TSTP Solution File: LAT379+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT379+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 Sep 17 18:33:37 EDT 2022
% Result : Theorem 0.22s 0.52s
% Output : Proof 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LAT379+1 : TPTP v8.1.0. Released v3.4.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Sep 1 16:38:54 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.22/0.52 % SZS status Theorem
% 0.22/0.52 % SZS output start Proof
% 0.22/0.52 tff(v1_finset_1_type, type, (
% 0.22/0.52 v1_finset_1: $i > $o)).
% 0.22/0.52 tff(k2_tarski_type, type, (
% 0.22/0.52 k2_tarski: ( $i * $i ) > $i)).
% 0.22/0.52 tff(tptp_fun_E_5_type, type, (
% 0.22/0.52 tptp_fun_E_5: ( $i * $i * $i ) > $i)).
% 0.22/0.52 tff(tptp_fun_A_0_type, type, (
% 0.22/0.52 tptp_fun_A_0: $i)).
% 0.22/0.52 tff(tptp_fun_B_1_type, type, (
% 0.22/0.52 tptp_fun_B_1: $i)).
% 0.22/0.52 tff(tptp_fun_C_2_type, type, (
% 0.22/0.52 tptp_fun_C_2: $i)).
% 0.22/0.52 tff(tptp_fun_D_4_type, type, (
% 0.22/0.52 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 0.22/0.52 tff(k2_struct_0_type, type, (
% 0.22/0.52 k2_struct_0: ( $i * $i * $i ) > $i)).
% 0.22/0.52 tff(m1_subset_1_type, type, (
% 0.22/0.52 m1_subset_1: ( $i * $i ) > $o)).
% 0.22/0.52 tff(u1_struct_0_type, type, (
% 0.22/0.52 u1_struct_0: $i > $i)).
% 0.22/0.52 tff(r4_waybel_0_type, type, (
% 0.22/0.52 r4_waybel_0: ( $i * $i * $i * $i ) > $o)).
% 0.22/0.52 tff(v20_waybel_0_type, type, (
% 0.22/0.52 v20_waybel_0: ( $i * $i * $i ) > $o)).
% 0.22/0.52 tff(m2_relset_1_type, type, (
% 0.22/0.52 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.22/0.52 tff(v1_funct_2_type, type, (
% 0.22/0.52 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.22/0.52 tff(v1_funct_1_type, type, (
% 0.22/0.52 v1_funct_1: $i > $o)).
% 0.22/0.52 tff(l1_orders_2_type, type, (
% 0.22/0.52 l1_orders_2: $i > $o)).
% 0.22/0.52 tff(v3_struct_0_type, type, (
% 0.22/0.52 v3_struct_0: $i > $o)).
% 0.22/0.52 tff(v4_waybel34_type, type, (
% 0.22/0.52 v4_waybel34: ( $i * $i * $i ) > $o)).
% 0.22/0.52 tff(v5_waybel34_type, type, (
% 0.22/0.52 v5_waybel34: ( $i * $i * $i ) > $o)).
% 0.22/0.52 tff(k1_pre_topc_type, type, (
% 0.22/0.52 k1_pre_topc: $i > $i)).
% 0.22/0.52 tff(k1_xboole_0_type, type, (
% 0.22/0.52 k1_xboole_0: $i)).
% 0.22/0.52 tff(v1_xboole_0_type, type, (
% 0.22/0.52 v1_xboole_0: $i > $o)).
% 0.22/0.52 tff(v2_waybel_0_type, type, (
% 0.22/0.52 v2_waybel_0: ( $i * $i ) > $o)).
% 0.22/0.52 tff(v1_waybel_0_type, type, (
% 0.22/0.52 v1_waybel_0: ( $i * $i ) > $o)).
% 0.22/0.52 tff(v5_orders_2_type, type, (
% 0.22/0.52 v5_orders_2: ( $i * $i ) > $o)).
% 0.22/0.52 tff(v5_membered_type, type, (
% 0.22/0.52 v5_membered: $i > $o)).
% 0.22/0.52 tff(v4_membered_type, type, (
% 0.22/0.52 v4_membered: $i > $o)).
% 0.22/0.52 tff(v3_membered_type, type, (
% 0.22/0.52 v3_membered: $i > $o)).
% 0.22/0.52 tff(v2_membered_type, type, (
% 0.22/0.52 v2_membered: $i > $o)).
% 0.22/0.52 tff(v1_membered_type, type, (
% 0.22/0.52 v1_membered: $i > $o)).
% 0.22/0.52 tff(k1_zfmisc_1_type, type, (
% 0.22/0.52 k1_zfmisc_1: $i > $i)).
% 0.22/0.52 tff(l1_struct_0_type, type, (
% 0.22/0.52 l1_struct_0: $i > $o)).
% 0.22/0.52 tff(tptp_fun_D_3_type, type, (
% 0.22/0.52 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.22/0.52 tff(1,plain,
% 0.22/0.52 (^[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))))))))))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(2,plain,
% 0.22/0.52 (![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))) | (~((~((~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)))))))))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.52 tff(3,plain,
% 0.22/0.52 (^[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)))))))))))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(4,plain,
% 0.22/0.52 (![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))) | (~((~((~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))))))))))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.52 tff(5,plain,
% 0.22/0.52 (^[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)))))))))))))),
% 0.22/0.52 inference(bind,[status(th)],[])).
% 0.22/0.52 tff(6,plain,
% 0.22/0.52 (![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))) | (~((~((~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))))))))))))),
% 0.22/0.52 inference(quant_intro,[status(thm)],[5])).
% 0.22/0.52 tff(7,plain,
% 0.22/0.52 (![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))) | (~((~((~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))))))))))))),
% 0.22/0.52 inference(transitivity,[status(thm)],[6, 4])).
% 0.22/0.52 tff(8,plain,
% 0.22/0.52 (^[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))))))))))))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(9,plain,
% 0.22/0.53 (![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)))) | (((~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))))))))))))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[8])).
% 0.22/0.53 tff(10,plain,
% 0.22/0.53 (^[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)))) | (((~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))))))))))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(11,plain,
% 0.22/0.53 (![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)))) | (((~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)))))))))))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.53 tff(12,plain,
% 0.22/0.53 (![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)))) | (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))))))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(13,plain,
% 0.22/0.53 (^[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((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))))))))))),
% 0.22/0.53 inference(bind,[status(th)],[])).
% 0.22/0.53 tff(14,plain,
% 0.22/0.53 (![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))) => (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))))))))),
% 0.22/0.53 inference(quant_intro,[status(thm)],[13])).
% 0.22/0.53 tff(15,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')).
% 0.22/0.53 tff(16,plain,
% 0.22/0.53 (![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)))) | (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))))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.22/0.53 tff(17,plain,
% 0.22/0.53 (![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)))) | (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))))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.22/0.53 tff(18,plain,(
% 0.22/0.53 ![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)))) | (((~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)))))))))))),
% 0.22/0.53 inference(skolemize,[status(sab)],[17])).
% 0.22/0.53 tff(19,plain,
% 0.22/0.53 (![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)))) | (((~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)))))))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.22/0.53 tff(20,plain,
% 0.22/0.53 (![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))) | (~((~((~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))))))))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.22/0.53 tff(21,plain,
% 0.22/0.53 (![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))) | (~((~((~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))))))))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[20, 7])).
% 0.22/0.53 tff(22,plain,
% 0.22/0.53 (![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))) | (~((~(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)))))))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[21, 2])).
% 0.22/0.53 tff(23,plain,
% 0.22/0.53 ((((~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)))))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(24,plain,
% 0.22/0.53 ((((~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)))))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(25,plain,
% 0.22/0.53 ((~((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))))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(26,plain,
% 0.22/0.53 ((~(~((~v3_struct_0(B!1)) & l1_orders_2(B!1)))) <=> ((~v3_struct_0(B!1)) & l1_orders_2(B!1))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(27,plain,
% 0.22/0.53 (((~(~((~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)))))))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[26, 25])).
% 0.22/0.53 tff(28,plain,
% 0.22/0.53 (((~(~((~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)))))))),
% 0.22/0.53 inference(transitivity,[status(thm)],[27, 24])).
% 0.22/0.53 tff(29,plain,
% 0.22/0.53 ((~(~((~v3_struct_0(A!0)) & l1_orders_2(A!0)))) <=> ((~v3_struct_0(A!0)) & l1_orders_2(A!0))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(30,plain,
% 0.22/0.53 (((~(~((~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))))))))),
% 0.22/0.53 inference(monotonicity,[status(thm)],[29, 28])).
% 0.22/0.53 tff(31,plain,
% 0.22/0.53 (((~(~((~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)))))))),
% 0.22/0.53 inference(transitivity,[status(thm)],[30, 23])).
% 0.22/0.53 tff(32,plain,
% 0.22/0.53 ((~![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))))))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(33,plain,
% 0.22/0.53 ((~![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) => (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))))))))),
% 0.22/0.53 inference(rewrite,[status(thm)],[])).
% 0.22/0.53 tff(34,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')).
% 0.22/0.53 tff(35,plain,
% 0.22/0.53 (~![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)))))))),
% 0.22/0.53 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.22/0.53 tff(36,plain,
% 0.22/0.53 (~![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)))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.22/0.54 tff(37,plain,
% 0.22/0.54 (~![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)))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.22/0.54 tff(38,plain,
% 0.22/0.54 (~![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)))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.22/0.54 tff(39,plain,
% 0.22/0.54 (~![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)))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[38, 32])).
% 0.22/0.54 tff(40,plain,
% 0.22/0.54 (~![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)))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.22/0.54 tff(41,plain,
% 0.22/0.54 (~![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)))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[40, 32])).
% 0.22/0.54 tff(42,plain,
% 0.22/0.54 ((~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))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.22/0.54 tff(43,plain,
% 0.22/0.54 (l1_orders_2(A!0)),
% 0.22/0.54 inference(and_elim,[status(thm)],[42])).
% 0.22/0.54 tff(44,plain,
% 0.22/0.54 (~v3_struct_0(A!0)),
% 0.22/0.54 inference(and_elim,[status(thm)],[42])).
% 0.22/0.54 tff(45,plain,
% 0.22/0.54 (((~![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))) | (~((~(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)) | (~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)))))))))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(46,plain,
% 0.22/0.54 ((~![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))) | (~((~(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)))))))))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(47,plain,
% 0.22/0.54 ((~![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))) | (~((~(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))))))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.22/0.54 tff(48,plain,
% 0.22/0.54 (![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))))))))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[47, 44, 43, 22])).
% 0.22/0.54 tff(49,plain,
% 0.22/0.54 (l1_orders_2(B!1)),
% 0.22/0.54 inference(and_elim,[status(thm)],[42])).
% 0.22/0.54 tff(50,plain,
% 0.22/0.54 (~v3_struct_0(B!1)),
% 0.22/0.54 inference(and_elim,[status(thm)],[42])).
% 0.22/0.54 tff(51,plain,
% 0.22/0.54 (((~![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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)) | (~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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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))))))))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(52,plain,
% 0.22/0.54 ((~![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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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))))))))))),
% 0.22/0.54 inference(quant_inst,[status(thm)],[])).
% 0.22/0.54 tff(53,plain,
% 0.22/0.54 ((~![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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)))))))))),
% 0.22/0.54 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.22/0.54 tff(54,plain,
% 0.22/0.54 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)))))))))),
% 0.22/0.54 inference(unit_resolution,[status(thm)],[53, 50, 49, 48])).
% 0.22/0.54 tff(55,plain,
% 0.22/0.54 (~((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)))))),
% 0.22/0.54 inference(and_elim,[status(thm)],[42])).
% 0.22/0.54 tff(56,plain,
% 0.22/0.54 (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))),
% 0.22/0.54 inference(or_elim,[status(thm)],[55])).
% 0.22/0.54 tff(57,plain,
% 0.22/0.54 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.22/0.54 inference(and_elim,[status(thm)],[56])).
% 0.22/0.54 tff(58,plain,
% 0.22/0.54 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.22/0.54 inference(and_elim,[status(thm)],[56])).
% 0.22/0.54 tff(59,plain,
% 0.22/0.54 (v1_funct_1(C!2)),
% 0.22/0.54 inference(and_elim,[status(thm)],[56])).
% 0.22/0.54 tff(60,plain,
% 0.22/0.54 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)))))))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(61,plain,
% 0.22/0.54 (((~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) | (~((~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))))))))) <=> ((~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)))))))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(62,plain,
% 0.22/0.54 (((~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)) | ![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)))))),
% 0.22/0.54 inference(rewrite,[status(thm)],[])).
% 0.22/0.54 tff(63,plain,
% 0.22/0.54 ((~((~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)) | ![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))))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[62])).
% 0.22/0.55 tff(64,plain,
% 0.22/0.55 ((~(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)))))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(65,plain,
% 0.22/0.55 (((~(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)) | ![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))))))) | (~((~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)))))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[64, 63])).
% 0.22/0.55 tff(66,plain,
% 0.22/0.55 ((~((~(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)) | ![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))))))) | (~((~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))))))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[65])).
% 0.22/0.55 tff(67,plain,
% 0.22/0.55 (((~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) | (~((~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))))))))) <=> ((~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) | (~((~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)))))))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[66])).
% 0.22/0.55 tff(68,plain,
% 0.22/0.55 (((~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) | (~((~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))))))))) <=> ((~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)))))))))),
% 0.22/0.55 inference(transitivity,[status(thm)],[67, 61])).
% 0.22/0.55 tff(69,plain,
% 0.22/0.55 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)) | (~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) | (~((~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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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))))))))))),
% 0.22/0.55 inference(monotonicity,[status(thm)],[68])).
% 0.22/0.55 tff(70,plain,
% 0.22/0.55 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)) | (~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) | (~((~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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)))))))))),
% 0.22/0.55 inference(transitivity,[status(thm)],[69, 60])).
% 0.22/0.55 tff(71,plain,
% 0.22/0.55 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)) | (~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) | (~((~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)))))))))),
% 0.22/0.55 inference(quant_inst,[status(thm)],[])).
% 0.22/0.55 tff(72,plain,
% 0.22/0.55 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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))))))))),
% 0.22/0.55 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.22/0.55 tff(73,plain,
% 0.22/0.55 (~((~(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)) | ![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)))))))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[72, 59, 58, 57, 54])).
% 0.22/0.55 tff(74,plain,
% 0.22/0.55 (((~(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)) | ![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))))))),
% 0.22/0.55 inference(tautology,[status(thm)],[])).
% 0.22/0.55 tff(75,plain,
% 0.22/0.55 (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)))))),
% 0.22/0.55 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.22/0.55 tff(76,plain,
% 0.22/0.55 (^[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)))))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(77,plain,
% 0.22/0.55 (![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))))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[76])).
% 0.22/0.55 tff(78,plain,
% 0.22/0.55 (^[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)))))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(79,plain,
% 0.22/0.55 (![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))))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[78])).
% 0.22/0.55 tff(80,plain,
% 0.22/0.55 (![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))))))),
% 0.22/0.55 inference(transitivity,[status(thm)],[79, 77])).
% 0.22/0.55 tff(81,plain,
% 0.22/0.55 (^[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))))))))),
% 0.22/0.55 inference(bind,[status(th)],[])).
% 0.22/0.55 tff(82,plain,
% 0.22/0.55 (![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))))))),
% 0.22/0.55 inference(quant_intro,[status(thm)],[81])).
% 0.22/0.55 tff(83,plain,
% 0.22/0.55 (![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))))))),
% 0.22/0.55 inference(rewrite,[status(thm)],[])).
% 0.22/0.55 tff(84,plain,
% 0.22/0.55 (^[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))))))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(85,plain,
% 0.22/0.56 (![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))))))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[84])).
% 0.22/0.56 tff(86,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')).
% 0.22/0.56 tff(87,plain,
% 0.22/0.56 (![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))))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.22/0.56 tff(88,plain,
% 0.22/0.56 (![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))))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.22/0.56 tff(89,plain,(
% 0.22/0.56 ![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))))))),
% 0.22/0.56 inference(skolemize,[status(sab)],[88])).
% 0.22/0.56 tff(90,plain,
% 0.22/0.56 (![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))))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.22/0.56 tff(91,plain,
% 0.22/0.56 (![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))))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.22/0.56 tff(92,plain,
% 0.22/0.56 (((~![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)) | (~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))) | (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)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0))))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(93,plain,
% 0.22/0.56 ((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)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0))))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(94,plain,
% 0.22/0.56 (((~![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)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0)))))))),
% 0.22/0.56 inference(monotonicity,[status(thm)],[93])).
% 0.22/0.56 tff(95,plain,
% 0.22/0.56 (((~![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)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0))))))),
% 0.22/0.56 inference(transitivity,[status(thm)],[94, 92])).
% 0.22/0.56 tff(96,plain,
% 0.22/0.56 ((~![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))))))),
% 0.22/0.56 inference(quant_inst,[status(thm)],[])).
% 0.22/0.56 tff(97,plain,
% 0.22/0.56 ((~![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)) | (~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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.22/0.56 tff(98,plain,
% 0.22/0.56 (![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))) | (v5_waybel34(C, A!0, B) <=> r4_waybel_0(A!0, B, C, k1_pre_topc(A!0)))))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[97, 44, 43, 91])).
% 0.22/0.56 tff(99,plain,
% 0.22/0.56 (((~![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))) | (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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)) | (~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))) | (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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(100,plain,
% 0.22/0.56 ((~![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))) | (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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)))))),
% 0.22/0.56 inference(quant_inst,[status(thm)],[])).
% 0.22/0.56 tff(101,plain,
% 0.22/0.56 ((~![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))) | (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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.22/0.56 tff(102,plain,
% 0.22/0.56 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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))))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[101, 50, 49, 98])).
% 0.22/0.56 tff(103,plain,
% 0.22/0.56 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(104,plain,
% 0.22/0.56 (((~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))) | (v5_waybel34(C!2, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C!2, 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))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(105,plain,
% 0.22/0.56 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)) | (~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))) | (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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)))))),
% 0.22/0.56 inference(monotonicity,[status(thm)],[104])).
% 0.22/0.56 tff(106,plain,
% 0.22/0.56 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)) | (~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))) | (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)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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))))),
% 0.22/0.56 inference(transitivity,[status(thm)],[105, 103])).
% 0.22/0.56 tff(107,plain,
% 0.22/0.56 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)) | (~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))) | (v5_waybel34(C!2, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0))))),
% 0.22/0.56 inference(quant_inst,[status(thm)],[])).
% 0.22/0.56 tff(108,plain,
% 0.22/0.56 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.22/0.56 tff(109,plain,
% 0.22/0.56 (v5_waybel34(C!2, A!0, B!1) <=> r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0))),
% 0.22/0.56 inference(unit_resolution,[status(thm)],[108, 59, 58, 57, 102])).
% 0.22/0.56 tff(110,plain,
% 0.22/0.56 (^[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))))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(111,plain,
% 0.22/0.56 (![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)))))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[110])).
% 0.22/0.56 tff(112,plain,
% 0.22/0.56 (^[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))))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(113,plain,
% 0.22/0.56 (![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)))))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[112])).
% 0.22/0.56 tff(114,plain,
% 0.22/0.56 (![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)))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(115,plain,
% 0.22/0.56 (^[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)))))),
% 0.22/0.56 inference(bind,[status(th)],[])).
% 0.22/0.56 tff(116,plain,
% 0.22/0.56 (![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)))),
% 0.22/0.56 inference(quant_intro,[status(thm)],[115])).
% 0.22/0.56 tff(117,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')).
% 0.22/0.56 tff(118,plain,
% 0.22/0.56 (![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)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.22/0.56 tff(119,plain,
% 0.22/0.56 (![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)))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.22/0.56 tff(120,plain,(
% 0.22/0.56 ![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)))),
% 0.22/0.56 inference(skolemize,[status(sab)],[119])).
% 0.22/0.56 tff(121,plain,
% 0.22/0.56 (![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)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.22/0.56 tff(122,plain,
% 0.22/0.56 (![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)))))),
% 0.22/0.56 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.22/0.56 tff(123,plain,
% 0.22/0.56 (((~![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)))))),
% 0.22/0.56 inference(rewrite,[status(thm)],[])).
% 0.22/0.56 tff(124,plain,
% 0.22/0.56 (((~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)))))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(125,plain,
% 0.22/0.57 (((~![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))))))),
% 0.22/0.57 inference(monotonicity,[status(thm)],[124])).
% 0.22/0.57 tff(126,plain,
% 0.22/0.57 (((~![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)))))),
% 0.22/0.57 inference(transitivity,[status(thm)],[125, 123])).
% 0.22/0.57 tff(127,plain,
% 0.22/0.57 ((~![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)))))),
% 0.22/0.57 inference(quant_inst,[status(thm)],[])).
% 0.22/0.57 tff(128,plain,
% 0.22/0.57 ((~![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))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.22/0.57 tff(129,plain,
% 0.22/0.57 (~((~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)))),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[128, 43, 122])).
% 0.22/0.57 tff(130,plain,
% 0.22/0.57 (((~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))),
% 0.22/0.57 inference(tautology,[status(thm)],[])).
% 0.22/0.57 tff(131,plain,
% 0.22/0.57 (v1_xboole_0(k1_pre_topc(A!0))),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.22/0.57 tff(132,plain,
% 0.22/0.57 (^[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)))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(133,plain,
% 0.22/0.57 (![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))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[132])).
% 0.22/0.57 tff(134,plain,
% 0.22/0.57 (^[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))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(135,plain,
% 0.22/0.57 (![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))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[134])).
% 0.22/0.57 tff(136,plain,
% 0.22/0.57 (![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)))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(137,plain,
% 0.22/0.57 (^[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))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(138,plain,
% 0.22/0.57 (![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)))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[137])).
% 0.22/0.57 tff(139,axiom,(![A: $i, B: $i] : (~((v1_xboole_0(A) & (~(A = B))) & v1_xboole_0(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 0.22/0.57 tff(140,plain,
% 0.22/0.57 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.22/0.57 tff(141,plain,
% 0.22/0.57 (![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.22/0.57 tff(142,plain,(
% 0.22/0.57 ![A: $i, B: $i] : (~(v1_xboole_0(A) & (~(A = B)) & v1_xboole_0(B)))),
% 0.22/0.57 inference(skolemize,[status(sab)],[141])).
% 0.22/0.57 tff(143,plain,
% 0.22/0.57 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.22/0.57 tff(144,plain,
% 0.22/0.57 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~v1_xboole_0(A)) | (A = B))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[143, 133])).
% 0.22/0.57 tff(145,plain,
% 0.22/0.57 (v1_xboole_0(k1_xboole_0) <=> v1_xboole_0(k1_xboole_0)),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(146,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')).
% 0.22/0.57 tff(147,plain,
% 0.22/0.57 ((((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)),
% 0.22/0.57 inference(and_elim,[status(thm)],[146])).
% 0.22/0.57 tff(148,plain,
% 0.22/0.57 (((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)) & v3_membered(k1_xboole_0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[147])).
% 0.22/0.57 tff(149,plain,
% 0.22/0.57 ((v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)) & v2_membered(k1_xboole_0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[148])).
% 0.22/0.57 tff(150,plain,
% 0.22/0.57 (v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[149])).
% 0.22/0.57 tff(151,plain,
% 0.22/0.57 (v1_xboole_0(k1_xboole_0)),
% 0.22/0.57 inference(and_elim,[status(thm)],[150])).
% 0.22/0.57 tff(152,plain,
% 0.22/0.57 (v1_xboole_0(k1_xboole_0)),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[151, 145])).
% 0.22/0.57 tff(153,plain,
% 0.22/0.57 (((~![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))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(154,plain,
% 0.22/0.57 ((~![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))),
% 0.22/0.57 inference(quant_inst,[status(thm)],[])).
% 0.22/0.57 tff(155,plain,
% 0.22/0.57 ((~![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)),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.22/0.57 tff(156,plain,
% 0.22/0.57 (k1_pre_topc(A!0) = k1_xboole_0),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[155, 152, 144, 131])).
% 0.22/0.57 tff(157,plain,
% 0.22/0.57 (k1_xboole_0 = k1_pre_topc(A!0)),
% 0.22/0.57 inference(symmetry,[status(thm)],[156])).
% 0.22/0.57 tff(158,plain,
% 0.22/0.57 (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))),
% 0.22/0.57 inference(monotonicity,[status(thm)],[157])).
% 0.22/0.57 tff(159,plain,
% 0.22/0.57 (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)))),
% 0.22/0.57 inference(monotonicity,[status(thm)],[157])).
% 0.22/0.57 tff(160,plain,
% 0.22/0.57 (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)))),
% 0.22/0.57 inference(symmetry,[status(thm)],[159])).
% 0.22/0.57 tff(161,plain,
% 0.22/0.57 (^[A: $i] : refl((l1_struct_0(A) | (~l1_orders_2(A))) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(162,plain,
% 0.22/0.57 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[161])).
% 0.22/0.57 tff(163,plain,
% 0.22/0.57 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(164,plain,
% 0.22/0.57 (^[A: $i] : rewrite((l1_orders_2(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_orders_2(A))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(165,plain,
% 0.22/0.57 (![A: $i] : (l1_orders_2(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[164])).
% 0.22/0.57 tff(166,axiom,(![A: $i] : (l1_orders_2(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_orders_2')).
% 0.22/0.57 tff(167,plain,
% 0.22/0.57 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.22/0.57 tff(168,plain,
% 0.22/0.57 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.22/0.57 tff(169,plain,(
% 0.22/0.57 ![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.57 inference(skolemize,[status(sab)],[168])).
% 0.22/0.57 tff(170,plain,
% 0.22/0.57 (![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.22/0.57 tff(171,plain,
% 0.22/0.57 (((~![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)))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(172,plain,
% 0.22/0.57 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | (l1_struct_0(A!0) | (~l1_orders_2(A!0)))),
% 0.22/0.57 inference(quant_inst,[status(thm)],[])).
% 0.22/0.57 tff(173,plain,
% 0.22/0.57 ((~![A: $i] : (l1_struct_0(A) | (~l1_orders_2(A)))) | l1_struct_0(A!0) | (~l1_orders_2(A!0))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.22/0.57 tff(174,plain,
% 0.22/0.57 (l1_struct_0(A!0)),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[173, 43, 170])).
% 0.22/0.57 tff(175,plain,
% 0.22/0.57 (^[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)))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(176,plain,
% 0.22/0.57 (![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))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[175])).
% 0.22/0.57 tff(177,plain,
% 0.22/0.57 (![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))))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(178,plain,
% 0.22/0.57 (^[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)))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(179,plain,
% 0.22/0.57 (![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))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[178])).
% 0.22/0.57 tff(180,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')).
% 0.22/0.57 tff(181,plain,
% 0.22/0.57 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.22/0.57 tff(182,plain,
% 0.22/0.57 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.22/0.57 tff(183,plain,(
% 0.22/0.57 ![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.22/0.57 inference(skolemize,[status(sab)],[182])).
% 0.22/0.57 tff(184,plain,
% 0.22/0.57 (![A: $i] : ((~l1_struct_0(A)) | m1_subset_1(k1_pre_topc(A), k1_zfmisc_1(u1_struct_0(A))))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.22/0.57 tff(185,plain,
% 0.22/0.57 (((~![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))))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(186,plain,
% 0.22/0.57 ((~![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))))),
% 0.22/0.57 inference(quant_inst,[status(thm)],[])).
% 0.22/0.57 tff(187,plain,
% 0.22/0.57 ((~![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)))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.22/0.57 tff(188,plain,
% 0.22/0.57 (m1_subset_1(k1_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.22/0.57 inference(unit_resolution,[status(thm)],[187, 184, 174])).
% 0.22/0.57 tff(189,plain,
% 0.22/0.57 (m1_subset_1(k1_xboole_0, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.22/0.57 inference(modus_ponens,[status(thm)],[188, 160])).
% 0.22/0.57 tff(190,plain,
% 0.22/0.57 (^[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))))))))))))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(191,plain,
% 0.22/0.57 (![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)))))))))))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[190])).
% 0.22/0.57 tff(192,plain,
% 0.22/0.57 (^[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))))))))))))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(193,plain,
% 0.22/0.57 (![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)))))))))))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[192])).
% 0.22/0.57 tff(194,plain,
% 0.22/0.57 (![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)))))))))))))),
% 0.22/0.57 inference(transitivity,[status(thm)],[193, 191])).
% 0.22/0.57 tff(195,plain,
% 0.22/0.57 (^[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)))))))))))))))),
% 0.22/0.57 inference(bind,[status(th)],[])).
% 0.22/0.57 tff(196,plain,
% 0.22/0.57 (![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)))))))))))))),
% 0.22/0.57 inference(quant_intro,[status(thm)],[195])).
% 0.22/0.57 tff(197,plain,
% 0.22/0.57 (![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))))))),
% 0.22/0.57 inference(rewrite,[status(thm)],[])).
% 0.22/0.57 tff(198,plain,
% 0.22/0.57 (^[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))))))))),
% 0.22/0.58 inference(bind,[status(th)],[])).
% 0.22/0.58 tff(199,plain,
% 0.22/0.58 (![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))))))),
% 0.22/0.58 inference(quant_intro,[status(thm)],[198])).
% 0.22/0.58 tff(200,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')).
% 0.22/0.58 tff(201,plain,
% 0.22/0.58 (![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))))))),
% 0.22/0.58 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.22/0.58 tff(202,plain,
% 0.22/0.58 (![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))))))),
% 0.22/0.58 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.22/0.58 tff(203,plain,(
% 0.22/0.58 ![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)))))))))),
% 0.22/0.58 inference(skolemize,[status(sab)],[202])).
% 0.22/0.58 tff(204,plain,
% 0.22/0.58 (![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)))))))))))))),
% 0.22/0.58 inference(modus_ponens,[status(thm)],[203, 196])).
% 0.22/0.58 tff(205,plain,
% 0.22/0.58 (![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)))))))))))))),
% 0.22/0.58 inference(modus_ponens,[status(thm)],[204, 194])).
% 0.22/0.58 tff(206,plain,
% 0.22/0.58 (((~![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] : ((~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) | (~(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)) | (~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] : ((~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) | (~(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)))))))))))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(207,plain,
% 0.22/0.58 ((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)) | (~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] : ((~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) | (~(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)))))))))))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(208,plain,
% 0.22/0.58 (((~![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)) | (~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] : ((~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) | (~(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))))))))))))))),
% 0.22/0.58 inference(monotonicity,[status(thm)],[207])).
% 0.22/0.58 tff(209,plain,
% 0.22/0.58 (((~![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)) | (~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] : ((~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) | (~(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)))))))))))))),
% 0.22/0.58 inference(transitivity,[status(thm)],[208, 206])).
% 0.22/0.58 tff(210,plain,
% 0.22/0.58 ((~![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)))))))))))))),
% 0.22/0.58 inference(quant_inst,[status(thm)],[])).
% 0.22/0.58 tff(211,plain,
% 0.22/0.58 ((~![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] : ((~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) | (~(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))))))))))))),
% 0.22/0.58 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.22/0.58 tff(212,plain,
% 0.22/0.58 (![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] : ((~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) | (~(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))))))))))))),
% 0.22/0.58 inference(unit_resolution,[status(thm)],[211, 44, 43, 205])).
% 0.22/0.58 tff(213,plain,
% 0.22/0.58 (((~![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] : ((~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) | (~(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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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))))))))))))) <=> ((~![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] : ((~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) | (~(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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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))))))))))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(214,plain,
% 0.22/0.58 ((v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))) <=> (v3_struct_0(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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))))))))))))),
% 0.22/0.58 inference(rewrite,[status(thm)],[])).
% 0.22/0.58 tff(215,plain,
% 0.22/0.58 (((~![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] : ((~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) | (~(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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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))))))))))))) <=> ((~![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] : ((~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) | (~(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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))))),
% 0.22/0.58 inference(monotonicity,[status(thm)],[214])).
% 0.22/0.58 tff(216,plain,
% 0.22/0.58 (((~![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] : ((~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) | (~(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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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))))))))))))) <=> ((~![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] : ((~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) | (~(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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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))))))))))))),
% 0.22/0.58 inference(transitivity,[status(thm)],[215, 213])).
% 0.22/0.58 tff(217,plain,
% 0.22/0.58 ((~![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] : ((~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) | (~(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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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))))))))))))),
% 0.22/0.59 inference(quant_inst,[status(thm)],[])).
% 0.22/0.59 tff(218,plain,
% 0.22/0.59 ((~![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] : ((~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) | (~(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(B!1) | (~l1_orders_2(B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))),
% 0.22/0.59 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.22/0.59 tff(219,plain,
% 0.22/0.59 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))),
% 0.22/0.59 inference(unit_resolution,[status(thm)],[218, 50, 49, 212])).
% 0.22/0.59 tff(220,plain,
% 0.22/0.59 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))) | ((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))) | (~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))))),
% 0.22/0.59 inference(rewrite,[status(thm)],[])).
% 0.22/0.59 tff(221,plain,
% 0.22/0.59 (((~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))) | (~((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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))))))))))) <=> ((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))))),
% 0.22/0.59 inference(rewrite,[status(thm)],[])).
% 0.22/0.59 tff(222,plain,
% 0.22/0.59 ((~(v4_waybel34(C!2, A!0, B!1) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))) <=> (~(v4_waybel34(C!2, A!0, B!1) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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))))))))),
% 0.22/0.59 inference(rewrite,[status(thm)],[])).
% 0.22/0.59 tff(223,plain,
% 0.22/0.59 (((~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)))),
% 0.22/0.59 inference(rewrite,[status(thm)],[])).
% 0.22/0.59 tff(224,plain,
% 0.22/0.59 ((~((~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))))),
% 0.22/0.59 inference(monotonicity,[status(thm)],[223])).
% 0.22/0.59 tff(225,plain,
% 0.22/0.59 (((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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))))))))) <=> ((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))),
% 0.22/0.59 inference(monotonicity,[status(thm)],[224, 222])).
% 0.22/0.59 tff(226,plain,
% 0.22/0.59 ((~((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))) <=> (~((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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))))))))))),
% 0.22/0.59 inference(monotonicity,[status(thm)],[225])).
% 0.22/0.59 tff(227,plain,
% 0.22/0.59 (((~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))) | (~((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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))))))))))) <=> ((~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))) | (~((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))))),
% 0.22/0.59 inference(monotonicity,[status(thm)],[226])).
% 0.22/0.59 tff(228,plain,
% 0.22/0.59 (((~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))) | (~((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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))))))))))) <=> ((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))))),
% 0.22/0.59 inference(transitivity,[status(thm)],[227, 221])).
% 0.22/0.59 tff(229,plain,
% 0.22/0.59 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))) | ((~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))) | (~((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))) | ((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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))))))))))))),
% 0.22/0.60 inference(monotonicity,[status(thm)],[228])).
% 0.22/0.60 tff(230,plain,
% 0.22/0.60 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))) | ((~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))) | (~((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))) | (~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))))),
% 0.22/0.60 inference(transitivity,[status(thm)],[229, 220])).
% 0.22/0.60 tff(231,plain,
% 0.22/0.60 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))) | ((~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))) | (~((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))))),
% 0.22/0.60 inference(quant_inst,[status(thm)],[])).
% 0.22/0.60 tff(232,plain,
% 0.22/0.60 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m2_relset_1(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) | (~(r4_waybel_0(A!0, B!1, C, tptp_fun_D_3(C, B!1, A!0)) | (~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)))))))))))) | (~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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))))))))))),
% 0.22/0.60 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.22/0.60 tff(233,plain,
% 0.22/0.60 (~((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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)))))))))),
% 0.22/0.60 inference(unit_resolution,[status(thm)],[232, 59, 58, 57, 219])).
% 0.22/0.60 tff(234,plain,
% 0.22/0.60 (((~((~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) | (~(r4_waybel_0(A!0, B!1, C!2, tptp_fun_D_3(C!2, B!1, A!0)) | (~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))))))))) | ((~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)))),
% 0.22/0.60 inference(tautology,[status(thm)],[])).
% 0.22/0.60 tff(235,plain,
% 0.22/0.60 ((~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))),
% 0.22/0.60 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.22/0.60 tff(236,plain,
% 0.22/0.60 (v4_waybel34(C!2, A!0, B!1)),
% 0.22/0.60 inference(or_elim,[status(thm)],[55])).
% 0.22/0.60 tff(237,plain,
% 0.22/0.60 ((~((~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))),
% 0.22/0.60 inference(tautology,[status(thm)],[])).
% 0.22/0.60 tff(238,plain,
% 0.22/0.60 ((~((~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))),
% 0.22/0.60 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.22/0.60 tff(239,plain,
% 0.22/0.60 (![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))),
% 0.22/0.60 inference(unit_resolution,[status(thm)],[238, 235])).
% 0.22/0.60 tff(240,plain,
% 0.22/0.60 (^[A: $i] : refl((v1_finset_1(A) | (~v1_xboole_0(A))) <=> (v1_finset_1(A) | (~v1_xboole_0(A))))),
% 0.22/0.60 inference(bind,[status(th)],[])).
% 0.22/0.60 tff(241,plain,
% 0.22/0.60 (![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A))) <=> ![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.22/0.60 inference(quant_intro,[status(thm)],[240])).
% 0.22/0.60 tff(242,plain,
% 0.22/0.60 (![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A))) <=> ![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.22/0.60 inference(rewrite,[status(thm)],[])).
% 0.22/0.60 tff(243,plain,
% 0.22/0.60 (^[A: $i] : rewrite((v1_xboole_0(A) => v1_finset_1(A)) <=> (v1_finset_1(A) | (~v1_xboole_0(A))))),
% 0.22/0.60 inference(bind,[status(th)],[])).
% 0.22/0.60 tff(244,plain,
% 0.22/0.60 (![A: $i] : (v1_xboole_0(A) => v1_finset_1(A)) <=> ![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.22/0.60 inference(quant_intro,[status(thm)],[243])).
% 0.22/0.60 tff(245,axiom,(![A: $i] : (v1_xboole_0(A) => v1_finset_1(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_finset_1')).
% 0.22/0.60 tff(246,plain,
% 0.22/0.60 (![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.22/0.60 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.22/0.60 tff(247,plain,
% 0.22/0.60 (![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.22/0.60 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.22/0.60 tff(248,plain,(
% 0.22/0.60 ![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.22/0.60 inference(skolemize,[status(sab)],[247])).
% 0.22/0.60 tff(249,plain,
% 0.22/0.60 (![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))),
% 0.22/0.60 inference(modus_ponens,[status(thm)],[248, 241])).
% 0.22/0.60 tff(250,plain,
% 0.22/0.60 (((~![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)))),
% 0.22/0.60 inference(rewrite,[status(thm)],[])).
% 0.22/0.60 tff(251,plain,
% 0.22/0.60 ((~![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))) | (v1_finset_1(k1_xboole_0) | (~v1_xboole_0(k1_xboole_0)))),
% 0.22/0.60 inference(quant_inst,[status(thm)],[])).
% 0.22/0.60 tff(252,plain,
% 0.22/0.60 ((~![A: $i] : (v1_finset_1(A) | (~v1_xboole_0(A)))) | v1_finset_1(k1_xboole_0) | (~v1_xboole_0(k1_xboole_0))),
% 0.22/0.60 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.22/0.60 tff(253,plain,
% 0.22/0.60 (v1_finset_1(k1_xboole_0)),
% 0.22/0.60 inference(unit_resolution,[status(thm)],[252, 249, 152])).
% 0.22/0.60 tff(254,plain,
% 0.22/0.60 (((~![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))),
% 0.22/0.60 inference(rewrite,[status(thm)],[])).
% 0.22/0.60 tff(255,plain,
% 0.22/0.60 ((~![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))),
% 0.22/0.60 inference(quant_inst,[status(thm)],[])).
% 0.22/0.60 tff(256,plain,
% 0.22/0.60 ((~![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)),
% 0.22/0.60 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.22/0.60 tff(257,plain,
% 0.22/0.60 ((~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)),
% 0.22/0.60 inference(unit_resolution,[status(thm)],[256, 253, 239])).
% 0.22/0.60 tff(258,plain,
% 0.22/0.60 (r4_waybel_0(A!0, B!1, C!2, k1_xboole_0)),
% 0.22/0.60 inference(unit_resolution,[status(thm)],[257, 189])).
% 0.22/0.60 tff(259,plain,
% 0.22/0.60 (r4_waybel_0(A!0, B!1, C!2, k1_pre_topc(A!0))),
% 0.22/0.60 inference(modus_ponens,[status(thm)],[258, 158])).
% 0.22/0.60 tff(260,plain,
% 0.22/0.60 ((~(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)))),
% 0.22/0.60 inference(tautology,[status(thm)],[])).
% 0.22/0.60 tff(261,plain,
% 0.22/0.60 (v5_waybel34(C!2, A!0, B!1)),
% 0.22/0.60 inference(unit_resolution,[status(thm)],[260, 259, 109])).
% 0.22/0.60 tff(262,plain,
% 0.22/0.60 ((~(~((~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)))),
% 0.22/0.60 inference(rewrite,[status(thm)],[])).
% 0.22/0.60 tff(263,plain,
% 0.22/0.60 ((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))))),
% 0.22/0.60 inference(rewrite,[status(thm)],[])).
% 0.22/0.60 tff(264,plain,
% 0.22/0.60 ((~(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)))))),
% 0.22/0.60 inference(monotonicity,[status(thm)],[263])).
% 0.22/0.60 tff(265,plain,
% 0.22/0.60 ((~(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)))),
% 0.22/0.60 inference(transitivity,[status(thm)],[264, 262])).
% 0.22/0.60 tff(266,plain,
% 0.22/0.60 (~(v20_waybel_0(C!2, A!0, B!1) & v5_waybel34(C!2, A!0, B!1))),
% 0.52/0.60 inference(or_elim,[status(thm)],[55])).
% 0.52/0.60 tff(267,plain,
% 0.52/0.60 ((~v20_waybel_0(C!2, A!0, B!1)) | (~v5_waybel34(C!2, A!0, B!1))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.52/0.60 tff(268,plain,
% 0.52/0.60 (~v20_waybel_0(C!2, A!0, B!1)),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[267, 261])).
% 0.52/0.60 tff(269,plain,
% 0.52/0.60 ((~(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)))))),
% 0.52/0.60 inference(tautology,[status(thm)],[])).
% 0.52/0.60 tff(270,plain,
% 0.52/0.60 (~((~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))))),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[269, 268, 75])).
% 0.52/0.60 tff(271,plain,
% 0.52/0.60 (((~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))),
% 0.52/0.60 inference(tautology,[status(thm)],[])).
% 0.52/0.60 tff(272,plain,
% 0.52/0.60 (m1_subset_1(tptp_fun_E_5(C!2, B!1, A!0), u1_struct_0(A!0))),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[271, 270])).
% 0.52/0.60 tff(273,plain,
% 0.52/0.60 (((~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))),
% 0.52/0.60 inference(tautology,[status(thm)],[])).
% 0.52/0.60 tff(274,plain,
% 0.52/0.60 (m1_subset_1(tptp_fun_D_4(C!2, B!1, A!0), u1_struct_0(A!0))),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[273, 270])).
% 0.52/0.60 tff(275,plain,
% 0.52/0.60 (^[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)))))),
% 0.52/0.60 inference(bind,[status(th)],[])).
% 0.52/0.60 tff(276,plain,
% 0.52/0.60 (![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))))),
% 0.52/0.60 inference(quant_intro,[status(thm)],[275])).
% 0.52/0.60 tff(277,plain,
% 0.52/0.60 (^[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))))))),
% 0.52/0.61 inference(bind,[status(th)],[])).
% 0.52/0.61 tff(278,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(quant_intro,[status(thm)],[277])).
% 0.52/0.61 tff(279,plain,
% 0.52/0.61 (![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)))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(280,plain,
% 0.52/0.61 (^[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)))))),
% 0.52/0.61 inference(bind,[status(th)],[])).
% 0.52/0.61 tff(281,plain,
% 0.52/0.61 (![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)))),
% 0.52/0.61 inference(quant_intro,[status(thm)],[280])).
% 0.52/0.61 tff(282,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')).
% 0.52/0.61 tff(283,plain,
% 0.52/0.61 (![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)))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.52/0.61 tff(284,plain,
% 0.52/0.61 (![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)))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[283, 279])).
% 0.52/0.61 tff(285,plain,(
% 0.52/0.61 ![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)))),
% 0.52/0.61 inference(skolemize,[status(sab)],[284])).
% 0.52/0.61 tff(286,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[285, 278])).
% 0.52/0.61 tff(287,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[286, 276])).
% 0.52/0.61 tff(288,plain,
% 0.52/0.61 (((~![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_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))) | (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_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))) | (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))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(289,plain,
% 0.52/0.61 ((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_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))) | (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))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(290,plain,
% 0.52/0.61 (((~![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_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))) | (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)))))),
% 0.52/0.61 inference(monotonicity,[status(thm)],[289])).
% 0.52/0.61 tff(291,plain,
% 0.52/0.61 (((~![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_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))) | (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))))),
% 0.52/0.61 inference(transitivity,[status(thm)],[290, 288])).
% 0.52/0.61 tff(292,plain,
% 0.52/0.61 ((~![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))))),
% 0.52/0.61 inference(quant_inst,[status(thm)],[])).
% 0.52/0.61 tff(293,plain,
% 0.52/0.61 ((~![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_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))) | (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)))),
% 0.52/0.61 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.52/0.61 tff(294,plain,
% 0.52/0.61 (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))),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[293, 44, 287, 174, 274, 272])).
% 0.52/0.61 tff(295,plain,
% 0.52/0.61 (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))),
% 0.52/0.61 inference(symmetry,[status(thm)],[294])).
% 0.52/0.61 tff(296,plain,
% 0.52/0.61 (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)))),
% 0.52/0.61 inference(monotonicity,[status(thm)],[295])).
% 0.52/0.61 tff(297,plain,
% 0.52/0.61 (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)))),
% 0.52/0.61 inference(symmetry,[status(thm)],[296])).
% 0.52/0.61 tff(298,plain,
% 0.52/0.61 ((~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))))),
% 0.52/0.61 inference(monotonicity,[status(thm)],[297])).
% 0.52/0.61 tff(299,plain,
% 0.52/0.61 (^[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)))))),
% 0.52/0.61 inference(bind,[status(th)],[])).
% 0.52/0.61 tff(300,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(quant_intro,[status(thm)],[299])).
% 0.52/0.61 tff(301,plain,
% 0.52/0.61 (^[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))))))),
% 0.52/0.61 inference(bind,[status(th)],[])).
% 0.52/0.61 tff(302,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(quant_intro,[status(thm)],[301])).
% 0.52/0.61 tff(303,plain,
% 0.52/0.61 (![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))))),
% 0.52/0.61 inference(rewrite,[status(thm)],[])).
% 0.52/0.61 tff(304,plain,
% 0.52/0.61 (^[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))))))),
% 0.52/0.62 inference(bind,[status(th)],[])).
% 0.52/0.62 tff(305,plain,
% 0.52/0.62 (![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))))),
% 0.52/0.62 inference(quant_intro,[status(thm)],[304])).
% 0.52/0.62 tff(306,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')).
% 0.52/0.62 tff(307,plain,
% 0.52/0.62 (![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))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.52/0.62 tff(308,plain,
% 0.52/0.62 (![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))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[307, 303])).
% 0.52/0.62 tff(309,plain,(
% 0.52/0.62 ![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))))),
% 0.52/0.62 inference(skolemize,[status(sab)],[308])).
% 0.52/0.62 tff(310,plain,
% 0.52/0.62 (![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))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[309, 302])).
% 0.52/0.62 tff(311,plain,
% 0.52/0.62 (![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))))),
% 0.52/0.62 inference(modus_ponens,[status(thm)],[310, 300])).
% 0.52/0.62 tff(312,plain,
% 0.52/0.62 (((~![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_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))) | 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_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))) | 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))))),
% 0.52/0.62 inference(rewrite,[status(thm)],[])).
% 0.52/0.62 tff(313,plain,
% 0.52/0.62 ((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_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))) | 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))))),
% 0.52/0.62 inference(rewrite,[status(thm)],[])).
% 0.52/0.62 tff(314,plain,
% 0.52/0.62 (((~![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_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))) | 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)))))),
% 0.52/0.62 inference(monotonicity,[status(thm)],[313])).
% 0.52/0.62 tff(315,plain,
% 0.52/0.62 (((~![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_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))) | 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))))),
% 0.52/0.62 inference(transitivity,[status(thm)],[314, 312])).
% 0.52/0.62 tff(316,plain,
% 0.52/0.62 ((~![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))))),
% 0.52/0.62 inference(quant_inst,[status(thm)],[])).
% 0.52/0.62 tff(317,plain,
% 0.52/0.62 ((~![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_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))) | 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)))),
% 0.54/0.62 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.54/0.62 tff(318,plain,
% 0.54/0.62 (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)))),
% 0.54/0.62 inference(unit_resolution,[status(thm)],[317, 44, 311, 174, 274, 272])).
% 0.54/0.62 tff(319,plain,
% 0.54/0.62 (((~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))))),
% 0.54/0.62 inference(tautology,[status(thm)],[])).
% 0.54/0.62 tff(320,plain,
% 0.54/0.62 (~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)))),
% 0.54/0.62 inference(unit_resolution,[status(thm)],[319, 270])).
% 0.54/0.62 tff(321,plain,
% 0.54/0.62 (((~![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))))),
% 0.54/0.62 inference(rewrite,[status(thm)],[])).
% 0.54/0.62 tff(322,plain,
% 0.54/0.62 ((~![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))))),
% 0.54/0.62 inference(quant_inst,[status(thm)],[])).
% 0.54/0.62 tff(323,plain,
% 0.54/0.62 ((~![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)))),
% 0.54/0.62 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.54/0.62 tff(324,plain,
% 0.54/0.62 ((~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))))),
% 0.54/0.62 inference(unit_resolution,[status(thm)],[323, 239, 320])).
% 0.54/0.62 tff(325,plain,
% 0.54/0.62 (~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)))),
% 0.54/0.62 inference(unit_resolution,[status(thm)],[324, 318])).
% 0.54/0.62 tff(326,plain,
% 0.54/0.62 (~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)))),
% 0.54/0.62 inference(modus_ponens,[status(thm)],[325, 298])).
% 0.54/0.62 tff(327,plain,
% 0.54/0.62 (^[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))))))),
% 0.54/0.62 inference(bind,[status(th)],[])).
% 0.54/0.62 tff(328,plain,
% 0.54/0.62 (![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)))))),
% 0.54/0.63 inference(quant_intro,[status(thm)],[327])).
% 0.54/0.63 tff(329,plain,
% 0.54/0.63 (^[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))))))),
% 0.54/0.63 inference(bind,[status(th)],[])).
% 0.54/0.63 tff(330,plain,
% 0.54/0.63 (![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)))))),
% 0.54/0.63 inference(quant_intro,[status(thm)],[329])).
% 0.54/0.63 tff(331,plain,
% 0.54/0.63 (![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)))),
% 0.54/0.63 inference(rewrite,[status(thm)],[])).
% 0.54/0.63 tff(332,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')).
% 0.54/0.63 tff(333,plain,
% 0.54/0.63 (![A: $i, B: $i] : ((~v1_xboole_0(k2_tarski(A, B))) & v1_finset_1(k2_tarski(A, B)))),
% 0.54/0.63 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.54/0.63 tff(334,plain,(
% 0.54/0.63 ![A: $i, B: $i] : ((~v1_xboole_0(k2_tarski(A, B))) & v1_finset_1(k2_tarski(A, B)))),
% 0.54/0.63 inference(skolemize,[status(sab)],[333])).
% 0.54/0.63 tff(335,plain,
% 0.54/0.63 (![A: $i, B: $i] : (~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B)))))),
% 0.54/0.63 inference(modus_ponens,[status(thm)],[334, 330])).
% 0.54/0.63 tff(336,plain,
% 0.54/0.63 (![A: $i, B: $i] : (~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B)))))),
% 0.54/0.63 inference(modus_ponens,[status(thm)],[335, 328])).
% 0.54/0.63 tff(337,plain,
% 0.54/0.63 ((~![A: $i, B: $i] : (~(v1_xboole_0(k2_tarski(A, B)) | (~v1_finset_1(k2_tarski(A, B)))))) | (~(v1_xboole_0(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) | (~v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))))),
% 0.54/0.63 inference(quant_inst,[status(thm)],[])).
% 0.54/0.63 tff(338,plain,
% 0.54/0.63 (~(v1_xboole_0(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) | (~v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))))),
% 0.54/0.63 inference(unit_resolution,[status(thm)],[337, 336])).
% 0.54/0.63 tff(339,plain,
% 0.54/0.63 ((v1_xboole_0(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))) | (~v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0))))) | v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))),
% 0.54/0.63 inference(tautology,[status(thm)],[])).
% 0.54/0.63 tff(340,plain,
% 0.54/0.63 (v1_finset_1(k2_tarski(tptp_fun_D_4(C!2, B!1, A!0), tptp_fun_E_5(C!2, B!1, A!0)))),
% 0.54/0.63 inference(unit_resolution,[status(thm)],[339, 338])).
% 0.54/0.63 tff(341,plain,
% 0.54/0.63 ($false),
% 0.54/0.63 inference(unit_resolution,[status(thm)],[340, 326])).
% 0.54/0.63 % SZS output end Proof
%------------------------------------------------------------------------------