TSTP Solution File: GRP621+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP621+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Fri Sep 16 22:28:52 EDT 2022
% Result : Theorem 1.34s 1.11s
% Output : Proof 1.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP621+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 18:18:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.34/1.11 % SZS status Theorem
% 1.34/1.11 % SZS output start Proof
% 1.34/1.11 tff(m2_relset_1_type, type, (
% 1.34/1.11 m2_relset_1: ( $i * $i * $i ) > $o)).
% 1.34/1.11 tff(u1_struct_0_type, type, (
% 1.34/1.11 u1_struct_0: $i > $i)).
% 1.34/1.11 tff(tptp_fun_A_0_type, type, (
% 1.34/1.11 tptp_fun_A_0: $i)).
% 1.34/1.11 tff(k5_relat_1_type, type, (
% 1.34/1.11 k5_relat_1: ( $i * $i ) > $i)).
% 1.34/1.11 tff(tptp_fun_B_1_type, type, (
% 1.34/1.11 tptp_fun_B_1: $i)).
% 1.34/1.11 tff(tptp_fun_C_2_type, type, (
% 1.34/1.11 tptp_fun_C_2: $i)).
% 1.34/1.11 tff(k7_funct_2_type, type, (
% 1.34/1.11 k7_funct_2: ( $i * $i * $i * $i * $i ) > $i)).
% 1.34/1.11 tff(m1_relset_1_type, type, (
% 1.34/1.11 m1_relset_1: ( $i * $i * $i ) > $o)).
% 1.34/1.11 tff(v1_group_6_type, type, (
% 1.34/1.11 v1_group_6: ( $i * $i * $i ) > $o)).
% 1.34/1.11 tff(v1_funct_2_type, type, (
% 1.34/1.11 v1_funct_2: ( $i * $i * $i ) > $o)).
% 1.34/1.11 tff(v1_funct_1_type, type, (
% 1.34/1.11 v1_funct_1: $i > $o)).
% 1.34/1.11 tff(m2_fraenkel_type, type, (
% 1.34/1.11 m2_fraenkel: ( $i * $i * $i * $i ) > $o)).
% 1.34/1.11 tff(k1_autgroup_type, type, (
% 1.34/1.11 k1_autgroup: $i > $i)).
% 1.34/1.11 tff(v3_group_6_type, type, (
% 1.34/1.11 v3_group_6: ( $i * $i * $i ) > $o)).
% 1.34/1.11 tff(v2_funct_1_type, type, (
% 1.34/1.11 v2_funct_1: $i > $o)).
% 1.34/1.11 tff(r2_hidden_type, type, (
% 1.34/1.11 r2_hidden: ( $i * $i ) > $o)).
% 1.34/1.11 tff(tptp_fun_C_4_type, type, (
% 1.34/1.11 tptp_fun_C_4: ( $i * $i ) > $i)).
% 1.34/1.11 tff(tptp_fun_C_3_type, type, (
% 1.34/1.11 tptp_fun_C_3: ( $i * $i ) > $i)).
% 1.34/1.11 tff(m1_fraenkel_type, type, (
% 1.34/1.11 m1_fraenkel: ( $i * $i * $i ) > $o)).
% 1.34/1.11 tff(v4_group_1_type, type, (
% 1.34/1.11 v4_group_1: $i > $o)).
% 1.34/1.11 tff(v3_group_1_type, type, (
% 1.34/1.11 v3_group_1: $i > $o)).
% 1.34/1.11 tff(v1_group_1_type, type, (
% 1.34/1.11 v1_group_1: $i > $o)).
% 1.34/1.11 tff(l1_group_1_type, type, (
% 1.34/1.11 l1_group_1: $i > $o)).
% 1.34/1.11 tff(v3_struct_0_type, type, (
% 1.34/1.11 v3_struct_0: $i > $o)).
% 1.34/1.11 tff(v1_xboole_0_type, type, (
% 1.34/1.11 v1_xboole_0: $i > $o)).
% 1.34/1.11 tff(l1_struct_0_type, type, (
% 1.34/1.11 l1_struct_0: $i > $o)).
% 1.34/1.11 tff(g1_group_1_type, type, (
% 1.34/1.11 g1_group_1: ( $i * $i ) > $i)).
% 1.34/1.11 tff(u1_group_1_type, type, (
% 1.34/1.11 u1_group_1: $i > $i)).
% 1.34/1.11 tff(k8_group_6_type, type, (
% 1.34/1.11 k8_group_6: ( $i * $i * $i * $i * $i ) > $i)).
% 1.34/1.11 tff(v4_group_6_type, type, (
% 1.34/1.11 v4_group_6: ( $i * $i * $i ) > $o)).
% 1.34/1.11 tff(m1_subset_1_type, type, (
% 1.34/1.11 m1_subset_1: ( $i * $i ) > $o)).
% 1.34/1.11 tff(v1_fraenkel_type, type, (
% 1.34/1.11 v1_fraenkel: $i > $o)).
% 1.34/1.11 tff(1,plain,
% 1.34/1.11 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 1.34/1.11 inference(bind,[status(th)],[])).
% 1.34/1.11 tff(2,plain,
% 1.34/1.11 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.34/1.11 inference(quant_intro,[status(thm)],[1])).
% 1.34/1.11 tff(3,plain,
% 1.34/1.11 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.34/1.11 inference(rewrite,[status(thm)],[])).
% 1.34/1.11 tff(4,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 1.34/1.11 tff(5,plain,
% 1.34/1.11 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.34/1.11 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.34/1.11 tff(6,plain,(
% 1.34/1.11 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.34/1.11 inference(skolemize,[status(sab)],[5])).
% 1.34/1.11 tff(7,plain,
% 1.34/1.11 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 1.34/1.11 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.34/1.11 tff(8,plain,
% 1.34/1.11 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.34/1.11 inference(quant_inst,[status(thm)],[])).
% 1.34/1.11 tff(9,plain,
% 1.34/1.11 (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.11 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.34/1.11 tff(10,plain,
% 1.34/1.11 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))))))))),
% 1.34/1.11 inference(bind,[status(th)],[])).
% 1.34/1.11 tff(11,plain,
% 1.34/1.11 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))),
% 1.34/1.11 inference(quant_intro,[status(thm)],[10])).
% 1.34/1.11 tff(12,plain,
% 1.34/1.11 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))))))),
% 1.34/1.11 inference(bind,[status(th)],[])).
% 1.34/1.11 tff(13,plain,
% 1.34/1.11 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))))))),
% 1.34/1.11 inference(quant_intro,[status(thm)],[12])).
% 1.34/1.11 tff(14,plain,
% 1.34/1.11 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))))))),
% 1.34/1.11 inference(bind,[status(th)],[])).
% 1.34/1.11 tff(15,plain,
% 1.34/1.11 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))))))),
% 1.34/1.11 inference(quant_intro,[status(thm)],[14])).
% 1.34/1.11 tff(16,plain,
% 1.34/1.11 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))))))),
% 1.34/1.12 inference(transitivity,[status(thm)],[15, 13])).
% 1.34/1.12 tff(17,plain,
% 1.34/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A)))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))))))), (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A)))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))))))))),
% 1.34/1.12 inference(bind,[status(th)],[])).
% 1.34/1.12 tff(18,plain,
% 1.34/1.12 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))))))),
% 1.34/1.12 inference(quant_intro,[status(thm)],[17])).
% 1.34/1.12 tff(19,plain,
% 1.34/1.12 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))),
% 1.34/1.12 inference(bind,[status(th)],[])).
% 1.34/1.12 tff(20,plain,
% 1.34/1.12 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))),
% 1.34/1.12 inference(quant_intro,[status(thm)],[19])).
% 1.34/1.12 tff(21,plain,
% 1.34/1.12 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 1.34/1.12 inference(rewrite,[status(thm)],[])).
% 1.34/1.12 tff(22,plain,
% 1.34/1.12 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) <=> ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))), ((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), rewrite((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))), ((m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))))), (![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))) <=> ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))))),
% 1.34/1.12 inference(bind,[status(th)],[])).
% 1.34/1.12 tff(23,plain,
% 1.34/1.12 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 1.34/1.12 inference(quant_intro,[status(thm)],[22])).
% 1.34/1.12 tff(24,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A)) => ((B = k1_autgroup(A)) <=> (![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B) => (((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(C, A, A)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_autgroup')).
% 1.34/1.12 tff(25,plain,
% 1.34/1.12 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.34/1.12 tff(26,plain,
% 1.34/1.12 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | ((B = k1_autgroup(A)) <=> (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A))))))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.34/1.12 tff(27,plain,(
% 1.34/1.12 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | ((~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A))))))))))),
% 1.34/1.12 inference(skolemize,[status(sab)],[26])).
% 1.34/1.12 tff(28,plain,
% 1.34/1.12 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (((~(B = k1_autgroup(A))) | (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) & ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(C, A, A) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(C, B) <=> (v2_funct_1(C) & v3_group_6(C, A, A)))))) & ((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (v1_funct_1(tptp_fun_C_3(B, A)) & v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_3(B, A), A, A) & m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))) | (~((~(v1_funct_1(tptp_fun_C_4(B, A)) & v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)) & v1_group_6(tptp_fun_C_4(B, A), A, A) & m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (v2_funct_1(tptp_fun_C_4(B, A)) & v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[27, 20])).
% 1.34/1.12 tff(29,plain,
% 1.34/1.12 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[28, 18])).
% 1.34/1.12 tff(30,plain,
% 1.34/1.12 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A))))))))))) | (~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A)))))))))))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[29, 16])).
% 1.34/1.12 tff(31,plain,
% 1.34/1.12 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[30, 11])).
% 1.34/1.12 tff(32,plain,
% 1.34/1.12 ((((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))))) <=> ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))))),
% 1.34/1.12 inference(rewrite,[status(thm)],[])).
% 1.34/1.12 tff(33,plain,
% 1.34/1.12 (((~(~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))) <=> (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))))),
% 1.34/1.12 inference(rewrite,[status(thm)],[])).
% 1.34/1.12 tff(34,plain,
% 1.34/1.12 ((~(~((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) <=> ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0))),
% 1.34/1.12 inference(rewrite,[status(thm)],[])).
% 1.34/1.12 tff(35,plain,
% 1.34/1.12 (((~(~((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) & ((~(~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))))) <=> (((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))))),
% 1.34/1.12 inference(monotonicity,[status(thm)],[34, 33])).
% 1.34/1.12 tff(36,plain,
% 1.34/1.12 (((~(~((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) & ((~(~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))))) <=> ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))))),
% 1.34/1.12 inference(transitivity,[status(thm)],[35, 32])).
% 1.34/1.12 tff(37,plain,
% 1.34/1.12 ((~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))))),
% 1.34/1.12 inference(rewrite,[status(thm)],[])).
% 1.34/1.12 tff(38,plain,
% 1.34/1.12 ((~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))))))),
% 1.34/1.12 inference(rewrite,[status(thm)],[])).
% 1.34/1.12 tff(39,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => ![C: $i] : (m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)) => m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_autgroup')).
% 1.34/1.12 tff(40,plain,
% 1.34/1.12 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.34/1.12 tff(41,plain,
% 1.34/1.12 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[40, 37])).
% 1.34/1.12 tff(42,plain,
% 1.34/1.12 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[41, 37])).
% 1.34/1.12 tff(43,plain,
% 1.34/1.12 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[42, 37])).
% 1.34/1.12 tff(44,plain,
% 1.34/1.12 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[43, 37])).
% 1.34/1.12 tff(45,plain,
% 1.34/1.12 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[44, 37])).
% 1.34/1.12 tff(46,plain,
% 1.34/1.12 (~![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m2_fraenkel(B, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), k1_autgroup(A))) | m2_fraenkel(k7_funct_2(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), C, B), u1_struct_0(A), u1_struct_0(A), k1_autgroup(A)))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[45, 37])).
% 1.34/1.12 tff(47,plain,
% 1.34/1.12 ((~v3_struct_0(A!0)) & v1_group_1(A!0) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) & (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))))),
% 1.34/1.12 inference(modus_ponens,[status(thm)],[46, 36])).
% 1.34/1.12 tff(48,plain,
% 1.34/1.12 (l1_group_1(A!0)),
% 1.34/1.12 inference(and_elim,[status(thm)],[47])).
% 1.34/1.12 tff(49,plain,
% 1.34/1.12 (v4_group_1(A!0)),
% 1.34/1.12 inference(and_elim,[status(thm)],[47])).
% 1.34/1.12 tff(50,plain,
% 1.34/1.12 (v3_group_1(A!0)),
% 1.34/1.12 inference(and_elim,[status(thm)],[47])).
% 1.34/1.12 tff(51,plain,
% 1.34/1.12 (v1_group_1(A!0)),
% 1.34/1.12 inference(and_elim,[status(thm)],[47])).
% 1.34/1.12 tff(52,plain,
% 1.34/1.12 (~v3_struct_0(A!0)),
% 1.34/1.12 inference(and_elim,[status(thm)],[47])).
% 1.34/1.12 tff(53,plain,
% 1.34/1.12 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))))))))),
% 1.34/1.13 inference(rewrite,[status(thm)],[])).
% 1.34/1.13 tff(54,plain,
% 1.34/1.13 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))))))))),
% 1.34/1.13 inference(quant_inst,[status(thm)],[])).
% 1.34/1.13 tff(55,plain,
% 1.34/1.13 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A), u1_struct_0(A))) | (~((~((B = k1_autgroup(A)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A))) | (~v1_funct_2(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(tptp_fun_C_3(B, A), A, A)) | (~m2_relset_1(tptp_fun_C_3(B, A), u1_struct_0(A), u1_struct_0(A))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A))) | (~v1_group_6(tptp_fun_C_4(B, A), A, A)) | (~v1_funct_2(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (~m2_relset_1(tptp_fun_C_4(B, A), u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(tptp_fun_C_4(B, A), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A))) | (~v3_group_6(tptp_fun_C_4(B, A), A, A))))))))) | (~((~(B = k1_autgroup(A))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A), u1_struct_0(A), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(C, A, A)) | (~m2_relset_1(C, u1_struct_0(A), u1_struct_0(A))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A, A)))))))))))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))),
% 1.34/1.13 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.34/1.13 tff(56,plain,
% 1.34/1.13 (![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))),
% 1.34/1.13 inference(unit_resolution,[status(thm)],[55, 52, 51, 50, 49, 48, 31])).
% 1.34/1.13 tff(57,plain,
% 1.34/1.13 (^[A: $i] : refl((v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 1.34/1.13 inference(bind,[status(th)],[])).
% 1.34/1.13 tff(58,plain,
% 1.34/1.13 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.34/1.13 inference(quant_intro,[status(thm)],[57])).
% 1.34/1.13 tff(59,plain,
% 1.34/1.13 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 1.34/1.13 inference(bind,[status(th)],[])).
% 1.34/1.13 tff(60,plain,
% 1.34/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.34/1.13 inference(quant_intro,[status(thm)],[59])).
% 1.34/1.13 tff(61,plain,
% 1.34/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.34/1.13 inference(rewrite,[status(thm)],[])).
% 1.34/1.13 tff(62,plain,
% 1.34/1.13 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))))),
% 1.34/1.13 inference(bind,[status(th)],[])).
% 1.34/1.13 tff(63,plain,
% 1.34/1.13 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.34/1.13 inference(quant_intro,[status(thm)],[62])).
% 1.34/1.13 tff(64,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_autgroup')).
% 1.34/1.13 tff(65,plain,
% 1.34/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.34/1.13 inference(modus_ponens,[status(thm)],[64, 63])).
% 1.34/1.13 tff(66,plain,
% 1.34/1.13 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.34/1.13 inference(modus_ponens,[status(thm)],[65, 61])).
% 1.34/1.13 tff(67,plain,(
% 1.34/1.13 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)))),
% 1.34/1.13 inference(skolemize,[status(sab)],[66])).
% 1.34/1.13 tff(68,plain,
% 1.34/1.13 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.34/1.13 inference(modus_ponens,[status(thm)],[67, 60])).
% 1.34/1.13 tff(69,plain,
% 1.34/1.13 (![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 1.34/1.13 inference(modus_ponens,[status(thm)],[68, 58])).
% 1.34/1.13 tff(70,plain,
% 1.34/1.13 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.34/1.13 inference(rewrite,[status(thm)],[])).
% 1.34/1.13 tff(71,plain,
% 1.34/1.13 ((v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.34/1.13 inference(rewrite,[status(thm)],[])).
% 1.34/1.13 tff(72,plain,
% 1.34/1.13 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.34/1.13 inference(monotonicity,[status(thm)],[71])).
% 1.34/1.13 tff(73,plain,
% 1.34/1.13 (((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.34/1.13 inference(transitivity,[status(thm)],[72, 70])).
% 1.34/1.13 tff(74,plain,
% 1.34/1.13 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | (v3_struct_0(A!0) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0)) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)))),
% 1.34/1.13 inference(quant_inst,[status(thm)],[])).
% 1.34/1.13 tff(75,plain,
% 1.34/1.13 ((~![A: $i] : (v3_struct_0(A) | m1_fraenkel(k1_autgroup(A), u1_struct_0(A), u1_struct_0(A)) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~v1_group_1(A!0)) | m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.13 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.34/1.13 tff(76,plain,
% 1.34/1.13 (m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.13 inference(unit_resolution,[status(thm)],[75, 52, 51, 50, 49, 48, 69])).
% 1.34/1.13 tff(77,plain,
% 1.34/1.13 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))),
% 1.34/1.13 inference(rewrite,[status(thm)],[])).
% 1.34/1.13 tff(78,plain,
% 1.34/1.13 (((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v1_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(k1_autgroup(A!0), A!0), k1_autgroup(A!0)) <=> (~((~v2_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0))))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))))))) <=> ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))),
% 1.34/1.13 inference(rewrite,[status(thm)],[])).
% 1.34/1.13 tff(79,plain,
% 1.34/1.13 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v1_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(k1_autgroup(A!0), A!0), k1_autgroup(A!0)) <=> (~((~v2_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0))))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))))),
% 1.34/1.13 inference(monotonicity,[status(thm)],[78])).
% 1.34/1.13 tff(80,plain,
% 1.34/1.13 (((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v1_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(k1_autgroup(A!0), A!0), k1_autgroup(A!0)) <=> (~((~v2_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0))))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) <=> ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))),
% 1.34/1.14 inference(transitivity,[status(thm)],[79, 77])).
% 1.34/1.14 tff(81,plain,
% 1.34/1.14 ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((k1_autgroup(A!0) = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(tptp_fun_C_3(k1_autgroup(A!0), A!0))) | (~v1_funct_2(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(k1_autgroup(A!0), A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v1_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(k1_autgroup(A!0), A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(k1_autgroup(A!0), A!0), k1_autgroup(A!0)) <=> (~((~v2_funct_1(tptp_fun_C_4(k1_autgroup(A!0), A!0))) | (~v3_group_6(tptp_fun_C_4(k1_autgroup(A!0), A!0), A!0, A!0))))))))) | (~((~(k1_autgroup(A!0) = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))),
% 1.34/1.14 inference(quant_inst,[status(thm)],[])).
% 1.34/1.14 tff(82,plain,
% 1.34/1.14 ((~![B: $i] : ((~m1_fraenkel(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~((B = k1_autgroup(A!0)) | (~((~m2_fraenkel(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(tptp_fun_C_3(B, A!0))) | (~v1_funct_2(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(tptp_fun_C_3(B, A!0), A!0, A!0)) | (~m2_relset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~((~v1_funct_1(tptp_fun_C_4(B, A!0))) | (~v1_group_6(tptp_fun_C_4(B, A!0), A!0, A!0)) | (~v1_funct_2(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(tptp_fun_C_4(B, A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_C_4(B, A!0), B) <=> (~((~v2_funct_1(tptp_fun_C_4(B, A!0))) | (~v3_group_6(tptp_fun_C_4(B, A!0), A!0, A!0))))))))) | (~((~(B = k1_autgroup(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), B)) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, B) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))))))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.34/1.14 tff(83,plain,
% 1.34/1.14 (~((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0))))))))),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[82, 76, 56])).
% 1.34/1.14 tff(84,plain,
% 1.34/1.14 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C, k1_autgroup(A!0)) <=> (~((~v2_funct_1(C)) | (~v3_group_6(C, A!0, A!0)))))))) | ![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.34/1.14 inference(tautology,[status(thm)],[])).
% 1.34/1.14 tff(85,plain,
% 1.34/1.14 (![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[84, 83])).
% 1.34/1.14 tff(86,plain,
% 1.34/1.14 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 1.34/1.14 inference(and_elim,[status(thm)],[47])).
% 1.34/1.14 tff(87,plain,
% 1.34/1.14 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)))))),
% 1.34/1.14 inference(rewrite,[status(thm)],[])).
% 1.34/1.14 tff(88,plain,
% 1.34/1.14 (((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)))))),
% 1.34/1.14 inference(rewrite,[status(thm)],[])).
% 1.34/1.14 tff(89,plain,
% 1.34/1.14 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0))))))),
% 1.34/1.14 inference(monotonicity,[status(thm)],[88])).
% 1.34/1.14 tff(90,plain,
% 1.34/1.14 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)))))),
% 1.34/1.14 inference(transitivity,[status(thm)],[89, 87])).
% 1.34/1.14 tff(91,plain,
% 1.34/1.14 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.34/1.14 inference(quant_inst,[status(thm)],[])).
% 1.34/1.14 tff(92,plain,
% 1.34/1.14 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0))))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.34/1.14 tff(93,plain,
% 1.34/1.14 (~((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)))),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[92, 86, 85])).
% 1.34/1.14 tff(94,plain,
% 1.34/1.14 (((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0))) | m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.14 inference(tautology,[status(thm)],[])).
% 1.34/1.14 tff(95,plain,
% 1.34/1.14 (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[94, 93])).
% 1.34/1.14 tff(96,plain,
% 1.34/1.14 ((~(m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.14 inference(tautology,[status(thm)],[])).
% 1.34/1.14 tff(97,plain,
% 1.34/1.14 ((~(m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[96, 95])).
% 1.34/1.14 tff(98,plain,
% 1.34/1.14 (m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[97, 9])).
% 1.34/1.14 tff(99,plain,
% 1.34/1.14 (~((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)))),
% 1.34/1.14 inference(and_elim,[status(thm)],[47])).
% 1.34/1.14 tff(100,plain,
% 1.34/1.14 (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 1.34/1.14 inference(or_elim,[status(thm)],[99])).
% 1.34/1.14 tff(101,plain,
% 1.34/1.14 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)))))),
% 1.34/1.14 inference(rewrite,[status(thm)],[])).
% 1.34/1.14 tff(102,plain,
% 1.34/1.14 (((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)))))),
% 1.34/1.14 inference(rewrite,[status(thm)],[])).
% 1.34/1.14 tff(103,plain,
% 1.34/1.14 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))))))),
% 1.34/1.14 inference(monotonicity,[status(thm)],[102])).
% 1.34/1.14 tff(104,plain,
% 1.34/1.14 (((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)))))),
% 1.34/1.14 inference(transitivity,[status(thm)],[103, 101])).
% 1.34/1.14 tff(105,plain,
% 1.34/1.14 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | ((~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.34/1.14 inference(quant_inst,[status(thm)],[])).
% 1.34/1.14 tff(106,plain,
% 1.34/1.14 ((~![C: $i] : ((~m2_fraenkel(C, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_1(C)) | (~v1_funct_2(C, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C, A!0, A!0)) | (~m2_relset_1(C, u1_struct_0(A!0), u1_struct_0(A!0))))))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | (~((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.34/1.14 tff(107,plain,
% 1.34/1.14 (~((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)))),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[106, 100, 85])).
% 1.34/1.14 tff(108,plain,
% 1.34/1.14 (((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))) | v1_funct_1(C!2)),
% 1.34/1.14 inference(tautology,[status(thm)],[])).
% 1.34/1.14 tff(109,plain,
% 1.34/1.14 (v1_funct_1(C!2)),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[108, 107])).
% 1.34/1.14 tff(110,plain,
% 1.34/1.14 (((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0))) | v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.14 inference(tautology,[status(thm)],[])).
% 1.34/1.14 tff(111,plain,
% 1.34/1.14 (v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[110, 93])).
% 1.34/1.14 tff(112,plain,
% 1.34/1.14 (((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0))) | v1_funct_1(B!1)),
% 1.34/1.14 inference(tautology,[status(thm)],[])).
% 1.34/1.14 tff(113,plain,
% 1.34/1.14 (v1_funct_1(B!1)),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[112, 93])).
% 1.34/1.14 tff(114,plain,
% 1.34/1.14 (((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))) | v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.14 inference(tautology,[status(thm)],[])).
% 1.34/1.14 tff(115,plain,
% 1.34/1.14 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[114, 107])).
% 1.34/1.14 tff(116,plain,
% 1.34/1.14 (^[A: $i] : refl((l1_struct_0(A) | (~l1_group_1(A))) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 1.34/1.14 inference(bind,[status(th)],[])).
% 1.34/1.14 tff(117,plain,
% 1.34/1.14 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.34/1.14 inference(quant_intro,[status(thm)],[116])).
% 1.34/1.14 tff(118,plain,
% 1.34/1.14 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.34/1.14 inference(rewrite,[status(thm)],[])).
% 1.34/1.14 tff(119,plain,
% 1.34/1.14 (^[A: $i] : rewrite((l1_group_1(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l1_group_1(A))))),
% 1.34/1.14 inference(bind,[status(th)],[])).
% 1.34/1.14 tff(120,plain,
% 1.34/1.14 (![A: $i] : (l1_group_1(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.34/1.14 inference(quant_intro,[status(thm)],[119])).
% 1.34/1.14 tff(121,axiom,(![A: $i] : (l1_group_1(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_group_1')).
% 1.34/1.14 tff(122,plain,
% 1.34/1.14 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.34/1.14 tff(123,plain,
% 1.34/1.14 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[122, 118])).
% 1.34/1.14 tff(124,plain,(
% 1.34/1.14 ![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.34/1.14 inference(skolemize,[status(sab)],[123])).
% 1.34/1.14 tff(125,plain,
% 1.34/1.14 (![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[124, 117])).
% 1.34/1.14 tff(126,plain,
% 1.34/1.14 (((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 1.34/1.14 inference(rewrite,[status(thm)],[])).
% 1.34/1.14 tff(127,plain,
% 1.34/1.14 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | (l1_struct_0(A!0) | (~l1_group_1(A!0)))),
% 1.34/1.14 inference(quant_inst,[status(thm)],[])).
% 1.34/1.14 tff(128,plain,
% 1.34/1.14 ((~![A: $i] : (l1_struct_0(A) | (~l1_group_1(A)))) | l1_struct_0(A!0) | (~l1_group_1(A!0))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.34/1.14 tff(129,plain,
% 1.34/1.14 (l1_struct_0(A!0)),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[128, 48, 125])).
% 1.34/1.14 tff(130,plain,
% 1.34/1.14 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 1.34/1.14 inference(bind,[status(th)],[])).
% 1.34/1.14 tff(131,plain,
% 1.34/1.14 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.34/1.14 inference(quant_intro,[status(thm)],[130])).
% 1.34/1.14 tff(132,plain,
% 1.34/1.14 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 1.34/1.14 inference(bind,[status(th)],[])).
% 1.34/1.14 tff(133,plain,
% 1.34/1.14 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.34/1.14 inference(quant_intro,[status(thm)],[132])).
% 1.34/1.14 tff(134,plain,
% 1.34/1.14 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.34/1.14 inference(rewrite,[status(thm)],[])).
% 1.34/1.14 tff(135,plain,
% 1.34/1.14 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 1.34/1.14 inference(bind,[status(th)],[])).
% 1.34/1.14 tff(136,plain,
% 1.34/1.14 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.34/1.14 inference(quant_intro,[status(thm)],[135])).
% 1.34/1.14 tff(137,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 1.34/1.14 tff(138,plain,
% 1.34/1.14 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.34/1.14 tff(139,plain,
% 1.34/1.14 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[138, 134])).
% 1.34/1.14 tff(140,plain,(
% 1.34/1.14 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.34/1.14 inference(skolemize,[status(sab)],[139])).
% 1.34/1.14 tff(141,plain,
% 1.34/1.14 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[140, 133])).
% 1.34/1.14 tff(142,plain,
% 1.34/1.14 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[141, 131])).
% 1.34/1.14 tff(143,plain,
% 1.34/1.14 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.34/1.14 inference(rewrite,[status(thm)],[])).
% 1.34/1.14 tff(144,plain,
% 1.34/1.14 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.34/1.14 inference(rewrite,[status(thm)],[])).
% 1.34/1.14 tff(145,plain,
% 1.34/1.14 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 1.34/1.14 inference(monotonicity,[status(thm)],[144])).
% 1.34/1.14 tff(146,plain,
% 1.34/1.14 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.34/1.14 inference(transitivity,[status(thm)],[145, 143])).
% 1.34/1.14 tff(147,plain,
% 1.34/1.14 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 1.34/1.14 inference(quant_inst,[status(thm)],[])).
% 1.34/1.14 tff(148,plain,
% 1.34/1.14 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 1.34/1.14 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.34/1.14 tff(149,plain,
% 1.34/1.14 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[148, 52, 142])).
% 1.34/1.14 tff(150,plain,
% 1.34/1.14 (~v1_xboole_0(u1_struct_0(A!0))),
% 1.34/1.14 inference(unit_resolution,[status(thm)],[149, 129])).
% 1.34/1.14 tff(151,plain,
% 1.34/1.14 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.34/1.15 inference(quant_inst,[status(thm)],[])).
% 1.34/1.15 tff(152,plain,
% 1.34/1.15 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[151, 7])).
% 1.34/1.15 tff(153,plain,
% 1.34/1.15 (((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))) | m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.15 inference(tautology,[status(thm)],[])).
% 1.34/1.15 tff(154,plain,
% 1.34/1.15 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[153, 107])).
% 1.34/1.15 tff(155,plain,
% 1.34/1.15 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.15 inference(tautology,[status(thm)],[])).
% 1.34/1.15 tff(156,plain,
% 1.34/1.15 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[155, 154])).
% 1.34/1.15 tff(157,plain,
% 1.34/1.15 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[156, 152])).
% 1.34/1.15 tff(158,plain,
% 1.34/1.15 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(159,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[158])).
% 1.34/1.15 tff(160,plain,
% 1.34/1.15 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) <=> (~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite(((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(161,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[160])).
% 1.34/1.15 tff(162,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(163,plain,
% 1.34/1.15 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(164,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[163])).
% 1.34/1.15 tff(165,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k7_funct_2')).
% 1.34/1.15 tff(166,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.34/1.15 tff(167,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[166, 162])).
% 1.34/1.15 tff(168,plain,(
% 1.34/1.15 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.34/1.15 inference(skolemize,[status(sab)],[167])).
% 1.34/1.15 tff(169,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[168, 161])).
% 1.34/1.15 tff(170,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[169, 159])).
% 1.34/1.15 tff(171,plain,
% 1.34/1.15 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(172,plain,
% 1.34/1.15 ((v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(173,plain,
% 1.34/1.15 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1))))),
% 1.34/1.15 inference(monotonicity,[status(thm)],[172])).
% 1.34/1.15 tff(174,plain,
% 1.34/1.15 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 1.34/1.15 inference(transitivity,[status(thm)],[173, 171])).
% 1.34/1.15 tff(175,plain,
% 1.34/1.15 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.34/1.15 inference(quant_inst,[status(thm)],[])).
% 1.34/1.15 tff(176,plain,
% 1.34/1.15 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (k7_funct_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.34/1.15 tff(177,plain,
% 1.34/1.15 (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1))),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[176, 170])).
% 1.34/1.15 tff(178,plain,
% 1.34/1.15 (k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1) = k5_relat_1(C!2, B!1)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[177, 157, 150, 115, 113, 111, 109, 98])).
% 1.34/1.15 tff(179,plain,
% 1.34/1.15 (k5_relat_1(C!2, B!1) = k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)),
% 1.34/1.15 inference(symmetry,[status(thm)],[178])).
% 1.34/1.15 tff(180,plain,
% 1.34/1.15 (m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.15 inference(monotonicity,[status(thm)],[179])).
% 1.34/1.15 tff(181,plain,
% 1.34/1.15 (m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.15 inference(symmetry,[status(thm)],[180])).
% 1.34/1.15 tff(182,plain,
% 1.34/1.15 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(183,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[182])).
% 1.34/1.15 tff(184,plain,
% 1.34/1.15 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) <=> (~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))))), rewrite((~(~(v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)))), ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))))), rewrite((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)) <=> (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))))), rewrite(((v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C))) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))), (((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(185,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[184])).
% 1.34/1.15 tff(186,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(187,plain,
% 1.34/1.15 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B))), (((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E))), ((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C))), (((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))), ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) <=> ((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)))), rewrite(((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)) <=> (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> (((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))))), rewrite((((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C)) => (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))), (((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(188,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[187])).
% 1.34/1.15 tff(189,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((((((((~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, A, B)) & m1_relset_1(D, A, B)) & v1_funct_1(E)) & v1_funct_2(E, B, C)) & m1_relset_1(E, B, C)) => ((v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k7_funct_2')).
% 1.34/1.15 tff(190,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[189, 188])).
% 1.34/1.15 tff(191,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[190, 186])).
% 1.34/1.15 tff(192,plain,(
% 1.34/1.15 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, A, B) & m1_relset_1(D, A, B) & v1_funct_1(E) & v1_funct_2(E, B, C) & m1_relset_1(E, B, C))) | (v1_funct_1(k7_funct_2(A, B, C, D, E)) & v1_funct_2(k7_funct_2(A, B, C, D, E), A, C) & m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))),
% 1.34/1.15 inference(skolemize,[status(sab)],[191])).
% 1.34/1.15 tff(193,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[192, 185])).
% 1.34/1.15 tff(194,plain,
% 1.34/1.15 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[193, 183])).
% 1.34/1.15 tff(195,plain,
% 1.34/1.15 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(196,plain,
% 1.34/1.15 ((v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(197,plain,
% 1.34/1.15 ((~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(198,plain,
% 1.34/1.15 ((v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[197])).
% 1.34/1.16 tff(199,plain,
% 1.34/1.16 ((v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.34/1.16 inference(transitivity,[status(thm)],[198, 196])).
% 1.34/1.16 tff(200,plain,
% 1.34/1.16 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[199])).
% 1.34/1.16 tff(201,plain,
% 1.34/1.16 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.34/1.16 inference(transitivity,[status(thm)],[200, 195])).
% 1.34/1.16 tff(202,plain,
% 1.34/1.16 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.34/1.16 inference(quant_inst,[status(thm)],[])).
% 1.34/1.16 tff(203,plain,
% 1.34/1.16 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v1_xboole_0(B) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v1_funct_2(D, A, B)) | (~m1_relset_1(D, A, B)) | (~v1_funct_2(E, B, C)) | (~m1_relset_1(E, B, C)) | (~((~v1_funct_1(k7_funct_2(A, B, C, D, E))) | (~v1_funct_2(k7_funct_2(A, B, C, D, E), A, C)) | (~m2_relset_1(k7_funct_2(A, B, C, D, E), A, C)))))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[202, 201])).
% 1.34/1.16 tff(204,plain,
% 1.34/1.16 (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[203, 194])).
% 1.34/1.16 tff(205,plain,
% 1.34/1.16 (~((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[204, 157, 150, 115, 113, 111, 109, 98])).
% 1.34/1.16 tff(206,plain,
% 1.34/1.16 (((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(tautology,[status(thm)],[])).
% 1.34/1.16 tff(207,plain,
% 1.34/1.16 (m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[206, 205])).
% 1.34/1.16 tff(208,plain,
% 1.34/1.16 (m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[207, 181])).
% 1.34/1.16 tff(209,plain,
% 1.34/1.16 (v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[179])).
% 1.34/1.16 tff(210,plain,
% 1.34/1.16 (v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(symmetry,[status(thm)],[209])).
% 1.34/1.16 tff(211,plain,
% 1.34/1.16 (((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(tautology,[status(thm)],[])).
% 1.34/1.16 tff(212,plain,
% 1.34/1.16 (v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[211, 205])).
% 1.34/1.16 tff(213,plain,
% 1.34/1.16 (v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[212, 210])).
% 1.34/1.16 tff(214,plain,
% 1.34/1.16 (v1_funct_1(k5_relat_1(C!2, B!1)) <=> v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[179])).
% 1.34/1.16 tff(215,plain,
% 1.34/1.16 (v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1)) <=> v1_funct_1(k5_relat_1(C!2, B!1))),
% 1.34/1.16 inference(symmetry,[status(thm)],[214])).
% 1.34/1.16 tff(216,plain,
% 1.34/1.16 (((~v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))) | (~v1_funct_2(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))) | v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 1.34/1.16 inference(tautology,[status(thm)],[])).
% 1.34/1.16 tff(217,plain,
% 1.34/1.16 (v1_funct_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1))),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[216, 205])).
% 1.34/1.16 tff(218,plain,
% 1.34/1.16 (v1_funct_1(k5_relat_1(C!2, B!1))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[217, 215])).
% 1.34/1.16 tff(219,plain,
% 1.34/1.16 (^[A: $i] : refl(((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A))))),
% 1.34/1.16 inference(bind,[status(th)],[])).
% 1.34/1.16 tff(220,plain,
% 1.34/1.16 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 1.34/1.16 inference(quant_intro,[status(thm)],[219])).
% 1.34/1.16 tff(221,plain,
% 1.34/1.16 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(222,plain,
% 1.34/1.16 (^[A: $i] : trans(monotonicity(rewrite((v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))) <=> ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> (l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))))), rewrite((l1_group_1(A) => ((~v1_group_1(A)) | (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))), ((l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))))),
% 1.34/1.16 inference(bind,[status(th)],[])).
% 1.34/1.16 tff(223,plain,
% 1.34/1.16 (![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A))))) <=> ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 1.34/1.16 inference(quant_intro,[status(thm)],[222])).
% 1.34/1.16 tff(224,axiom,(![A: $i] : (l1_group_1(A) => (v1_group_1(A) => (A = g1_group_1(u1_struct_0(A), u1_group_1(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v1_group_1')).
% 1.34/1.16 tff(225,plain,
% 1.34/1.16 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[224, 223])).
% 1.34/1.16 tff(226,plain,
% 1.34/1.16 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[225, 221])).
% 1.34/1.16 tff(227,plain,(
% 1.34/1.16 ![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 1.34/1.16 inference(skolemize,[status(sab)],[226])).
% 1.34/1.16 tff(228,plain,
% 1.34/1.16 (![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[227, 220])).
% 1.34/1.16 tff(229,plain,
% 1.34/1.16 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(230,plain,
% 1.34/1.16 (((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0))) <=> ((~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(231,plain,
% 1.34/1.16 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[230])).
% 1.34/1.16 tff(232,plain,
% 1.34/1.16 (((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))) <=> ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(transitivity,[status(thm)],[231, 229])).
% 1.34/1.16 tff(233,plain,
% 1.34/1.16 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | ((A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)))),
% 1.34/1.16 inference(quant_inst,[status(thm)],[])).
% 1.34/1.16 tff(234,plain,
% 1.34/1.16 ((~![A: $i] : ((A = g1_group_1(u1_struct_0(A), u1_group_1(A))) | (~l1_group_1(A)) | (~v1_group_1(A)))) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[233, 232])).
% 1.34/1.16 tff(235,plain,
% 1.34/1.16 (A!0 = g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[234, 51, 48, 228])).
% 1.34/1.16 tff(236,plain,
% 1.34/1.16 (k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1)),
% 1.34/1.16 inference(monotonicity,[status(thm)],[235])).
% 1.34/1.16 tff(237,plain,
% 1.34/1.16 (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1)),
% 1.34/1.16 inference(symmetry,[status(thm)],[236])).
% 1.34/1.16 tff(238,plain,
% 1.34/1.16 (g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)) = A!0),
% 1.34/1.16 inference(symmetry,[status(thm)],[235])).
% 1.34/1.16 tff(239,plain,
% 1.34/1.16 (u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) = u1_struct_0(A!0)),
% 1.34/1.16 inference(monotonicity,[status(thm)],[238])).
% 1.34/1.16 tff(240,plain,
% 1.34/1.16 (m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[239, 239])).
% 1.34/1.16 tff(241,plain,
% 1.34/1.16 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(symmetry,[status(thm)],[240])).
% 1.34/1.16 tff(242,plain,
% 1.34/1.16 (m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[157, 241])).
% 1.34/1.16 tff(243,plain,
% 1.34/1.16 (m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[239, 239])).
% 1.34/1.16 tff(244,plain,
% 1.34/1.16 (m1_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(symmetry,[status(thm)],[243])).
% 1.34/1.16 tff(245,plain,
% 1.34/1.16 (m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[98, 244])).
% 1.34/1.16 tff(246,plain,
% 1.34/1.16 (v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_6(B!1, A!0, A!0)),
% 1.34/1.16 inference(monotonicity,[status(thm)],[238, 238])).
% 1.34/1.16 tff(247,plain,
% 1.34/1.16 (v1_group_6(B!1, A!0, A!0) <=> v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(symmetry,[status(thm)],[246])).
% 1.34/1.16 tff(248,plain,
% 1.34/1.16 (((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0))) | v1_group_6(B!1, A!0, A!0)),
% 1.34/1.16 inference(tautology,[status(thm)],[])).
% 1.34/1.16 tff(249,plain,
% 1.34/1.16 (v1_group_6(B!1, A!0, A!0)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[248, 93])).
% 1.34/1.16 tff(250,plain,
% 1.34/1.16 (v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[249, 247])).
% 1.34/1.16 tff(251,plain,
% 1.34/1.16 (v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[239, 239])).
% 1.34/1.16 tff(252,plain,
% 1.34/1.16 (v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(symmetry,[status(thm)],[251])).
% 1.34/1.16 tff(253,plain,
% 1.34/1.16 (v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[111, 252])).
% 1.34/1.16 tff(254,plain,
% 1.34/1.16 (v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_6(C!2, A!0, A!0)),
% 1.34/1.16 inference(monotonicity,[status(thm)],[238, 238])).
% 1.34/1.16 tff(255,plain,
% 1.34/1.16 (v1_group_6(C!2, A!0, A!0) <=> v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(symmetry,[status(thm)],[254])).
% 1.34/1.16 tff(256,plain,
% 1.34/1.16 (((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0))) | v1_group_6(C!2, A!0, A!0)),
% 1.34/1.16 inference(tautology,[status(thm)],[])).
% 1.34/1.16 tff(257,plain,
% 1.34/1.16 (v1_group_6(C!2, A!0, A!0)),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[256, 107])).
% 1.34/1.16 tff(258,plain,
% 1.34/1.16 (v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[257, 255])).
% 1.34/1.16 tff(259,plain,
% 1.34/1.16 (v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[239, 239])).
% 1.34/1.16 tff(260,plain,
% 1.34/1.16 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(symmetry,[status(thm)],[259])).
% 1.34/1.16 tff(261,plain,
% 1.34/1.16 (v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[115, 260])).
% 1.34/1.16 tff(262,plain,
% 1.34/1.16 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_1(A!0)),
% 1.34/1.16 inference(monotonicity,[status(thm)],[238])).
% 1.34/1.16 tff(263,plain,
% 1.34/1.16 (v4_group_1(A!0) <=> v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(symmetry,[status(thm)],[262])).
% 1.34/1.16 tff(264,plain,
% 1.34/1.16 (v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[49, 263])).
% 1.34/1.16 tff(265,plain,
% 1.34/1.16 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_group_1(A!0)),
% 1.34/1.16 inference(monotonicity,[status(thm)],[238])).
% 1.34/1.16 tff(266,plain,
% 1.34/1.16 (v3_group_1(A!0) <=> v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(symmetry,[status(thm)],[265])).
% 1.34/1.16 tff(267,plain,
% 1.34/1.16 (v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[50, 266])).
% 1.34/1.16 tff(268,plain,
% 1.34/1.16 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> l1_group_1(A!0)),
% 1.34/1.16 inference(monotonicity,[status(thm)],[238])).
% 1.34/1.16 tff(269,plain,
% 1.34/1.16 (l1_group_1(A!0) <=> l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(symmetry,[status(thm)],[268])).
% 1.34/1.16 tff(270,plain,
% 1.34/1.16 (l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[48, 269])).
% 1.34/1.16 tff(271,plain,
% 1.34/1.16 (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v3_struct_0(A!0)),
% 1.34/1.16 inference(monotonicity,[status(thm)],[238])).
% 1.34/1.16 tff(272,plain,
% 1.34/1.16 (v3_struct_0(A!0) <=> v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(symmetry,[status(thm)],[271])).
% 1.34/1.16 tff(273,plain,
% 1.34/1.16 ((~v3_struct_0(A!0)) <=> (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[272])).
% 1.34/1.16 tff(274,plain,
% 1.34/1.16 (~v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[52, 273])).
% 1.34/1.16 tff(275,plain,
% 1.34/1.16 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))),
% 1.34/1.16 inference(bind,[status(th)],[])).
% 1.34/1.16 tff(276,plain,
% 1.34/1.16 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))),
% 1.34/1.16 inference(quant_intro,[status(thm)],[275])).
% 1.34/1.16 tff(277,plain,
% 1.34/1.16 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (~(~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), rewrite((~(~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite(((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))),
% 1.34/1.16 inference(bind,[status(th)],[])).
% 1.34/1.16 tff(278,plain,
% 1.34/1.16 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))),
% 1.34/1.16 inference(quant_intro,[status(thm)],[277])).
% 1.34/1.16 tff(279,plain,
% 1.34/1.16 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(280,plain,
% 1.34/1.16 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))) & v3_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))) & v3_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) & (~v3_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) & (~v3_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))))), (((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))) & v3_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))) & v3_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C))), (((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)))), ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C))), ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)))), (((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))), (((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)))), ((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) & v1_funct_1(D)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) & v1_funct_1(D)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D))), ((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)))), (((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)))), (((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))))), ((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B))), ((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)))), (((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)))), (((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), ((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E))), ((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)))), (((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)))), (((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))))), ((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C))), ((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)))), (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))), (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), ((((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))), ((((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))))),
% 1.34/1.17 inference(bind,[status(th)],[])).
% 1.34/1.17 tff(281,plain,
% 1.34/1.17 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.34/1.17 inference(quant_intro,[status(thm)],[280])).
% 1.34/1.17 tff(282,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k8_group_6')).
% 1.34/1.17 tff(283,plain,
% 1.34/1.17 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[282, 281])).
% 1.34/1.17 tff(284,plain,
% 1.34/1.17 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[283, 279])).
% 1.34/1.17 tff(285,plain,(
% 1.34/1.17 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)))),
% 1.34/1.17 inference(skolemize,[status(sab)],[284])).
% 1.34/1.17 tff(286,plain,
% 1.34/1.17 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[285, 278])).
% 1.34/1.17 tff(287,plain,
% 1.34/1.17 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[286, 276])).
% 1.34/1.17 tff(288,plain,
% 1.34/1.17 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | ((~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(289,plain,
% 1.34/1.17 ((v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(290,plain,
% 1.34/1.17 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | ((~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1))))),
% 1.34/1.17 inference(monotonicity,[status(thm)],[289])).
% 1.34/1.17 tff(291,plain,
% 1.34/1.17 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)))),
% 1.34/1.17 inference(transitivity,[status(thm)],[290, 288])).
% 1.34/1.17 tff(292,plain,
% 1.34/1.17 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.34/1.18 inference(quant_inst,[status(thm)],[])).
% 1.34/1.18 tff(293,plain,
% 1.34/1.18 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (k8_group_6(A, B, C, D, E) = k5_relat_1(D, E)) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) | (~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1))),
% 1.34/1.18 inference(modus_ponens,[status(thm)],[292, 291])).
% 1.34/1.18 tff(294,plain,
% 1.34/1.18 ((~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1))),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[293, 287, 109, 113, 274, 270, 267, 264, 261, 258, 253, 250])).
% 1.34/1.18 tff(295,plain,
% 1.34/1.18 (k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1) = k5_relat_1(C!2, B!1)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[294, 245, 242])).
% 1.34/1.18 tff(296,plain,
% 1.34/1.18 (k5_relat_1(C!2, B!1) = k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1)),
% 1.34/1.18 inference(symmetry,[status(thm)],[295])).
% 1.34/1.18 tff(297,plain,
% 1.34/1.18 (k5_relat_1(C!2, B!1) = k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1)),
% 1.34/1.18 inference(transitivity,[status(thm)],[296, 237])).
% 1.34/1.18 tff(298,plain,
% 1.34/1.18 (v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0) <=> v1_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.18 inference(monotonicity,[status(thm)],[297, 235, 235])).
% 1.34/1.18 tff(299,plain,
% 1.34/1.18 (v1_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)),
% 1.34/1.18 inference(symmetry,[status(thm)],[298])).
% 1.34/1.18 tff(300,plain,
% 1.34/1.18 (v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.34/1.18 inference(monotonicity,[status(thm)],[237])).
% 1.34/1.18 tff(301,plain,
% 1.34/1.18 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))))),
% 1.34/1.18 inference(bind,[status(th)],[])).
% 1.34/1.18 tff(302,plain,
% 1.34/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))),
% 1.34/1.18 inference(quant_intro,[status(thm)],[301])).
% 1.34/1.18 tff(303,plain,
% 1.34/1.18 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (~(~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), rewrite((~(~(v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), rewrite((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) <=> (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))))), rewrite(((v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))))),
% 1.34/1.18 inference(bind,[status(th)],[])).
% 1.34/1.18 tff(304,plain,
% 1.34/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))),
% 1.34/1.18 inference(quant_intro,[status(thm)],[303])).
% 1.34/1.18 tff(305,plain,
% 1.34/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))),
% 1.34/1.18 inference(rewrite,[status(thm)],[])).
% 1.34/1.18 tff(306,plain,
% 1.34/1.18 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & (~v3_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))) & v3_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B))) & v3_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B))), ((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))), (((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) & (~v3_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) & (~v3_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)))), ((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))))), (((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))) & v3_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C))) & v3_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C))), (((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)))), ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C))), ((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)))), (((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))), (((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)))), ((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) & v1_funct_1(D)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) & v1_funct_1(D)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D))), ((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)))), (((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)))), (((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))))), ((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B))), ((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)))), (((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)))), (((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), ((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E))), ((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)))), (((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)))), (((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))))), ((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C))), ((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)))), (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))), (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), trans(monotonicity(rewrite(((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) <=> (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C))), ((((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) <=> ((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))), rewrite(((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) <=> (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))), ((((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) <=> (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))), ((((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))), ((((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))),
% 1.47/1.18 inference(bind,[status(th)],[])).
% 1.47/1.18 tff(307,plain,
% 1.47/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))),
% 1.47/1.18 inference(quant_intro,[status(thm)],[306])).
% 1.47/1.18 tff(308,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : (((((((((((((((((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & (~v3_struct_0(B))) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) & (~v3_struct_0(C))) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) & v1_funct_1(D)) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) & v1_funct_1(E)) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => (((v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) & v1_group_6(k8_group_6(A, B, C, D, E), A, C)) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_group_6')).
% 1.47/1.18 tff(309,plain,
% 1.47/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[308, 307])).
% 1.47/1.18 tff(310,plain,
% 1.47/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[309, 305])).
% 1.47/1.18 tff(311,plain,(
% 1.47/1.18 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & (~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & (~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) & v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m1_relset_1(D, u1_struct_0(A), u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m1_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) | (v1_funct_1(k8_group_6(A, B, C, D, E)) & v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C)) & v1_group_6(k8_group_6(A, B, C, D, E), A, C) & m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))),
% 1.47/1.18 inference(skolemize,[status(sab)],[310])).
% 1.47/1.18 tff(312,plain,
% 1.47/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[311, 304])).
% 1.47/1.18 tff(313,plain,
% 1.47/1.18 (![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))),
% 1.47/1.18 inference(modus_ponens,[status(thm)],[312, 302])).
% 1.47/1.18 tff(314,plain,
% 1.47/1.18 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(315,plain,
% 1.47/1.19 ((v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(316,plain,
% 1.47/1.19 ((~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.47/1.19 inference(rewrite,[status(thm)],[])).
% 1.47/1.19 tff(317,plain,
% 1.47/1.19 ((v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) <=> (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.47/1.19 inference(monotonicity,[status(thm)],[316])).
% 1.47/1.19 tff(318,plain,
% 1.47/1.19 ((v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.47/1.19 inference(transitivity,[status(thm)],[317, 315])).
% 1.47/1.19 tff(319,plain,
% 1.47/1.19 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))))),
% 1.47/1.19 inference(monotonicity,[status(thm)],[318])).
% 1.47/1.19 tff(320,plain,
% 1.47/1.19 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.47/1.20 inference(transitivity,[status(thm)],[319, 314])).
% 1.47/1.20 tff(321,plain,
% 1.47/1.20 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v1_funct_1(B!1)) | (~v1_funct_1(C!2)) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.47/1.20 inference(quant_inst,[status(thm)],[])).
% 1.47/1.20 tff(322,plain,
% 1.47/1.20 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : (v3_struct_0(C) | v3_struct_0(B) | v3_struct_0(A) | (~v1_funct_1(E)) | (~v1_funct_1(D)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | (~v3_group_1(B)) | (~v4_group_1(B)) | (~l1_group_1(B)) | (~v3_group_1(C)) | (~v4_group_1(C)) | (~l1_group_1(C)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m1_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m1_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~((~v1_funct_1(k8_group_6(A, B, C, D, E))) | (~v1_funct_2(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))) | (~v1_group_6(k8_group_6(A, B, C, D, E), A, C)) | (~m2_relset_1(k8_group_6(A, B, C, D, E), u1_struct_0(A), u1_struct_0(C))))))) | (~v1_funct_1(C!2)) | (~v1_funct_1(B!1)) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[321, 320])).
% 1.47/1.20 tff(323,plain,
% 1.47/1.20 ((~m1_relset_1(C!2, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~m1_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[322, 313, 109, 113, 274, 270, 267, 264, 261, 258, 253, 250])).
% 1.47/1.20 tff(324,plain,
% 1.47/1.20 (~((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[323, 245, 242])).
% 1.47/1.20 tff(325,plain,
% 1.47/1.20 (((~v1_funct_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1))) | (~v1_funct_2(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.47/1.20 inference(tautology,[status(thm)],[])).
% 1.47/1.20 tff(326,plain,
% 1.47/1.20 (v1_group_6(k8_group_6(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[325, 324])).
% 1.47/1.20 tff(327,plain,
% 1.47/1.20 (v1_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[326, 300])).
% 1.47/1.20 tff(328,plain,
% 1.47/1.20 (v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[327, 299])).
% 1.47/1.20 tff(329,plain,
% 1.47/1.20 (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))),
% 1.47/1.20 inference(monotonicity,[status(thm)],[179])).
% 1.47/1.20 tff(330,plain,
% 1.47/1.20 (r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)) <=> r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0))),
% 1.47/1.20 inference(symmetry,[status(thm)],[329])).
% 1.47/1.20 tff(331,plain,
% 1.47/1.20 ((~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))) <=> (~r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)))),
% 1.47/1.20 inference(monotonicity,[status(thm)],[330])).
% 1.47/1.20 tff(332,plain,
% 1.47/1.20 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(333,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[332])).
% 1.47/1.20 tff(334,plain,
% 1.47/1.20 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(335,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[334])).
% 1.47/1.20 tff(336,plain,
% 1.47/1.20 (^[A: $i, B: $i, C: $i] : rewrite((v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(337,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[336])).
% 1.47/1.20 tff(338,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.47/1.20 inference(transitivity,[status(thm)],[337, 335])).
% 1.47/1.20 tff(339,plain,
% 1.47/1.20 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) <=> (~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)))), ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) <=> (v1_xboole_0(B) | (~m1_fraenkel(C, A, B))))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))), rewrite(((v1_xboole_0(B) | (~m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))), (((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(340,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[339])).
% 1.47/1.20 tff(341,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(342,plain,
% 1.47/1.20 (^[A: $i, B: $i, C: $i] : rewrite((((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(343,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[342])).
% 1.47/1.20 tff(344,axiom,(![A: $i, B: $i, C: $i] : (((~v1_xboole_0(B)) & m1_fraenkel(C, A, B)) => ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_fraenkel')).
% 1.47/1.20 tff(345,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[344, 343])).
% 1.47/1.20 tff(346,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[345, 341])).
% 1.47/1.20 tff(347,plain,(
% 1.47/1.20 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(B)) & m1_fraenkel(C, A, B))) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.47/1.20 inference(skolemize,[status(sab)],[346])).
% 1.47/1.20 tff(348,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[347, 340])).
% 1.47/1.20 tff(349,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)) | (~m1_fraenkel(C, A, B)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[348, 338])).
% 1.47/1.20 tff(350,plain,
% 1.47/1.20 (![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[349, 333])).
% 1.47/1.20 tff(351,plain,
% 1.47/1.20 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(352,plain,
% 1.47/1.20 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0))))),
% 1.47/1.20 inference(quant_inst,[status(thm)],[])).
% 1.47/1.20 tff(353,plain,
% 1.47/1.20 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(B) | (~m1_fraenkel(C, A, B)) | ![D: $i] : (m2_fraenkel(D, A, B, C) <=> m1_subset_1(D, C)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | ![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[352, 351])).
% 1.47/1.20 tff(354,plain,
% 1.47/1.20 (![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[353, 350, 150, 76])).
% 1.47/1.20 tff(355,plain,
% 1.47/1.20 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))) | (m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))),
% 1.47/1.20 inference(quant_inst,[status(thm)],[])).
% 1.47/1.20 tff(356,plain,
% 1.47/1.20 (m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[355, 354])).
% 1.47/1.20 tff(357,plain,
% 1.47/1.20 (~m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))),
% 1.47/1.20 inference(or_elim,[status(thm)],[99])).
% 1.47/1.20 tff(358,plain,
% 1.47/1.20 ((~(m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))) | m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) | (~m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))),
% 1.47/1.20 inference(tautology,[status(thm)],[])).
% 1.47/1.20 tff(359,plain,
% 1.47/1.20 ((~(m2_fraenkel(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))) | (~m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[358, 357])).
% 1.47/1.20 tff(360,plain,
% 1.47/1.20 (~m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[359, 356])).
% 1.47/1.20 tff(361,plain,
% 1.47/1.20 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(362,plain,
% 1.47/1.20 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[361])).
% 1.47/1.20 tff(363,plain,
% 1.47/1.20 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(364,plain,
% 1.47/1.20 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(365,plain,
% 1.47/1.20 (![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[364])).
% 1.47/1.20 tff(366,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 1.47/1.20 tff(367,plain,
% 1.47/1.20 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[366, 365])).
% 1.47/1.20 tff(368,plain,
% 1.47/1.20 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[367, 363])).
% 1.47/1.20 tff(369,plain,(
% 1.47/1.20 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.47/1.20 inference(skolemize,[status(sab)],[368])).
% 1.47/1.20 tff(370,plain,
% 1.47/1.20 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[369, 362])).
% 1.47/1.20 tff(371,plain,
% 1.47/1.20 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))) | m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))) | m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))),
% 1.47/1.20 inference(rewrite,[status(thm)],[])).
% 1.47/1.20 tff(372,plain,
% 1.47/1.20 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))) | m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0)))),
% 1.47/1.20 inference(quant_inst,[status(thm)],[])).
% 1.47/1.20 tff(373,plain,
% 1.47/1.20 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))) | m1_subset_1(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[372, 371])).
% 1.47/1.20 tff(374,plain,
% 1.47/1.20 (~r2_hidden(k7_funct_2(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), C!2, B!1), k1_autgroup(A!0))),
% 1.47/1.20 inference(unit_resolution,[status(thm)],[373, 370, 360])).
% 1.47/1.20 tff(375,plain,
% 1.47/1.20 (~r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0))),
% 1.47/1.20 inference(modus_ponens,[status(thm)],[374, 331])).
% 1.47/1.20 tff(376,plain,
% 1.47/1.20 (v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0) <=> v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.47/1.20 inference(monotonicity,[status(thm)],[297, 235])).
% 1.47/1.20 tff(377,plain,
% 1.47/1.20 (v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)),
% 1.47/1.20 inference(symmetry,[status(thm)],[376])).
% 1.47/1.20 tff(378,plain,
% 1.47/1.20 (v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_6(C!2, A!0, A!0)),
% 1.47/1.20 inference(monotonicity,[status(thm)],[238])).
% 1.47/1.20 tff(379,plain,
% 1.47/1.20 (v4_group_6(C!2, A!0, A!0) <=> v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.47/1.20 inference(symmetry,[status(thm)],[378])).
% 1.47/1.20 tff(380,plain,
% 1.47/1.20 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(381,plain,
% 1.47/1.20 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[380])).
% 1.47/1.20 tff(382,plain,
% 1.47/1.20 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))))),
% 1.47/1.20 inference(bind,[status(th)],[])).
% 1.47/1.20 tff(383,plain,
% 1.47/1.20 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 1.47/1.20 inference(quant_intro,[status(thm)],[382])).
% 1.47/1.20 tff(384,plain,
% 1.47/1.20 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 1.47/1.20 inference(transitivity,[status(thm)],[383, 381])).
% 1.47/1.20 tff(385,plain,
% 1.47/1.20 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))), ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))), ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))), (((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))), (((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))))), (![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))))),
% 1.47/1.21 inference(bind,[status(th)],[])).
% 1.47/1.21 tff(386,plain,
% 1.47/1.21 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 1.47/1.21 inference(quant_intro,[status(thm)],[385])).
% 1.47/1.21 tff(387,plain,
% 1.47/1.21 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))),
% 1.47/1.21 inference(rewrite,[status(thm)],[])).
% 1.47/1.21 tff(388,plain,
% 1.47/1.21 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) <=> (v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A))), ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) <=> ((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) <=> (v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))), ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) <=> (v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))))), (((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))), (((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))))), (![B: $i] : ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))) <=> ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> (((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))))), rewrite((((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))), (((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))))),
% 1.47/1.21 inference(bind,[status(th)],[])).
% 1.47/1.21 tff(389,plain,
% 1.47/1.21 (![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))),
% 1.47/1.21 inference(quant_intro,[status(thm)],[388])).
% 1.47/1.21 tff(390,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v1_group_1(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) & v1_group_6(B, A, A)) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A))) => (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_autgroup')).
% 1.47/1.21 tff(391,plain,
% 1.47/1.21 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[390, 389])).
% 1.47/1.21 tff(392,plain,
% 1.47/1.21 (![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[391, 387])).
% 1.47/1.21 tff(393,plain,(
% 1.47/1.21 ![A: $i] : ((~((~v3_struct_0(A)) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & v1_group_6(B, A, A) & m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))) | (r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A))))),
% 1.47/1.21 inference(skolemize,[status(sab)],[392])).
% 1.47/1.21 tff(394,plain,
% 1.47/1.21 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[393, 386])).
% 1.47/1.21 tff(395,plain,
% 1.47/1.21 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))),
% 1.47/1.21 inference(modus_ponens,[status(thm)],[394, 384])).
% 1.47/1.21 tff(396,plain,
% 1.47/1.21 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.50/1.21 inference(rewrite,[status(thm)],[])).
% 1.50/1.21 tff(397,plain,
% 1.50/1.21 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.50/1.21 inference(rewrite,[status(thm)],[])).
% 1.50/1.21 tff(398,plain,
% 1.50/1.21 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 1.50/1.21 inference(monotonicity,[status(thm)],[397])).
% 1.50/1.21 tff(399,plain,
% 1.50/1.21 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.50/1.21 inference(transitivity,[status(thm)],[398, 396])).
% 1.50/1.21 tff(400,plain,
% 1.50/1.21 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 1.50/1.21 inference(quant_inst,[status(thm)],[])).
% 1.50/1.21 tff(401,plain,
% 1.50/1.21 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((r2_hidden(B, k1_autgroup(A)) <=> v4_group_6(B, A, A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A), u1_struct_0(A))) | (~v1_group_6(B, A, A)) | (~m2_relset_1(B, u1_struct_0(A), u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.50/1.21 inference(modus_ponens,[status(thm)],[400, 399])).
% 1.50/1.21 tff(402,plain,
% 1.50/1.21 (![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.50/1.21 inference(unit_resolution,[status(thm)],[401, 52, 51, 50, 49, 48, 395])).
% 1.50/1.21 tff(403,plain,
% 1.50/1.21 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)))),
% 1.50/1.21 inference(rewrite,[status(thm)],[])).
% 1.50/1.21 tff(404,plain,
% 1.50/1.21 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)))),
% 1.50/1.21 inference(rewrite,[status(thm)],[])).
% 1.50/1.21 tff(405,plain,
% 1.50/1.21 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0))))),
% 1.50/1.21 inference(monotonicity,[status(thm)],[404])).
% 1.50/1.21 tff(406,plain,
% 1.50/1.21 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)))),
% 1.50/1.21 inference(transitivity,[status(thm)],[405, 403])).
% 1.50/1.21 tff(407,plain,
% 1.50/1.21 ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)) | (~v1_group_6(C!2, A!0, A!0)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.50/1.21 inference(quant_inst,[status(thm)],[])).
% 1.50/1.21 tff(408,plain,
% 1.50/1.21 ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_funct_1(C!2)) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(C!2, A!0, A!0)) | (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0))),
% 1.50/1.21 inference(modus_ponens,[status(thm)],[407, 406])).
% 1.50/1.21 tff(409,plain,
% 1.50/1.21 (r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0)),
% 1.50/1.21 inference(unit_resolution,[status(thm)],[408, 402, 115, 109, 154, 257])).
% 1.50/1.21 tff(410,plain,
% 1.50/1.21 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))) | (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0)))),
% 1.50/1.21 inference(quant_inst,[status(thm)],[])).
% 1.50/1.21 tff(411,plain,
% 1.50/1.21 (m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.50/1.21 inference(unit_resolution,[status(thm)],[410, 354])).
% 1.50/1.21 tff(412,plain,
% 1.50/1.21 ((~(m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0)))) | (~m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.50/1.21 inference(tautology,[status(thm)],[])).
% 1.50/1.21 tff(413,plain,
% 1.50/1.21 ((~(m2_fraenkel(C!2, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(C!2, k1_autgroup(A!0)))) | m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.50/1.21 inference(unit_resolution,[status(thm)],[412, 100])).
% 1.50/1.21 tff(414,plain,
% 1.50/1.21 (m1_subset_1(C!2, k1_autgroup(A!0))),
% 1.50/1.21 inference(unit_resolution,[status(thm)],[413, 411])).
% 1.50/1.21 tff(415,plain,
% 1.50/1.21 (^[A: $i, B: $i, C: $i] : refl(((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))) <=> ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))))),
% 1.50/1.21 inference(bind,[status(th)],[])).
% 1.50/1.21 tff(416,plain,
% 1.50/1.21 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.50/1.21 inference(quant_intro,[status(thm)],[415])).
% 1.50/1.21 tff(417,plain,
% 1.50/1.21 (^[A: $i, B: $i, C: $i] : rewrite(((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C))))))),
% 1.50/1.21 inference(bind,[status(th)],[])).
% 1.50/1.21 tff(418,plain,
% 1.50/1.21 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.50/1.21 inference(quant_intro,[status(thm)],[417])).
% 1.50/1.21 tff(419,plain,
% 1.50/1.21 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.50/1.21 inference(rewrite,[status(thm)],[])).
% 1.50/1.21 tff(420,plain,
% 1.50/1.21 (^[A: $i, B: $i, C: $i] : rewrite((m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C))))),
% 1.50/1.21 inference(bind,[status(th)],[])).
% 1.50/1.21 tff(421,plain,
% 1.50/1.21 (![A: $i, B: $i, C: $i] : (m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.50/1.21 inference(quant_intro,[status(thm)],[420])).
% 1.50/1.21 tff(422,axiom,(![A: $i, B: $i, C: $i] : (m1_fraenkel(C, A, B) => ((~v1_xboole_0(C)) & v1_fraenkel(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_fraenkel')).
% 1.50/1.21 tff(423,plain,
% 1.50/1.21 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.50/1.21 inference(modus_ponens,[status(thm)],[422, 421])).
% 1.50/1.21 tff(424,plain,
% 1.50/1.21 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.50/1.21 inference(modus_ponens,[status(thm)],[423, 419])).
% 1.50/1.21 tff(425,plain,(
% 1.50/1.21 ![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | ((~v1_xboole_0(C)) & v1_fraenkel(C)))),
% 1.50/1.21 inference(skolemize,[status(sab)],[424])).
% 1.50/1.21 tff(426,plain,
% 1.50/1.21 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.50/1.21 inference(modus_ponens,[status(thm)],[425, 418])).
% 1.50/1.21 tff(427,plain,
% 1.50/1.21 (![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))),
% 1.50/1.21 inference(modus_ponens,[status(thm)],[426, 416])).
% 1.50/1.21 tff(428,plain,
% 1.50/1.21 (((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 1.50/1.21 inference(rewrite,[status(thm)],[])).
% 1.50/1.21 tff(429,plain,
% 1.50/1.21 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | ((~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))))),
% 1.50/1.21 inference(quant_inst,[status(thm)],[])).
% 1.50/1.21 tff(430,plain,
% 1.50/1.21 ((~![A: $i, B: $i, C: $i] : ((~m1_fraenkel(C, A, B)) | (~(v1_xboole_0(C) | (~v1_fraenkel(C)))))) | (~m1_fraenkel(k1_autgroup(A!0), u1_struct_0(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))))),
% 1.50/1.21 inference(modus_ponens,[status(thm)],[429, 428])).
% 1.50/1.21 tff(431,plain,
% 1.50/1.21 (~(v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0))))),
% 1.50/1.21 inference(unit_resolution,[status(thm)],[430, 427, 76])).
% 1.50/1.21 tff(432,plain,
% 1.50/1.21 ((v1_xboole_0(k1_autgroup(A!0)) | (~v1_fraenkel(k1_autgroup(A!0)))) | (~v1_xboole_0(k1_autgroup(A!0)))),
% 1.50/1.21 inference(tautology,[status(thm)],[])).
% 1.50/1.21 tff(433,plain,
% 1.50/1.21 (~v1_xboole_0(k1_autgroup(A!0))),
% 1.50/1.21 inference(unit_resolution,[status(thm)],[432, 431])).
% 1.50/1.21 tff(434,plain,
% 1.50/1.21 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 1.50/1.21 inference(bind,[status(th)],[])).
% 1.50/1.21 tff(435,plain,
% 1.50/1.21 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.50/1.21 inference(quant_intro,[status(thm)],[434])).
% 1.50/1.21 tff(436,plain,
% 1.50/1.21 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.50/1.21 inference(rewrite,[status(thm)],[])).
% 1.50/1.21 tff(437,plain,
% 1.50/1.21 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 1.50/1.21 inference(bind,[status(th)],[])).
% 1.50/1.21 tff(438,plain,
% 1.50/1.21 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.50/1.21 inference(quant_intro,[status(thm)],[437])).
% 1.50/1.21 tff(439,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 1.50/1.21 tff(440,plain,
% 1.50/1.21 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.50/1.21 inference(modus_ponens,[status(thm)],[439, 438])).
% 1.50/1.21 tff(441,plain,
% 1.50/1.21 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.50/1.21 inference(modus_ponens,[status(thm)],[440, 436])).
% 1.50/1.21 tff(442,plain,(
% 1.50/1.21 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.50/1.21 inference(skolemize,[status(sab)],[441])).
% 1.50/1.21 tff(443,plain,
% 1.50/1.21 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 1.50/1.21 inference(modus_ponens,[status(thm)],[442, 435])).
% 1.50/1.21 tff(444,plain,
% 1.50/1.21 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, k1_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, k1_autgroup(A!0)))),
% 1.50/1.21 inference(rewrite,[status(thm)],[])).
% 1.50/1.21 tff(445,plain,
% 1.50/1.21 ((r2_hidden(C!2, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0)))) <=> (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, k1_autgroup(A!0)))),
% 1.50/1.21 inference(rewrite,[status(thm)],[])).
% 1.50/1.21 tff(446,plain,
% 1.50/1.21 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, k1_autgroup(A!0))))),
% 1.50/1.21 inference(monotonicity,[status(thm)],[445])).
% 1.50/1.21 tff(447,plain,
% 1.50/1.21 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, k1_autgroup(A!0)))),
% 1.50/1.21 inference(transitivity,[status(thm)],[446, 444])).
% 1.50/1.21 tff(448,plain,
% 1.50/1.21 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(C!2, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0))))),
% 1.50/1.21 inference(quant_inst,[status(thm)],[])).
% 1.50/1.21 tff(449,plain,
% 1.50/1.21 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(C!2, k1_autgroup(A!0))) | r2_hidden(C!2, k1_autgroup(A!0))),
% 1.50/1.21 inference(modus_ponens,[status(thm)],[448, 447])).
% 1.50/1.21 tff(450,plain,
% 1.50/1.21 (r2_hidden(C!2, k1_autgroup(A!0))),
% 1.50/1.21 inference(unit_resolution,[status(thm)],[449, 443, 433, 414])).
% 1.50/1.21 tff(451,plain,
% 1.50/1.21 ((~(r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0))) | (~r2_hidden(C!2, k1_autgroup(A!0))) | v4_group_6(C!2, A!0, A!0)),
% 1.50/1.21 inference(tautology,[status(thm)],[])).
% 1.50/1.21 tff(452,plain,
% 1.50/1.21 ((~(r2_hidden(C!2, k1_autgroup(A!0)) <=> v4_group_6(C!2, A!0, A!0))) | v4_group_6(C!2, A!0, A!0)),
% 1.50/1.21 inference(unit_resolution,[status(thm)],[451, 450])).
% 1.50/1.21 tff(453,plain,
% 1.50/1.21 (v4_group_6(C!2, A!0, A!0)),
% 1.50/1.21 inference(unit_resolution,[status(thm)],[452, 409])).
% 1.50/1.21 tff(454,plain,
% 1.50/1.21 (v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.50/1.22 inference(modus_ponens,[status(thm)],[453, 379])).
% 1.50/1.22 tff(455,plain,
% 1.50/1.22 (v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v4_group_6(B!1, A!0, A!0)),
% 1.50/1.22 inference(monotonicity,[status(thm)],[238, 238])).
% 1.50/1.22 tff(456,plain,
% 1.50/1.22 (v4_group_6(B!1, A!0, A!0) <=> v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.50/1.22 inference(symmetry,[status(thm)],[455])).
% 1.50/1.22 tff(457,plain,
% 1.50/1.22 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)))),
% 1.50/1.22 inference(rewrite,[status(thm)],[])).
% 1.50/1.22 tff(458,plain,
% 1.50/1.22 (((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)))) <=> ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)))),
% 1.50/1.22 inference(rewrite,[status(thm)],[])).
% 1.50/1.22 tff(459,plain,
% 1.50/1.22 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0))))),
% 1.50/1.22 inference(monotonicity,[status(thm)],[458])).
% 1.50/1.22 tff(460,plain,
% 1.50/1.22 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)))),
% 1.50/1.22 inference(transitivity,[status(thm)],[459, 457])).
% 1.50/1.22 tff(461,plain,
% 1.50/1.22 ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)) | (~v1_group_6(B!1, A!0, A!0)) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.50/1.22 inference(quant_inst,[status(thm)],[])).
% 1.50/1.22 tff(462,plain,
% 1.50/1.22 ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))) | (~v1_group_6(B!1, A!0, A!0)) | (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0))),
% 1.50/1.22 inference(modus_ponens,[status(thm)],[461, 460])).
% 1.50/1.22 tff(463,plain,
% 1.50/1.22 (r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0)),
% 1.50/1.22 inference(unit_resolution,[status(thm)],[462, 402, 113, 111, 95, 249])).
% 1.50/1.22 tff(464,plain,
% 1.50/1.22 ((~![D: $i] : (m2_fraenkel(D, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(D, k1_autgroup(A!0)))) | (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))),
% 1.50/1.22 inference(quant_inst,[status(thm)],[])).
% 1.50/1.22 tff(465,plain,
% 1.50/1.22 (m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.50/1.22 inference(unit_resolution,[status(thm)],[464, 354])).
% 1.50/1.22 tff(466,plain,
% 1.50/1.22 ((~(m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))) | (~m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0))) | m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.50/1.22 inference(tautology,[status(thm)],[])).
% 1.50/1.22 tff(467,plain,
% 1.50/1.22 ((~(m2_fraenkel(B!1, u1_struct_0(A!0), u1_struct_0(A!0), k1_autgroup(A!0)) <=> m1_subset_1(B!1, k1_autgroup(A!0)))) | m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.50/1.22 inference(unit_resolution,[status(thm)],[466, 86])).
% 1.50/1.22 tff(468,plain,
% 1.50/1.22 (m1_subset_1(B!1, k1_autgroup(A!0))),
% 1.50/1.22 inference(unit_resolution,[status(thm)],[467, 465])).
% 1.50/1.22 tff(469,plain,
% 1.50/1.22 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0)))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0)))),
% 1.50/1.22 inference(rewrite,[status(thm)],[])).
% 1.50/1.22 tff(470,plain,
% 1.50/1.22 ((r2_hidden(B!1, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0)))) <=> (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0)))),
% 1.50/1.22 inference(rewrite,[status(thm)],[])).
% 1.50/1.22 tff(471,plain,
% 1.50/1.22 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(B!1, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0))))),
% 1.50/1.22 inference(monotonicity,[status(thm)],[470])).
% 1.50/1.22 tff(472,plain,
% 1.50/1.22 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(B!1, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0)))),
% 1.50/1.22 inference(transitivity,[status(thm)],[471, 469])).
% 1.50/1.22 tff(473,plain,
% 1.50/1.22 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(B!1, k1_autgroup(A!0)) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))))),
% 1.50/1.22 inference(quant_inst,[status(thm)],[])).
% 1.50/1.22 tff(474,plain,
% 1.50/1.22 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(k1_autgroup(A!0)) | (~m1_subset_1(B!1, k1_autgroup(A!0))) | r2_hidden(B!1, k1_autgroup(A!0))),
% 1.50/1.22 inference(modus_ponens,[status(thm)],[473, 472])).
% 1.50/1.22 tff(475,plain,
% 1.50/1.22 (r2_hidden(B!1, k1_autgroup(A!0))),
% 1.50/1.22 inference(unit_resolution,[status(thm)],[474, 443, 433, 468])).
% 1.50/1.22 tff(476,plain,
% 1.50/1.22 ((~(r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0))) | (~r2_hidden(B!1, k1_autgroup(A!0))) | v4_group_6(B!1, A!0, A!0)),
% 1.50/1.22 inference(tautology,[status(thm)],[])).
% 1.50/1.22 tff(477,plain,
% 1.50/1.22 ((~(r2_hidden(B!1, k1_autgroup(A!0)) <=> v4_group_6(B!1, A!0, A!0))) | v4_group_6(B!1, A!0, A!0)),
% 1.50/1.22 inference(unit_resolution,[status(thm)],[476, 475])).
% 1.50/1.22 tff(478,plain,
% 1.50/1.22 (v4_group_6(B!1, A!0, A!0)),
% 1.50/1.22 inference(unit_resolution,[status(thm)],[477, 463])).
% 1.50/1.22 tff(479,plain,
% 1.50/1.22 (v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.50/1.22 inference(modus_ponens,[status(thm)],[478, 456])).
% 1.50/1.22 tff(480,plain,
% 1.50/1.22 (m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.50/1.22 inference(monotonicity,[status(thm)],[239, 239])).
% 1.50/1.22 tff(481,plain,
% 1.50/1.22 (m2_relset_1(B!1, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.50/1.22 inference(symmetry,[status(thm)],[480])).
% 1.50/1.22 tff(482,plain,
% 1.50/1.22 (m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.50/1.22 inference(modus_ponens,[status(thm)],[95, 481])).
% 1.50/1.22 tff(483,plain,
% 1.50/1.22 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.50/1.22 inference(monotonicity,[status(thm)],[239])).
% 1.50/1.22 tff(484,plain,
% 1.50/1.22 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.50/1.22 inference(symmetry,[status(thm)],[483])).
% 1.50/1.22 tff(485,plain,
% 1.50/1.22 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.50/1.22 inference(modus_ponens,[status(thm)],[115, 484])).
% 1.50/1.22 tff(486,plain,
% 1.50/1.22 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0))),
% 1.50/1.22 inference(monotonicity,[status(thm)],[239])).
% 1.50/1.22 tff(487,plain,
% 1.50/1.22 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(A!0)) <=> m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.50/1.22 inference(symmetry,[status(thm)],[486])).
% 1.50/1.22 tff(488,plain,
% 1.50/1.22 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.50/1.22 inference(modus_ponens,[status(thm)],[154, 487])).
% 1.50/1.22 tff(489,plain,
% 1.50/1.22 (v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) <=> v1_group_6(C!2, A!0, A!0)),
% 1.50/1.22 inference(monotonicity,[status(thm)],[238])).
% 1.50/1.22 tff(490,plain,
% 1.50/1.22 (v1_group_6(C!2, A!0, A!0) <=> v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.50/1.22 inference(symmetry,[status(thm)],[489])).
% 1.50/1.22 tff(491,plain,
% 1.50/1.22 (v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.50/1.22 inference(modus_ponens,[status(thm)],[257, 490])).
% 1.50/1.22 tff(492,plain,
% 1.50/1.22 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))))),
% 1.50/1.22 inference(bind,[status(th)],[])).
% 1.50/1.22 tff(493,plain,
% 1.50/1.22 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.50/1.22 inference(quant_intro,[status(thm)],[492])).
% 1.50/1.22 tff(494,plain,
% 1.50/1.22 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))))),
% 1.50/1.22 inference(bind,[status(th)],[])).
% 1.50/1.22 tff(495,plain,
% 1.50/1.22 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.50/1.22 inference(quant_intro,[status(thm)],[494])).
% 1.50/1.22 tff(496,plain,
% 1.50/1.22 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.50/1.22 inference(transitivity,[status(thm)],[495, 493])).
% 1.50/1.22 tff(497,plain,
% 1.50/1.22 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) <=> (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))), ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) <=> (~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)))), ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) <=> (~(v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))))), ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) <=> (~(~(v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))))))), rewrite((~(~(v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))))) <=> (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)))), ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) <=> (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> (~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))), ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) <=> (~(~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))))), rewrite((~(~((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))))), quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((v4_group_6(D, A, B) & v4_group_6(E, B, C)) <=> (~((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))), ((~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) <=> (~(~((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))), rewrite((~(~((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))) <=> ((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))), ((~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) <=> ((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))), trans(monotonicity(rewrite((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (~((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), ((~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> (~(~((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), rewrite((~(~((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))) <=> ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), ((~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))) <=> ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), ((v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) <=> (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | ((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))) | ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))), rewrite((v4_group_6(k8_group_6(A, B, C, D, E), A, C) | ((~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))) | ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) <=> (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))), ((v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) <=> (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))), (![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))) <=> ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))), (((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))) <=> (((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))), rewrite((((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))), (((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))), (![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))) <=> ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))), (((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))) <=> ((v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))), rewrite(((v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))) <=> (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))), (((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))) <=> (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))), (![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))) <=> ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))) <=> ((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))), rewrite(((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B))) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))))),
% 1.50/1.22 inference(bind,[status(th)],[])).
% 1.50/1.22 tff(498,plain,
% 1.50/1.22 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.50/1.22 inference(quant_intro,[status(thm)],[497])).
% 1.50/1.22 tff(499,plain,
% 1.50/1.22 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))),
% 1.50/1.22 inference(rewrite,[status(thm)],[])).
% 1.50/1.22 tff(500,plain,
% 1.50/1.22 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B))), (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> (((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)))), rewrite((((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))), (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) <=> ((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C))), (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> (((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)))), rewrite((((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))), (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) <=> ((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) <=> (v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B))), ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> ((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))), ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) <=> (v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))))), quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) <=> (v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C))), ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> ((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), rewrite(((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))), ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) <=> (v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))), rewrite(((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)) <=> ((~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | v4_group_6(k8_group_6(A, B, C, D, E), A, C))), (((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))) <=> ((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | v4_group_6(k8_group_6(A, B, C, D, E), A, C))))), rewrite(((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | v4_group_6(k8_group_6(A, B, C, D, E), A, C))) <=> (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))), (((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))) <=> (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), (![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))) <=> ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))), (((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))) <=> ((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))), (((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))), (![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))) <=> ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), ((((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))) <=> (((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))), rewrite((((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C)) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))) <=> ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))), ((((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))) <=> ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))), (![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))) <=> ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))), ((((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))))) <=> (((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) => ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))), rewrite((((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B)) => ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))), ((((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))))), (![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))))),
% 1.50/1.23 inference(bind,[status(th)],[])).
% 1.50/1.23 tff(501,plain,
% 1.50/1.23 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))),
% 1.50/1.23 inference(quant_intro,[status(thm)],[500])).
% 1.50/1.23 tff(502,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : (((((~v3_struct_0(C)) & v3_group_1(C)) & v4_group_1(C)) & l1_group_1(C)) => ![D: $i] : ((((v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(D, A, B)) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) => ![E: $i] : ((((v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) & v1_group_6(E, B, C)) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) => ((v4_group_6(D, A, B) & v4_group_6(E, B, C)) => v4_group_6(k8_group_6(A, B, C, D, E), A, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t74_group_6')).
% 1.50/1.23 tff(503,plain,
% 1.50/1.23 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))),
% 1.50/1.23 inference(modus_ponens,[status(thm)],[502, 501])).
% 1.50/1.23 tff(504,plain,
% 1.50/1.23 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))),
% 1.50/1.23 inference(modus_ponens,[status(thm)],[503, 499])).
% 1.50/1.23 tff(505,plain,(
% 1.50/1.23 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~((~v3_struct_0(C)) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(D, A, B) & m2_relset_1(D, u1_struct_0(A), u1_struct_0(B)))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~(v4_group_6(D, A, B) & v4_group_6(E, B, C))) | (~(v1_funct_1(E) & v1_funct_2(E, u1_struct_0(B), u1_struct_0(C)) & v1_group_6(E, B, C) & m2_relset_1(E, u1_struct_0(B), u1_struct_0(C)))))))))),
% 1.50/1.23 inference(skolemize,[status(sab)],[504])).
% 1.50/1.23 tff(506,plain,
% 1.50/1.23 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.50/1.23 inference(modus_ponens,[status(thm)],[505, 498])).
% 1.50/1.23 tff(507,plain,
% 1.50/1.23 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))),
% 1.50/1.23 inference(modus_ponens,[status(thm)],[506, 496])).
% 1.50/1.23 tff(508,plain,
% 1.50/1.23 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B)))))))),
% 1.50/1.23 inference(rewrite,[status(thm)],[])).
% 1.50/1.23 tff(509,plain,
% 1.50/1.23 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A!0, B)) | (~v4_group_6(E, B, C))))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B)))))))),
% 1.50/1.23 inference(rewrite,[status(thm)],[])).
% 1.50/1.23 tff(510,plain,
% 1.50/1.23 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A!0, B)) | (~v4_group_6(E, B, C)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))))),
% 1.50/1.23 inference(monotonicity,[status(thm)],[509])).
% 1.50/1.23 tff(511,plain,
% 1.50/1.23 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A!0, B)) | (~v4_group_6(E, B, C)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B)))))))),
% 1.50/1.23 inference(transitivity,[status(thm)],[510, 508])).
% 1.50/1.23 tff(512,plain,
% 1.50/1.23 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A!0, B)) | (~v4_group_6(E, B, C)))))))),
% 1.50/1.23 inference(quant_inst,[status(thm)],[])).
% 1.50/1.23 tff(513,plain,
% 1.50/1.23 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A), u1_struct_0(B))) | (~v1_group_6(D, A, B)) | (~m2_relset_1(D, u1_struct_0(A), u1_struct_0(B))) | ![E: $i] : (v4_group_6(k8_group_6(A, B, C, D, E), A, C) | (~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(D, A, B)) | (~v4_group_6(E, B, C)))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))),
% 1.50/1.23 inference(modus_ponens,[status(thm)],[512, 511])).
% 1.50/1.23 tff(514,plain,
% 1.50/1.23 (![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[513, 52, 50, 49, 48, 507])).
% 1.50/1.23 tff(515,plain,
% 1.50/1.23 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.50/1.23 inference(rewrite,[status(thm)],[])).
% 1.50/1.23 tff(516,plain,
% 1.50/1.23 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))))),
% 1.50/1.23 inference(quant_inst,[status(thm)],[])).
% 1.50/1.23 tff(517,plain,
% 1.50/1.23 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~v4_group_1(B)) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(B))) | (~v1_group_6(D, A!0, B)) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(B))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(B), u1_struct_0(C))) | (~v1_group_6(E, B, C)) | (~m2_relset_1(E, u1_struct_0(B), u1_struct_0(C))) | (~v4_group_6(E, B, C)) | v4_group_6(k8_group_6(A!0, B, C, D, E), A!0, C) | (~v4_group_6(D, A!0, B))))))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.50/1.23 inference(modus_ponens,[status(thm)],[516, 515])).
% 1.50/1.23 tff(518,plain,
% 1.50/1.23 (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[517, 514])).
% 1.50/1.23 tff(519,plain,
% 1.50/1.23 (![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.50/1.23 inference(unit_resolution,[status(thm)],[518, 270, 267, 264, 274])).
% 1.50/1.23 tff(520,plain,
% 1.50/1.23 (((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(521,plain,
% 1.50/1.24 ((v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))) <=> (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.50/1.24 inference(rewrite,[status(thm)],[])).
% 1.50/1.24 tff(522,plain,
% 1.50/1.24 (((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.50/1.24 inference(monotonicity,[status(thm)],[521])).
% 1.50/1.24 tff(523,plain,
% 1.50/1.24 (((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.50/1.24 inference(transitivity,[status(thm)],[522, 520])).
% 1.50/1.24 tff(524,plain,
% 1.50/1.24 ((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | (v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))),
% 1.50/1.24 inference(quant_inst,[status(thm)],[])).
% 1.50/1.24 tff(525,plain,
% 1.50/1.24 ((~![C: $i] : (v3_struct_0(C) | (~l1_group_1(C)) | (~v3_group_1(C)) | (~v4_group_1(C)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(C))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C)) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C, D, E), A!0, C) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))))) | v3_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))) | (~l1_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v3_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_1(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.50/1.24 inference(modus_ponens,[status(thm)],[524, 523])).
% 1.50/1.24 tff(526,plain,
% 1.50/1.24 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.50/1.24 inference(unit_resolution,[status(thm)],[525, 274, 270, 267, 264, 519])).
% 1.50/1.24 tff(527,plain,
% 1.50/1.24 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(528,plain,
% 1.53/1.24 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.53/1.24 inference(rewrite,[status(thm)],[])).
% 1.53/1.24 tff(529,plain,
% 1.53/1.24 (^[E: $i] : rewrite(((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.53/1.24 inference(bind,[status(th)],[])).
% 1.53/1.24 tff(530,plain,
% 1.53/1.24 (![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.53/1.25 inference(quant_intro,[status(thm)],[529])).
% 1.53/1.25 tff(531,plain,
% 1.53/1.25 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.53/1.25 inference(monotonicity,[status(thm)],[530])).
% 1.53/1.25 tff(532,plain,
% 1.53/1.25 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.53/1.25 inference(transitivity,[status(thm)],[531, 528])).
% 1.53/1.25 tff(533,plain,
% 1.53/1.25 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))))),
% 1.53/1.25 inference(monotonicity,[status(thm)],[532])).
% 1.53/1.25 tff(534,plain,
% 1.53/1.25 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.53/1.25 inference(transitivity,[status(thm)],[533, 527])).
% 1.53/1.25 tff(535,plain,
% 1.53/1.25 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.53/1.25 inference(quant_inst,[status(thm)],[])).
% 1.53/1.25 tff(536,plain,
% 1.53/1.25 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(D, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v4_group_6(D, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), D, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.53/1.25 inference(modus_ponens,[status(thm)],[535, 534])).
% 1.53/1.25 tff(537,plain,
% 1.53/1.25 ((~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.53/1.25 inference(unit_resolution,[status(thm)],[536, 109, 526])).
% 1.53/1.25 tff(538,plain,
% 1.53/1.25 (![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.53/1.25 inference(unit_resolution,[status(thm)],[537, 491, 488, 485])).
% 1.53/1.25 tff(539,plain,
% 1.53/1.25 (((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ((~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.53/1.25 inference(rewrite,[status(thm)],[])).
% 1.53/1.25 tff(540,plain,
% 1.53/1.25 (((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) <=> ((~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.53/1.26 inference(rewrite,[status(thm)],[])).
% 1.53/1.26 tff(541,plain,
% 1.53/1.26 (((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ((~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))))),
% 1.53/1.26 inference(monotonicity,[status(thm)],[540])).
% 1.53/1.26 tff(542,plain,
% 1.53/1.26 (((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) <=> ((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.53/1.26 inference(transitivity,[status(thm)],[541, 539])).
% 1.53/1.26 tff(543,plain,
% 1.53/1.26 ((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | ((~v1_funct_1(B!1)) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))),
% 1.53/1.26 inference(quant_inst,[status(thm)],[])).
% 1.53/1.26 tff(544,plain,
% 1.53/1.26 ((~![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(E, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(E, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, E), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_funct_1(B!1)) | (~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.53/1.26 inference(modus_ponens,[status(thm)],[543, 542])).
% 1.53/1.26 tff(545,plain,
% 1.53/1.26 ((~v4_group_6(C!2, A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~v1_funct_2(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v1_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | (~m2_relset_1(B!1, u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))), u1_struct_0(g1_group_1(u1_struct_0(A!0), u1_group_1(A!0))))) | (~v4_group_6(B!1, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))) | v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.53/1.26 inference(unit_resolution,[status(thm)],[544, 113, 538])).
% 1.53/1.26 tff(546,plain,
% 1.53/1.26 (v4_group_6(k8_group_6(A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)), C!2, B!1), A!0, g1_group_1(u1_struct_0(A!0), u1_group_1(A!0)))),
% 1.53/1.26 inference(unit_resolution,[status(thm)],[545, 253, 250, 482, 479, 454])).
% 1.53/1.26 tff(547,plain,
% 1.53/1.26 (v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)),
% 1.53/1.26 inference(modus_ponens,[status(thm)],[546, 377])).
% 1.53/1.26 tff(548,plain,
% 1.53/1.26 ((~(r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0))) | r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) | (~v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0))),
% 1.53/1.27 inference(tautology,[status(thm)],[])).
% 1.53/1.27 tff(549,plain,
% 1.53/1.27 (~(r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0))),
% 1.53/1.27 inference(unit_resolution,[status(thm)],[548, 547, 375])).
% 1.53/1.27 tff(550,plain,
% 1.53/1.27 (((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(k5_relat_1(C!2, B!1))) | (~v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k5_relat_1(C!2, B!1))) | (~v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.53/1.27 inference(rewrite,[status(thm)],[])).
% 1.53/1.27 tff(551,plain,
% 1.53/1.27 ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | ((~v1_funct_1(k5_relat_1(C!2, B!1))) | (~v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))))),
% 1.53/1.27 inference(quant_inst,[status(thm)],[])).
% 1.53/1.27 tff(552,plain,
% 1.53/1.27 ((~![B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(B, k1_autgroup(A!0)) <=> v4_group_6(B, A!0, A!0)) | (~v1_group_6(B, A!0, A!0)) | (~m2_relset_1(B, u1_struct_0(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k5_relat_1(C!2, B!1))) | (~v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.53/1.27 inference(modus_ponens,[status(thm)],[551, 550])).
% 1.53/1.27 tff(553,plain,
% 1.53/1.27 ((~v1_funct_1(k5_relat_1(C!2, B!1))) | (~v1_funct_2(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0))) | (r2_hidden(k5_relat_1(C!2, B!1), k1_autgroup(A!0)) <=> v4_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~v1_group_6(k5_relat_1(C!2, B!1), A!0, A!0)) | (~m2_relset_1(k5_relat_1(C!2, B!1), u1_struct_0(A!0), u1_struct_0(A!0)))),
% 1.53/1.27 inference(unit_resolution,[status(thm)],[552, 402])).
% 1.53/1.27 tff(554,plain,
% 1.53/1.27 ($false),
% 1.53/1.27 inference(unit_resolution,[status(thm)],[553, 549, 328, 218, 213, 208])).
% 1.53/1.27 % SZS output end Proof
%------------------------------------------------------------------------------