%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT379+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:14:35 AM UTC 2025
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT379+1 : TPTP v9.0.0. Released v3.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 20:49:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(v1_finset_1_type, type, (
% 0.20/0.48 v1_finset_1: $i > $o)).
% 0.20/0.48 tff(k2_tarski_type, type, (
% 0.20/0.48 k2_tarski: ( $i * $i ) > $i)).
% 0.20/0.48 tff(tptp_fun_E_5_type, type, (
% 0.20/0.48 tptp_fun_E_5: ( $i * $i * $i ) > $i)).
% 0.20/0.48 tff(tptp_fun_A_0_type, type, (
% 0.20/0.48 tptp_fun_A_0: $i)).
% 0.20/0.48 tff(tptp_fun_B_1_type, type, (
% 0.20/0.48 tptp_fun_B_1: $i)).
% 0.20/0.48 tff(tptp_fun_C_2_type, type, (
% 0.20/0.48 tptp_fun_C_2: $i)).
% 0.20/0.48 tff(tptp_fun_D_4_type, type, (
% 0.20/0.48 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 0.20/0.48 tff(k2_struct_0_type, type, (
% 0.20/0.48 k2_struct_0: ( $i * $i * $i ) > $i)).
% 0.20/0.48 tff(m1_subset_1_type, type, (
% 0.20/0.48 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.48 tff(u1_struct_0_type, type, (
% 0.20/0.48 u1_struct_0: $i > $i)).
% 0.20/0.48 tff(r4_waybel_0_type, type, (
% 0.20/0.48 r4_waybel_0: ( $i * $i * $i * $i ) > $o)).
% 0.20/0.48 tff(v20_waybel_0_type, type, (
% 0.20/0.48 v20_waybel_0: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(v1_funct_2_type, type, (
% 0.20/0.48 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(m2_relset_1_type, type, (
% 0.20/0.48 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(v1_funct_1_type, type, (
% 0.20/0.48 v1_funct_1: $i > $o)).
% 0.20/0.48 tff(l1_orders_2_type, type, (
% 0.20/0.48 l1_orders_2: $i > $o)).
% 0.20/0.48 tff(v3_struct_0_type, type, (
% 0.20/0.48 v3_struct_0: $i > $o)).
% 0.20/0.48 tff(v4_waybel34_type, type, (
% 0.20/0.48 v4_waybel34: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(v5_waybel34_type, type, (
% 0.20/0.48 v5_waybel34: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(k1_pre_topc_type, type, (
% 0.20/0.48 k1_pre_topc: $i > $i)).
% 0.20/0.48 tff(k1_xboole_0_type, type, (
% 0.20/0.48 k1_xboole_0: $i)).
% 0.20/0.48 tff(v1_xboole_0_type, type, (
% 0.20/0.48 v1_xboole_0: $i > $o)).
% 0.20/0.48 tff(v2_waybel_0_type, type, (
% 0.20/0.48 v2_waybel_0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(v1_waybel_0_type, type, (
% 0.20/0.48 v1_waybel_0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(v5_orders_2_type, type, (
% 0.20/0.48 v5_orders_2: ( $i * $i ) > $o)).
% 0.20/0.48 tff(v5_membered_type, type, (
% 0.20/0.48 v5_membered: $i > $o)).
% 0.20/0.48 tff(v4_membered_type, type, (
% 0.20/0.48 v4_membered: $i > $o)).
% 0.20/0.48 tff(v3_membered_type, type, (
% 0.20/0.48 v3_membered: $i > $o)).
% 0.20/0.48 tff(v2_membered_type, type, (
% 0.20/0.48 v2_membered: $i > $o)).
% 0.20/0.48 tff(v1_membered_type, type, (
% 0.20/0.48 v1_membered: $i > $o)).
% 0.20/0.48 tff(k1_zfmisc_1_type, type, (
% 0.20/0.48 k1_zfmisc_1: $i > $i)).
% 0.20/0.48 tff(l1_struct_0_type, type, (
% 0.20/0.48 l1_struct_0: $i > $o)).
% 0.20/0.48 tff(tptp_fun_D_3_type, type, (
% 0.20/0.48 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.20/0.48 tff(1,plain,
% 0.20/0.48 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) | (~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) | (~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 (^[A: $i] : refl((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(4,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(6,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (^[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))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & l1_orders_2(B)) <=> (~(v3_struct_0(B) | (~l1_orders_2(B))))), ((~((~v3_struct_0(B)) & l1_orders_2(B))) <=> (~(~(v3_struct_0(B) | (~l1_orders_2(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_orders_2(B))))) <=> (v3_struct_0(B) | (~l1_orders_2(B)))), ((~((~v3_struct_0(B)) & l1_orders_2(B))) <=> (v3_struct_0(B) | (~l1_orders_2(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(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)))))), trans(monotonicity(rewrite(((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) <=> ((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))), trans(monotonicity(rewrite((m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))) <=> (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))), ((v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) <=> (v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))), rewrite((v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))) <=> (v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))), ((v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) <=> (v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))), ((((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) <=> (((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))), rewrite((((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) <=> (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))), ((((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) <=> (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))), (((~(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)))) | (((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))) <=> (((~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)))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))), 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)))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))) <=> ((~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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))), (((~(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)))) | (((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))) <=> ((~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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))))), (![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)))) | (((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))) <=> ![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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))), (((~((~v3_struct_0(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)))) | (((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))) <=> ((v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))))), rewrite(((v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))) <=> (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))), (((~((~v3_struct_0(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)))) | (((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))) <=> (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))))), (![B: $i] : ((~((~v3_struct_0(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)))) | (((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))) <=> ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))) <=> ((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(9,plain,
% 0.20/0.49 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(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)))), rewrite((v20_waybel_0(C, A, B) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) <=> (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))), ((((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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) <=> ((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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))), 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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) <=> ((~(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))), ((((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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) <=> ((~(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))))), (![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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) <=> ![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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))), ((((~v3_struct_0(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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))) <=> (((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))))), rewrite((((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))) <=> ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))), ((((~v3_struct_0(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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))) <=> ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))), (![B: $i] : (((~v3_struct_0(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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))) <=> ![B: $i] : ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))) <=> (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))), rewrite((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 (![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.49 tff(13,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v20_waybel_0(C, A, B) <=> ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(A)) => r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d35_waybel_0')).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v20_waybel_0(C, A, B) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.49 tff(16,plain,(
% 0.20/0.49 ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E))))) & (v20_waybel_0(C, A, B) | (m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[15])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.20/0.49 tff(18,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))) | (~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) | (~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 ((((~v3_struct_0(A!0)) & l1_orders_2(A!0)) & ((~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(A!0)) & l1_orders_2(A!0) & (~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 ((((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 ((~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 ((((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> (((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 ((((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[23, 21])).
% 0.20/0.50 tff(25,plain,
% 0.20/0.50 ((((~v3_struct_0(A!0)) & l1_orders_2(A!0)) & (((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))) <=> (((~v3_struct_0(A!0)) & l1_orders_2(A!0)) & ((~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[24])).
% 0.20/0.50 tff(26,plain,
% 0.20/0.50 ((((~v3_struct_0(A!0)) & l1_orders_2(A!0)) & (((~v3_struct_0(B!1)) & l1_orders_2(B!1)) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))) <=> ((~v3_struct_0(A!0)) & l1_orders_2(A!0) & (~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[25, 20])).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 ((~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((v20_waybel_0(C, A, B) & v5_waybel34(C, A, B)) | (~v4_waybel34(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] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((v20_waybel_0(C, A, B) & v5_waybel34(C, A, B)) | (~v4_waybel34(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))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(28,plain,
% 0.20/0.50 ((~![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v4_waybel34(C, A, B) => (v20_waybel_0(C, A, B) & v5_waybel34(C, A, B))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((v20_waybel_0(C, A, B) & v5_waybel34(C, A, B)) | (~v4_waybel34(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))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(29,axiom,(~![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v4_waybel34(C, A, B) => (v20_waybel_0(C, A, B) & v5_waybel34(C, A, B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t65_waybel34')).
% 0.20/0.50 tff(30,plain,
% 0.20/0.50 (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((v20_waybel_0(C, A, B) & v5_waybel34(C, A, B)) | (~v4_waybel34(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)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((v20_waybel_0(C, A, B) & v5_waybel34(C, A, B)) | (~v4_waybel34(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)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((v20_waybel_0(C, A, B) & v5_waybel34(C, A, B)) | (~v4_waybel34(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)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.50 tff(33,plain,
% 0.20/0.50 (~![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & l1_orders_2(B))) | ![C: $i] : ((v20_waybel_0(C, A, B) & v5_waybel34(C, A, B)) | (~v4_waybel34(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)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 ((~v3_struct_0(A!0)) & l1_orders_2(A!0) & (~v3_struct_0(B!1)) & l1_orders_2(B!1) & (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (l1_orders_2(A!0)),
% 0.20/0.50 inference(and_elim,[status(thm)],[34])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 (~v3_struct_0(A!0)),
% 0.20/0.50 inference(and_elim,[status(thm)],[34])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.50 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) | (~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) | (~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(38,plain,
% 0.20/0.50 ((v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E))))))))))) <=> (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(39,plain,
% 0.20/0.50 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) | (~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) | (~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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)))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.50 tff(40,plain,
% 0.20/0.50 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) | (~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) | (~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[39, 37])).
% 0.20/0.50 tff(41,plain,
% 0.20/0.50 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) | (~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(42,plain,
% 0.20/0.50 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~(v20_waybel_0(C, A, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_E_5(C, B, A), u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))))) | (~((~v20_waybel_0(C, A, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A))) | r4_waybel_0(A, B, C, k2_struct_0(A, D, E)))))))))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.50 tff(43,plain,
% 0.20/0.50 (![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[42, 36, 35, 19])).
% 0.20/0.50 tff(44,plain,
% 0.20/0.50 (l1_orders_2(B!1)),
% 0.20/0.50 inference(and_elim,[status(thm)],[34])).
% 0.20/0.50 tff(45,plain,
% 0.20/0.50 (~v3_struct_0(B!1)),
% 0.20/0.50 inference(and_elim,[status(thm)],[34])).
% 0.20/0.50 tff(46,plain,
% 0.20/0.50 (((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E))))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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)))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(47,plain,
% 0.20/0.50 ((v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E)))))))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(48,plain,
% 0.20/0.50 (((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E)))))))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E)))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[47])).
% 0.20/0.51 tff(49,plain,
% 0.20/0.51 (((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E)))))))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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)))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[48, 46])).
% 0.20/0.51 tff(50,plain,
% 0.20/0.51 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E)))))))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(51,plain,
% 0.20/0.51 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~((~(v20_waybel_0(C, A!0, B) | (~((~m1_subset_1(tptp_fun_D_4(C, B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0))))))) | (~((~v20_waybel_0(C, A!0, B)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B, C, k2_struct_0(A!0, D, E)))))))) | (~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)))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E)))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.51 tff(52,plain,
% 0.20/0.51 (![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E)))))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[51, 45, 44, 43])).
% 0.20/0.51 tff(53,plain,
% 0.20/0.51 (~((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) | (~v4_waybel34(C!2, A!0, B!1)) | (~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 0.20/0.51 inference(and_elim,[status(thm)],[34])).
% 0.20/0.51 tff(54,plain,
% 0.20/0.51 (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.20/0.51 inference(or_elim,[status(thm)],[53])).
% 0.20/0.51 tff(55,plain,
% 0.20/0.51 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.20/0.51 inference(and_elim,[status(thm)],[54])).
% 0.20/0.51 tff(56,plain,
% 0.20/0.51 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.20/0.51 inference(and_elim,[status(thm)],[54])).
% 0.20/0.51 tff(57,plain,
% 0.20/0.51 (v1_funct_1(C!2)),
% 0.20/0.51 inference(and_elim,[status(thm)],[54])).
% 0.20/0.51 tff(58,plain,
% 0.20/0.51 (((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E)))))))))) | ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))))) | (~((~v20_waybel_0(C!2, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, D, E)))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E)))))))))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))))) | (~((~v20_waybel_0(C!2, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, D, E)))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E)))))))))) | ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))))) | (~((~v20_waybel_0(C!2, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, D, E)))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(60,plain,
% 0.20/0.51 ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, tptp_fun_D_4(C, B!1, A!0), tptp_fun_E_5(C, B!1, A!0))))))) | (~((~v20_waybel_0(C, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C, k2_struct_0(A!0, D, E)))))))))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~(v20_waybel_0(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))))) | (~((~v20_waybel_0(C!2, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, D, E))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.51 tff(61,plain,
% 0.20/0.51 (~((~(v20_waybel_0(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))))) | (~((~v20_waybel_0(C!2, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, D, E)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[60, 57, 56, 55, 52])).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 (((~(v20_waybel_0(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))))) | (~((~v20_waybel_0(C!2, A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, D, E))))))) | (v20_waybel_0(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(63,plain,
% 0.20/0.51 (v20_waybel_0(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 (^[A: $i] : refl((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(65,plain,
% 0.20/0.51 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.51 tff(66,plain,
% 0.20/0.51 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(67,plain,
% 0.20/0.51 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.51 tff(68,plain,
% 0.20/0.51 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[67, 65])).
% 0.20/0.51 tff(69,plain,
% 0.20/0.51 (^[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))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & l1_orders_2(B)) <=> (~(v3_struct_0(B) | (~l1_orders_2(B))))), ((~((~v3_struct_0(B)) & l1_orders_2(B))) <=> (~(~(v3_struct_0(B) | (~l1_orders_2(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_orders_2(B))))) <=> (v3_struct_0(B) | (~l1_orders_2(B)))), ((~((~v3_struct_0(B)) & l1_orders_2(B))) <=> (v3_struct_0(B) | (~l1_orders_2(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(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)))))), (((~(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))) <=> (((~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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))), 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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))) <=> ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))) <=> ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))) <=> ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))) <=> ((v3_struct_0(B) | (~l1_orders_2(B))) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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(((v3_struct_0(B) | (~l1_orders_2(B))) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))) <=> (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))) <=> ((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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(((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(70,plain,
% 0.20/0.51 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.51 tff(71,plain,
% 0.20/0.51 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(72,plain,
% 0.20/0.51 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(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)))), ((((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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))) <=> ((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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))), 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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))) <=> ((~(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))), ((((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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))) <=> ((~(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))))), (![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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))) <=> ![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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))), ((((~v3_struct_0(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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))) <=> (((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))))), rewrite((((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))) <=> ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))), ((((~v3_struct_0(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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))) <=> ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))))), (![B: $i] : (((~v3_struct_0(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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))) <=> ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))) <=> (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))))), rewrite((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(73,plain,
% 0.20/0.51 (![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.52 tff(74,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d16_waybel34')).
% 0.20/0.52 tff(75,plain,
% 0.20/0.52 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.52 tff(76,plain,
% 0.20/0.52 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.52 tff(77,plain,(
% 0.20/0.52 ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[76])).
% 0.20/0.52 tff(78,plain,
% 0.20/0.52 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.20/0.52 tff(79,plain,
% 0.20/0.52 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.20/0.52 tff(80,plain,
% 0.20/0.52 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(81,plain,
% 0.20/0.52 ((v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B)))))) <=> (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(82,plain,
% 0.20/0.52 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0)))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[81])).
% 0.20/0.52 tff(83,plain,
% 0.20/0.52 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[82, 80])).
% 0.20/0.52 tff(84,plain,
% 0.20/0.52 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0))) | (~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(85,plain,
% 0.20/0.52 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((v5_waybel34(C, A, B) <=> r4_waybel_0(A, B, C, k1_pre_topc(A))) | (~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_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.52 tff(86,plain,
% 0.20/0.52 (![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[85, 36, 35, 79])).
% 0.20/0.52 tff(87,plain,
% 0.20/0.52 (((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C, k1_pre_topc(A!0)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0)))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C, k1_pre_topc(A!0)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(88,plain,
% 0.20/0.52 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0)))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C, k1_pre_topc(A!0)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(89,plain,
% 0.20/0.52 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0)))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C, k1_pre_topc(A!0))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.52 tff(90,plain,
% 0.20/0.52 (![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C, k1_pre_topc(A!0))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[89, 45, 44, 86])).
% 0.20/0.52 tff(91,plain,
% 0.20/0.52 (((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C, k1_pre_topc(A!0))))) | ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C!2, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C, k1_pre_topc(A!0))))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C!2, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(92,plain,
% 0.20/0.52 ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C, k1_pre_topc(A!0))))) | ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C!2, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(93,plain,
% 0.20/0.52 ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C, k1_pre_topc(A!0))))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (v5_waybel34(C!2, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.52 tff(94,plain,
% 0.20/0.52 (v5_waybel34(C!2, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[93, 57, 56, 55, 90])).
% 0.20/0.52 tff(95,plain,
% 0.20/0.52 (^[A: $i] : refl(((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A))))) <=> ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(96,plain,
% 0.20/0.52 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A))))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.52 tff(97,plain,
% 0.20/0.52 (^[A: $i] : rewrite(((~l1_orders_2(A)) | (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A))) <=> ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(98,plain,
% 0.20/0.52 (![A: $i] : ((~l1_orders_2(A)) | (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A))) <=> ![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.52 tff(99,plain,
% 0.20/0.52 (![A: $i] : ((~l1_orders_2(A)) | (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A))) <=> ![A: $i] : ((~l1_orders_2(A)) | (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(100,plain,
% 0.20/0.52 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)))), ((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) <=> ((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))))), rewrite(((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)))), ((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A))))), (((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) <=> ((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))))), rewrite(((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)))), (((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A))))), ((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) <=> ((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))))), rewrite(((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)))), ((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A))))), (((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) <=> ((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))))), rewrite(((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)))), (((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A))))), ((((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))) <=> ((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))))), rewrite(((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)))), ((((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A))))), (((((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))) & v1_waybel_0(k1_pre_topc(A), A)) <=> ((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A))) & v1_waybel_0(k1_pre_topc(A), A)))), rewrite(((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A))) & v1_waybel_0(k1_pre_topc(A), A)) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A))), (((((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))) & v1_waybel_0(k1_pre_topc(A), A)) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A)))), ((((((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))) & v1_waybel_0(k1_pre_topc(A), A)) & v2_waybel_0(k1_pre_topc(A), A)) <=> ((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A)) & v2_waybel_0(k1_pre_topc(A), A)))), rewrite(((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A)) & v2_waybel_0(k1_pre_topc(A), A)) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A))), ((((((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))) & v1_waybel_0(k1_pre_topc(A), A)) & v2_waybel_0(k1_pre_topc(A), A)) <=> (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A)))), ((l1_orders_2(A) => (((((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))) & v1_waybel_0(k1_pre_topc(A), A)) & v2_waybel_0(k1_pre_topc(A), A))) <=> (l1_orders_2(A) => (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A))))), rewrite((l1_orders_2(A) => (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A))) <=> ((~l1_orders_2(A)) | (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A)))), ((l1_orders_2(A) => (((((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))) & v1_waybel_0(k1_pre_topc(A), A)) & v2_waybel_0(k1_pre_topc(A), A))) <=> ((~l1_orders_2(A)) | (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(101,plain,
% 0.20/0.52 (![A: $i] : (l1_orders_2(A) => (((((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))) & v1_waybel_0(k1_pre_topc(A), A)) & v2_waybel_0(k1_pre_topc(A), A))) <=> ![A: $i] : ((~l1_orders_2(A)) | (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.52 tff(102,axiom,(![A: $i] : (l1_orders_2(A) => (((((((((v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A)) & v1_finset_1(k1_pre_topc(A))) & v1_membered(k1_pre_topc(A))) & v2_membered(k1_pre_topc(A))) & v3_membered(k1_pre_topc(A))) & v4_membered(k1_pre_topc(A))) & v5_membered(k1_pre_topc(A))) & v1_waybel_0(k1_pre_topc(A), A)) & v2_waybel_0(k1_pre_topc(A), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_waybel_0')).
% 0.20/0.52 tff(103,plain,
% 0.20/0.52 (![A: $i] : ((~l1_orders_2(A)) | (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.52 tff(104,plain,
% 0.20/0.52 (![A: $i] : ((~l1_orders_2(A)) | (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.52 tff(105,plain,(
% 0.20/0.52 ![A: $i] : ((~l1_orders_2(A)) | (v1_xboole_0(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A), A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v1_waybel_0(k1_pre_topc(A), A) & v2_waybel_0(k1_pre_topc(A), A)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[104])).
% 0.20/0.52 tff(106,plain,
% 0.20/0.52 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.20/0.52 tff(107,plain,
% 0.20/0.52 (![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.20/0.52 tff(108,plain,
% 0.20/0.52 (((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))) | ((~l1_orders_2(A!0)) | (~((~v1_membered(k1_pre_topc(A!0))) | (~v1_xboole_0(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0)))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))) | (~l1_orders_2(A!0)) | (~((~v1_membered(k1_pre_topc(A!0))) | (~v1_xboole_0(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(109,plain,
% 0.20/0.52 (((~l1_orders_2(A!0)) | (~((~v1_xboole_0(k1_pre_topc(A!0))) | (~v1_membered(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0))))) <=> ((~l1_orders_2(A!0)) | (~((~v1_membered(k1_pre_topc(A!0))) | (~v1_xboole_0(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(110,plain,
% 0.20/0.52 (((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))) | ((~l1_orders_2(A!0)) | (~((~v1_xboole_0(k1_pre_topc(A!0))) | (~v1_membered(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0)))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))) | ((~l1_orders_2(A!0)) | (~((~v1_membered(k1_pre_topc(A!0))) | (~v1_xboole_0(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.52 tff(111,plain,
% 0.20/0.52 (((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))) | ((~l1_orders_2(A!0)) | (~((~v1_xboole_0(k1_pre_topc(A!0))) | (~v1_membered(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0)))))) <=> ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))) | (~l1_orders_2(A!0)) | (~((~v1_membered(k1_pre_topc(A!0))) | (~v1_xboole_0(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[110, 108])).
% 0.20/0.53 tff(112,plain,
% 0.20/0.53 ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))) | ((~l1_orders_2(A!0)) | (~((~v1_xboole_0(k1_pre_topc(A!0))) | (~v1_membered(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(113,plain,
% 0.20/0.53 ((~![A: $i] : ((~l1_orders_2(A)) | (~((~v1_xboole_0(k1_pre_topc(A))) | (~v1_membered(k1_pre_topc(A))) | (~v2_membered(k1_pre_topc(A))) | (~v3_membered(k1_pre_topc(A))) | (~v4_membered(k1_pre_topc(A))) | (~v5_membered(k1_pre_topc(A))) | (~v1_finset_1(k1_pre_topc(A))) | (~v5_orders_2(k1_pre_topc(A), A)) | (~v1_waybel_0(k1_pre_topc(A), A)) | (~v2_waybel_0(k1_pre_topc(A), A)))))) | (~l1_orders_2(A!0)) | (~((~v1_membered(k1_pre_topc(A!0))) | (~v1_xboole_0(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.53 tff(114,plain,
% 0.20/0.53 (~((~v1_membered(k1_pre_topc(A!0))) | (~v1_xboole_0(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[113, 35, 107])).
% 0.20/0.53 tff(115,plain,
% 0.20/0.53 (((~v1_membered(k1_pre_topc(A!0))) | (~v1_xboole_0(k1_pre_topc(A!0))) | (~v2_membered(k1_pre_topc(A!0))) | (~v3_membered(k1_pre_topc(A!0))) | (~v4_membered(k1_pre_topc(A!0))) | (~v5_membered(k1_pre_topc(A!0))) | (~v1_finset_1(k1_pre_topc(A!0))) | (~v5_orders_2(k1_pre_topc(A!0), A!0)) | (~v1_waybel_0(k1_pre_topc(A!0), A!0)) | (~v2_waybel_0(k1_pre_topc(A!0), A!0))) | v1_xboole_0(k1_pre_topc(A!0))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(116,plain,
% 0.20/0.53 (v1_xboole_0(k1_pre_topc(A!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.20/0.53 tff(117,plain,
% 0.20/0.53 (^[A: $i, B: $i] : refl(((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)) <=> ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(118,plain,
% 0.20/0.53 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)) <=> ![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.53 tff(119,plain,
% 0.20/0.53 (^[A: $i, B: $i] : trans(monotonicity(rewrite((v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)) <=> (~((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))), ((~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> (~(~((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))))), rewrite((~(~((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B)))) <=> ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))), ((~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(120,plain,
% 0.20/0.53 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.53 tff(121,plain,
% 0.20/0.53 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(122,plain,
% 0.20/0.53 (^[A: $i, B: $i] : rewrite((~((v1_xboole_0(A) & (~(A = B))) & v1_xboole_0(B))) <=> (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(123,plain,
% 0.20/0.53 (![A: $i, B: $i] : (~((v1_xboole_0(A) & (~(A = B))) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.53 tff(124,axiom,(![A: $i, B: $i] : (~((v1_xboole_0(A) & (~(A = B))) & v1_xboole_0(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 0.20/0.53 tff(125,plain,
% 0.20/0.53 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.53 tff(126,plain,
% 0.20/0.53 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.20/0.53 tff(127,plain,(
% 0.20/0.53 ![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[126])).
% 0.20/0.53 tff(128,plain,
% 0.20/0.53 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.20/0.53 tff(129,plain,
% 0.20/0.53 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[128, 118])).
% 0.20/0.53 tff(130,plain,
% 0.20/0.53 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(131,axiom,(((((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)) & v4_membered(k1_xboole_0)) & v5_membered(k1_xboole_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc6_membered')).
% 0.20/0.53 tff(132,plain,
% 0.20/0.53 ((((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)) & v4_membered(k1_xboole_0)),
% 0.20/0.53 inference(and_elim,[status(thm)],[131])).
% 0.20/0.53 tff(133,plain,
% 0.20/0.53 (((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)),
% 0.20/0.53 inference(and_elim,[status(thm)],[132])).
% 0.20/0.53 tff(134,plain,
% 0.20/0.53 ((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)),
% 0.20/0.53 inference(and_elim,[status(thm)],[133])).
% 0.20/0.53 tff(135,plain,
% 0.20/0.53 (v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)),
% 0.20/0.53 inference(and_elim,[status(thm)],[134])).
% 0.20/0.53 tff(136,plain,
% 0.20/0.53 (v1_xboole_0(k1_xboole_0)),
% 0.20/0.53 inference(and_elim,[status(thm)],[135])).
% 0.20/0.53 tff(137,plain,
% 0.20/0.53 (v1_xboole_0(k1_xboole_0)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[136, 130])).
% 0.20/0.53 tff(138,plain,
% 0.20/0.53 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(k1_pre_topc(A!0))) | (k1_pre_topc(A!0) = k1_xboole_0))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(k1_pre_topc(A!0))) | (k1_pre_topc(A!0) = k1_xboole_0))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(139,plain,
% 0.20/0.53 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | ((~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(k1_pre_topc(A!0))) | (k1_pre_topc(A!0) = k1_xboole_0))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(140,plain,
% 0.20/0.53 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))) | (~v1_xboole_0(k1_xboole_0)) | (~v1_xboole_0(k1_pre_topc(A!0))) | (k1_pre_topc(A!0) = k1_xboole_0)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.53 tff(141,plain,
% 0.20/0.53 (k1_pre_topc(A!0) = k1_xboole_0),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[140, 137, 129, 116])).
% 0.20/0.53 tff(142,plain,
% 0.20/0.53 (k1_xboole_0 = k1_pre_topc(A!0)),
% 0.20/0.53 inference(symmetry,[status(thm)],[141])).
% 0.20/0.53 tff(143,plain,
% 0.20/0.53 (r4_waybel_0(A!0, B!1, C!2, k1_xboole_0) <=> r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.53 tff(144,plain,
% 0.20/0.53 (m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k1_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.53 tff(145,plain,
% 0.20/0.53 (m1_subset_1(k1_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[144])).
% 0.20/0.53 tff(146,plain,
% 0.20/0.53 (^[A: $i] : refl((l1_struct_0(A) | (~l1_orders_2(A))) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(147,plain,
% 0.20/0.53 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[146])).
% 0.20/0.53 tff(148,plain,
% 0.20/0.53 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(149,plain,
% 0.20/0.53 (^[A: $i] : rewrite((l1_orders_2(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(150,plain,
% 0.20/0.53 (![A: $i] : (l1_orders_2(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[149])).
% 0.20/0.53 tff(151,axiom,(![A: $i] : (l1_orders_2(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 0.20/0.53 tff(152,plain,
% 0.20/0.53 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.53 tff(153,plain,
% 0.20/0.53 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.20/0.53 tff(154,plain,(
% 0.20/0.53 ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[153])).
% 0.20/0.53 tff(155,plain,
% 0.20/0.53 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.20/0.53 tff(156,plain,
% 0.20/0.53 (((~![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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(157,plain,
% 0.20/0.53 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(A!0) | (~l1_orders_2(A!0)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(158,plain,
% 0.20/0.53 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(A!0) | (~l1_orders_2(A!0))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.53 tff(159,plain,
% 0.20/0.53 (l1_struct_0(A!0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[158, 35, 155])).
% 0.20/0.53 tff(160,plain,
% 0.20/0.53 (^[A: $i] : refl(((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(161,plain,
% 0.20/0.53 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[160])).
% 0.20/0.53 tff(162,plain,
% 0.20/0.53 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(163,plain,
% 0.20/0.53 (^[A: $i] : rewrite((l1_struct_0(A) => m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(164,plain,
% 0.20/0.53 (![A: $i] : (l1_struct_0(A) => m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[163])).
% 0.20/0.53 tff(165,axiom,(![A: $i] : (l1_struct_0(A) => m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_pre_topc')).
% 0.20/0.53 tff(166,plain,
% 0.20/0.53 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.53 tff(167,plain,
% 0.20/0.53 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.20/0.53 tff(168,plain,(
% 0.20/0.53 ![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[167])).
% 0.20/0.53 tff(169,plain,
% 0.20/0.53 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.20/0.53 tff(170,plain,
% 0.20/0.53 (((~![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))) | ((~l1_struct_0(A!0)) | m1_subset_1(k1_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))) | (~l1_struct_0(A!0)) | m1_subset_1(k1_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(171,plain,
% 0.20/0.53 ((~![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))) | ((~l1_struct_0(A!0)) | m1_subset_1(k1_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(172,plain,
% 0.20/0.53 ((~![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))) | (~l1_struct_0(A!0)) | m1_subset_1(k1_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.53 tff(173,plain,
% 0.20/0.53 (m1_subset_1(k1_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[172, 169, 159])).
% 0.20/0.53 tff(174,plain,
% 0.20/0.53 (m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[173, 145])).
% 0.20/0.53 tff(175,plain,
% 0.20/0.53 (^[A: $i] : refl((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(176,plain,
% 0.20/0.53 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[175])).
% 0.20/0.53 tff(177,plain,
% 0.20/0.53 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(178,plain,
% 0.20/0.53 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[177])).
% 0.20/0.53 tff(179,plain,
% 0.20/0.53 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[178, 176])).
% 0.20/0.53 tff(180,plain,
% 0.20/0.53 (^[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))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & l1_orders_2(B)) <=> (~(v3_struct_0(B) | (~l1_orders_2(B))))), ((~((~v3_struct_0(B)) & l1_orders_2(B))) <=> (~(~(v3_struct_0(B) | (~l1_orders_2(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_orders_2(B))))) <=> (v3_struct_0(B) | (~l1_orders_2(B)))), ((~((~v3_struct_0(B)) & l1_orders_2(B))) <=> (v3_struct_0(B) | (~l1_orders_2(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(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)))))), trans(monotonicity(rewrite(((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) <=> ((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))), trans(monotonicity(rewrite((~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)))) <=> (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))), ((v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A))))) <=> (v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))) <=> (v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))), ((v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A))))) <=> (v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))), ((((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)))))) <=> (((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & (v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite((((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))))) & (v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))) <=> (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))), ((((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)))))) <=> (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))), (((~(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)))) | (((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A))))))) <=> (((~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)))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))), 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)))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))) <=> ((~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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))), (((~(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)))) | (((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A))))))) <=> ((~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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))), (![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)))) | (((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A))))))) <=> ![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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))), (((~((~v3_struct_0(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)))) | (((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)))))))) <=> ((v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))), rewrite(((v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))) <=> (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))), (((~((~v3_struct_0(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)))) | (((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)))))))) <=> (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))))), (![B: $i] : ((~((~v3_struct_0(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)))) | (((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)))))))) <=> ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A))))))))) <=> ((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))))), rewrite(((v3_struct_0(A) | (~l1_orders_2(A))) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))), (((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A))))))))) <=> (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(181,plain,
% 0.20/0.53 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[180])).
% 0.20/0.53 tff(182,plain,
% 0.20/0.53 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(183,plain,
% 0.20/0.53 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(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)))), rewrite((v4_waybel34(C, A, B) <=> ![D: $i] : ((v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => r4_waybel_0(A, B, C, D))) <=> (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D)))), ((((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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => r4_waybel_0(A, B, C, D)))) <=> ((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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D)))))), 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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D)))) <=> ((~(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))))), ((((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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => r4_waybel_0(A, B, C, D)))) <=> ((~(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))))))), (![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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => r4_waybel_0(A, B, C, D)))) <=> ![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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D)))))), ((((~v3_struct_0(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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => r4_waybel_0(A, B, C, D))))) <=> (((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))))))), rewrite((((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))))) <=> ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D)))))), ((((~v3_struct_0(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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => r4_waybel_0(A, B, C, D))))) <=> ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D)))))))), (![B: $i] : (((~v3_struct_0(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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => r4_waybel_0(A, B, C, D))))) <=> ![B: $i] : ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => r4_waybel_0(A, B, C, D)))))) <=> (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D)))))))), rewrite((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D)))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))))))), ((((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => r4_waybel_0(A, B, C, D)))))) <=> ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(184,plain,
% 0.20/0.53 (![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => r4_waybel_0(A, B, C, D)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[183])).
% 0.20/0.53 tff(185,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_orders_2(A)) => ![B: $i] : (((~v3_struct_0(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))) => (v4_waybel34(C, A, B) <=> ![D: $i] : ((v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => r4_waybel_0(A, B, C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d15_waybel34')).
% 0.20/0.53 tff(186,plain,
% 0.20/0.53 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.54 tff(187,plain,
% 0.20/0.54 (![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (v4_waybel34(C, A, B) <=> ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.20/0.54 tff(188,plain,(
% 0.20/0.54 ![A: $i] : ((~((~v3_struct_0(A)) & l1_orders_2(A))) | ![B: $i] : ((~((~v3_struct_0(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)))) | (((~v4_waybel34(C, A, B)) | ![D: $i] : ((~(v1_finset_1(D) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, D))) & (v4_waybel34(C, A, B) | (~((~(v1_finset_1(tptp_fun_D_3(C, B, A)) & m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A))))) | r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)))))))))),
% 0.20/0.54 inference(skolemize,[status(sab)],[187])).
% 0.20/0.54 tff(189,plain,
% 0.20/0.54 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.20/0.54 tff(190,plain,
% 0.20/0.54 (![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[189, 179])).
% 0.20/0.54 tff(191,plain,
% 0.20/0.54 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0)))))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(192,plain,
% 0.20/0.54 ((v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : (r4_waybel_0(A!0, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~(r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0)) | (~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0))))))))))))) <=> (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0)))))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(193,plain,
% 0.20/0.54 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : (r4_waybel_0(A!0, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~(r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0)) | (~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0))))))))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[192])).
% 0.20/0.54 tff(194,plain,
% 0.20/0.54 (((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : (r4_waybel_0(A!0, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~(r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0)) | (~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0)))))))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[193, 191])).
% 0.20/0.54 tff(195,plain,
% 0.20/0.54 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))) | (v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B))) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : (r4_waybel_0(A!0, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~(r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0)) | (~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(196,plain,
% 0.20/0.54 ((~![A: $i] : (v3_struct_0(A) | (~l1_orders_2(A)) | ![B: $i] : (v3_struct_0(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))) | (~((~((~v4_waybel34(C, A, B)) | ![D: $i] : (r4_waybel_0(A, B, C, D) | (~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))))) | (~(v4_waybel34(C, A, B) | (~(r4_waybel_0(A, B, C, tptp_fun_D_3(C, B, A)) | (~v1_finset_1(tptp_fun_D_3(C, B, A))) | (~m1_subset_1(tptp_fun_D_3(C, B, A), k1_zfmisc_1(u1_struct_0(A)))))))))))))) | v3_struct_0(A!0) | (~l1_orders_2(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0))))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.54 tff(197,plain,
% 0.20/0.54 (![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0))))))))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[196, 36, 35, 190])).
% 0.20/0.54 tff(198,plain,
% 0.20/0.54 (((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0))))))))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, D)))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0))))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0))))))))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, D)))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0))))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(199,plain,
% 0.20/0.54 ((v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B!1, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)))))))))) <=> (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, D)))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0))))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(200,plain,
% 0.20/0.54 (((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0))))))))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B!1, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0))))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0))))))))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, D)))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)))))))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[199])).
% 0.20/0.54 tff(201,plain,
% 0.20/0.54 (((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0))))))))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B!1, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0))))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0))))))))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, D)))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0))))))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[200, 198])).
% 0.20/0.54 tff(202,plain,
% 0.20/0.54 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0))))))))))) | (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B!1, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0))))))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(203,plain,
% 0.20/0.54 ((~![B: $i] : (v3_struct_0(B) | (~l1_orders_2(B)) | ![C: $i] : ((~v1_funct_1(C)) | (~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))) | (~((~((~v4_waybel34(C, A!0, B)) | ![D: $i] : ((~v1_finset_1(D)) | r4_waybel_0(A!0, B, C, D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0))))))) | (~(v4_waybel34(C, A!0, B) | (~((~v1_finset_1(tptp_fun_D_3(C, B, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B, C, tptp_fun_D_3(C, B, A!0))))))))))) | v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, D)))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.54 tff(204,plain,
% 0.20/0.54 (![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, D)))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)))))))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[203, 45, 44, 197])).
% 0.20/0.54 tff(205,plain,
% 0.20/0.54 (((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, D)))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)))))))))) | ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C!2, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D)))) | (~(v4_waybel34(C!2, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C!2, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, D)))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)))))))))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C!2, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D)))) | (~(v4_waybel34(C!2, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C!2, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(206,plain,
% 0.20/0.54 ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, D)))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)))))))))) | ((~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C!2, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D)))) | (~(v4_waybel34(C!2, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C!2, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)))))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(207,plain,
% 0.20/0.54 ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, D)))) | (~(v4_waybel34(C, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)))))))))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~((~((~v4_waybel34(C!2, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D)))) | (~(v4_waybel34(C!2, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C!2, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.20/0.55 tff(208,plain,
% 0.20/0.55 (~((~((~v4_waybel34(C!2, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D)))) | (~(v4_waybel34(C!2, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C!2, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[207, 57, 56, 55, 204])).
% 0.20/0.55 tff(209,plain,
% 0.20/0.55 (((~((~v4_waybel34(C!2, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D)))) | (~(v4_waybel34(C!2, A!0, B!1) | (~((~v1_finset_1(tptp_fun_D_3(C!2, B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(C!2, B!1, A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0))))))) | ((~v4_waybel34(C!2, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(210,plain,
% 0.20/0.55 ((~v4_waybel34(C!2, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.20/0.55 tff(211,plain,
% 0.20/0.55 (v4_waybel34(C!2, A!0, B!1)),
% 0.20/0.55 inference(or_elim,[status(thm)],[53])).
% 0.20/0.55 tff(212,plain,
% 0.20/0.55 ((~((~v4_waybel34(C!2, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D)))) | (~v4_waybel34(C!2, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(213,plain,
% 0.20/0.55 ((~((~v4_waybel34(C!2, A!0, B!1)) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D)))) | ![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.20/0.55 tff(214,plain,
% 0.20/0.55 (![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[213, 210])).
% 0.20/0.55 tff(215,plain,
% 0.20/0.55 (^[A: $i] : refl((v1_finset_1(A) | (~v1_xboole_0(A))) <=> (v1_finset_1(A) | (~v1_xboole_0(A))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(216,plain,
% 0.20/0.55 (![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A))) <=> ![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[215])).
% 0.20/0.55 tff(217,plain,
% 0.20/0.55 (![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A))) <=> ![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(218,plain,
% 0.20/0.55 (^[A: $i] : rewrite((v1_xboole_0(A) => v1_finset_1(A)) <=> (v1_finset_1(A) | (~v1_xboole_0(A))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(219,plain,
% 0.20/0.55 (![A: $i] : (v1_xboole_0(A) => v1_finset_1(A)) <=> ![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[218])).
% 0.20/0.55 tff(220,axiom,(![A: $i] : (v1_xboole_0(A) => v1_finset_1(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_finset_1')).
% 0.20/0.55 tff(221,plain,
% 0.20/0.55 (![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.20/0.55 tff(222,plain,
% 0.20/0.55 (![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.20/0.55 tff(223,plain,(
% 0.20/0.55 ![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.20/0.55 inference(skolemize,[status(sab)],[222])).
% 0.20/0.55 tff(224,plain,
% 0.20/0.55 (![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[223, 216])).
% 0.20/0.55 tff(225,plain,
% 0.20/0.55 (((~![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))) | (v1_finset_1(k1_xboole_0) | (~v1_xboole_0(k1_xboole_0)))) <=> ((~![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))) | v1_finset_1(k1_xboole_0) | (~v1_xboole_0(k1_xboole_0)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(226,plain,
% 0.20/0.55 ((~![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))) | (v1_finset_1(k1_xboole_0) | (~v1_xboole_0(k1_xboole_0)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(227,plain,
% 0.20/0.55 ((~![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))) | v1_finset_1(k1_xboole_0) | (~v1_xboole_0(k1_xboole_0))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.20/0.55 tff(228,plain,
% 0.20/0.55 (v1_finset_1(k1_xboole_0)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[227, 224, 137])).
% 0.20/0.55 tff(229,plain,
% 0.20/0.55 (((~![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))) | ((~v1_finset_1(k1_xboole_0)) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, k1_xboole_0))) <=> ((~![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))) | (~v1_finset_1(k1_xboole_0)) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, k1_xboole_0))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(230,plain,
% 0.20/0.55 ((~![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))) | ((~v1_finset_1(k1_xboole_0)) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, k1_xboole_0))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(231,plain,
% 0.20/0.55 ((~![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))) | (~v1_finset_1(k1_xboole_0)) | (~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, k1_xboole_0)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.20/0.55 tff(232,plain,
% 0.20/0.55 ((~m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, k1_xboole_0)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[231, 228, 214])).
% 0.20/0.55 tff(233,plain,
% 0.20/0.55 (r4_waybel_0(A!0, B!1, C!2, k1_xboole_0)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[232, 174])).
% 0.20/0.55 tff(234,plain,
% 0.20/0.55 (r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[233, 143])).
% 0.20/0.55 tff(235,plain,
% 0.20/0.55 ((~(v5_waybel34(C!2, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0)))) | v5_waybel34(C!2, A!0, B!1) | (~r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(236,plain,
% 0.20/0.55 (v5_waybel34(C!2, A!0, B!1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[235, 234, 94])).
% 0.20/0.55 tff(237,plain,
% 0.20/0.55 ((~(~((~v20_waybel_0(C!2, A!0, B!1)) | (~v5_waybel34(C!2, A!0, B!1))))) <=> ((~v20_waybel_0(C!2, A!0, B!1)) | (~v5_waybel34(C!2, A!0, B!1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(238,plain,
% 0.20/0.55 ((v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1)) <=> (~((~v20_waybel_0(C!2, A!0, B!1)) | (~v5_waybel34(C!2, A!0, B!1))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(239,plain,
% 0.20/0.55 ((~(v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1))) <=> (~(~((~v20_waybel_0(C!2, A!0, B!1)) | (~v5_waybel34(C!2, A!0, B!1)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[238])).
% 0.20/0.55 tff(240,plain,
% 0.20/0.55 ((~(v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1))) <=> ((~v20_waybel_0(C!2, A!0, B!1)) | (~v5_waybel34(C!2, A!0, B!1)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[239, 237])).
% 0.20/0.55 tff(241,plain,
% 0.20/0.55 (~(v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1))),
% 0.20/0.55 inference(or_elim,[status(thm)],[53])).
% 0.20/0.55 tff(242,plain,
% 0.20/0.55 ((~v20_waybel_0(C!2, A!0, B!1)) | (~v5_waybel34(C!2, A!0, B!1))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.20/0.55 tff(243,plain,
% 0.20/0.55 (~v20_waybel_0(C!2, A!0, B!1)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[242, 236])).
% 0.20/0.55 tff(244,plain,
% 0.20/0.55 ((~(v20_waybel_0(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))))) | v20_waybel_0(C!2, A!0, B!1) | (~((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(245,plain,
% 0.20/0.55 (~((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[244, 243, 63])).
% 0.20/0.55 tff(246,plain,
% 0.20/0.55 (((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))) | m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(247,plain,
% 0.20/0.55 (m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.20/0.55 tff(248,plain,
% 0.20/0.55 (((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))) | m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(249,plain,
% 0.20/0.55 (m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[248, 245])).
% 0.20/0.55 tff(250,plain,
% 0.20/0.55 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(251,plain,
% 0.20/0.55 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[250])).
% 0.20/0.55 tff(252,plain,
% 0.20/0.55 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C))) <=> ((v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C))))), rewrite(((v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C))) <=> (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C))) <=> (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(253,plain,
% 0.20/0.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[252])).
% 0.20/0.55 tff(254,plain,
% 0.20/0.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(255,plain,
% 0.20/0.55 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k2_struct_0(A, B, C) = k2_tarski(B, C))) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k2_struct_0(A, B, C) = k2_tarski(B, C))))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k2_struct_0(A, B, C) = k2_tarski(B, C))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C)))), ((((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k2_struct_0(A, B, C) = k2_tarski(B, C))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(256,plain,
% 0.20/0.55 (![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k2_struct_0(A, B, C) = k2_tarski(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[255])).
% 0.20/0.55 tff(257,axiom,(![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k2_struct_0(A, B, C) = k2_tarski(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k2_struct_0')).
% 0.20/0.55 tff(258,plain,
% 0.20/0.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.20/0.55 tff(259,plain,
% 0.20/0.55 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[258, 254])).
% 0.20/0.55 tff(260,plain,(
% 0.20/0.55 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k2_struct_0(A, B, C) = k2_tarski(B, C)))),
% 0.20/0.55 inference(skolemize,[status(sab)],[259])).
% 0.20/0.55 tff(261,plain,
% 0.20/0.55 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[260, 253])).
% 0.20/0.55 tff(262,plain,
% 0.20/0.55 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[261, 251])).
% 0.20/0.55 tff(263,plain,
% 0.20/0.55 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(264,plain,
% 0.20/0.55 ((v3_struct_0(A!0) | (k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(265,plain,
% 0.20/0.55 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[264])).
% 0.20/0.55 tff(266,plain,
% 0.20/0.55 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[265, 263])).
% 0.20/0.55 tff(267,plain,
% 0.20/0.55 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(268,plain,
% 0.20/0.55 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k2_struct_0(A, B, C) = k2_tarski(B, C)) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.20/0.55 tff(269,plain,
% 0.20/0.55 (k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[268, 36, 262, 159, 249, 247])).
% 0.20/0.55 tff(270,plain,
% 0.20/0.55 (k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)) = k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))),
% 0.20/0.55 inference(symmetry,[status(thm)],[269])).
% 0.20/0.55 tff(271,plain,
% 0.20/0.55 (v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) <=> v1_finset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[270])).
% 0.20/0.55 tff(272,plain,
% 0.20/0.55 (v1_finset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) <=> v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))),
% 0.20/0.55 inference(symmetry,[status(thm)],[271])).
% 0.20/0.55 tff(273,plain,
% 0.20/0.55 ((~v1_finset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))) <=> (~v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[272])).
% 0.20/0.55 tff(274,plain,
% 0.20/0.55 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(275,plain,
% 0.20/0.55 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[274])).
% 0.20/0.56 tff(276,plain,
% 0.20/0.56 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A)))))), rewrite(((v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(277,plain,
% 0.20/0.56 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[276])).
% 0.20/0.56 tff(278,plain,
% 0.20/0.56 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(279,plain,
% 0.20/0.56 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))))), ((((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(280,plain,
% 0.20/0.56 (![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[279])).
% 0.20/0.56 tff(281,axiom,(![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l1_struct_0(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_struct_0')).
% 0.20/0.56 tff(282,plain,
% 0.20/0.56 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.20/0.56 tff(283,plain,
% 0.20/0.56 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[282, 278])).
% 0.20/0.56 tff(284,plain,(
% 0.20/0.56 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))))),
% 0.20/0.56 inference(skolemize,[status(sab)],[283])).
% 0.20/0.56 tff(285,plain,
% 0.20/0.56 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[284, 277])).
% 0.20/0.56 tff(286,plain,
% 0.20/0.56 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[285, 275])).
% 0.20/0.56 tff(287,plain,
% 0.20/0.56 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(288,plain,
% 0.20/0.56 ((v3_struct_0(A!0) | m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(289,plain,
% 0.20/0.56 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[288])).
% 0.20/0.56 tff(290,plain,
% 0.20/0.56 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[289, 287])).
% 0.20/0.56 tff(291,plain,
% 0.20/0.56 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0))) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(292,plain,
% 0.20/0.56 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_struct_0(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.20/0.56 tff(293,plain,
% 0.20/0.56 (m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[292, 36, 286, 159, 249, 247])).
% 0.20/0.56 tff(294,plain,
% 0.20/0.56 (((~m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))) | (~r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(295,plain,
% 0.20/0.56 (~r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[294, 245])).
% 0.20/0.56 tff(296,plain,
% 0.20/0.56 (((~![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))) | ((~v1_finset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))) | (~m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))) <=> ((~![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))) | (~v1_finset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))) | (~m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(297,plain,
% 0.20/0.56 ((~![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))) | ((~v1_finset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))) | (~m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(298,plain,
% 0.20/0.56 ((~![D: $i] : ((~v1_finset_1(D)) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, D))) | (~v1_finset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))) | (~m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | r4_waybel_0(A!0, B!1, C!2, k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.20/0.56 tff(299,plain,
% 0.20/0.56 ((~v1_finset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))) | (~m1_subset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[298, 214, 295])).
% 0.20/0.56 tff(300,plain,
% 0.20/0.56 (~v1_finset_1(k2_struct_0(A!0, tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[299, 293])).
% 0.20/0.56 tff(301,plain,
% 0.20/0.56 (~v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[300, 273])).
% 0.20/0.56 tff(302,plain,
% 0.20/0.56 (^[A: $i, B: $i] : refl((~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B))))) <=> (~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(303,plain,
% 0.20/0.56 (![A: $i, B: $i] : (~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B))))) <=> ![A: $i, B: $i] : (~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B)))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[302])).
% 0.20/0.56 tff(304,plain,
% 0.20/0.56 (^[A: $i, B: $i] : rewrite(((~v1_xboole_0(k2_tarski(A, B))) & v1_finset_1(k2_tarski(A, B))) <=> (~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(305,plain,
% 0.20/0.57 (![A: $i, B: $i] : ((~v1_xboole_0(k2_tarski(A, B))) & v1_finset_1(k2_tarski(A, B))) <=> ![A: $i, B: $i] : (~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B)))))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[304])).
% 0.20/0.57 tff(306,plain,
% 0.20/0.57 (![A: $i, B: $i] : ((~v1_xboole_0(k2_tarski(A, B))) & v1_finset_1(k2_tarski(A, B))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(k2_tarski(A, B))) & v1_finset_1(k2_tarski(A, B)))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(307,axiom,(![A: $i, B: $i] : ((~v1_xboole_0(k2_tarski(A, B))) & v1_finset_1(k2_tarski(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc2_finset_1')).
% 0.20/0.57 tff(308,plain,
% 0.20/0.57 (![A: $i, B: $i] : ((~v1_xboole_0(k2_tarski(A, B))) & v1_finset_1(k2_tarski(A, B)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.20/0.57 tff(309,plain,(
% 0.20/0.57 ![A: $i, B: $i] : ((~v1_xboole_0(k2_tarski(A, B))) & v1_finset_1(k2_tarski(A, B)))),
% 0.20/0.57 inference(skolemize,[status(sab)],[308])).
% 0.20/0.57 tff(310,plain,
% 0.20/0.57 (![A: $i, B: $i] : (~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B)))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[309, 305])).
% 0.20/0.57 tff(311,plain,
% 0.20/0.57 (![A: $i, B: $i] : (~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B)))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[310, 303])).
% 0.20/0.57 tff(312,plain,
% 0.20/0.57 ((~![A: $i, B: $i] : (~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B)))))) | (~(v1_xboole_0(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) | (~v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(313,plain,
% 0.20/0.57 (~(v1_xboole_0(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) | (~v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[312, 311])).
% 0.20/0.57 tff(314,plain,
% 0.20/0.57 ((v1_xboole_0(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) | (~v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))) | v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(315,plain,
% 0.20/0.57 (v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[314, 313])).
% 0.20/0.57 tff(316,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[315, 301])).
% 0.20/0.57 % SZS output end Proof
% 0.40/0.57 % E exiting
%------------------------------------------------------------------------------