%------------------------------------------------------------------------------ % File : SET007+368 : TPTP v7.5.0. Released v3.4.0. % Domain : Set Theory % Axioms : Subspaces of Real Linear Space Generated by Vectors % Version : [Urb08] axioms. % English : % Refs : [Mat90] Matuszewski (1990), Formalized Mathematics % : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In % : [Urb08] Urban (2006), Email to G. Sutcliffe % Source : [Urb08] % Names : rlvect_4 [Urb08] % Status : Satisfiable % Syntax : Number of formulae : 43 ( 2 unit) % Number of atoms : 535 ( 94 equality) % Maximal formula depth : 19 ( 12 average) % Number of connectives : 566 ( 74 ~ ; 34 |; 283 &) % ( 7 <=>; 168 =>; 0 <=) % ( 0 <~>; 0 ~|; 0 ~&) % Number of predicates : 19 ( 1 propositional; 0-3 arity) % Number of functors : 41 ( 26 constant; 0-4 arity) % Number of variables : 169 ( 0 singleton; 153 !; 16 ?) % Maximal term depth : 6 ( 1 average) % SPC : % Comments : The individual reference can be found in [Mat90] by looking for % the name provided by [Urb08]. % : Translated by MPTP from the Mizar Mathematical Library 4.48.930. % : These set theory axioms are used in encodings of problems in % various domains, including ALG, CAT, GRP, LAT, SET, and TOP. %------------------------------------------------------------------------------ fof(t1_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_rlvect_1(A,k4_rlvect_1(A,B,C),B) = C & k6_rlvect_1(A,k4_rlvect_1(A,C,B),B) = C & k4_rlvect_1(A,k6_rlvect_1(A,B,B),C) = C & k4_rlvect_1(A,k6_rlvect_1(A,C,B),B) = C & k4_rlvect_1(A,B,k6_rlvect_1(A,C,B)) = C & k4_rlvect_1(A,C,k6_rlvect_1(A,B,B)) = C & k6_rlvect_1(A,B,k6_rlvect_1(A,B,C)) = C ) ) ) ) )). fof(t2_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k6_rlvect_1(A,k4_rlvect_1(A,B,C),D) = k4_rlvect_1(A,k6_rlvect_1(A,B,D),C) ) ) ) ) )). fof(t3_rlvect_4,axiom,( $true )). fof(t4_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k6_rlvect_1(A,B,C) = k6_rlvect_1(A,D,C) => B = D ) ) ) ) ) )). fof(t5_rlvect_4,axiom,( $true )). fof(t6_rlvect_4,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k5_rlvect_1(B,k3_rlvect_1(B,C,A)) = k3_rlvect_1(B,C,k1_real_1(A)) ) ) ) )). fof(t7_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ( m1_rlsub_1(C,D) => r1_tarski(k3_rlsub_1(A,B,C),k3_rlsub_1(A,B,D)) ) ) ) ) ) )). fof(t8_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ( r2_hidden(B,k3_rlsub_1(A,C,D)) => k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,D) ) ) ) ) ) )). fof(t9_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m2_rlvect_2(E,A,k9_rlvect_2(A,B,C,D)) => ~ ( B != C & B != D & C != D & k13_rlvect_2(A,E) != k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,E,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,E,C))),k3_rlvect_1(A,D,k8_funct_2(u1_struct_0(A),k1_numbers,E,D))) ) ) ) ) ) ) )). fof(t10_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( B != C & B != D & C != D & v1_rlvect_3(k9_rlvect_2(A,B,C,D),A) ) <=> ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ! [G] : ( m1_subset_1(G,k1_numbers) => ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A) => ( E = np__0 & F = np__0 & G = np__0 ) ) ) ) ) ) ) ) ) ) )). fof(t11_rlvect_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( r1_rlvect_1(k1_rlvect_3(B,k7_rlvect_2(B,C)),A) <=> ? [D] : ( m1_subset_1(D,k1_numbers) & A = k3_rlvect_1(B,C,D) ) ) ) ) )). fof(t12_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_rlvect_1(k1_rlvect_3(A,k7_rlvect_2(A,B)),B) ) ) )). fof(t13_rlvect_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(A,k3_rlsub_1(B,C,k1_rlvect_3(B,k7_rlvect_2(B,D)))) <=> ? [E] : ( m1_subset_1(E,k1_numbers) & A = k4_rlvect_1(B,C,k3_rlvect_1(B,D,E)) ) ) ) ) ) )). fof(t14_rlvect_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_rlvect_1(k1_rlvect_3(B,k8_rlvect_2(B,C,D)),A) <=> ? [E] : ( m1_subset_1(E,k1_numbers) & ? [F] : ( m1_subset_1(F,k1_numbers) & A = k4_rlvect_1(B,k3_rlvect_1(B,C,E),k3_rlvect_1(B,D,F)) ) ) ) ) ) ) )). fof(t15_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,B,C)),B) & r1_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,B,C)),C) ) ) ) ) )). fof(t16_rlvect_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(A,k3_rlsub_1(B,C,k1_rlvect_3(B,k8_rlvect_2(B,D,E)))) <=> ? [F] : ( m1_subset_1(F,k1_numbers) & ? [G] : ( m1_subset_1(G,k1_numbers) & A = k4_rlvect_1(B,k4_rlvect_1(B,C,k3_rlvect_1(B,D,F)),k3_rlvect_1(B,E,G)) ) ) ) ) ) ) ) )). fof(t17_rlvect_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_rlvect_1(k1_rlvect_3(B,k9_rlvect_2(B,C,D,E)),A) <=> ? [F] : ( m1_subset_1(F,k1_numbers) & ? [G] : ( m1_subset_1(G,k1_numbers) & ? [H] : ( m1_subset_1(H,k1_numbers) & A = k4_rlvect_1(B,k4_rlvect_1(B,k3_rlvect_1(B,C,F),k3_rlvect_1(B,D,G)),k3_rlvect_1(B,E,H)) ) ) ) ) ) ) ) ) )). fof(t18_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_rlvect_1(k1_rlvect_3(A,k9_rlvect_2(A,B,C,D)),B) & r1_rlvect_1(k1_rlvect_3(A,k9_rlvect_2(A,B,C,D)),C) & r1_rlvect_1(k1_rlvect_3(A,k9_rlvect_2(A,B,C,D)),D) ) ) ) ) ) )). fof(t19_rlvect_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( r2_hidden(A,k3_rlsub_1(B,C,k1_rlvect_3(B,k9_rlvect_2(B,D,E,F)))) <=> ? [G] : ( m1_subset_1(G,k1_numbers) & ? [H] : ( m1_subset_1(H,k1_numbers) & ? [I] : ( m1_subset_1(I,k1_numbers) & A = k4_rlvect_1(B,k4_rlvect_1(B,k4_rlvect_1(B,C,k3_rlvect_1(B,D,G)),k3_rlvect_1(B,E,H)),k3_rlvect_1(B,F,I)) ) ) ) ) ) ) ) ) ) )). fof(t20_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v1_rlvect_3(k8_rlvect_2(A,B,C),A) => ( B = C | v1_rlvect_3(k8_rlvect_2(A,B,k6_rlvect_1(A,C,B)),A) ) ) ) ) ) )). fof(t21_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v1_rlvect_3(k8_rlvect_2(A,B,C),A) => ( B = C | v1_rlvect_3(k8_rlvect_2(A,B,k4_rlvect_1(A,C,B)),A) ) ) ) ) ) )). fof(t22_rlvect_4,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( v1_rlvect_3(k8_rlvect_2(B,C,D),B) => ( C = D | A = np__0 | v1_rlvect_3(k8_rlvect_2(B,C,k3_rlvect_1(B,D,A)),B) ) ) ) ) ) ) )). fof(t23_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v1_rlvect_3(k8_rlvect_2(A,B,C),A) => ( B = C | v1_rlvect_3(k8_rlvect_2(A,B,k5_rlvect_1(A,C)),A) ) ) ) ) ) )). fof(t24_rlvect_4,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( ( ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ~ ( A != B & v1_rlvect_3(k8_rlvect_2(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)),C) ) ) ) ) ) )). fof(t25_rlvect_4,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ~ ( A != np__1 & v1_rlvect_3(k8_rlvect_2(B,C,k3_rlvect_1(B,C,A)),B) ) ) ) ) )). fof(t26_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A) => ( B = D | B = C | D = C | v1_rlvect_3(k9_rlvect_2(A,B,C,k6_rlvect_1(A,D,B)),A) ) ) ) ) ) ) )). fof(t27_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A) => ( B = D | B = C | D = C | v1_rlvect_3(k9_rlvect_2(A,B,k6_rlvect_1(A,C,B),k6_rlvect_1(A,D,B)),A) ) ) ) ) ) ) )). fof(t28_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A) => ( B = D | B = C | D = C | v1_rlvect_3(k9_rlvect_2(A,B,C,k4_rlvect_1(A,D,B)),A) ) ) ) ) ) ) )). fof(t29_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A) => ( B = D | B = C | D = C | v1_rlvect_3(k9_rlvect_2(A,B,k4_rlvect_1(A,C,B),k4_rlvect_1(A,D,B)),A) ) ) ) ) ) ) )). fof(t30_rlvect_4,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( v1_rlvect_3(k9_rlvect_2(B,C,D,E),B) => ( C = E | C = D | E = D | A = np__0 | v1_rlvect_3(k9_rlvect_2(B,C,D,k3_rlvect_1(B,E,A)),B) ) ) ) ) ) ) ) )). fof(t31_rlvect_4,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( ( ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ( v1_rlvect_3(k9_rlvect_2(C,D,E,F),C) => ( D = F | D = E | F = E | A = np__0 | B = np__0 | v1_rlvect_3(k9_rlvect_2(C,D,k3_rlvect_1(C,E,A),k3_rlvect_1(C,F,B)),C) ) ) ) ) ) ) ) ) )). fof(t32_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A) => ( B = D | B = C | D = C | v1_rlvect_3(k9_rlvect_2(A,B,C,k5_rlvect_1(A,D)),A) ) ) ) ) ) ) )). fof(t33_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A) => ( B = D | B = C | D = C | v1_rlvect_3(k9_rlvect_2(A,B,k5_rlvect_1(A,C),k5_rlvect_1(A,D)),A) ) ) ) ) ) ) )). fof(t34_rlvect_4,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( ( ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ~ ( A != B & v1_rlvect_3(k9_rlvect_2(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B),E),C) ) ) ) ) ) ) )). fof(t35_rlvect_4,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ~ ( A != np__1 & v1_rlvect_3(k9_rlvect_2(B,C,k3_rlvect_1(B,C,A),D),B) ) ) ) ) ) )). fof(t36_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_rlvect_1(k1_rlvect_3(A,k7_rlvect_2(A,C)),B) => ( B = k1_rlvect_1(A) | k1_rlvect_3(A,k7_rlvect_2(A,B)) = k1_rlvect_3(A,k7_rlvect_2(A,C)) ) ) ) ) ) )). fof(t37_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( v1_rlvect_3(k8_rlvect_2(A,B,C),A) & r1_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,D,E)),B) & r1_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,D,E)),C) ) => ( B = C | ( k1_rlvect_3(A,k8_rlvect_2(A,D,E)) = k1_rlvect_3(A,k8_rlvect_2(A,B,C)) & v1_rlvect_3(k8_rlvect_2(A,D,E),A) & D != E ) ) ) ) ) ) ) ) )). fof(t38_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != k1_rlvect_1(A) & ~ v1_rlvect_3(k8_rlvect_2(A,C,B),A) & ! [D] : ( m1_subset_1(D,k1_numbers) => C != k3_rlvect_1(A,B,D) ) ) ) ) ) )). fof(t39_rlvect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != C & v1_rlvect_3(k8_rlvect_2(A,B,C),A) & ~ v1_rlvect_3(k9_rlvect_2(A,D,B,C),A) & ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => D != k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) ) ) ) ) ) ) ) )). fof(s1_rlvect_4,axiom, ( ( f3_s1_rlvect_4 != f4_s1_rlvect_4 & f3_s1_rlvect_4 != f5_s1_rlvect_4 & f4_s1_rlvect_4 != f5_s1_rlvect_4 ) => ? [A] : ( v1_funct_1(A) & v1_funct_2(A,f1_s1_rlvect_4,f2_s1_rlvect_4) & m2_relset_1(A,f1_s1_rlvect_4,f2_s1_rlvect_4) & k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,f3_s1_rlvect_4) = f6_s1_rlvect_4 & k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,f4_s1_rlvect_4) = f7_s1_rlvect_4 & k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,f5_s1_rlvect_4) = f8_s1_rlvect_4 & ! [B] : ( m1_subset_1(B,f1_s1_rlvect_4) => ~ ( B != f3_s1_rlvect_4 & B != f4_s1_rlvect_4 & B != f5_s1_rlvect_4 & k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,B) != f9_s1_rlvect_4(B) ) ) ) )). fof(s2_rlvect_4,axiom,( ? [A] : ( m2_rlvect_2(A,f1_s2_rlvect_4,k7_rlvect_2(f1_s2_rlvect_4,f2_s2_rlvect_4)) & k8_funct_2(u1_struct_0(f1_s2_rlvect_4),k1_numbers,A,f2_s2_rlvect_4) = f3_s2_rlvect_4 ) )). fof(s3_rlvect_4,axiom, ( f2_s3_rlvect_4 != f3_s3_rlvect_4 => ? [A] : ( m2_rlvect_2(A,f1_s3_rlvect_4,k8_rlvect_2(f1_s3_rlvect_4,f2_s3_rlvect_4,f3_s3_rlvect_4)) & k8_funct_2(u1_struct_0(f1_s3_rlvect_4),k1_numbers,A,f2_s3_rlvect_4) = f4_s3_rlvect_4 & k8_funct_2(u1_struct_0(f1_s3_rlvect_4),k1_numbers,A,f3_s3_rlvect_4) = f5_s3_rlvect_4 ) )). fof(s4_rlvect_4,axiom, ( ( f2_s4_rlvect_4 != f3_s4_rlvect_4 & f2_s4_rlvect_4 != f4_s4_rlvect_4 & f3_s4_rlvect_4 != f4_s4_rlvect_4 ) => ? [A] : ( m2_rlvect_2(A,f1_s4_rlvect_4,k9_rlvect_2(f1_s4_rlvect_4,f2_s4_rlvect_4,f3_s4_rlvect_4,f4_s4_rlvect_4)) & k8_funct_2(u1_struct_0(f1_s4_rlvect_4),k1_numbers,A,f2_s4_rlvect_4) = f5_s4_rlvect_4 & k8_funct_2(u1_struct_0(f1_s4_rlvect_4),k1_numbers,A,f3_s4_rlvect_4) = f6_s4_rlvect_4 & k8_funct_2(u1_struct_0(f1_s4_rlvect_4),k1_numbers,A,f4_s4_rlvect_4) = f7_s4_rlvect_4 ) )). %------------------------------------------------------------------------------