1142=1. f1146=1. f1147=1. f1154=1. f1155=1. f1156=1. f1172=1. f1177=1. f1178=1. f1201=1. f1202=1. f1203=1. f1204=1. f1205=1. f1206=1. f1237=1. f1238=1. f1239=1. f1240=1. f1247=1. f1248=1. f1249=1. f1250=1. f1251=1. f1252=1. f1253=1. f1262=1. f1263=1. f1264=1. f1265=1. f1266=1. f1267=1. f1268=1. f1269=1. f1289=1. f1292=1. f1299=1. f1301=1. f1305=1. f1306=1. f1307=1. f1324=1. f1325=1. f1326=1. f1327=1. f1328=1. f1329=1. f1337=1. f1338=1. f1339=1. f1340=1. f1341=1. f1342=1. f1343=1. f1344=1. f1345=1. f1346=1. f1347=1. f1348=1. f1349=1. f1350=1. f1361=1. f1371=1. f1373=1. f1374=1. f1375=1. f1378=1. f1379=1. f1395=1. f1396=1. f1397=1. f1398=1. f1399=1. f1402=1. f1403=1. f1426=1. f1427=1. f1428=1. f1429=1. f1430=1. f1437=1. f1438=1. f1439=1. f1440=1. f1441=1. f1451=1. f1452=1. f1453=1. f1454=1. f1455=1. f1456=1. f1457=1. f1458=1. f1460=1. f1461=1. f1476=1. f1477=1. f1483=1. f1484=1. f1501=1. f1502=1. f1503=1. f1504=1. f1513=1. f1514=1. f1518=1. f1519=1. f1520=1. f1521=1. f1522=1. f1524=1. f1525=1. f1535=1. f1542=1. f1543=1. f1544=1. f1545=1. f1546=1. f1551=1. f1552=1. f1553=1. f1554=1. f1555=1. f1568=1. f1569=1. f1570=1. f1602=1. f1603=1. f1604=1. f1605=1. f1628=1. f1629=1. f1630=1. f1631=1. f1632=1. f1633=1. f1660=1. f1722=1. f1723=1. f1724=1. f1754=1. f1757=1. f1758=1. f1759=1. f1760=1. f1761=1. f1765=1. f1776=1. f1777=1. f1782=1. f1791=1. f1792=1. f1797=1. f1829=1. f1830=1. f1831=1. f1832=1. f1833=1. f1844=1. f1845=1. f1846=1. f1847=1. f1848=1. f1860=1. f1861=1. f1862=1. f1885=1. f1906=1. f1907=1. f1908=1. f1909=1. f1910=1. f1911=1. f1912=1. f1913=1. f1918=1. f1919=1. f1920=1. f1925=1. f1926=1. f1927=1. f1928=1. f1929=1. f1930=1. f1942=1. f1943=1. f1944=1. f1945=1. f1946=1. f1947=1. f1948=1. f1949=1. f1950=1. f1972=1. f1973=1. f1974=1. f1975=1. f1976=1. f1977=1. f1978=1. f1986=1. f1990=1. f2029=1. f2030=1. f2031=1. f2046=1. f2052=1. f2053=1. f2079=1. f2094=1. f2100=1. f2101=1. f2102=1. f2103=1. f2119=1. f2120=1. f2121=1. f2122=1. f2123=1. f2124=1. f2151=1. f2152=1. f2153=1. f2154=1. f2160=1. f2171=1. f2172=1. f2173=1. f2174=1. f2175=1. f2183=1. f2184=1. f2186=1. f2187=1. f2211=1. f2212=1. f2213=1. f2214=1. f2215=1. f2216=1. f2249=1. f2250=1. f2253=1. f2297=1. f2298=1. f2299=1. f2300=1. f2304=1. f2305=1. f2306=1. f2307=1. f2318=1. f2319=1. f2320=1. f2321=1. f2328=1. f2329=1. f2330=1. f2336=1. f2337=1. f2338=1. f2349=1. f2350=1. f2354=1. f2355=1. f2356=1. f2357=1. f2358=1. f2394=1. f2395=1. f2396=1. f2397=1. f2402=1. f2410=1. f2411=1. f2412=1. f2413=1. f2419=1. f2420=1. f2422=1. f2423=1. f2424=1. f2428=1. f2429=1. f2430=1. f2431=1. f2432=1. f2448=1. f2449=1. f2450=1. f2451=1. f2458=1. f2459=1. f2460=1. f2461=1. f2462=1. f2463=1. f2474=1. f2475=1. f2476=1. f2477=1. f2487=1. f2488=1. f2489=1. f2513=1. f2516=1. f2517=1. f2518=1. f2519=1. f2540=1. f2541=1. f2542=1. f2543=1. f2544=1. f2550=1. f2551=1. f2552=1. f2555=1. f2556=1. f2557=1. f2558=1. f2567=1. f2576=1. f2577=1. f2578=1. f2580=1. f2586=1. f2587=1. f2642=1. f2643=1. f2644=1. f2645=1. f2650=1. f2651=1. f2652=1. f2659=1. f2660=1. f2661=1. f2662=1. f2663=1. f2664=1. f2676=1. f2677=1. f2678=1. f2679=1. f2680=1. f2681=1. f2689=1. f2690=1. f2691=1. f2692=1. f2697=1. f2698=1. f2699=1. f2704=1. f2706=1. f2707=1. f2722=1. f2723=1. f2729=1. f2737=1. f2738=1. f2739=1. f2740=1. f2741=1. f2778=1. f2793=1. f2794=1. f2806=1. f2807=1. f2814=1. f2825=1. f2854=1. f2855=1. f2856=1. f2857=1. f2869=1. f2962=1. f2967=1. f2972=1. f2973=1. f2974=1. f2975=1. f2979=1. f2980=1. f2981=1. f2982=1. f2983=1. f2984=1. f2992=1. f2993=1. f2994=1. f3005=1. f3006=1. f3007=1. f3008=1. f3009=1. f3010=1. f3011=1. f3012=1. f3013=1. f3025=1. f3029=1. f3030=1. f3031=1. f3032=1. f3033=1. f3035=1. f3061=1. f3062=1. f3063=1. f3064=1. f3065=1. f3068=1. f3069=1. f3070=1. f3071=1. f3075=1. f3076=1. f3127=1. f3128=1. f3129=1. f3130=1. f3131=1. f3132=1. f3133=1. f3149=1. f3150=1. f3151=1. f3158=1. f3165=1. f3182=1. f3191=1. f3194=1. f3195=1. f3196=1. f3197=1. f3202=1. f3203=1. f3204=1. f3205=1. f3212=1. f3213=1. f3218=1. f3219=1. f3220=1. f3252=1. f3254=1. f3255=1. f3299=1. f3300=1. f3302=1. f3303=1. f3304=1. f3305=1. f3322=1. f3334=1. f3335=1. f3336=1. f3337=1. f3338=1. f3339=1. f3347=1. f3351=1. f3352=1. f3353=1. f3354=1. f3355=1. f3356=1. f3362=1. f3365=1. f3366=1. f3367=1. f3368=1. f3369=1. f3370=1. f3382=1. f3383=1. f3384=1. f3387=1. f3388=1. f3392=1. f3393=1. f3394=1. f3395=1. f3396=1. f3397=1. f3398=1. f3399=1. f3402=1. f3404=1. f3405=1. f3406=1. f3407=1. f3408=1. f3409=1. f3410=1. f3412=1. f3414=1. f3415=1. f3422=1. f3423=1. f3424=1. f3427=1. f3428=1. f3429=1. f3430=1. f3431=1. f3432=1. f3445=1. f3446=1. f3452=1. f3453=1. f3454=1. f3455=1. f3456=1. f3457=1. f3469=1. f3483=1. f3484=1. f3485=1. f3486=1. f3487=1. f3491=1. f3492=1. f3496=1. f3497=1. f3498=1. f3501=1. f3502=1. f3503=1. f3510=1. f3511=1. f3512=1. f3513=1. f3520=1. f3521=1. f3522=1. f3525=1. f3529=1. f3530=1. f3531=1. f3532=1. f3533=1. f3534=1. f3542=1. f3543=1. f3549=1. f3558=1. f3559=1. f3560=1. f3561=1. f3562=1. f3605=1. f3608=1. f3609=1. f3610=1. f3622=1. f3623=1. f3624=1. f3628=1. f3629=1. f3630=1. f3643=1. f3644=1. f3645=1. f3646=1. f3661=1. f3662=1. f3663=1. f3664=1. f3665=1. f3666=1. f3667=1. f3668=1. f3669=1. f3672=1. f3676=1. f3679=1. f3680=1. f3681=1. f3684=1. f3685=1. f3686=1. f3687=1. f3688=1. f3689=1. f3693=1. f3707=1. f3708=1. f3709=1. f3710=1. f3716=1. f3717=1. f3718=1. f3719=1. f3720=1. f3721=1. f3725=1. f3726=1. f3727=1. f3728=1. f3729=1. f3760=1. f3768=1. f3774=1. f3775=1. f3783=1. f3784=1. f3785=1. f3786=1. f3813=1. f3814=1. f3816=1. f3825=1. f3826=1. f3834=1. f3839=1. f3844=1. f3845=1. f3846=1. f3847=1. f3851=1. f3852=1. f3853=1. f3854=1. f3855=1. f3856=1. f3857=1. f3858=1. f3859=1. f3865=1. f3866=1. f3867=1. f3871=1. f3872=1. f3874=1. f3876=1. f3877=1. f3878=1. f3900=1. f3901=1. f3903=1. f3904=1. f3905=1. f3906=1. f3907=1. f3912=1. f3913=1. f3914=1. f3920=1. f3921=1. f3923=1. f3933=1. f3934=1. f3935=1. f3937=1. f3938=1. f3939=1. f3940=1. f3941=1. f3942=1. f3943=1. f3944=1. f3945=1. f3946=1. f3947=1. f3948=1. f3949=1. f3950=1. f3961=1. f3962=1. f3963=1. f3966=1. f3967=1. f3968=1. f3969=1. f3977=1. f3978=1. f3979=1. f3982=1. f3985=1. f3988=1. f3989=1. f3990=1. f3999=1. f4000=1. f4001=1. f4002=1. f4003=1. f4004=1. f4009=1. f4010=1. f4011=1. f4012=1. f4013=1. f4014=1. f4015=1. f4028=1. f4029=1. f4030=1. f4031=1. f4032=1. f4041=1. f4049=1. f4050=1. f4061=1. f4062=1. f4063=1. f4071=1. f4072=1. f4073=1. f4086=1. f4087=1. f4088=1. f4089=1. f4090=1. f4091=1. f4092=1. f4093=1. f4102=1. f4103=1. f4104=1. f4105=1. f4106=1. f4107=1. f4111=1. f4112=1. f4113=1. f4115=1. f4116=1. f4117=1. f4118=1. f4119=1. f4120=1. f4121=1. f4122=1. f4124=1. f4125=1. f4126=1. f4127=1. f4136=1. f4137=1. f4138=1. f4139=1. f4161=1. f4162=1. f4163=1. f4173=1. f4174=1. f4175=1. f4176=1. f4180=1. f4181=1. f4182=1. f4183=1. f4191=1. f4192=1. f4193=1. f4194=1. f4200=1. f4201=1. f4209=1. f4210=1. f4215=1. f4216=1. f4221=1. f4232=1. f4233=1. f4236=1. f4237=1. f4238=1. f4239=1. f4240=1. f4242=1. f4251=1. f4252=1. f4257=1. f4258=1. f4264=1. f4265=1. f4266=1. f4267=1. f4270=1. f4271=1. f4285=1. f4286=1. f4288=1. f4289=1. f4296=1. f4297=1. f4298=1. f4300=1. f4301=1. f4302=1. f4303=1. f4305=1. f4311=1. f4312=1. f4317=1. f4318=1. f4330=1. f4331=1. f4335=1. f4336=1. f4357=1. f4363=1. f4364=1. f4365=1. f4366=1. f4370=1. f4373=1. f4374=1. f4375=1. f4376=1. f4381=1. f4382=1. f4383=1. f4384=1. f4399=1. f4400=1. f4403=1. f4404=1. f4405=1. f4406=1. f4415=1. f4416=1. f4417=1. f4419=1. f4420=1. f4421=1. f4422=1. f4424=1. f4426=1. f4427=1. f4428=1. f4431=1. f4432=1. f4433=1. f4434=1. f1=1. f2=1. f5=1. f6=1. f7=1. f73=1. f74=1. f75=1. f80=1. f81=1. f82=1. f83=1. f105=1. f134=1. f135=1. f136=1. f137=1. f138=1. f142=1. f143=1. f144=1. f145=1. f146=1. f147=1. f174=1. f175=1. f176=1. f177=1. f178=1. f179=1. f188=1. f189=1. f190=1. f192=1. f193=1. f213=1. f220=1. f222=1. f223=1. f224=1. f225=1. f254=1. f255=1. f256=1. f257=1. f258=1. f259=1. f260=1. f268=1. f274=1. f278=1. f279=1. f280=1. f291=1. f294=1. f296=1. f315=1. f316=1. f317=1. f319=1. f320=1. f321=1. f322=1. f323=1. f330=1. f331=1. f332=1. f341=1. f351=1. f352=1. f353=1. f354=1. f372=1. f373=1. f404=1. f405=1. f415=1. f416=1. f417=1. f418=1. f419=1. f430=1. f431=1. f437=1. f438=1. f439=1. f440=1. f441=1. f446=1. f447=1. f448=1. f450=1. f451=1. f452=1. f453=1. f454=1. f455=1. f456=1. f521=1. f522=1. f523=1. f524=1. f525=1. f528=1. f529=1. f545=1. f546=1. f550=1. f551=1. f552=1. f554=1. f565=1. f566=1. f567=1. f591=1. f605=1. f672=1. f673=1. f674=1. f675=1. f676=1. f677=1. f702=1. f703=1. f704=1. f705=1. f706=1. f707=1. f763=1. f764=1. f765=1. f766=1. f793=1. f794=1. f795=1. f796=1. f799=1. f800=1. f807=1. f808=1. f809=1. f810=1. f811=1. f834=1. f846=1. f847=1. f848=1. f852=1. f856=1. f857=1. f867=1. f869=1. f870=1. f879=1. f880=1. f887=1. f888=1. f896=1. f897=1. f898=1. f899=1. f955=1. f956=1. f957=1. f958=1. f962=1. f963=1. f983=1. f984=1. f985=1. f986=1. f987=1. f997=1. f998=1. f999=1. f1000=1. f1003=1. f1004=1. f1005=1. f1006=1. f1025=1. f1035=1. f1036=1. f1037=1. f1038=1. f1039=1. f1040=1. f1041=1. f1043=1. f1044=1. f1045=1. f1057=1. f1058=1. f1059=1. f1060=1. f1061=1. f1062=1. f1093=1. f1100=1. f1115=1. f1116=1. f1117=1. f1126=1. f1127=1. f1128=1. f1136=1. f1137=1. f1138=1. f1148=1. f1149=1. f1150=1. f1151=1. f1157=1. f1159=1. f1160=1. f1164=1. f1165=1. f1166=1. f1167=1. f1180=1. f1181=1. f1182=1. f1208=1. f1209=1. f1210=1. f1211=1. f1215=1. f1218=1. f1219=1. f1220=1. f1221=1. f1222=1. f1226=1. f1227=1. f1228=1. f1229=1. f1230=1. f1241=1. f1242=1. f1243=1. f1244=1. f1270=1. f1271=1. f1272=1. f1273=1. f1274=1. f1275=1. f1276=1. f1284=1. f1295=1. f1302=1. f1303=1. f1304=1. f1351=1. f1352=1. f1353=1. f1362=1. f1363=1. f1372=1. f1376=1. f1377=1. f1380=1. f1381=1. f1382=1. f1383=1. f1384=1. f1385=1. f1386=1. f1387=1. f1388=1. f1389=1. f1432=1. f1433=1. f1434=1. f1435=1. f1442=1. f1450=1. f1498=1. f1505=1. f1515=1. f1526=1. f1527=1. f1528=1. f1529=1. f1530=1. f1556=1. f1557=1. f1558=1. f1559=1. f1574=1. f1575=1. f1576=1. f1577=1. f1578=1. f1579=1. f1580=1. f1606=1. f1607=1. f1613=1. f1614=1. f1615=1. f1616=1. f1617=1. f1618=1. f1619=1. f1634=1. f1635=1. f1636=1. f1637=1. f1638=1. f1639=1. f1650=1. f1651=1. f1652=1. f1653=1. f1661=1. f1662=1. f1665=1. f1666=1. f1703=1. f1721=1. f1725=1. f1726=1. f1727=1. f1728=1. f1729=1. f1730=1. f1748=1. f1749=1. f1750=1. f1751=1. f1774=1. f1775=1. f1783=1. f1809=1. f1810=1. f1811=1. f1815=1. f1835=1. f1836=1. f1837=1. f1838=1. f1853=1. f1854=1. f1857=1. f1863=1. f1864=1. f1865=1. f1866=1. f1881=1. f1889=1. f1890=1. f1891=1. f1892=1. f1900=1. f1921=1. f1922=1. f1923=1. f1924=1. f1931=1. f1932=1. f1933=1. f1934=1. f1951=1. f1952=1. f1953=1. f1954=1. f1962=1. f1963=1. f1964=1. f1965=1. f1969=1. f1984=1. f1985=1. f1987=1. f1995=1. f1996=1. f1997=1. f1998=1. f1999=1. f2000=1. f2014=1. f2015=1. f2054=1. f2055=1. f2059=1. f2060=1. f2061=1. f2077=1. f2078=1. f2080=1. f2081=1. f2082=1. f2083=1. f2084=1. f2085=1. f2086=1. f2099=1. f2104=1. f2105=1. f2106=1. f2125=1. f2126=1. f2127=1. f2141=1. f2155=1. f2156=1. f2176=1. f2177=1. f2178=1. f2179=1. f2190=1. f2191=1. f2192=1. f2210=1. f2218=1. f2316=1. f2323=1. f2324=1. f2325=1. f2326=1. f2360=1. f2361=1. f2362=1. f2363=1. f2364=1. f2366=1. f2370=1. f2371=1. f2372=1. f2373=1. f2374=1. f2399=1. f2400=1. f2401=1. f2407=1. f2414=1. f2415=1. f2416=1. f2445=1. f2446=1. f2452=1. f2453=1. f2454=1. f2455=1. f2456=1. f2464=1. f2465=1. f2466=1. f2467=1. f2468=1. f2469=1. f2485=1. f2486=1. f2490=1. f2491=1. f2492=1. f2514=1. f2530=1. f2533=1. f2548=1. f2559=1. f2560=1. f2561=1. f2562=1. f2563=1. f2566=1. f2574=1. f2575=1. f2583=1. f2631=1. f2646=1. f2647=1. f2648=1. f2649=1. f2656=1. f2671=1. f2672=1. f2695=1. f2696=1. f2717=1. f2718=1. f2719=1. f2724=1. f2725=1. f2733=1. f2801=1. f2811=1. f2812=1. f2815=1. f2823=1. f2843=1. f2844=1. f2845=1. f2846=1. f2853=1. f2865=1. f2922=1. f2924=1. f2925=1. f2926=1. f2932=1. f2950=1. f2957=1. f2958=1. f2959=1. f2968=1. f2995=1. f2996=1. f3039=1. f3040=1. f3041=1. f3046=1. f3047=1. f3048=1. f3049=1. f3072=1. f3078=1. f3079=1. f3082=1. f3083=1. f3136=1. f3137=1. f3138=1. f3141=1. f3159=1. f3170=1. f3171=1. f3178=1. f3193=1. f3198=1. f3199=1. f3200=1. f3201=1. f3206=1. f3207=1. f3208=1. f3253=1. f3256=1. f3306=1. f3307=1. f3308=1. f3309=1. f3310=1. f3311=1. f3312=1. f3314=1. f3315=1. f3340=1. f3341=1. f3342=1. f3343=1. f3344=1. f3345=1. f3403=1. f3411=1. f3413=1. f3421=1. f3433=1. f3434=1. f3435=1. f3436=1. f3458=1. f3459=1. f3460=1. f3472=1. f3473=1. f3474=1. f3475=1. f3476=1. f3477=1. f3499=1. f3500=1. f3514=1. f3515=1. f3516=1. f3523=1. f3524=1. f3535=1. f3536=1. f3556=1. f3557=1. f3563=1. f3564=1. f3565=1. f3611=1. f3612=1. f3613=1. f3614=1. f3615=1. f3625=1. f3626=1. f3627=1. f3631=1. f3632=1. f3633=1. f3634=1. f3635=1. f3677=1. f3678=1. f3682=1. f3683=1. f3690=1. f3691=1. f3692=1. f3706=1. f3711=1. f3712=1. f3713=1. f3736=1. f3737=1. f3738=1. f3739=1. f3740=1. f3741=1. f3752=1. f3753=1. f3757=1. f3776=1. f3777=1. f3778=1. f3779=1. f3782=1. f3787=1. f3788=1. f3789=1. f3799=1. f3800=1. f3801=1. f3807=1. f3811=1. f3812=1. f3824=1. f3830=1. f3843=1. f3848=1. f3849=1. f3850=1. f3860=1. f3861=1. f3862=1. f3879=1. f3880=1. f3884=1. f3885=1. f3886=1. f3887=1. f3888=1. f3889=1. f3890=1. f3911=1. f3916=1. f3917=1. f3918=1. f3919=1. f3926=1. f3929=1. f3932=1. f3951=1. f3952=1. f3971=1. f3972=1. f3973=1. f3983=1. f3984=1. f3991=1. f3992=1. f3993=1. f4016=1. f4017=1. f4018=1. f4019=1. f4024=1. f4025=1. f4026=1. f4027=1. f4033=1. f4034=1. f4035=1. f4036=1. f4043=1. f4051=1. f4052=1. f4053=1. f4054=1. f4055=1. f4060=1. f4064=1. f4065=1. f4066=1. f4109=1. f4110=1. f4114=1. f4128=1. f4129=1. f4130=1. f4140=1. f4141=1. f4142=1. f4144=1. f4145=1. f4146=1. f4147=1. f4177=1. f4178=1. f4179=1. f4186=1. f4195=1. f4196=1. f4208=1. f4222=1. f4223=1. f4224=1. f4225=1. f4226=1. f4227=1. f4274=1. f4275=1. f4283=1. f4295=1. f4304=1. f4326=1. f4327=1. f4328=1. f4329=1. f4340=1. f4341=1. f4342=1. f4362=1. f4371=1. f4385=1. f4386=1. f4387=1. f4392=1. f4393=1. f4394=1. f4395=1. f4402=1. f4407=1. f4408=1. f4409=1. f4410=1. f4418=1. f4423=1. f4425=1. f4429=1. f4430=1. f4435=1. f3=1. f4=1. f11=1. f89=1. f94=1. f95=1. f96=1. f107=1. f108=1. f109=1. f112=1. f113=1. f139=1. f140=1. f141=1. f180=1. f181=1. f182=1. f212=1. f214=1. f229=1. f230=1. f234=1. f235=1. f300=1. f301=1. f324=1. f325=1. f326=1. f355=1. f357=1. f394=1. f395=1. f396=1. f397=1. f398=1. f412=1. f457=1. f458=1. f471=1. f480=1. f481=1. f482=1. f483=1. f484=1. f485=1. f486=1. f518=1. f530=1. f531=1. f575=1. f576=1. f678=1. f679=1. f680=1. f708=1. f709=1. f710=1. f711=1. f778=1. f779=1. f812=1. f813=1. f814=1. f815=1. f845=1. f895=1. f910=1. f911=1. f968=1. f969=1. f981=1. f982=1. f1024=1. f1026=1. f1029=1. f1046=1. f1047=1. f1064=1. f1065=1. f1066=1. f1067=1. f1129=1. f1130=1. f1131=1. f1152=1. f1153=1. f1161=1. f1183=1. f1184=1. f1193=1. f1194=1. f1195=1. f1196=1. f1197=1. f1198=1. f1199=1. f1207=1. f1216=1. f1217=1. f1277=1. f1278=1. f1293=1. f1308=1. f1309=1. f1354=1. f1355=1. f1356=1. f1357=1. f1358=1. f1359=1. f1364=1. f1365=1. f1390=1. f1391=1. f1407=1. f1431=1. f1436=1. f1470=1. f1471=1. f1481=1. f1485=1. f1516=1. f1523=1. f1583=1. f1584=1. f1585=1. f1586=1. f1587=1. f1593=1. f1640=1. f1641=1. f1642=1. f1654=1. f1655=1. f1667=1. f1668=1. f1669=1. f1670=1. f1675=1. f1676=1. f1704=1. f1705=1. f1706=1. f1707=1. f1708=1. f1709=1. f1710=1. f1711=1. f1731=1. f1732=1. f1733=1. f1734=1. f1752=1. f1753=1. f1772=1. f1773=1. f1819=1. f1820=1. f1821=1. f1822=1. f1823=1. f1824=1. f1834=1. f1839=1. f1883=1. f1893=1. f1894=1. f1901=1. f1902=1. f1903=1. f1904=1. f1905=1. f1941=1. f1994=1. f2016=1. f2017=1. f2018=1. f2032=1. f2033=1. f2034=1. f2035=1. f2036=1. f2062=1. f2063=1. f2089=1. f2090=1. f2091=1. f2092=1. f2093=1. f2095=1. f2096=1. f2097=1. f2107=1. f2109=1. f2110=1. f2128=1. f2129=1. f2130=1. f2131=1. f2132=1. f2133=1. f2144=1. f2185=1. f2193=1. f2194=1. f2217=1. f2222=1. f2223=1. f2224=1. f2225=1. f2256=1. f2257=1. f2258=1. f2259=1. f2260=1. f2261=1. f2262=1. f2263=1. f2264=1. f2265=1. f2266=1. f2322=1. f2359=1. f2375=1. f2376=1. f2377=1. f2378=1. f2398=1. f2421=1. f2433=1. f2434=1. f2435=1. f2470=1. f2471=1. f2472=1. f2493=1. f2494=1. f2495=1. f2520=1. f2521=1. f2534=1. f2568=1. f2569=1. f2570=1. f2590=1. f2591=1. f2592=1. f2593=1. f2597=1. f2598=1. f2599=1. f2600=1. f2601=1. f2641=1. f2682=1. f2693=1. f2694=1. f2813=1. f2819=1. f2820=1. f2821=1. f2822=1. f2824=1. f2858=1. f2859=1. f2880=1. f2881=1. f2882=1. f2883=1. f2923=1. f2933=1. f2934=1. f2935=1. f2936=1. f2937=1. f2938=1. f2939=1. f2940=1. f2969=1. f2976=1. f2977=1. f2978=1. f2985=1. f2989=1. f2990=1. f3001=1. f3002=1. f3019=1. f3050=1. f3051=1. f3052=1. f3053=1. f3054=1. f3055=1. f3066=1. f3067=1. f3084=1. f3085=1. f3086=1. f3087=1. f3092=1. f3093=1. f3123=1. f3124=1. f3134=1. f3135=1. f3152=1. f3153=1. f3154=1. f3155=1. f3175=1. f3176=1. f3177=1. f3185=1. f3186=1. f3187=1. f3189=1. f3190=1. f3324=1. f3325=1. f3326=1. f3327=1. f3328=1. f3329=1. f3348=1. f3349=1. f3350=1. f3360=1. f3361=1. f3437=1. f3438=1. f3439=1. f3440=1. f3441=1. f3442=1. f3461=1. f3462=1. f3463=1. f3468=1. f3478=1. f3479=1. f3480=1. f3481=1. f3488=1. f3508=1. f3509=1. f3526=1. f3566=1. f3567=1. f3568=1. f3569=1. f3722=1. f3723=1. f3742=1. f3743=1. f3744=1. f3745=1. f3751=1. f3754=1. f3790=1. f3802=1. f3803=1. f3804=1. f3817=1. f3833=1. f3840=1. f3841=1. f3842=1. f3891=1. f3892=1. f3893=1. f3894=1. f3902=1. f3974=1. f4020=1. f4021=1. f4022=1. f4023=1. f4037=1. f4038=1. f4056=1. f4057=1. f4058=1. f4059=1. f4074=1. f4075=1. f4076=1. f4077=1. f4123=1. f4131=1. f4132=1. f4133=1. f4135=1. f4143=1. f4148=1. f4149=1. f4150=1. f4151=1. f4152=1. f4153=1. f4184=1. f4185=1. f4228=1. f4229=1. f4230=1. f4231=1. f4241=1. f4272=1. f4273=1. f4284=1. f4299=1. f4313=1. f4314=1. f4315=1. f4316=1. f4339=1. f4396=1. f4397=1. f4398=1. f84=1. f85=1. f114=1. f121=1. f122=1. f123=1. f124=1. f150=1. f236=1. f356=1. f487=1. f488=1. f489=1. f490=1. f526=1. f527=1. f532=1. f609=1. f610=1. f611=1. f612=1. f613=1. f614=1. f615=1. f616=1. f681=1. f682=1. f683=1. f684=1. f685=1. f686=1. f690=1. f691=1. f712=1. f713=1. f714=1. f839=1. f920=1. f921=1. f922=1. f923=1. f924=1. f925=1. f926=1. f988=1. f989=1. f990=1. f1014=1. f1015=1. f1016=1. f1017=1. f1027=1. f1028=1. f1048=1. f1049=1. f1063=1. f1085=1. f1086=1. f1087=1. f1088=1. f1185=1. f1186=1. f1223=1. f1224=1. f1225=1. f1330=1. f1331=1. f1366=1. f1469=1. f1531=1. f1581=1. f1582=1. f1643=1. f1644=1. f1645=1. f1646=1. f1647=1. f1648=1. f1659=1. f1663=1. f1664=1. f1677=1. f1678=1. f1679=1. f1680=1. f1681=1. f1682=1. f1715=1. f1716=1. f1717=1. f1718=1. f1719=1. f1720=1. f1735=1. f1736=1. f1737=1. f1855=1. f1856=1. f2001=1. f2002=1. f2003=1. f2004=1. f2028=1. f2037=1. f2038=1. f2039=1. f2040=1. f2075=1. f2076=1. f2087=1. f2088=1. f2108=1. f2137=1. f2138=1. f2139=1. f2226=1. f2227=1. f2228=1. f2274=1. f2275=1. f2339=1. f2340=1. f2341=1. f2342=1. f2343=1. f2344=1. f2345=1. f2346=1. f2347=1. f2365=1. f2379=1. f2380=1. f2381=1. f2535=1. f2536=1. f2537=1. f2538=1. f2564=1. f2579=1. f2602=1. f2603=1. f2604=1. f2605=1. f2666=1. f2667=1. f2673=1. f2674=1. f2873=1. f2874=1. f2875=1. f2876=1. f2877=1. f2878=1. f2879=1. f2884=1. f2885=1. f2886=1. f2944=1. f2945=1. f2946=1. f2947=1. f2948=1. f2949=1. f2960=1. f3056=1. f3057=1. f3058=1. f3059=1. f3080=1. f3081=1. f3094=1. f3095=1. f3096=1. f3097=1. f3098=1. f3099=1. f3143=1. f3144=1. f3145=1. f3146=1. f3147=1. f3148=1. f3172=1. f3173=1. f3174=1. f3188=1. f3224=1. f3225=1. f3226=1. f3227=1. f3228=1. f3371=1. f3372=1. f3464=1. f3465=1. f3466=1. f3537=1. f3538=1. f3570=1. f3571=1. f3572=1. f3647=1. f3648=1. f3649=1. f3650=1. f3651=1. f3652=1. f3656=1. f3657=1. f3746=1. f3747=1. f3748=1. f3749=1. f3750=1. f3791=1. f3792=1. f3793=1. f3794=1. f3795=1. f3796=1. f3797=1. f3798=1. f3805=1. f3806=1. f3820=1. f3821=1. f3822=1. f3823=1. f3895=1. f3896=1. f3897=1. f4154=1. f4155=1. f4156=1. f4164=1. f4165=1. f4167=1. f4169=1. f4170=1. f4172=1. f4287=1. f4388=1. f25=1. f26=1. f27=1. f28=1. f110=1. f111=1. f115=1. f116=1. f117=1. f118=1. f119=1. f120=1. f125=1. f126=1. f127=1. f338=1. f339=1. f340=1. f360=1. f361=1. f362=1. f491=1. f492=1. f493=1. f494=1. f495=1. f533=1. f534=1. f535=1. f536=1. f602=1. f617=1. f618=1. f619=1. f620=1. f621=1. f622=1. f650=1. f651=1. f652=1. f653=1. f654=1. f655=1. f688=1. f689=1. f692=1. f693=1. f715=1. f716=1. f717=1. f718=1. f719=1. f720=1. f725=1. f726=1. f727=1. f728=1. f927=1. f928=1. f929=1. f930=1. f931=1. f1042=1. f1089=1. f1090=1. f1091=1. f1111=1. f1200=1. f1367=1. f1368=1. f1465=1. f1466=1. f1620=1. f1671=1. f1672=1. f1673=1. f1674=1. f1683=1. f1688=1. f1689=1. f1712=1. f1713=1. f1714=1. f1738=1. f1739=1. f1740=1. f1741=1. f1742=1. f1743=1. f1825=1. f1826=1. f1827=1. f1828=1. f2140=1. f2142=1. f2143=1. f2229=1. f2230=1. f2382=1. f2383=1. f2606=1. f2607=1. f2608=1. f2609=1. f2610=1. f2742=1. f2743=1. f2744=1. f2745=1. f2746=1. f2747=1. f2748=1. f2826=1. f2827=1. f2828=1. f2829=1. f2847=1. f2887=1. f2888=1. f2889=1. f2890=1. f2891=1. f2892=1. f2941=1. f2942=1. f2943=1. f2963=1. f2964=1. f2965=1. f2966=1. f3088=1. f3089=1. f3090=1. f3091=1. f3100=1. f3105=1. f3106=1. f3117=1. f3118=1. f3119=1. f3120=1. f3229=1. f3230=1. f3231=1. f3232=1. f3257=1. f3258=1. f3259=1. f3260=1. f3330=1. f3331=1. f3332=1. f3333=1. f3346=1. f3573=1. f3574=1. f3575=1. f3576=1. f3927=1. f3928=1. f4134=1. f4166=1. f4168=1. f4171=1. f29=1. f30=1. f31=1. f183=1. f496=1. f497=1. f537=1. f538=1. f539=1. f540=1. f541=1. f542=1. f543=1. f544=1. f623=1. f624=1. f625=1. f626=1. f627=1. f628=1. f656=1. f657=1. f658=1. f659=1. f660=1. f721=1. f722=1. f723=1. f724=1. f729=1. f730=1. f731=1. f932=1. f933=1. f934=1. f935=1. f936=1. f1369=1. f1690=1. f1691=1. f1692=1. f1693=1. f1744=1. f1745=1. f1746=1. f1747=1. f2019=1. f2020=1. f2021=1. f2022=1. f2023=1. f2024=1. f2025=1. f2026=1. f2027=1. f2145=1. f2146=1. f2147=1. f2231=1. f2232=1. f2233=1. f2234=1. f2235=1. f2384=1. f2385=1. f2386=1. f2387=1. f2408=1. f2409=1. f2473=1. f2539=1. f2611=1. f2612=1. f2720=1. f2749=1. f2750=1. f2751=1. f2752=1. f2753=1. f2754=1. f2830=1. f2831=1. f2832=1. f2893=1. f2894=1. f2895=1. f2896=1. f3003=1. f3004=1. f3107=1. f3108=1. f3109=1. f3110=1. f3233=1. f3234=1. f3235=1. f3261=1. f3262=1. f3263=1. f3577=1. f3578=1. f3579=1. f4211=1. f4212=1. f4213=1. f4214=1. f4411=1. f4412=1. f32=1. f33=1. f34=1. f35=1. f36=1. f37=1. f498=1. f499=1. f500=1. f501=1. f629=1. f630=1. f631=1. f632=1. f633=1. f661=1. f662=1. f663=1. f664=1. f665=1. f732=1. f733=1. f734=1. f735=1. f736=1. f937=1. f938=1. f939=1. f940=1. f1279=1. f1280=1. f1360=1. f1684=1. f1685=1. f1686=1. f1687=1. f1694=1. f2005=1. f2006=1. f2007=1. f2008=1. f2009=1. f2010=1. f2011=1. f2012=1. f2013=1. f2064=1. f2065=1. f2134=1. f2195=1. f2196=1. f2197=1. f2236=1. f2237=1. f2388=1. f2389=1. f2390=1. f2524=1. f2525=1. f2526=1. f2613=1. f2614=1. f2615=1. f2616=1. f2755=1. f2756=1. f2757=1. f2758=1. f2759=1. f2833=1. f2834=1. f2835=1. f2836=1. f2849=1. f2850=1. f2851=1. f2852=1. f2897=1. f2898=1. f2899=1. f2900=1. f3101=1. f3102=1. f3103=1. f3104=1. f3111=1. f3236=1. f3237=1. f3264=1. f3265=1. f3266=1. f3267=1. f3268=1. f3269=1. f3580=1. f3898=1. f3899=1. f4157=1. f38=1. f39=1. f40=1. f41=1. f363=1. f364=1. f365=1. f366=1. f367=1. f368=1. f369=1. f370=1. f371=1. f502=1. f503=1. f504=1. f505=1. f506=1. f508=1. f509=1. f666=1. f667=1. f668=1. f669=1. f687=1. f737=1. f738=1. f1486=1. f1487=1. f1649=1. f1695=1. f1696=1. f1697=1. f1698=1. f2238=1. f2239=1. f2240=1. f2241=1. f2617=1. f2618=1. f2619=1. f2620=1. f2621=1. f2623=1. f2624=1. f2760=1. f2761=1. f2762=1. f2763=1. f2837=1. f2838=1. f2839=1. f2901=1. f2902=1. f2903=1. f3060=1. f3112=1. f3113=1. f3114=1. f3115=1. f3238=1. f3239=1. f3240=1. f3241=1. f3270=1. f3271=1. f3272=1. f3273=1. f3581=1. f3582=1. f3583=1. f3584=1. f3585=1. f3586=1. f3587=1. f3588=1. f3589=1. f3590=1. f3591=1. f3592=1. f3593=1. f3594=1. f3595=1. f3596=1. f3597=1. f3598=1. f3599=1. f3600=1. f3601=1. f3602=1. f3603=1. f3604=1. f42=1. f43=1. f44=1. f45=1. f510=1. f511=1. f512=1. f513=1. f739=1. f740=1. f741=1. f742=1. f1699=1. f2242=1. f2243=1. f2244=1. f2245=1. f2246=1. f2625=1. f2626=1. f2627=1. f2628=1. f2764=1. f2765=1. f2766=1. f2767=1. f2768=1. f2769=1. f2904=1. f2905=1. f2906=1. f2907=1. f2908=1. f2909=1. f3116=1. f3242=1. f3243=1. f3244=1. f3274=1. f3275=1. f3276=1. f3277=1. f46=1. f47=1. f48=1. f507=1. f743=1. f744=1. f745=1. f746=1. f748=1. f749=1. f2247=1. f2248=1. f2523=1. f2622=1. f2770=1. f2771=1. f2772=1. f2773=1. f2774=1. f2910=1. f2911=1. f2912=1. f2913=1. f3278=1. f3279=1. f3280=1. f49=1. f50=1. f51=1. f52=1. f53=1. f54=1. f750=1. f751=1. f752=1. f2914=1. f2915=1. f2916=1. f2917=1. f2918=1. f3281=1. f3282=1. f3283=1. f3284=1. f3285=1. f3286=1. f55=1. f56=1. f57=1. f58=1. f747=1. f2919=1. f2920=1. f2921=1. f3287=1. f3288=1. f3289=1. f3290=1. f59=1. f60=1. f61=1. f62=1. f63=1. f941=1. f942=1. f943=1. f944=1. f945=1. f946=1. f947=1. f948=1. f3291=1. f3292=1. f3293=1. f3294=1. f3295=1. f64=1. f65=1. f66=1. f634=1. f635=1. f636=1. f637=1. f638=1. f639=1. f640=1. f641=1. f3296=1. f3297=1. f3298=1. 47.06/47.06 47.06/47.06 ============================== STATISTICS ============================ 47.06/47.06 47.06/47.06 Given=0. Generated=1247. Kept=1240. proofs=0. 47.06/47.06 Usable=0. Sos=0. Demods=127. Limbo=1239, Disabled=1247. Hints=0. 47.06/47.06 Kept_by_rule=0, Deleted_by_rule=0. 47.06/47.06 Forward_subsumed=7. Back_subsumed=0. 47.06/47.06 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 47.06/47.06 New_demodulators=127 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 47.06/47.06 Demod_attempts=433981. Demod_rewrites=99. 47.06/47.06 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 47.06/47.06 Nonunit_fsub_feature_tests=483. Nonunit_bsub_feature_tests=0. 47.06/47.06 Megabytes=419.43. 47.06/47.06 User_CPU=35.02, System_CPU=0.13, Wall_clock=35. 47.06/47.06 47.06/47.06 Megs malloced by palloc(): 400. 47.06/47.06 type (bytes each) gets frees in use bytes 47.06/47.06 chunk ( 104) 639335 639335 0 0.0 K 47.06/47.06 string_buf ( 8) 588114 588114 0 0.0 K 47.06/47.06 token ( 20) 1512436 1512436 0 0.0 K 47.06/47.06 pterm ( 16) 1112589 1112589 0 0.0 K 47.06/47.06 hashtab ( 8) 3514 3514 0 0.0 K 47.06/47.06 hashnode ( 8) 19526 19526 0 0.0 K 47.06/47.06 term ( 20) 17680871 11128311 6552560 127979.7 K 47.06/47.06 term arg arrays: 39507.4 K 47.06/47.06 attribute ( 12) 41350 10 41340 484.5 K 47.06/47.06 ilist ( 8) 45281378 45256724 24654 192.6 K 47.06/47.06 plist ( 8) 171794 101982 69812 545.4 K 47.06/47.06 i2list ( 12) 422551 422551 0 0.0 K 47.06/47.06 just ( 12) 20434 1020 19414 227.5 K 47.06/47.06 parajust ( 16) 0 0 0 0.0 K 47.06/47.06 instancejust ( 8) 0 0 0 0.0 K 47.06/47.06 ivyjust ( 24) 0 0 0 0.0 K 47.06/47.06 formula ( 28) 261709 196293 65416 1788.7 K 47.06/47.06 formula arg arrays: 228.1 K 47.06/47.06 topform ( 52) 19154 7 19147 972.3 K 47.06/47.06 clist_pos ( 20) 17006 1247 15759 307.8 K 47.06/47.06 clist ( 16) 8 0 8 0.1 K 47.06/47.06 context ( 808) 23816 23816 0 0.0 K 47.06/47.06 trail ( 12) 3854 3854 0 0.0 K 47.06/47.06 ac_match_pos (70044) 0 0 0 0.0 K 47.06/47.06 ac_match_free_vars_pos (20020) 47.06/47.06 0 0 0 0.0 K 47.06/47.06 btm_state ( 60) 0 0 0 0.0 K 47.06/47.06 btu_state ( 60) 0 0 0 0.0 K 47.06/47.06 ac_position (285432) 0 0 0 0.0 K 47.06/47.06 fpa_trie ( 20) 19168 0 19168 374.4 K 47.06/47.06 fpa_state ( 28) 293 293 0 0.0 K 47.06/47.06 fpa_index ( 12) 10 0 10 0.1 K 47.06/47.06 fpa_chunk ( 20) 34016 14000 20016 390.9 K 47.06/47.06 fpa_list ( 16) 9562 0 9562 149.4 K 47.06/47.06 fpa_list chunks: 669.0 K 47.06/47.06 discrim ( 12) 13317 0 13317 156.1 K 47.06/47.06 discrim_pos ( 16) 101 101 0 0.0 K 47.06/47.06 flat2 ( 32) 180030 180030 0 0.0 K 47.06/47.06 flat ( 48) 0 0 0 0.0 K 47.06/47.06 flatterm ( 32) 675755 675755 0 0.0 K 47.06/47.06 mindex ( 28) 13 0 13 0.4 K 47.06/47.06 mindex_pos ( 56) 19916 19916 0 0.0 K 47.06/47.06 lindex ( 12) 5 0 5 0.1 K 47.06/47.06 clash ( 40) 0 0 0 0.0 K 47.06/47.06 di_tree ( 12) 19933033 0 19933033 233590.2 K 47.06/47.06 avl_node ( 20) 0 0 0 0.0 K 47.06/47.06 47.06/47.06 Memory report, 20 @ 20 = 400 megs (400.00 megs used). 47.06/47.06 List 1, length 13, 0.1 K 47.06/47.06 List 4, length 612, 9.6 K 47.06/47.06 List 5, length 66, 1.3 K 47.06/47.06 List 7, length 254, 6.9 K 47.06/47.06 List 8, length 298, 9.3 K 47.06/47.06 List 10, length 24, 0.9 K 47.06/47.06 List 11, length 16, 0.7 K 47.06/47.06 List 13, length 8, 0.4 K 47.06/47.06 List 14, length 1, 0.1 K 47.06/47.06 List 15, length 1034, 60.6 K 47.06/47.06 List 19, length 16, 1.2 K 47.06/47.06 List 21, length 28, 2.3 K 47.06/47.06 List 22, length 240, 20.6 K 47.06/47.06 List 23, length 156, 14.0 K 47.06/47.06 List 24, length 56, 5.2 K 47.06/47.06 List 25, length 8, 0.8 K 47.06/47.06 List 26, length 3611, 366.7 K 47.06/47.06 List 27, length 2, 0.2 K 47.06/47.06 List 28, length 2, 0.2 K 47.06/47.06 List 29, length 2, 0.2 K 47.06/47.06 List 30, length 2, 0.2 K 47.06/47.06 List 33, length 2, 0.3 K 47.06/47.06 List 34, length 2, 0.3 K 47.06/47.06 List 35, length 2, 0.3 K 47.06/47.06 List 36, length 2, 0.3 K 47.06/47.06 List 40, length 2, 0.3 K 47.06/47.06 List 48, length 2, 0.4 K 47.06/47.06 List 49, length 2, 0.4 K 47.06/47.06 List 54, length 2, 0.4 K 47.06/47.06 List 60, length 2, 0.5 K 47.06/47.06 List 63, length 2, 0.5 K 47.06/47.06 List 70, length 2, 0.5 K 47.06/47.06 List 72, length 2, 0.6 K 47.06/47.06 List 80, length 2, 0.6 K 47.06/47.06 List 96, length 2, 0.8 K 47.06/47.06 List 98, length 2, 0.8 K 47.06/47.06 List 108, length 2, 0.8 K 47.06/47.07 List 112, length 2, 0.9 K 47.06/47.07 List 125, length 2, 1.0 K 47.06/47.07 List 126, length 2, 1.0 K 47.06/47.07 List 202, length 2, 1.6 K 47.06/47.07 List 288, length 2, 2.2 K 47.06/47.07 List 296, length 2, 2.3 K 47.06/47.07 List 490, length 2, 3.8 K 47.06/47.07 47.06/47.07 ============================== SELECTOR REPORT ======================= 47.06/47.07 Sos_deleted=0, Sos_displaced=0, Sos_size=0 47.06/47.07 SELECTOR PART PRIORITY ORDER SIZE SELECTED 47.06/47.07 I 2147483647 high age 0 0 47.06/47.07 H 1 high weight 0 0 47.06/47.07 A 1 low age 0 0 47.06/47.07 F 4 low weight 0 0 47.06/47.07 T 4 low weight 0 0 47.06/47.07 ============================== end of selector report ================ 47.06/47.07 47.06/47.07 ============================== end of statistics ===================== 47.06/47.07 47.06/47.07 Exiting with failure. 47.06/47.07 47.06/47.07 Process 47289 exit (max_megs) Sat Jul 14 06:33:58 2018 47.06/47.07 Prover9 interrupted 47.06/47.07 EOF