%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT356+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:29 AM UTC 2025
% Result : Theorem 1.02s 1.19s
% Output : Proof 1.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT356+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 20:35:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.02/1.19 % SZS status Theorem
% 1.02/1.19 % SZS output start Proof
% 1.02/1.19 tff(k7_grcat_1_type, type, (
% 1.02/1.19 k7_grcat_1: $i > $i)).
% 1.02/1.19 tff(tptp_fun_A_0_type, type, (
% 1.02/1.19 tptp_fun_A_0: $i)).
% 1.02/1.19 tff(k1_waybel34_type, type, (
% 1.02/1.19 k1_waybel34: ( $i * $i * $i ) > $i)).
% 1.02/1.19 tff(v3_waybel_1_type, type, (
% 1.02/1.19 v3_waybel_1: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(k1_waybel_1_type, type, (
% 1.02/1.19 k1_waybel_1: ( $i * $i * $i * $i ) > $i)).
% 1.02/1.19 tff(m2_relset_1_type, type, (
% 1.02/1.19 m2_relset_1: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(u1_struct_0_type, type, (
% 1.02/1.19 u1_struct_0: $i > $i)).
% 1.02/1.19 tff(v1_funct_2_type, type, (
% 1.02/1.19 v1_funct_2: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(v1_funct_1_type, type, (
% 1.02/1.19 v1_funct_1: $i > $o)).
% 1.02/1.19 tff(v17_waybel_0_type, type, (
% 1.02/1.19 v17_waybel_0: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(v3_lattice3_type, type, (
% 1.02/1.19 v3_lattice3: $i > $o)).
% 1.02/1.19 tff(v4_orders_2_type, type, (
% 1.02/1.19 v4_orders_2: $i > $o)).
% 1.02/1.19 tff(v3_orders_2_type, type, (
% 1.02/1.19 v3_orders_2: $i > $o)).
% 1.02/1.19 tff(v2_orders_2_type, type, (
% 1.02/1.19 v2_orders_2: $i > $o)).
% 1.02/1.19 tff(v2_lattice3_type, type, (
% 1.02/1.19 v2_lattice3: $i > $o)).
% 1.02/1.19 tff(v1_lattice3_type, type, (
% 1.02/1.19 v1_lattice3: $i > $o)).
% 1.02/1.19 tff(l1_orders_2_type, type, (
% 1.02/1.19 l1_orders_2: $i > $o)).
% 1.02/1.19 tff(k2_waybel34_type, type, (
% 1.02/1.19 k2_waybel34: ( $i * $i * $i ) > $i)).
% 1.02/1.19 tff(l1_struct_0_type, type, (
% 1.02/1.19 l1_struct_0: $i > $o)).
% 1.02/1.19 tff(v22_waybel_0_type, type, (
% 1.02/1.19 v22_waybel_0: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(v21_waybel_0_type, type, (
% 1.02/1.19 v21_waybel_0: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(v20_waybel_0_type, type, (
% 1.02/1.19 v20_waybel_0: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(v19_waybel_0_type, type, (
% 1.02/1.19 v19_waybel_0: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(v18_waybel_0_type, type, (
% 1.02/1.19 v18_waybel_0: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(v11_quantal1_type, type, (
% 1.02/1.19 v11_quantal1: $i > $o)).
% 1.02/1.19 tff(v8_waybel_1_type, type, (
% 1.02/1.19 v8_waybel_1: ( $i * $i ) > $o)).
% 1.02/1.19 tff(v7_waybel_1_type, type, (
% 1.02/1.19 v7_waybel_1: ( $i * $i ) > $o)).
% 1.02/1.19 tff(v6_waybel_1_type, type, (
% 1.02/1.19 v6_waybel_1: ( $i * $i ) > $o)).
% 1.02/1.19 tff(v5_orders_3_type, type, (
% 1.02/1.19 v5_orders_3: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(v1_partfun1_type, type, (
% 1.02/1.19 v1_partfun1: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(v2_funct_1_type, type, (
% 1.02/1.19 v2_funct_1: $i > $o)).
% 1.02/1.19 tff(v23_waybel_0_type, type, (
% 1.02/1.19 v23_waybel_0: ( $i * $i * $i ) > $o)).
% 1.02/1.19 tff(v1_relat_1_type, type, (
% 1.02/1.19 v1_relat_1: $i > $o)).
% 1.02/1.19 tff(v1_xboole_0_type, type, (
% 1.02/1.19 v1_xboole_0: $i > $o)).
% 1.02/1.19 tff(v3_struct_0_type, type, (
% 1.02/1.19 v3_struct_0: $i > $o)).
% 1.02/1.19 tff(1,plain,
% 1.02/1.19 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))))))))),
% 1.02/1.19 inference(bind,[status(th)],[])).
% 1.02/1.19 tff(2,plain,
% 1.02/1.19 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))),
% 1.02/1.19 inference(quant_intro,[status(thm)],[1])).
% 1.02/1.19 tff(3,plain,
% 1.02/1.19 (^[A: $i] : refl(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 1.02/1.19 inference(bind,[status(th)],[])).
% 1.02/1.19 tff(4,plain,
% 1.02/1.19 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 1.02/1.19 inference(quant_intro,[status(thm)],[3])).
% 1.02/1.19 tff(5,plain,
% 1.02/1.19 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 1.02/1.19 inference(bind,[status(th)],[])).
% 1.02/1.19 tff(6,plain,
% 1.02/1.19 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 1.02/1.19 inference(quant_intro,[status(thm)],[5])).
% 1.02/1.19 tff(7,plain,
% 1.02/1.19 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 1.02/1.19 inference(transitivity,[status(thm)],[6, 4])).
% 1.02/1.19 tff(8,plain,
% 1.02/1.19 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)) <=> (~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) <=> (~(~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))))), rewrite((~(~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)) <=> (~((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))), ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) <=> (~(~((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))))), rewrite((~(~((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)))), ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) <=> (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))), ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) <=> (~(~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))), rewrite((~(~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))))), ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))), (((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) <=> (((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))), rewrite((((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) <=> (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))))), (((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) <=> (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))))))), (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) <=> ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))), trans(monotonicity(rewrite((v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B)) <=> (~((~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B))))), ((~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) <=> (~(~((~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B))))))), rewrite((~(~((~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B))))) <=> ((~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)))), ((~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) <=> ((~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B))))), trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> (![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B))) | ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), rewrite((![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B))) | ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))), ((![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> (((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), rewrite((((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), (((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), (![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) <=> (((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))),
% 1.02/1.19 inference(bind,[status(th)],[])).
% 1.02/1.19 tff(9,plain,
% 1.02/1.19 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 1.02/1.19 inference(quant_intro,[status(thm)],[8])).
% 1.02/1.19 tff(10,plain,
% 1.02/1.19 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(11,plain,
% 1.02/1.19 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v2_lattice3(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v2_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)) & l1_orders_2(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B))), ((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)) & v1_lattice3(B)))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)) & v1_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B))), ((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)))), (((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)) & v2_lattice3(B)))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)) & v2_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B))), (((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)))), ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)) & l1_orders_2(B)))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)) & l1_orders_2(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))), ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))), trans(monotonicity(rewrite(((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) <=> (v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) <=> (v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))), ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) <=> ((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)))), ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)))))), (![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) <=> ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))), ((((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)))) <=> ((v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B)) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)))))), rewrite(((v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B)) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)))) <=> ((~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))), ((((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)))) <=> ((~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)))))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ((~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))) <=> (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))) <=> (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), (![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))) <=> ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)))))) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)) => ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)) => ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))), (((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)))))) <=> ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))), (![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)))))) <=> ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))))) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)) => ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)) => ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))))),
% 1.02/1.19 inference(bind,[status(th)],[])).
% 1.02/1.19 tff(12,plain,
% 1.02/1.19 (![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))))))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 1.02/1.19 inference(quant_intro,[status(thm)],[11])).
% 1.02/1.19 tff(13,axiom,(![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => (((v3_lattice3(A) & v3_lattice3(B)) & v17_waybel_0(C, A, B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A))) => ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_waybel34')).
% 1.02/1.19 tff(14,plain,
% 1.02/1.19 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.02/1.19 tff(15,plain,
% 1.02/1.19 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[14, 10])).
% 1.02/1.19 tff(16,plain,(
% 1.02/1.19 ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | ((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v17_waybel_0(C, A, B))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))))))),
% 1.02/1.19 inference(skolemize,[status(sab)],[15])).
% 1.02/1.19 tff(17,plain,
% 1.02/1.19 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[16, 9])).
% 1.02/1.19 tff(18,plain,
% 1.02/1.19 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))))))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[17, 7])).
% 1.02/1.19 tff(19,plain,
% 1.02/1.19 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[18, 2])).
% 1.02/1.19 tff(20,plain,
% 1.02/1.19 ((~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ((k1_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A)) & (k2_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A))))) <=> (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ((k1_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A)) & (k2_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A)))))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(21,plain,
% 1.02/1.19 ((~![A: $i] : (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & v3_lattice3(A)) & l1_orders_2(A)) => ((k1_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A)) & (k2_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A))))) <=> (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ((k1_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A)) & (k2_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A)))))),
% 1.02/1.19 inference(rewrite,[status(thm)],[])).
% 1.02/1.19 tff(22,axiom,(~![A: $i] : (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & v3_lattice3(A)) & l1_orders_2(A)) => ((k1_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A)) & (k2_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_waybel34')).
% 1.02/1.19 tff(23,plain,
% 1.02/1.19 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ((k1_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A)) & (k2_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A))))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.02/1.19 tff(24,plain,
% 1.02/1.19 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ((k1_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A)) & (k2_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A))))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[23, 20])).
% 1.02/1.19 tff(25,plain,
% 1.02/1.19 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ((k1_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A)) & (k2_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A))))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[24, 20])).
% 1.02/1.19 tff(26,plain,
% 1.02/1.19 (~![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A))) | ((k1_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A)) & (k2_waybel34(A, A, k7_grcat_1(A)) = k7_grcat_1(A))))),
% 1.02/1.19 inference(modus_ponens,[status(thm)],[25, 20])).
% 1.02/1.19 tff(27,plain,(
% 1.02/1.19 ~((~(v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_lattice3(A!0) & v2_lattice3(A!0) & v3_lattice3(A!0) & l1_orders_2(A!0))) | ((k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)) & (k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))))),
% 1.02/1.20 inference(skolemize,[status(sab)],[26])).
% 1.02/1.20 tff(28,plain,
% 1.02/1.20 (v2_orders_2(A!0) & v3_orders_2(A!0) & v4_orders_2(A!0) & v1_lattice3(A!0) & v2_lattice3(A!0) & v3_lattice3(A!0) & l1_orders_2(A!0)),
% 1.02/1.20 inference(or_elim,[status(thm)],[27])).
% 1.02/1.20 tff(29,plain,
% 1.02/1.20 (l1_orders_2(A!0)),
% 1.02/1.20 inference(and_elim,[status(thm)],[28])).
% 1.02/1.20 tff(30,plain,
% 1.02/1.20 (v2_lattice3(A!0)),
% 1.02/1.20 inference(and_elim,[status(thm)],[28])).
% 1.02/1.20 tff(31,plain,
% 1.02/1.20 (v1_lattice3(A!0)),
% 1.02/1.20 inference(and_elim,[status(thm)],[28])).
% 1.02/1.20 tff(32,plain,
% 1.02/1.20 (v4_orders_2(A!0)),
% 1.02/1.20 inference(and_elim,[status(thm)],[28])).
% 1.02/1.20 tff(33,plain,
% 1.02/1.20 (v3_orders_2(A!0)),
% 1.02/1.20 inference(and_elim,[status(thm)],[28])).
% 1.02/1.20 tff(34,plain,
% 1.02/1.20 (v2_orders_2(A!0)),
% 1.02/1.20 inference(and_elim,[status(thm)],[28])).
% 1.02/1.20 tff(35,plain,
% 1.02/1.20 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0)))))))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(36,plain,
% 1.02/1.20 (((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v17_waybel_0(C, A!0, B)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))) <=> ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0)))))))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(37,plain,
% 1.02/1.20 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v17_waybel_0(C, A!0, B)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[36])).
% 1.02/1.20 tff(38,plain,
% 1.02/1.20 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v17_waybel_0(C, A!0, B)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0)))))))),
% 1.02/1.20 inference(transitivity,[status(thm)],[37, 35])).
% 1.02/1.20 tff(39,plain,
% 1.02/1.20 ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v17_waybel_0(C, A!0, B)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0)))))))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(40,plain,
% 1.02/1.20 ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) | (~v17_waybel_0(C, A, B)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) | ![D: $i] : (((D = k1_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, C, D), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A)))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.02/1.20 tff(41,plain,
% 1.02/1.20 (![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[40, 34, 33, 32, 31, 30, 29, 19])).
% 1.02/1.20 tff(42,plain,
% 1.02/1.20 (((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(43,plain,
% 1.02/1.20 (((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(44,plain,
% 1.02/1.20 (((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[43])).
% 1.02/1.20 tff(45,plain,
% 1.02/1.20 (((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.02/1.20 inference(transitivity,[status(thm)],[44, 42])).
% 1.02/1.20 tff(46,plain,
% 1.02/1.20 ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(47,plain,
% 1.02/1.20 ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~v17_waybel_0(C, A!0, B)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k1_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, C, D), A!0, B)) | (~v1_funct_2(D, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(B), u1_struct_0(A!0))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[46, 45])).
% 1.02/1.20 tff(48,plain,
% 1.02/1.20 (![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[47, 34, 33, 32, 31, 30, 29, 41])).
% 1.02/1.20 tff(49,plain,
% 1.02/1.20 (^[A: $i] : refl((l1_struct_0(A) | (~l1_orders_2(A))) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(50,plain,
% 1.02/1.20 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[49])).
% 1.02/1.20 tff(51,plain,
% 1.02/1.20 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(52,plain,
% 1.02/1.20 (^[A: $i] : rewrite((l1_orders_2(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(53,plain,
% 1.02/1.20 (![A: $i] : (l1_orders_2(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[52])).
% 1.02/1.20 tff(54,axiom,(![A: $i] : (l1_orders_2(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 1.02/1.20 tff(55,plain,
% 1.02/1.20 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.02/1.20 tff(56,plain,
% 1.02/1.20 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[55, 51])).
% 1.02/1.20 tff(57,plain,(
% 1.02/1.20 ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 1.02/1.20 inference(skolemize,[status(sab)],[56])).
% 1.02/1.20 tff(58,plain,
% 1.02/1.20 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[57, 50])).
% 1.02/1.20 tff(59,plain,
% 1.02/1.20 (((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(A!0) | (~l1_orders_2(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(A!0) | (~l1_orders_2(A!0)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(60,plain,
% 1.02/1.20 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(A!0) | (~l1_orders_2(A!0)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(61,plain,
% 1.02/1.20 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(A!0) | (~l1_orders_2(A!0))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.02/1.20 tff(62,plain,
% 1.02/1.20 (l1_struct_0(A!0)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[61, 29, 58])).
% 1.02/1.20 tff(63,plain,
% 1.02/1.20 (^[A: $i] : refl(((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))))) <=> ((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(64,plain,
% 1.02/1.20 (![A: $i] : ((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[63])).
% 1.02/1.20 tff(65,plain,
% 1.02/1.20 (^[A: $i] : rewrite(((~l1_struct_0(A)) | (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))) <=> ((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(66,plain,
% 1.02/1.20 (![A: $i] : ((~l1_struct_0(A)) | (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[65])).
% 1.02/1.20 tff(67,plain,
% 1.02/1.20 (![A: $i] : ((~l1_struct_0(A)) | (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(68,plain,
% 1.02/1.20 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) <=> (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))), ((l1_struct_0(A) => ((v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))) <=> (l1_struct_0(A) => (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))))), rewrite((l1_struct_0(A) => (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))) <=> ((~l1_struct_0(A)) | (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))), ((l1_struct_0(A) => ((v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))) <=> ((~l1_struct_0(A)) | (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(69,plain,
% 1.02/1.20 (![A: $i] : (l1_struct_0(A) => ((v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[68])).
% 1.02/1.20 tff(70,axiom,(![A: $i] : (l1_struct_0(A) => ((v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_grcat_1')).
% 1.02/1.20 tff(71,plain,
% 1.02/1.20 (![A: $i] : ((~l1_struct_0(A)) | (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.02/1.20 tff(72,plain,
% 1.02/1.20 (![A: $i] : ((~l1_struct_0(A)) | (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[71, 67])).
% 1.02/1.20 tff(73,plain,(
% 1.02/1.20 ![A: $i] : ((~l1_struct_0(A)) | (v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))),
% 1.02/1.20 inference(skolemize,[status(sab)],[72])).
% 1.02/1.20 tff(74,plain,
% 1.02/1.20 (![A: $i] : ((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[73, 66])).
% 1.02/1.20 tff(75,plain,
% 1.02/1.20 (![A: $i] : ((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[74, 64])).
% 1.02/1.20 tff(76,plain,
% 1.02/1.20 (((~![A: $i] : ((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))))) | ((~l1_struct_0(A!0)) | (~((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))))) | (~l1_struct_0(A!0)) | (~((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(77,plain,
% 1.02/1.20 ((~![A: $i] : ((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))))) | ((~l1_struct_0(A!0)) | (~((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(78,plain,
% 1.02/1.20 ((~![A: $i] : ((~l1_struct_0(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))))) | (~l1_struct_0(A!0)) | (~((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.02/1.20 tff(79,plain,
% 1.02/1.20 (~((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[78, 75, 62])).
% 1.02/1.20 tff(80,plain,
% 1.02/1.20 (((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.02/1.20 inference(tautology,[status(thm)],[])).
% 1.02/1.20 tff(81,plain,
% 1.02/1.20 (m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[80, 79])).
% 1.02/1.20 tff(82,plain,
% 1.02/1.20 (^[A: $i] : refl(((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(83,plain,
% 1.02/1.20 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[82])).
% 1.02/1.20 tff(84,plain,
% 1.02/1.20 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(85,plain,
% 1.02/1.20 (^[A: $i] : trans(monotonicity(rewrite((v2_lattice3(A) => (~v3_struct_0(A))) <=> ((~v2_lattice3(A)) | (~v3_struct_0(A)))), ((l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> (l1_orders_2(A) => ((~v2_lattice3(A)) | (~v3_struct_0(A)))))), rewrite((l1_orders_2(A) => ((~v2_lattice3(A)) | (~v3_struct_0(A)))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))), ((l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(86,plain,
% 1.02/1.20 (![A: $i] : (l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A)))) <=> ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[85])).
% 1.02/1.20 tff(87,axiom,(![A: $i] : (l1_orders_2(A) => (v2_lattice3(A) => (~v3_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc2_lattice3')).
% 1.02/1.20 tff(88,plain,
% 1.02/1.20 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.02/1.20 tff(89,plain,
% 1.02/1.20 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[88, 84])).
% 1.02/1.20 tff(90,plain,(
% 1.02/1.20 ![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.02/1.20 inference(skolemize,[status(sab)],[89])).
% 1.02/1.20 tff(91,plain,
% 1.02/1.20 (![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[90, 83])).
% 1.02/1.20 tff(92,plain,
% 1.02/1.20 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(93,plain,
% 1.02/1.20 (((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0))) <=> ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 1.02/1.20 inference(rewrite,[status(thm)],[])).
% 1.02/1.20 tff(94,plain,
% 1.02/1.20 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0))))),
% 1.02/1.20 inference(monotonicity,[status(thm)],[93])).
% 1.02/1.20 tff(95,plain,
% 1.02/1.20 (((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))) <=> ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0)))),
% 1.02/1.20 inference(transitivity,[status(thm)],[94, 92])).
% 1.02/1.20 tff(96,plain,
% 1.02/1.20 ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | ((~v3_struct_0(A!0)) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)))),
% 1.02/1.20 inference(quant_inst,[status(thm)],[])).
% 1.02/1.20 tff(97,plain,
% 1.02/1.20 ((~![A: $i] : ((~v3_struct_0(A)) | (~l1_orders_2(A)) | (~v2_lattice3(A)))) | (~l1_orders_2(A!0)) | (~v2_lattice3(A!0)) | (~v3_struct_0(A!0))),
% 1.02/1.20 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.02/1.20 tff(98,plain,
% 1.02/1.20 (~v3_struct_0(A!0)),
% 1.02/1.20 inference(unit_resolution,[status(thm)],[97, 30, 29, 91])).
% 1.02/1.20 tff(99,plain,
% 1.02/1.20 (^[A: $i] : refl((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A))))))),
% 1.02/1.20 inference(bind,[status(th)],[])).
% 1.02/1.20 tff(100,plain,
% 1.02/1.20 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))),
% 1.02/1.20 inference(quant_intro,[status(thm)],[99])).
% 1.02/1.20 tff(101,plain,
% 1.02/1.20 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A)) <=> (~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A))))), ((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) <=> (~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)))), ((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A))))), rewrite((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A)) <=> (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A))))), (((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A))) <=> ((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A))) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A))))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A))) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))), (((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))))),
% 1.02/1.21 inference(bind,[status(th)],[])).
% 1.02/1.21 tff(102,plain,
% 1.02/1.21 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))),
% 1.02/1.21 inference(quant_intro,[status(thm)],[101])).
% 1.02/1.21 tff(103,plain,
% 1.02/1.21 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A)))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(104,plain,
% 1.02/1.21 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_orders_2(A)) & l1_orders_2(A)) <=> ((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)))), ((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))))), ((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A)))))), (((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))), (((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))), ((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))), ((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))))), (((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)))), (((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A))))), ((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A))), ((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A)))), (((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A))), (((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A)))), ((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A))), ((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A)))), (((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A))), (((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A)))), ((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A))), ((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A)))), (((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A))), (((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A)))), ((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A))), ((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A)))), (((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A))), (((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A)))), ((((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A))), ((((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A)))), (((((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)) & v7_waybel_1(k7_grcat_1(A), A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A)) & v7_waybel_1(k7_grcat_1(A), A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A)) & v7_waybel_1(k7_grcat_1(A), A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A))), (((((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)) & v7_waybel_1(k7_grcat_1(A), A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A)))), ((((((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)) & v7_waybel_1(k7_grcat_1(A), A)) & v8_waybel_1(k7_grcat_1(A), A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A)) & v8_waybel_1(k7_grcat_1(A), A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A)) & v8_waybel_1(k7_grcat_1(A), A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A))), ((((((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)) & v7_waybel_1(k7_grcat_1(A), A)) & v8_waybel_1(k7_grcat_1(A), A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A)))), (((((~v3_struct_0(A)) & v2_orders_2(A)) & l1_orders_2(A)) => (((((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)) & v7_waybel_1(k7_grcat_1(A), A)) & v8_waybel_1(k7_grcat_1(A), A))) <=> (((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A)) => (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A))))), rewrite((((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A)) => (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A))) <=> ((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A)))), (((((~v3_struct_0(A)) & v2_orders_2(A)) & l1_orders_2(A)) => (((((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)) & v7_waybel_1(k7_grcat_1(A), A)) & v8_waybel_1(k7_grcat_1(A), A))) <=> ((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A)))))),
% 1.02/1.21 inference(bind,[status(th)],[])).
% 1.02/1.21 tff(105,plain,
% 1.02/1.21 (![A: $i] : ((((~v3_struct_0(A)) & v2_orders_2(A)) & l1_orders_2(A)) => (((((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)) & v7_waybel_1(k7_grcat_1(A), A)) & v8_waybel_1(k7_grcat_1(A), A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A)))),
% 1.02/1.21 inference(quant_intro,[status(thm)],[104])).
% 1.02/1.21 tff(106,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_orders_2(A)) & l1_orders_2(A)) => (((((((((((((((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v2_funct_1(k7_grcat_1(A))) & (~v1_xboole_0(k7_grcat_1(A)))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v11_quantal1(k7_grcat_1(A))) & v5_orders_3(k7_grcat_1(A), A, A)) & v17_waybel_0(k7_grcat_1(A), A, A)) & v18_waybel_0(k7_grcat_1(A), A, A)) & v19_waybel_0(k7_grcat_1(A), A, A)) & v20_waybel_0(k7_grcat_1(A), A, A)) & v21_waybel_0(k7_grcat_1(A), A, A)) & v22_waybel_0(k7_grcat_1(A), A, A)) & v23_waybel_0(k7_grcat_1(A), A, A)) & v6_waybel_1(k7_grcat_1(A), A)) & v7_waybel_1(k7_grcat_1(A), A)) & v8_waybel_1(k7_grcat_1(A), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc4_waybel10')).
% 1.02/1.21 tff(107,plain,
% 1.02/1.21 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A)))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[106, 105])).
% 1.02/1.21 tff(108,plain,
% 1.02/1.21 (![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A)))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[107, 103])).
% 1.02/1.21 tff(109,plain,(
% 1.02/1.21 ![A: $i] : ((~((~v3_struct_0(A)) & v2_orders_2(A) & l1_orders_2(A))) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & (~v1_xboole_0(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A), A, A) & v17_waybel_0(k7_grcat_1(A), A, A) & v18_waybel_0(k7_grcat_1(A), A, A) & v19_waybel_0(k7_grcat_1(A), A, A) & v20_waybel_0(k7_grcat_1(A), A, A) & v21_waybel_0(k7_grcat_1(A), A, A) & v22_waybel_0(k7_grcat_1(A), A, A) & v23_waybel_0(k7_grcat_1(A), A, A) & v6_waybel_1(k7_grcat_1(A), A) & v7_waybel_1(k7_grcat_1(A), A) & v8_waybel_1(k7_grcat_1(A), A)))),
% 1.02/1.21 inference(skolemize,[status(sab)],[108])).
% 1.02/1.21 tff(110,plain,
% 1.02/1.21 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[109, 102])).
% 1.02/1.21 tff(111,plain,
% 1.02/1.21 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))),
% 1.02/1.21 inference(modus_ponens,[status(thm)],[110, 100])).
% 1.02/1.21 tff(112,plain,
% 1.02/1.21 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0)))))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(113,plain,
% 1.02/1.21 ((v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0))))) <=> (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0)))))),
% 1.02/1.21 inference(rewrite,[status(thm)],[])).
% 1.02/1.21 tff(114,plain,
% 1.02/1.21 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0))))))),
% 1.02/1.21 inference(monotonicity,[status(thm)],[113])).
% 1.02/1.21 tff(115,plain,
% 1.02/1.21 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0)))))),
% 1.02/1.22 inference(transitivity,[status(thm)],[114, 112])).
% 1.02/1.22 tff(116,plain,
% 1.02/1.22 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)))))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(117,plain,
% 1.02/1.22 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | (~v2_orders_2(A)) | (~(v1_xboole_0(k7_grcat_1(A)) | (~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)) | (~v2_funct_1(k7_grcat_1(A))) | (~v1_partfun1(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v5_orders_3(k7_grcat_1(A), A, A)) | (~v6_waybel_1(k7_grcat_1(A), A)) | (~v11_quantal1(k7_grcat_1(A))) | (~v17_waybel_0(k7_grcat_1(A), A, A)) | (~v18_waybel_0(k7_grcat_1(A), A, A)) | (~v19_waybel_0(k7_grcat_1(A), A, A)) | (~v20_waybel_0(k7_grcat_1(A), A, A)) | (~v21_waybel_0(k7_grcat_1(A), A, A)) | (~v22_waybel_0(k7_grcat_1(A), A, A)) | (~v7_waybel_1(k7_grcat_1(A), A)) | (~v8_waybel_1(k7_grcat_1(A), A)))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | (~v2_orders_2(A!0)) | (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0))))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.02/1.22 tff(118,plain,
% 1.02/1.22 (v3_struct_0(A!0) | (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0))))),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[117, 34, 29, 111])).
% 1.02/1.22 tff(119,plain,
% 1.02/1.22 (~(v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0)))),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[118, 98])).
% 1.02/1.22 tff(120,plain,
% 1.02/1.22 ((v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0))) | v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)),
% 1.02/1.22 inference(tautology,[status(thm)],[])).
% 1.02/1.22 tff(121,plain,
% 1.02/1.22 (v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[120, 119])).
% 1.02/1.22 tff(122,plain,
% 1.02/1.22 (^[A: $i] : refl(((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A))))) <=> ((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A))))))),
% 1.02/1.22 inference(bind,[status(th)],[])).
% 1.02/1.22 tff(123,plain,
% 1.02/1.22 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)))))),
% 1.02/1.22 inference(quant_intro,[status(thm)],[122])).
% 1.02/1.22 tff(124,plain,
% 1.02/1.22 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A))) <=> ((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A))))))),
% 1.02/1.22 inference(bind,[status(th)],[])).
% 1.02/1.22 tff(125,plain,
% 1.02/1.22 (![A: $i] : ((~l1_orders_2(A)) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)))))),
% 1.02/1.22 inference(quant_intro,[status(thm)],[124])).
% 1.02/1.22 tff(126,plain,
% 1.02/1.22 (![A: $i] : ((~l1_orders_2(A)) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A))) <=> ![A: $i] : ((~l1_orders_2(A)) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(127,plain,
% 1.02/1.22 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)))), ((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v23_waybel_0(k7_grcat_1(A), A, A)) <=> ((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v23_waybel_0(k7_grcat_1(A), A, A)))), rewrite(((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v23_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A))), ((((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v23_waybel_0(k7_grcat_1(A), A, A)) <=> (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A)))), ((l1_orders_2(A) => (((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v23_waybel_0(k7_grcat_1(A), A, A))) <=> (l1_orders_2(A) => (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A))))), rewrite((l1_orders_2(A) => (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A))) <=> ((~l1_orders_2(A)) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A)))), ((l1_orders_2(A) => (((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v23_waybel_0(k7_grcat_1(A), A, A))) <=> ((~l1_orders_2(A)) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A)))))),
% 1.02/1.22 inference(bind,[status(th)],[])).
% 1.02/1.22 tff(128,plain,
% 1.02/1.22 (![A: $i] : (l1_orders_2(A) => (((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v23_waybel_0(k7_grcat_1(A), A, A))) <=> ![A: $i] : ((~l1_orders_2(A)) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A)))),
% 1.02/1.22 inference(quant_intro,[status(thm)],[127])).
% 1.02/1.22 tff(129,axiom,(![A: $i] : (l1_orders_2(A) => (((v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A))) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) & v23_waybel_0(k7_grcat_1(A), A, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_waybel_1')).
% 1.02/1.22 tff(130,plain,
% 1.02/1.22 (![A: $i] : ((~l1_orders_2(A)) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A)))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.02/1.22 tff(131,plain,
% 1.02/1.22 (![A: $i] : ((~l1_orders_2(A)) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A)))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[130, 126])).
% 1.02/1.22 tff(132,plain,(
% 1.02/1.22 ![A: $i] : ((~l1_orders_2(A)) | (v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A), A, A)))),
% 1.02/1.22 inference(skolemize,[status(sab)],[131])).
% 1.02/1.22 tff(133,plain,
% 1.02/1.22 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)))))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[132, 125])).
% 1.02/1.22 tff(134,plain,
% 1.02/1.22 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)))))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[133, 123])).
% 1.02/1.22 tff(135,plain,
% 1.02/1.22 (((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)))))) | ((~l1_orders_2(A!0)) | (~((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)))))) | (~l1_orders_2(A!0)) | (~((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)))))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(136,plain,
% 1.02/1.22 ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)))))) | ((~l1_orders_2(A!0)) | (~((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)))))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(137,plain,
% 1.02/1.22 ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_funct_1(k7_grcat_1(A))) | (~v1_funct_2(k7_grcat_1(A), u1_struct_0(A), u1_struct_0(A))) | (~v1_relat_1(k7_grcat_1(A))) | (~v23_waybel_0(k7_grcat_1(A), A, A)))))) | (~l1_orders_2(A!0)) | (~((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0))))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.02/1.22 tff(138,plain,
% 1.02/1.22 (~((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)))),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[137, 29, 134])).
% 1.02/1.22 tff(139,plain,
% 1.02/1.22 (((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0))) | v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.02/1.22 inference(tautology,[status(thm)],[])).
% 1.02/1.22 tff(140,plain,
% 1.02/1.22 (v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[139, 138])).
% 1.02/1.22 tff(141,plain,
% 1.02/1.22 (((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0))) | v1_funct_1(k7_grcat_1(A!0))),
% 1.02/1.22 inference(tautology,[status(thm)],[])).
% 1.02/1.22 tff(142,plain,
% 1.02/1.22 (v1_funct_1(k7_grcat_1(A!0))),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[141, 138])).
% 1.02/1.22 tff(143,plain,
% 1.02/1.22 (v3_lattice3(A!0)),
% 1.02/1.22 inference(and_elim,[status(thm)],[28])).
% 1.02/1.22 tff(144,plain,
% 1.02/1.22 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) | ((~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0))))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(145,plain,
% 1.02/1.22 (((~v1_funct_1(k7_grcat_1(A!0))) | (~v3_lattice3(A!0)) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)))) <=> ((~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0))))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(146,plain,
% 1.02/1.22 (^[D: $i] : rewrite(((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0))))),
% 1.02/1.22 inference(bind,[status(th)],[])).
% 1.02/1.22 tff(147,plain,
% 1.02/1.22 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)))),
% 1.02/1.22 inference(quant_intro,[status(thm)],[146])).
% 1.02/1.22 tff(148,plain,
% 1.02/1.22 (((~v1_funct_1(k7_grcat_1(A!0))) | (~v3_lattice3(A!0)) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~v1_funct_1(k7_grcat_1(A!0))) | (~v3_lattice3(A!0)) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[147])).
% 1.02/1.22 tff(149,plain,
% 1.02/1.22 (((~v1_funct_1(k7_grcat_1(A!0))) | (~v3_lattice3(A!0)) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0))))),
% 1.02/1.22 inference(transitivity,[status(thm)],[148, 145])).
% 1.02/1.22 tff(150,plain,
% 1.02/1.22 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) | ((~v1_funct_1(k7_grcat_1(A!0))) | (~v3_lattice3(A!0)) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) | ((~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)))))),
% 1.02/1.22 inference(monotonicity,[status(thm)],[149])).
% 1.02/1.22 tff(151,plain,
% 1.02/1.22 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) | ((~v1_funct_1(k7_grcat_1(A!0))) | (~v3_lattice3(A!0)) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0))))),
% 1.02/1.22 inference(transitivity,[status(thm)],[150, 144])).
% 1.02/1.22 tff(152,plain,
% 1.02/1.22 ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) | ((~v1_funct_1(k7_grcat_1(A!0))) | (~v3_lattice3(A!0)) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.02/1.22 inference(quant_inst,[status(thm)],[])).
% 1.02/1.22 tff(153,plain,
% 1.02/1.22 ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, C, D), A!0, A!0)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) | (~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)))),
% 1.02/1.22 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.02/1.22 tff(154,plain,
% 1.02/1.22 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)))),
% 1.02/1.22 inference(unit_resolution,[status(thm)],[153, 143, 142, 140, 121, 81, 48])).
% 1.02/1.22 tff(155,plain,
% 1.02/1.22 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)))) | ((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ((k7_grcat_1(A!0) = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)))) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ((k7_grcat_1(A!0) = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)))),
% 1.02/1.22 inference(rewrite,[status(thm)],[])).
% 1.02/1.22 tff(156,plain,
% 1.02/1.22 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)))) | ((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ((k7_grcat_1(A!0) = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)))),
% 1.02/1.23 inference(quant_inst,[status(thm)],[])).
% 1.02/1.23 tff(157,plain,
% 1.02/1.23 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), D), A!0, A!0)))) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ((k7_grcat_1(A!0) = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))),
% 1.02/1.23 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.02/1.23 tff(158,plain,
% 1.02/1.23 ((k7_grcat_1(A!0) = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[157, 142, 140, 81, 154])).
% 1.02/1.23 tff(159,plain,
% 1.02/1.23 (^[A: $i] : refl((v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A))) <=> (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A))))),
% 1.02/1.23 inference(bind,[status(th)],[])).
% 1.02/1.23 tff(160,plain,
% 1.02/1.23 (![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A))) <=> ![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))),
% 1.02/1.23 inference(quant_intro,[status(thm)],[159])).
% 1.02/1.23 tff(161,plain,
% 1.02/1.23 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_orders_2(A)) <=> (~(v3_struct_0(A) | (~l1_orders_2(A))))), ((~((~v3_struct_0(A)) & l1_orders_2(A))) <=> (~(~(v3_struct_0(A) | (~l1_orders_2(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_orders_2(A))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)))), ((~((~v3_struct_0(A)) & l1_orders_2(A))) <=> (v3_struct_0(A) | (~l1_orders_2(A))))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A)) <=> ((v3_struct_0(A) | (~l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A)))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A)) <=> (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A)) <=> (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))))),
% 1.02/1.23 inference(bind,[status(th)],[])).
% 1.02/1.23 tff(162,plain,
% 1.02/1.23 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A)) <=> ![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))),
% 1.02/1.23 inference(quant_intro,[status(thm)],[161])).
% 1.02/1.23 tff(163,plain,
% 1.02/1.23 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A))),
% 1.02/1.23 inference(rewrite,[status(thm)],[])).
% 1.02/1.23 tff(164,plain,
% 1.02/1.23 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_orders_2(A)) => v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A)) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A)))),
% 1.02/1.23 inference(bind,[status(th)],[])).
% 1.02/1.23 tff(165,plain,
% 1.02/1.23 (![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A))),
% 1.02/1.23 inference(quant_intro,[status(thm)],[164])).
% 1.02/1.23 tff(166,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t6_waybel34')).
% 1.02/1.23 tff(167,plain,
% 1.02/1.23 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A))),
% 1.02/1.23 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.02/1.23 tff(168,plain,
% 1.02/1.23 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A))),
% 1.02/1.23 inference(modus_ponens,[status(thm)],[167, 163])).
% 1.02/1.23 tff(169,plain,(
% 1.02/1.23 ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A))),
% 1.02/1.23 inference(skolemize,[status(sab)],[168])).
% 1.02/1.23 tff(170,plain,
% 1.02/1.23 (![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))),
% 1.02/1.23 inference(modus_ponens,[status(thm)],[169, 162])).
% 1.02/1.23 tff(171,plain,
% 1.02/1.23 (![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))),
% 1.02/1.23 inference(modus_ponens,[status(thm)],[170, 160])).
% 1.02/1.23 tff(172,plain,
% 1.02/1.23 (((~![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))) | ((~l1_orders_2(A!0)) | v3_struct_0(A!0) | v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))) <=> ((~![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))) | (~l1_orders_2(A!0)) | v3_struct_0(A!0) | v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))),
% 1.02/1.23 inference(rewrite,[status(thm)],[])).
% 1.02/1.23 tff(173,plain,
% 1.02/1.23 ((v3_struct_0(A!0) | v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0) | (~l1_orders_2(A!0))) <=> ((~l1_orders_2(A!0)) | v3_struct_0(A!0) | v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))),
% 1.02/1.23 inference(rewrite,[status(thm)],[])).
% 1.02/1.23 tff(174,plain,
% 1.02/1.23 (((~![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))) | (v3_struct_0(A!0) | v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0) | (~l1_orders_2(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))) | ((~l1_orders_2(A!0)) | v3_struct_0(A!0) | v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)))),
% 1.02/1.23 inference(monotonicity,[status(thm)],[173])).
% 1.02/1.23 tff(175,plain,
% 1.02/1.23 (((~![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))) | (v3_struct_0(A!0) | v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0) | (~l1_orders_2(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))) | (~l1_orders_2(A!0)) | v3_struct_0(A!0) | v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))),
% 1.02/1.23 inference(transitivity,[status(thm)],[174, 172])).
% 1.02/1.23 tff(176,plain,
% 1.02/1.23 ((~![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))) | (v3_struct_0(A!0) | v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0) | (~l1_orders_2(A!0)))),
% 1.02/1.23 inference(quant_inst,[status(thm)],[])).
% 1.02/1.23 tff(177,plain,
% 1.02/1.23 ((~![A: $i] : (v3_struct_0(A) | v3_waybel_1(k1_waybel_1(A, A, k7_grcat_1(A), k7_grcat_1(A)), A, A) | (~l1_orders_2(A)))) | (~l1_orders_2(A!0)) | v3_struct_0(A!0) | v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)),
% 1.02/1.23 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.02/1.23 tff(178,plain,
% 1.02/1.23 (v3_struct_0(A!0) | v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[177, 29, 171])).
% 1.02/1.23 tff(179,plain,
% 1.02/1.23 (v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[178, 98])).
% 1.02/1.23 tff(180,plain,
% 1.02/1.23 ((~((k7_grcat_1(A!0) = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))) | (k7_grcat_1(A!0) = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) | (~v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))),
% 1.02/1.23 inference(tautology,[status(thm)],[])).
% 1.02/1.23 tff(181,plain,
% 1.02/1.23 ((~((k7_grcat_1(A!0) = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))) | (k7_grcat_1(A!0) = k1_waybel34(A!0, A!0, k7_grcat_1(A!0)))),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[180, 179])).
% 1.02/1.23 tff(182,plain,
% 1.02/1.23 (k7_grcat_1(A!0) = k1_waybel34(A!0, A!0, k7_grcat_1(A!0))),
% 1.02/1.23 inference(unit_resolution,[status(thm)],[181, 158])).
% 1.02/1.23 tff(183,plain,
% 1.02/1.23 (k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)),
% 1.02/1.23 inference(symmetry,[status(thm)],[182])).
% 1.02/1.23 tff(184,plain,
% 1.02/1.23 ((k7_grcat_1(A!0) = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> (k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))),
% 1.02/1.23 inference(commutativity,[status(thm)],[])).
% 1.02/1.23 tff(185,plain,
% 1.02/1.23 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))))))),
% 1.02/1.23 inference(bind,[status(th)],[])).
% 1.02/1.23 tff(186,plain,
% 1.02/1.23 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))),
% 1.02/1.23 inference(quant_intro,[status(thm)],[185])).
% 1.02/1.23 tff(187,plain,
% 1.02/1.23 (^[A: $i] : refl(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 1.02/1.23 inference(bind,[status(th)],[])).
% 1.02/1.23 tff(188,plain,
% 1.02/1.23 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 1.02/1.23 inference(quant_intro,[status(thm)],[187])).
% 1.02/1.23 tff(189,plain,
% 1.02/1.23 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 1.02/1.23 inference(bind,[status(th)],[])).
% 1.02/1.23 tff(190,plain,
% 1.02/1.23 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 1.02/1.23 inference(quant_intro,[status(thm)],[189])).
% 1.02/1.23 tff(191,plain,
% 1.02/1.23 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 1.02/1.23 inference(transitivity,[status(thm)],[190, 188])).
% 1.02/1.23 tff(192,plain,
% 1.02/1.23 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)) <=> (~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) <=> (~(~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))))), rewrite((~(~((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)))), ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)) <=> (~((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))), ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) <=> (~(~((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))))), rewrite((~(~((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)))), ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))), ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))), (((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> (((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))), rewrite((((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), (((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))))), (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))), trans(monotonicity(rewrite((v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A)) <=> (~((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))))), ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) <=> (~(~((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))))))), rewrite((~(~((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))))) <=> ((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)))), ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) <=> ((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))))), trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))), ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), ((![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> (![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))) | ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), rewrite((![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A))) | ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))), ((![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), (((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> (((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), rewrite((((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B))) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), (((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), (![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> (((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), rewrite((((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A))) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(193,plain,
% 1.07/1.23 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[192])).
% 1.07/1.23 tff(194,plain,
% 1.07/1.23 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(195,plain,
% 1.07/1.23 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A))), ((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v2_lattice3(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A)) & v2_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A))), (((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)) & l1_orders_2(A)))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))), ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) <=> (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B))), ((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)) & v1_lattice3(B)))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B)) & v1_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B))), ((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)))), (((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)) & v2_lattice3(B)))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B)) & v2_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B))), (((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)))), ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)) & l1_orders_2(B)))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B)) & l1_orders_2(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))), ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) <=> (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) <=> (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))), trans(monotonicity(rewrite(((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) <=> (v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> ((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))), ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))), (![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) <=> ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))), ((((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))) <=> ((v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A)) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))), rewrite(((v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A)) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))) <=> ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))), ((((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))) <=> ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))) <=> ((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => ((~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))) <=> (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))), ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))) <=> (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), (![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))) <=> ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))) <=> ((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)) => ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), rewrite(((v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B)) => ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))) <=> ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))), (((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))) <=> ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))))), (![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))) <=> ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))))) <=> ((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)) => ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))))), rewrite(((v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A)) => ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))), (((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))))) <=> ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(196,plain,
% 1.07/1.23 (![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))))))) <=> ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[195])).
% 1.07/1.23 tff(197,axiom,(![A: $i] : ((((((v2_orders_2(A) & v3_orders_2(A)) & v4_orders_2(A)) & v1_lattice3(A)) & v2_lattice3(A)) & l1_orders_2(A)) => ![B: $i] : ((((((v2_orders_2(B) & v3_orders_2(B)) & v4_orders_2(B)) & v1_lattice3(B)) & v2_lattice3(B)) & l1_orders_2(B)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) => (((v3_lattice3(A) & v3_lattice3(B)) & v18_waybel_0(C, B, A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_waybel34')).
% 1.07/1.23 tff(198,plain,
% 1.07/1.23 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.07/1.23 tff(199,plain,
% 1.07/1.23 (![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[198, 194])).
% 1.07/1.23 tff(200,plain,(
% 1.07/1.23 ![A: $i] : ((~(v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A))) | ![B: $i] : ((~(v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B))) | ![C: $i] : (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B))) | (~(v3_lattice3(A) & v3_lattice3(B) & v18_waybel_0(C, B, A))) | (~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & m2_relset_1(C, u1_struct_0(B), u1_struct_0(A)))))))),
% 1.07/1.23 inference(skolemize,[status(sab)],[199])).
% 1.07/1.23 tff(201,plain,
% 1.07/1.23 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[200, 193])).
% 1.07/1.23 tff(202,plain,
% 1.07/1.23 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[201, 191])).
% 1.07/1.24 tff(203,plain,
% 1.07/1.24 (![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[202, 186])).
% 1.07/1.24 tff(204,plain,
% 1.07/1.24 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(205,plain,
% 1.07/1.24 (((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | ![D: $i] : (((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) <=> ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(206,plain,
% 1.07/1.24 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | ![D: $i] : (((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[205])).
% 1.07/1.24 tff(207,plain,
% 1.07/1.24 (((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | ![D: $i] : (((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))),
% 1.07/1.24 inference(transitivity,[status(thm)],[206, 204])).
% 1.07/1.24 tff(208,plain,
% 1.07/1.24 ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A!0)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | ![D: $i] : (((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B)))))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(209,plain,
% 1.07/1.24 ((~![A: $i] : ((~l1_orders_2(A)) | (~v1_lattice3(A)) | (~v2_lattice3(A)) | (~v2_orders_2(A)) | (~v3_orders_2(A)) | (~v4_orders_2(A)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A)) | (~v3_lattice3(B)) | (~v18_waybel_0(C, B, A)) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A))) | ![D: $i] : (((D = k2_waybel34(A, B, C)) <=> v3_waybel_1(k1_waybel_1(A, B, D, C), A, B)) | (~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[208, 207])).
% 1.07/1.24 tff(210,plain,
% 1.07/1.24 (![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[209, 34, 33, 32, 31, 30, 29, 203])).
% 1.07/1.24 tff(211,plain,
% 1.07/1.24 (((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0)))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0)))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(212,plain,
% 1.07/1.24 (((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0)))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(213,plain,
% 1.07/1.24 (((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0))))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[212])).
% 1.07/1.24 tff(214,plain,
% 1.07/1.24 (((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0)))))),
% 1.08/1.24 inference(transitivity,[status(thm)],[213, 211])).
% 1.08/1.24 tff(215,plain,
% 1.08/1.24 ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | ((~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.08/1.24 inference(quant_inst,[status(thm)],[])).
% 1.08/1.24 tff(216,plain,
% 1.08/1.24 ((~![B: $i] : ((~l1_orders_2(B)) | (~v1_lattice3(B)) | (~v2_lattice3(B)) | (~v2_orders_2(B)) | (~v3_orders_2(B)) | (~v4_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(B)) | (~v3_lattice3(A!0)) | (~m2_relset_1(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v1_funct_2(C, u1_struct_0(B), u1_struct_0(A!0))) | (~v18_waybel_0(C, B, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | ((D = k2_waybel34(A!0, B, C)) <=> v3_waybel_1(k1_waybel_1(A!0, B, D, C), A!0, B)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))))))) | (~l1_orders_2(A!0)) | (~v1_lattice3(A!0)) | (~v2_lattice3(A!0)) | (~v2_orders_2(A!0)) | (~v3_orders_2(A!0)) | (~v4_orders_2(A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0))))),
% 1.08/1.24 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.08/1.24 tff(217,plain,
% 1.08/1.24 (![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0))))),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[216, 34, 33, 32, 31, 30, 29, 210])).
% 1.08/1.24 tff(218,plain,
% 1.08/1.24 ((v1_xboole_0(k7_grcat_1(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_relat_1(k7_grcat_1(A!0))) | (~v23_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v2_funct_1(k7_grcat_1(A!0))) | (~v1_partfun1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v5_orders_3(k7_grcat_1(A!0), A!0, A!0)) | (~v6_waybel_1(k7_grcat_1(A!0), A!0)) | (~v7_waybel_1(k7_grcat_1(A!0), A!0)) | (~v8_waybel_1(k7_grcat_1(A!0), A!0)) | (~v11_quantal1(k7_grcat_1(A!0))) | (~v17_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v19_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v20_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v21_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~v22_waybel_0(k7_grcat_1(A!0), A!0, A!0))) | v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)),
% 1.08/1.24 inference(tautology,[status(thm)],[])).
% 1.08/1.24 tff(219,plain,
% 1.08/1.24 (v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)),
% 1.08/1.24 inference(unit_resolution,[status(thm)],[218, 119])).
% 1.08/1.24 tff(220,plain,
% 1.08/1.24 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0))))) | ((~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0))))) | (~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0))))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(221,plain,
% 1.08/1.24 (((~v1_funct_1(k7_grcat_1(A!0))) | (~v3_lattice3(A!0)) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0)))) <=> ((~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0))))),
% 1.08/1.24 inference(rewrite,[status(thm)],[])).
% 1.08/1.24 tff(222,plain,
% 1.08/1.24 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0))))) | ((~v1_funct_1(k7_grcat_1(A!0))) | (~v3_lattice3(A!0)) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0))))) | ((~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0)))))),
% 1.08/1.24 inference(monotonicity,[status(thm)],[221])).
% 1.08/1.24 tff(223,plain,
% 1.08/1.24 (((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0))))) | ((~v1_funct_1(k7_grcat_1(A!0))) | (~v3_lattice3(A!0)) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0))))) | (~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0))))),
% 1.08/1.25 inference(transitivity,[status(thm)],[222, 220])).
% 1.08/1.25 tff(224,plain,
% 1.08/1.25 ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0))))) | ((~v1_funct_1(k7_grcat_1(A!0))) | (~v3_lattice3(A!0)) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0))))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(225,plain,
% 1.08/1.25 ((~![C: $i] : ((~v1_funct_1(C)) | (~v3_lattice3(A!0)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(C, A!0, A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, C)) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, C), A!0, A!0))))) | (~v3_lattice3(A!0)) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v18_waybel_0(k7_grcat_1(A!0), A!0, A!0)) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.08/1.25 tff(226,plain,
% 1.08/1.25 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0)))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[225, 143, 142, 140, 219, 81, 217])).
% 1.08/1.25 tff(227,plain,
% 1.08/1.25 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0)))) | ((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ((k7_grcat_1(A!0) = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0)))) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ((k7_grcat_1(A!0) = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(228,plain,
% 1.08/1.25 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0)))) | ((~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ((k7_grcat_1(A!0) = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)))),
% 1.08/1.25 inference(quant_inst,[status(thm)],[])).
% 1.08/1.25 tff(229,plain,
% 1.08/1.25 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(A!0))) | ((D = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, D, k7_grcat_1(A!0)), A!0, A!0)))) | (~v1_funct_1(k7_grcat_1(A!0))) | (~v1_funct_2(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_grcat_1(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ((k7_grcat_1(A!0) = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[228, 227])).
% 1.08/1.25 tff(230,plain,
% 1.08/1.25 ((k7_grcat_1(A!0) = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0)),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[229, 142, 140, 81, 226])).
% 1.08/1.25 tff(231,plain,
% 1.08/1.25 ((~((k7_grcat_1(A!0) = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))) | (k7_grcat_1(A!0) = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) | (~v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))),
% 1.08/1.25 inference(tautology,[status(thm)],[])).
% 1.08/1.25 tff(232,plain,
% 1.08/1.25 ((~((k7_grcat_1(A!0) = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))) <=> v3_waybel_1(k1_waybel_1(A!0, A!0, k7_grcat_1(A!0), k7_grcat_1(A!0)), A!0, A!0))) | (k7_grcat_1(A!0) = k2_waybel34(A!0, A!0, k7_grcat_1(A!0)))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[231, 179])).
% 1.08/1.25 tff(233,plain,
% 1.08/1.25 (k7_grcat_1(A!0) = k2_waybel34(A!0, A!0, k7_grcat_1(A!0))),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[232, 230])).
% 1.08/1.25 tff(234,plain,
% 1.08/1.25 (k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[233, 184])).
% 1.08/1.25 tff(235,plain,
% 1.08/1.25 ((~(~((~(k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))) | (~(k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)))))) <=> ((~(k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))) | (~(k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(236,plain,
% 1.08/1.25 (((k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)) & (k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))) <=> (~((~(k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))) | (~(k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)))))),
% 1.08/1.25 inference(rewrite,[status(thm)],[])).
% 1.08/1.25 tff(237,plain,
% 1.08/1.25 ((~((k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)) & (k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)))) <=> (~(~((~(k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))) | (~(k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))))))),
% 1.08/1.25 inference(monotonicity,[status(thm)],[236])).
% 1.08/1.25 tff(238,plain,
% 1.08/1.25 ((~((k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)) & (k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)))) <=> ((~(k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))) | (~(k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))))),
% 1.08/1.25 inference(transitivity,[status(thm)],[237, 235])).
% 1.08/1.25 tff(239,plain,
% 1.08/1.25 (~((k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)) & (k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)))),
% 1.08/1.25 inference(or_elim,[status(thm)],[27])).
% 1.08/1.25 tff(240,plain,
% 1.08/1.25 ((~(k1_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0))) | (~(k2_waybel34(A!0, A!0, k7_grcat_1(A!0)) = k7_grcat_1(A!0)))),
% 1.08/1.25 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.08/1.25 tff(241,plain,
% 1.08/1.25 ($false),
% 1.08/1.25 inference(unit_resolution,[status(thm)],[240, 234, 183])).
% 1.08/1.25 % SZS output end Proof
% 1.08/1.26 % E exiting
%------------------------------------------------------------------------------